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CAESAR II Statics Training

CAESAR II Version 2011 - Statics Training

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CAESAR II Statics Training Introduction

Contents Introduction ..................................................................................................................... 6 Interface .............................................................................................................................................. 6 Default Data Directory .................................................................................................................... 6 Units .................................................................................................................................................... 7 Create Custom Units File................................................................................................................. 7 F = Kx Example .................................................................................................................................... 9 Model Input .................................................................................................................................. 12 Load Case Editor............................................................................................................................ 16 Hand Calculation ........................................................................................................................... 18 Output Processor .......................................................................................................................... 19 Axial ............................................................................................................................................... 21

Theory and Development of Pipe Stress Requirements ................................................... 25 Basic Stress Concepts ........................................................................................................................ 25 Example ......................................................................................................................................... 30 3D State of Stress in the Pipe Wall.................................................................................................... 33 Failure Theories................................................................................................................................. 36 Maximum Stress Intensity Criterion ................................................................................................. 38 Code Stress Equations....................................................................................................................... 40 B31.1 Power Piping ....................................................................................................................... 40

Pipe 1 ............................................................................................................................. 42 Input Model ...................................................................................................................................... 43 Error Checking ................................................................................................................................... 52 Review Load Cases ............................................................................................................................ 54 Review Results .................................................................................................................................. 55

Supt 01 ........................................................................................................................... 64 Locating Supports ............................................................................................................................. 65 Adding Supports to Model ............................................................................................................ 69 Analyse .............................................................................................................................................. 75 Fix Model........................................................................................................................................... 80 Place Spring Hangers..................................................................................................................... 87

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CAESAR II Statics Training Introduction

Turbo ............................................................................................................................. 92 Model Inlet ........................................................................................................................................ 93 Combine Models ............................................................................................................................... 98 NEMA SM23 .................................................................................................................................... 100

Manifold ...................................................................................................................... 111 API 610 Analysis .............................................................................................................................. 120

Tutor ............................................................................................................................ 128 Boundary Conditions................................................................................................................... 130 API 610 Analysis .............................................................................................................................. 136 Fix Model – Part 1 ........................................................................................................................... 139 Include WRC 297 flexibilities....................................................................................................... 139 Review Results ............................................................................................................................ 141 Fix Model – Part 2 ........................................................................................................................... 143 Build Steel Structure ................................................................................................................... 144 Combine Pipe and Steel models ................................................................................................. 154 Review Results ............................................................................................................................ 157 Fix Model – Part 3 ........................................................................................................................... 158 Loop Optimisation Wizard .......................................................................................................... 161 Fix Model – Part 4 ........................................................................................................................... 166 Model the Expansion Joint Assembly ......................................................................................... 170 Document the Analysis ................................................................................................................... 174 Custom Reports........................................................................................................................... 174 Filters........................................................................................................................................... 178 Generate Report ......................................................................................................................... 179 ISOGEN Stress Isometrics ............................................................................................................ 182

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CAESAR II Statics Training Introduction

Cool H20 – FRP Piping.................................................................................................... 194 Basics of Fibreglass Piping Analysis ................................................................................................. 195 CAESAR II’s Orthotropic Model for Piping Systems ........................................................................ 198 Requirements of the ISO 14692 Code............................................................................................. 199 Allowable Stress Data for this Model.............................................................................................. 202 Configuration Options for FRP Piping: ............................................................................................ 204 Model the system ........................................................................................................................... 206 Load Case Setup .............................................................................................................................. 213 Review Results ................................................................................................................................ 213 Solving Expansion Problems ........................................................................................................... 214 Static Seismic Using the ASCE 7-05: ................................................................................................ 214 Inertial Loads ............................................................................................................................... 214 Seismic Data Input ...................................................................................................................... 219 Load Case Setup .......................................................................................................................... 223 Review Results ............................................................................................................................ 225

Gas Transmission Pipeline - Buried Pipe ........................................................................ 228 B31.8 Design Code .......................................................................................................................... 229 Modelling the system ..................................................................................................................... 229 Material Database........................................................................................................................... 234 Buried Pipe Modeller ...................................................................................................................... 237 Restraint Parameters .................................................................................................................. 237 American Lifelines Alliance Clay Model ...................................................................................... 238 American Lifelines Alliance sand model: .................................................................................... 240 Meshing Parameters ................................................................................................................... 241 Virtual Anchor Length (VAL):....................................................................................................... 243 Bury Pipe ..................................................................................................................................... 244 Load Case Setup .............................................................................................................................. 249 Results Review ................................................................................................................................ 250 Fatigue ............................................................................................................................................ 251 Setting up the Fatigue Load cases............................................................................................... 251

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CAESAR II Statics Training Introduction

Riser ............................................................................................................................. 254 Modelling ........................................................................................................................................ 255 Injection Line ............................................................................................................................... 256 Product Line ................................................................................................................................ 260 Jacket .............................................................................................................................................. 261 Hydrodynamic Theory..................................................................................................................... 264 B31.4 Code Requirements .............................................................................................................. 265 Hydrodynamic Input ....................................................................................................................... 266 Wave Solution ................................................................................................................................. 267 Hydrodynamic Coefficients ......................................................................................................... 272 Wind Loading .................................................................................................................................. 274 Load Case Setup .............................................................................................................................. 277 Analysis ........................................................................................................................................... 278

SUPT01 – Water Hammer ............................................................................................. 280 Edit the Model ................................................................................................................................ 281 Determine the Load ........................................................................................................................ 282 Define the Occasion Load ........................................................................................................... 283 Load Case Setup .............................................................................................................................. 283 Check the Results ............................................................................................................................ 284 Reset the Load Cases ...................................................................................................................... 284 Check Results .................................................................................................................................. 285 Correct model ................................................................................................................................. 286

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CAESAR II Statics Training Introduction

Introduction CAESAR II is pipe stress analysis software which uses beam theory to evaluate piping systems to numerous international standards. CAESAR II is not Finite Element Analysis (FEA) software, but instead uses a stick model built up of elements connected by nodes. This course will introduce CAESAR II and demonstrate various modelling and analysis methods in order to evaluate and correct piping systems.

Interface When starting CAESAR II, the Main Window appears. This is the window where all tasks are started from. This includes opening/creating an input file, reviewing Load Cases, reviewing results or accessing any auxiliary modules such as WRC 107/297 processor or the ISOGEN stress isometrics module. All modules open up in their own separate window.

When opening a new file, the file will open, but you will return to the Main Window. You can then choose to go to the Input processor, Output processor or the results for this file. These modules (and other auxiliary modules) and their interfaces will be introduced as they occur throughout the training. Default Data Directory CAESAR II has the option to specify the default working directory – that is all files working with will be saved/opened from this default location. Of course it is still possible to navigate using windows explorer functions, this setting is just the default location when selecting New/Open. Select File > Set Default Data Directory from the CAESAR II Main window

Click on the ellipsis button at the end of the text field and browse to E:\Training\CAESAR II\Exercises

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CAESAR II Statics Training Introduction

Units CAESAR II performs all internal calculations in English units. To enable the entry and review of data in alternative units (such as SI), units files are used by CAESAR II. These units files simply convert the internal CAESAR II English units to the user’s preferred unit. Each CAESAR II file (referred to as a “Job File”) uses a particular units file which is specified on creation of the job. Files can be converted from one units file to another if required. The units files have the extension *.FIL and are located in the CAESAR II System directory, or in the same directory as the job file. The file to use is specified in the Configuration file. Create Custom Units File Throughout this course, we wish to use specific units for various parameters such as Pressure, Density etc. As such we require a units file which is different to the supplied default files. So we will create our own CAESAR II units file. Select Tool > Make Units Files from the Main Window

This allows the creation of new units files, or the review of existing units files, useful if you receive a units file from a colleague and wish to check the units in use in the file. Choose to Create New Units File and for the template file to use as a start point, select *MM.FIL. Give the new file a name and click View/Edit file.

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CAESAR II Statics Training Introduction

In the Units File dialogue box, change the following units from the MM defaults: Stress Pressure Elastic Modulus Pipe Density Insul. Density Fluid density Transl. Stiffness Uniform Load

N/sq.mm. bars N/sq.mm. kg/cu.m. kg/cu.m. kg/cu.m. N/mm N/mm

Ensure Nominals is set to ON. This allows the entry of pipe nominal sizes and schedules into the input, which will be converted to actual diameters and wall thicknesses (e.g. enter 4 into the diameter field and CAESAR II will convert this to 114.3mm). Give the file a label as well to easily identify the file.

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CAESAR II Statics Training Introduction

F = Kx Example As CAESAR II uses a stick model, and beam theory, it is easy to prove this using a simple cantilever example. This example will introduce the basic modelling methods in CAESAR II and introduce the Input Spread Sheet, Load Case editor and the Output Processor. In addition, we can check the CAESAR II results against some simple hand calculations. CAESAR II calculates forces using . Using the example below, we will create a simple cantilever model, fixed at one end, and apply a displacement of 2mm at the other end. We can then calculate the force required to generate this 2mm displacement – and see this in the results.

First we will create the model in CAESAR II. Create a new file in CAESAR II, called FKLateral

After creating the new job file, the first time it has opened, the units will be displayed to the user for confirmation. You will notice that the units file displayed here for our file is English (CAESAR II default units) not the units file we have just created. By default, CAESAR II uses the units file set in the Configuration/Setup as the default file for new jobs (and also as the units to use to display the output results).

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CAESAR II Statics Training Introduction

Click OK on the units review screen and the input spread sheet will open. To confirm/check the units, hover over any field in the input – the units used in this field will be displayed in the tooltips. For example, we changed the pressure units to bars, but the pressure field displays the units as lb./sq.in.

Close the input screen – we will change the units and return to the input with the correct units displayed. In the CAESAR II main window select Tools > Configure/Setup

In the window which appears, select Database Definitions from the categories tree on the left.

Now change the Units File Name setting to the units file just created.

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CAESAR II Statics Training Introduction

Save and exit.

Return to the Piping Input. Again, the units file to be used will be displayed – this should now be your custom units file.

Verify that the correct units are in use via the tooltips

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CAESAR II Statics Training Introduction Model Input We will now create the simple cantilever model and apply a 2mm displacement at the free end. The model will be as follows: One element 10m in length going from node 10 to node 20 in the X direction, anchored at one end. 8” pipe with Standard wall thickness.

The input spread sheet will have defaulted to nodes 10 to 20, so simply enter 10000 in the DX field. We are in mm units already. Enter the pipe diameter and wall thickness – this is 8” NS and STD wall thickness. As we have “nominals” set to ON, simply type in 8 in the diameter and hit enter. The actual OD for 8” pipe will be inserted. Repeat for the wall thickness, simply type in “S” and press enter.

Now we must fill in the pipe properties. We need to know the material properties to carry out the analysis. Select A106 – B from the list of materials. Notice that all materials have a number to identify it, you can simply type in the material number here - in the case of A106-B this is 106. Selecting the material will fill in the Elastic modulus and Poisson ratio and various material allowables under the Allowable Stress area, depending on the design code selected (B31.3 default).

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CAESAR II Statics Training Introduction

That is our pipe itself. We now need to anchor it at one end (node 10) and apply a displacement at the other end (node 20). Place the anchor by double clicking the Restraints check box. All the check boxes shown in the middle column on the spread sheet must be double clicked to check/uncheck.

To define a restraint you must specify a minimum of the node that the restraint will be attached to, plus the type of restraint. Press F1 for more information on the different restraint types. We need an anchor, so select ANC and locate it at node 10.

Now we will apply the 2mm displacement at the opposite end. Double click the Displacements check box to apply a displacement.

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CAESAR II Statics Training Introduction Specify the displacement at node 20, and specify a 2mm displacement downwards in the Y direction – i.e. enter -2 in the DY row. Leave the remaining rows empty – do not specify 0. Specifying 0 fixes the node in the specified direction. Entering 0 in each row would be the same as an anchor. Leaving the values blank leaves the remaining directions free.

Finally to complete the analysis we must specify a design temperature and pressure. In our case these are not really relevant as we are only concerned with displacement, so just enter 21°C in T1 and 1bar in P1 fields.

The file can now be analysed. Before analysis the input must be error checked in order to identify any issues which may prevent the analysis running (such as specifying both an anchor and an applied displacement at the same point), or anything which may provide incorrect results (such as Stress Intensification factors not present at a geometric intersection). Run the error checker to check the model.

You should see only one note in the error checker report – the C of G. This can be useful for identifying problems such as incorrect densities applied – giving an incorrect weight for example.

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CAESAR II Statics Training Introduction

If you receive anything other than this C of G, review the model for any issues. A common error on this exercise is the following:

This indicates that the displacement and the anchor have been specified at the same location. Check that the Anchor is specified at Node 10 and the displacement is specified at Node 20.

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CAESAR II Statics Training Introduction Load Case Editor Once the error check is successful, we can create load cases to analyse the system. Access the load case editor. This button is only available after a successful error check.

The load case editor will be shown.

The default load cases are the Operating, Sustained and Expansion cases, as required by the design codes such as B31.3. Remove all these load cases, as we are only concerned with the displacement.

Add one new row.

Into the load case we can add any of the loads defined in the input into the load case. As we are only concerned with the displacement, drag in D1 – Displacement Case #1 into the L1 row.

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CAESAR II Statics Training Introduction

Also select the stress type as SUS(tained).

The analysis will now take into account only the displacement reaction. Before we analyse the piping system, let us first perform the hand calculation in order to check.

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CAESAR II Statics Training Introduction Hand Calculation As we know,

The stiffness K is

; Where D = Pipe OD and d = Pipe ID E being Modulus of Elasticity and L being the length. So if we wish to know what force is required to displace the cantilever 2mm, we can calculate this quite easily.

So for a 2mm displacement, the force required is

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CAESAR II Statics Training Introduction Output Processor Back in CAESAR II, run the analysis by clicking on the “Running Man” icon from within the load case editor.

You will see the following message explaining that certain loads have been defined in the model but are not included in any of the load cases to be analysed – this is OK in our case, but can serve as a useful warning if you have may loads/load cases defined. Select OK as is…Continue and click OK to analyse.

Once the analysis is complete, the Output Processor will be shown. We can view various results for any load case from here, plus general model reports such as the Input Echo. These reports can be viewed on screen, or output to Word/Excel/Text or straight to a printer. In addition Custom report templates can be created, and any available report can be selected and added to the Output viewer Wizard, and exported/viewed to create/view a comprehensive report very quickly. For now we will just check the displacement at node 20 to verify that it is 2mm, and the force at node 20 to check against out hand calculation. Select the load case (SUS) D1 and the Displacements standard report and click to show on screen:

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CAESAR II Statics Training Introduction The DY at Node 20 is -2mm, as we specified.

Now to check the force at node 20; view the Global Element Forces report.

37 N as we calculated.

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CAESAR II Statics Training Introduction Axial We can repeat this exercise for axial forces. This is a simple change in the model changing the displacement from the Y to the X direction.

The analysis can be quickly re-run in cases where a change such as this has been made by using the Batch Run “Double Running Man” icon. This will run the error checker followed immediately by the analysis (providing there are no Errors).

The force should be as follows: We are still using F = Kx, but we are using the Axial stiffness.

Therefore:

110,021 N/mm So for an axial extension of 2mm, the force required is

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CAESAR II Statics Training Introduction

The CAESAR II results, Global Element forces report should verify this:

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CAESAR II Statics Training Introduction The forces calculated such as in the previous example produce bending moments throughout the piping system. Bending moment is produced when a Force is applied at a distance – MB = F x L Once the bending moment has been calculated, beam theory is used in order to calculate the stress at this point.

rearranges to is the section modulus Z. So this reduces further to

The stresses are calculated using this basic theory and compared to the allowable stresses in the design codes. CAESAR II has many design codes available, all of which have evolved separately over time, thus the way the stresses are calculated for each specific code are slightly different. However, looking at one of the most common piping codes – B31.3 – it can be seen that the equations used are based on the basic bending as detailed above. B31.3 Chemical Plant and Petroleum Refinery Piping Sustained:

Expansion:

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CAESAR II Statics Training Introduction As can be seen, the equations essentially use bending stress M/Z. The equations are a little more complicated than the basic cantilever example for the following reasons:

To address piping systems in 3 dimensions To address areas in a piping system where particular geometry/components, such as at a branch connection or a bend, can increase the stress, and therefore the likelihood of failure. At these points, the stress is increased by a Stress Intensification Factor (SIF) known as i. The design codes contain formulae to calculate these SIFs. Stresses can also be caused by Pressure and Axial Forces The Stresses are categorised into Sustained, Expansion and Occasional, as detailed below.

Sustained Stress: This is primary stresses caused by primary loadings such as the weight and pressure of the piping system. Expansion Stress: Expansion stresses are secondary stresses caused by secondary loadings such as the thermal expansion and applied displacements. Occasional Stress: Combines sustained stresses with those produced by an occasional loading such as earthquake of relief valve operation. As these are occasional loads, the allowable can be increased by a scalability factor, k. k is usually dependant of the duration or frequency of the occasional load.

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Theory and Development of Pipe Stress Requirements Basic Stress Concepts Normal Stresses: Normal stresses are those acting in a direction normal to the face of the crystal structure of the material, and may either be tensile or compressive in nature. In fact in piping, normal stresses tend more to be in tension due to the predominant nature of internal pressure as a load case. Normal stresses may be applied in more than one direction, and may develop from a number of different types of loads. For a piping system these are: Longitudinal Stress: Longitudinal or axial stress is the normal stress acting along the axis of the pipe. This may be caused by an internal force acting axially in the pipe.

Where: Longitudinal Stress Internal axial force acting on cross section Cross sectional area of pipe (

) Outer diameter Inner diameter

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements A specific instance of longitudinal stress is that due to internal pressure:

⁄ Design pressure Internal area of pipe ⁄ Replacing the terms for the internal and metal areas of the pipe, the previous equation may be written as ⁄

Or:

⁄ For convenience the longitudinal pressure stress is often conservatively approximated as

Bending Stress: Another component of axial normal stress is bending stress. Bending stress is zero at the neutral axis of the pipe and varies linearly across the cross-section from the maximum compressive outer fibre to the maximum tensile outer fibre. Calculating the stress as linearly proportional to the distance from the neutral axis:

⁄ Where: Bending moment acting on cross section Distance of point of interest from neutral axis of cross section Moment of inertial of cross section

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements The maximum bending stress occurs where c is highest – the maximum value c can be is equal to the radius of the pipe. ⁄

=

Where: Outer radius of pipe. Section modulus of pipe

Summing all components of longitudinal normal stress (for axial and bending):

Hoop Stress: Hoop stress is another of the normal stresses present in the pipe and is caused by internal pressure. This stress acts in a direction parallel to the pipe circumference.

The magnitude of the hoop stress varies through the pipe wall and can be calculated by Lame’s equation as: (

)

Where: Hoop stress due to pressure Inner radius of pipe Outer Radius of pipe Radial position where stress is being considered The hoop stress can be approximated conservatively for thin-wall cylinders by assuming that the pressure force applied over an arbitrary length of pipe, l is resisted uniformly by the pipe wall over that same arbitrary length.

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Or conservatively

Radial Stress: Radial Stress is the third normal stress present in the pipe wall. It acts in the third orthogonal direction – parallel to the pipe radius. Radial stress is caused by internal pressure and varies between a stress equal to the internal pressure at the pipe’s inner surface, and a stress equal the atmospheric pressure at the pipe’s external surface. Assuming that there is no external pressure, radial stress is calculated as:

Where Radial stress due to pressure Note that radial stress is zero at the outer radius of the pipe, where the bending stresses are maximised. For this reason, this stress component has traditionally been ignored during the stress calculations. Shear Stresses: Shear Stresses are applied in a direction parallel to the face of the plane of the crystal structure of the material and tend to cause adjacent planes of the crystal to slip against each other. Shear stresses may be caused by more than one type of applied load. For example, shear stress may be caused by shear forces acting on the cross section.

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Where: Maximum shear stress shear force shear form factor. Dimensionless quantity (1.333 for solid circular section) These shear stresses are distributed such that they are at the maximum at the neutral axis of the pipe and zero at the maximum distance from the neutral axis. Since this is the opposite of the case with bending stresses and since these Shear stresses are usually small, shear stresses due to forces are traditionally neglected during pipe stress analysis. Shear Stresses may also be caused by torsional loads.

⁄ Where: Internal torsional moment acting on cross-section distance of point of interest from torsional centre (intersection of neutral axes) or cross section torsional resistance of cross section

(

)

Maximum torsional stress occurs where c is maximised. Again at the outer radius. ⁄ Summing the individual components of the shear stress, the maximum shear stress acting on the pipe cross section is:

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements As noted above, a number of the stress components described above have been neglected for convenience during calculation of pipe stresses. Most piping codes require stresses to be calculated using some form of the following equations: Longitudinal Stress: Shear Stress: Hoop Stress: Example This example calculation illustrates for a 6” nominal diameter, standard schedule pipe (assuming the piping loads are known): Cross sectional properties Outside diameter Mean thickness Inside diameter 154.076mm Cross sectional Area

–

(

–

(

Moment of Inertia

–

(

)

) –

(

Section Modulus

)

)

⁄

⁄

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Piping loads Bending Moment Axial Force Internal Pressure Torsional Moment

Stresses Longitudinal Stress

Shear Stress

Hoop Stress

Bending Component of Longitudinal stress is the radius where the stress is being considered. This will be at a maximum value at the outer surface where ⁄ (

)

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Torsional Stress

The maximum torsional stress occurs at the outer radius where again

– at the outer surface

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

3D State of Stress in the Pipe Wall During operation, pipes are subject to all these types of stresses. Examining a small cube of metal form the most highly stressed point of the pipe wall, the stresses are distributed as so:

There are an infinite number of orientations in which this cube could have been selected, each with a different combination of normal and shear stresses on the faces. For example, there is one orientation of the orthogonal stress axes for which one normal stress is maximised and another for which one normal stress is minimised – in both cases; all shear stress components are zero. In orientation in which the shear stress is zero, the resulting normal components of the stress are termed the principal stresses. For 3-dimensional analyses, there are three of them and they are designated S1 (the maximum), S2 and S3 (the minimum). Note that regardless of the orientation of the stress axes, the sum of the orthogonal stress components is always equal, i.e.:

The converse of these orientations is that in which the shear stress component is maximised (there is also an orientation in which the shear stress is minimised, but this is ignored since the magnitudes of the minimum and maximum shear stresses are the same); this is appropriately called the orientation of maximum shear stress. The maximum shear stress in a three dimensional state of stress is equal to ½ the difference between the largest and smallest of the principal stresses (S1 and S3). The values of the principal and maximum shear stress can be determined through the use of Mohr’s circle. The Mohr’s circle analysis can be simplified by neglecting the radial stress component, therefore considering a less complex (i.e. 2D) state of stress. A Mohr’s circle can be developed by plotting the normal vs. shear stresses for the two known orientations (i.e. longitudinal stress vs. shear and hoop stress vs. shear), and constructing a circle through the two points. The infinite combinations of normal and shear stresses around the circle represent the combinations present in the infinite number of possible orientations of the local stress axes. A differential element at the outer radius of the pipe (where bending and torsional stresses are maximised and the radial normal and force-induced shear stresses are usually zero) is subject to 2D plane stress and thus the principal stress terms can be computed from the following Mohr’s circle:

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

The centre of the circle is at

and the radius is equal to(*

+

)

. Therefore

the principal stresses S1 and S2 are equal to the centre of the circle, plus or minus the radius respectively. The principal stresses are calculated as: *(

)

+

*(

)

+

and

As noted above, the maximum shear stress present in any orientation is equal to

Continuing our example: Mohr’s Circle of Stress Centre of circle

Radius of Circle

√( √(

) )

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or :

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Maximum Principal Stress S1 √(

√(

)

)

Or from the Mohr’s circle above, S1 = 78.07 + 50.59 = 128.66 MPa Maximum Principal Stresses S2 and S3 √(

√(

)

)

Or from the Mohr’s circle, S2 = 78.07 – 50.59 = 27.48 MPa S3 = S2

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Failure Theories The calculated stresses are not much use on their own, until they are compared to material allowables. Material allowable stresses are related to strengths as determined by material uniaxial tests, therefore calculated stresses must also be related to the uniaxial tensile test. This relationship can be developed by looking at available failure theories.

There are three generally accepted failure theories which may be used to predict the onset of yielding in a material:

Octahedral Shear or Von Mises theory Maximum Shear or Tresca Theory Maximum Stress or Rankine Theory

These theories relate failure in an arbitrary 3D stress state in a material to failure in the stress state found in a uniaxial tensile test specimen, since it is that test that is most commonly used to determine the allowable strength of commonly used materials. Failure of a uniaxial tensile test specimen is deemed to occur when plastic deformation occurs, i.e. when the specimen yields; that is, release of the load does not result in the specimen returning to its original state. The three failure theories state: Von Mises:

“Failure occurs when the octahedral shear stress in a body is equal to the octahedral shear stress at yield in a uniaxial tension test”

The octahedral shear stress is calculated as: √ In a uniaxial tensile test specimen at the point of yield:

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Therefore the octahedral shear stress in a uniaxial tensile test specimen at failure is calculated as: √(

)

(

)

√ Therefore under the Von Mises theory: Plastic deformation occurs in a 3-Dimensional stress state whenever the octahedral shear stress 𝑆𝑦𝑖𝑒𝑙𝑑

exceeds √

Tresca:

“Failure occurs when the maximum shear stress in a body is equal to the maximum shear stress at yield in a uniaxial tension test.

The maximum shear stress is calculated as:

In a uniaxial tensile test specimen at the point of yield:

Therefore

Therefore, under Tresca theory Plastic deformation occurs in a 3-Dimensional stress state whenever the maximum shear stress exceeds

𝑆𝑦𝑖𝑒𝑙𝑑

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Rankine:

“Failure occurs when the maximum tensile stress in a body is equal to the maximum tensile stress at yield in a uniaxial tension test”

The maximum tensile stress is the largest, positive principal stress, S1 (by definition, S1 is always the largest of the principal stresses.) In a uniaxial tensile test specimen at the point of yield:

Therefore, under Rankine theory: Plastic deformation occurs in a 3-Dimensional stress state whenever the maximum shear stress exceeds 𝑆𝑦𝑖𝑒𝑙𝑑

Maximum Stress Intensity Criterion Most of the piping codes use a slight modification of the maximum shear stress theory for flexibility related failures. Repeating, the maximum shear stress theory predicts that failure occurs when the maximum shear stress in a body equals

, the maximum shear stress existing at failure during

the uniaxial tensile test. Recapping, the maximum shear stress in a body is given by:

For a differential element at the outer surface of the pipe, the principal stresses were computed earlier as: √(

)

√(

)

As seen previously, the maximum shear stress theory states that during the uniaxial tensile test the maximum shear stress at failure is equal to one-half of the yield stress, so the following requirement is necessary: √

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Multiplying both sides by 2 creates the stress intensity, which is an artificial parameter defined simply as twice the maximum shear stress. Therefore the Maximum Stress Intensity Criterion, as adopted by most piping codes, dictates the following requirement: √ Note that when calculating only the varying stresses for fatigue evaluation purposes, the pressure components drop out of the equation. If an allowable stress based upon a suitable factor of safety is used, the Maximum Stress Intensity criterion yields an expression very similar to that specified by the B31.3 code: √ Where: longitudinal normal stress due to bending shear stress due to torsion allowable stress for loading case Continuing our example for the 6” diameter, standard wall pipe, in which longitudinal, shear and hoop stresses were calculated:

Assuming that the yield stress of the pipe material is 206 MPa (30,000 psi) at operating temperature, and a factor of safely of 2/3 is to be used, the following calculations must be made: √ √

The 101.185 MPa is the calculated stress intensity in the pipe wall, while the 137.33 MPa is the allowable stress intensity for the material at the specified temperature. In this case, the pipe would appear to be safely loaded under these conditions.

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Code Stress Equations The piping code stress equations are a direct outgrowth of the theoretical and investigative work discussed above, with specific limitations established by Markl in his 1955 paper. The stress equations were quite similar throughout the piping codes (i.e. between B31.1 and B31.3) until the winter of 1974 when the power codes having observed that Markl was incorrect in neglecting intensification of the torsional moment in a manner analogous to the bending component, combined the bending and torsional stress terms, thus intensifying torsion. It should be noted that the piping codes calculate exactly the stress intensity (twice the maximum shear stress) only for the expansion stress, since this load case contains no hoop or radial components and thus becomes an easy calculation. Including hoop and radial stresses (present in sustained loadings only) in the stress intensity calculation makes the calculation much more difficult. When considering the hoop and radial stresses, it is no longer clear which of the principal stresses is largest and which is the smallest. Additionally the subtraction of S1 – S3 does not produce a simple expression for the stress intensity. As it turns out the inclusion of the pressure term can be simplified by adding only the longitudinal component of the pressure stress directly to the stress intensity produced moment loading only. This provides an equally easy to use equation and sacrifices little as far as accuracy is concerned. The explicit stress requirements for the B31.1 piping code addressed by CAESAR II follows. Note that most codes allow for the exact expression for pressure stress

to be using in place of

in

the sustained stress calculations. Note also that there are many additional piping codes addressed by CAESAR II. B31.1 Power Piping The B31.1 code requires that the engineer calculate sustained, expansion and occasional stresses, exactly defined as below: Sustained

Where: = sustained stress = intensification factor = resultant moment due to sustained (primary) loads √ = basic allowable material stress at the hot (operating) temperature, as per Appendix A of B31.1 Code. Sh is roughly defined as the minimum of: 1. ¼ of the ultimate tensile strength of the material at operating temperature 2. ¼ of the ultimate tensile strength of the material at room temperature 3. 5/8 of the yield strength of the material at operating temperature (90% of the yield stress for austenitic stainless steels) 4. 5/8 of the yield strength of the material at room temperature (90% of the yield stress for austenitic stainless steels) 5. 100% of the average stress for a 0.01% creep rate per 1000 hours

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Expansion

Where: = expansion stress range = resultant range of moments due to expansion (secondary) loads =√ = Allowable expansion stress = basic allowable material stress at the cold (installation) temperature, as per Appendix A of B31.1 Code

Occasional:

Where: = Occasional Stresses = resultant moment due to occasional loads =√ = occasional load factor = 1.2 for loads occurring less than 1% of the time = 1.15 for loads occurring less than 10% of the time.

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CAESAR II Statics Training Pipe 1

Pipe 1 This exercise will provide further practise with the piping input, and introduce alternative editing tools which may increase productivity in creating models. We will also investigate and review the results to see what to look for and see how the piping system is behaving, and how to correct any issues which may arise during the design. The first stage of this exercise is to input the model. The model is below; you will also have the same isometric printed on a separate hand-out in a larger format. As before with the cantilever example, the model will be input using the node numbering system. Each section between two nodes is called an element. i.e. node 10 to node 20 are linked together by an element, referred to by ‘element 10 to 20’. Prior to entering geometry, it can be very useful and is a good idea to mark up the isometric drawing with the intended node number sequence.

We will use a slightly different method of inputting the data, which will allow us to maximise the graphics area during input. In the main “Classic Piping Input”, on each area, notice the “>>” symbol in the top right corner:

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CAESAR II Statics Training Pipe 1 Double click this symbol to “tear off” the particular section of the input spread sheet. This will allow the Classic window to be minimised for the most part thus maximising the graphics. Tear off the Node Numbers, Dimension Deltas and Pipe Sizes areas. As the material temperatures and pressures do not change throughout the model we can enter these on the first element and then we will not need them again.

Input Model Enter A106-B as the material, 330°C as the temperature and 17 bars as the pressure

In this model we also require insulation; 65mm thick Calcium Silicate.

The rest of the information we will need to enter for our model can be done via the three windows we have “torn off”. Minimise the Classic piping input (of course this can always be maximised at any point if needed).

Finally we can enter the pipe size and schedule, along with the densities and corrosion allowance, as per the isometric. The fluid density can be entered as 0.72SG and CAESAR II will convert this specific gravity to the correct units. As before the pipe size can be entered as 10 for 10” and S for STD schedule piping.

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CAESAR II Statics Training Pipe 1

We will begin at the bottom “right” pipe where it is connected to a pump. This will be node 10. Note that this is an anchor, a fixed point in our system. Element 10 to 20 is 400mm in length, in the -Z direction. Enter DZ as -400mm

Node 10 is also fixed so we need to specify an anchor. Use the toolbar on the left hand side of the graphics window (default location) to specify a restraint.

The Auxiliary Data – Restraints window will appear. Specify that the anchor is at node 10. The auxiliary data window can now be closed.

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CAESAR II Statics Training Pipe 1

Our first element is complete, and should look like the one below:

Use the Continue button to create a new element:

This next element is a 300# flanged gate valve. We could enter this in a number of ways. The valve will be rigid relative to the surrounding piping, so must be specified as a “rigid element” with a weight. This can be done either as 3 separate elements (flange – valve – flange), or as one overall element with the total length and combined weight specified. This can be done manually or by using the valve flange database to obtain the length/weight automatically from CAESAR II’s catalogue, which we will do. Select the Valve flange database button and select a gate valve with flanged ends, class 300.

The Flange – Valve – Flange check box can be used to split the component into 3 elements ifrequired.

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CAESAR II Statics Training Pipe 1

The element will appear in node 20 to 30.

The correct length will be inserted (and the element will continue in the same direction as the previous element). Also note that the Rigid check box is checked and the rigid weight has been entered with the relevant weight for a 300# gate valve and flanges. (Hover briefly over the Classic piping input where it is docked).

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CAESAR II Statics Training Pipe 1 Continue to the next element

.

Enter the DZ as -825mm. This element also leads into a bend, so press the Bend button on the right hand toolbar. If using the classic piping input we could check the bend check box to achieve the same result.

The bend auxiliary data window will appear.

The default bend type is a long radius (1.5D) bend This radius can be changed. Common bend radii are available in the drop down, alternatively any radius required can simply be typed in here.

In addition, further data can also be entered such as if the bend is flanged or mitred etc. Accept the default long radius bend. The graphics will not display the bend yet, as there is no following element.

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CAESAR II Statics Training Pipe 1 Continue to the next element

.

This time we are now continuing in the –X direction. DX is -1050. The bend will now be visible in the graphics. Continue to the next element

.

This element is a 10”x12” concentric reducer and is 203mm in length. Enter DX as -203mm and specify that this is a reducer.

The Reducer Auxiliary will appear and we can specify further data, including the second end size. A s before, entering a nominal size in here will be converted to the actual OD. Enter 12 in the diameter 2 and S in the thickness 2 fields, which will be converted to the actual values. Continue to the next element

.

Finally continue from the end of the reducer to the centre of the tee, 254mm as shown on the isometric. DX is -254mm The model at this point should now resemble the image below, note the node numbers in the image:

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CAESAR II Statics Training Pipe 1 We can now take advantage of the fact that the model is symmetrical and use the functions in CAESAR II to mirror the piping to create the opposite leg. Use the Select group function to activate the graphical selection mode and draw a window around the model.

All elements will turn yellow to indicate that they are currently selected. Ensure all components are selected. The Duplicate function can be used to copy, and mirror if required, selected elements.

Duplicate the selected elements and choose to mirror about the Y-Z plane.

We also need to increment the node numbers so that we do not have duplicate nodes. Currently our model goes from node 10 through to node 70. If we increase the node numbers by 70, node 10 will become node 80, 20 becomes 90 and so on. Therefore the second leg will be node 80 through to node 140. The only issue with this is that there are no common nodes, so the piping will not actually be connected. This can easily be fixed by chaging node 140 (the centre of the tee on the second leg) to become node 70 (the node at the centre of the tee on the first leg). This will connect up the piping at the common node, 70 – the centre of the tee.

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CAESAR II Statics Training Pipe 1

Click OK and the pipe will be duplicated, but as already stated there is no common node so CAESAR II does not know where to place the pipe. As such it locates it at the origin. The resulting model looks like the following.

All we need to do is connect element 130 – 140 to element 60 – 70. This can be done by changing 140 to become node 70. Select element 140. There are various ways of doing this – either double click in the graphics area, or user the navigation buttons to navigate to the correct element (as this is the last element the end button will quickly take you to the correct element).

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CAESAR II Statics Training Pipe 1 The Edit Node numbers window should now read 13 to 140 and the element will be highlighted in the model.

Simply change the “To” node from 140 to 70. The model will now be connected as should look like the one below:

We can now complete the model by adding the vertical leg and connection to the vessel. Skip to the last element. This can be done by again using the Last Element navigation button or using the Ctrl + End buttons on the keyboard. Click “Continue” to move to the next element need to change this to 70 to 140.

. The node numbers will default to 70 to 80. We

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CAESAR II Statics Training Pipe 1 This element is the vertical leg, and is 7m in the Y direction. DY is therefore 7000. This also leads into a bend so select the Bend icon as well.

.

Click “continue” and place the final element 140 to 150 in the –Z direction, 2000mm. The final element connects to the vessel, so we will place an anchor at this point. Click the retsraint button and specify an anchor at node 150 Notice in the isometric that at the vessel connection, there are DY and DZ displacements. These are due to the thermal expansion of the vessel.

Select the Displacements button and enter in the required values 3mm in DZ and 12mm in DY.

Error Checking The model is now complete, so run the error checker.

We will receive a fatal error and three warnings. We must correct the errors before we can analyse the model. The warnings may be acceptable but we should check to confirm that the input is as intended.

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CAESAR II Statics Training Pipe 1 So our error is mentioning that we have both an anchor and displacements speciified at node 150. This cannot be possible as the anchor fixes the point, but the displacements move the same point. We cannot have both at the same time. Remove the anchor and edit the displacements. Double click the error message to go straight to the area of concern. Now click the restraints button to remove restraints. Click OK in the message which appears. Now edit the displacements and fill in 0 in all other field (DX,RX,RY,RZ). A displacement of zero will fix the node in that direction, so now our node is fixed in all directions, except for DY and DZ where the relevant displacements are applied.

Re run the error checker and investigate the warnings. The second two warnings are regarding the reducer alpha angle which is not specified. CAESAR II is therefore using a default computed value. This is acceptable here for us. The first warning is stating that there is a geomtric intersectaion at node 70 (the tee) but we have not specified a type of tee, and therefore a SIF. This can sometimes be correct but is most often the result of an oversight, as in this case. Return to the input and locate node 70. The Find tool can be used to do this:

The Zoom to Node if found check box will also zoom into that node/element if it is found, useful on larger models.

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CAESAR II Statics Training Pipe 1 On node 70 use the SIFs/Tees button to specify a SIF at this point. This only needs to be done on one of the elements connecting to node 70, it is not necessary to do this on all three.

Select an unreinforced tee.

Re-run the error checker. All should now be OK, only the reducer alpha warnings will remain, plus the C of G report.

Review Load Cases Access the load case editor

Recall from earlier the design code (we are using B31.3) addresses the stresses produced by the various loads. In our model we have the following loads applied: Weight Pressure Temperature Displacement B31.3 requires that two checks are performed – Sustained and Expansion Sustained – Weight and Pressure Expansion – Temperature and Displacement

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CAESAR II Statics Training Pipe 1 These load cases are defined by CAESAR II as the default (recommended) load cases, shown in rows L2 and L3.

Row L1 is an operating case (OPE) and is the “Hot” case consisting of the ‘real world’ loads. This case is not required by B31.3 (although some codes do require this case also). However as this case is a “real world” scenario it is used to estalish restraint loads and loads on equipment conections. In addition, it is used to derive the Expansion case. The expansion case is the algebraic difference between L1 and L2 (L1 – L2). Accept these load cases and run the analysis by clicking the “Running Man” icon.

Review Results After the analysis has run, the output processor will appear. The first thing to notice is that the EXP case is coloured red. This indicates that this case has failed to code stress check. That is, the computed stresses in the system at some point are greater than the allowables published in the code. We need to fix this. Select the Expansion case and view the results for the Stresses report.

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CAESAR II Statics Training Pipe 1

The report shows that the code stress check failed and highlights in red where the check failed. Double clikcing on any column will order the report by that coluumn. Double click on the Code Stress column header to order by highest stress.

The overstress points are at nodes 70, 10 and 80.

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CAESAR II Statics Training Pipe 1 First we will check node 70. This is the tee. Look at the SIFs here. The in-plane SIF is 4.625 and the Out-Plane is 5.833. The stresses at this point are therefore being multipled by 4 and 5 times. If we can reduce these SIFs then the stress will reduce and can easily be reduced below the code allowable.

Return to the input and return back to node 70. Pick the Intersection SIF scratchpad and choose node 70.

Change the unreinforced tee to a reinforced tee. Specify a pad thickness of 10mm

Click the Recalculate button and notice the SIFs reduce dramatically. Now the stresses will be multplied by 2.887 and 2.415 rather than 4 and 5.

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CAESAR II Statics Training Pipe 1 Re-run the analysis using the batch run feature. The Expansion case is still shown in red, indicating the system is still overstressed. But check the Stress report for the Expansion case and notice that only nodes 10 and 80 are overstressed.

So what is happening at nodes 10 and 80? Nodes 10 and 80 are the initial anchor locations, so we need to find out what is causing the overstress. This is in the expansion case, so if we recall the code equation for the expansion case:

From this equation it can be seen that the dominant factor in the code equation is the bending moment – it is the only factor in the expansion case. So which bending moment is this, Mi, Mo or Mt? Mt is torsion, Mz and Mi and Mo are inplane and outplane – so vary dependant on the location. What we can see from the results though, is which bending moment is the highest in terms of our axes. View the Expansion case, Restraint Summary report.

We can see from this report that at nodes 10 and 80, the highest bending moment is the MY moment, at 116 kN.m. The MX is also rather high at 88 kN.m.

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CAESAR II Statics Training Pipe 1

So we know what is causing the overstress, but how do we correct this and reduce the bending moment (and therefore the stress)? Let us look at the 3D plot to view what is causing the bending moment. Close the report and view the 3D plot

In the 3D plot window which appears, ensure that the Load case we are viewing is the expansion case and select to Show the deflected shape. You may need to Adjust the deflection scale to get a more exaggerated deflected shape.

View the pipe from the bottom, using the standard views available

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CAESAR II Statics Training Pipe 1

We are looking upwards at the pipe from below. The Y axis is pointing upwards (away from us). The pipe is undergoing thermal expansion and causing the pipe to bend at the anchor points. Looking at the model from the side view will also explain the MX moment. As can be seen, the riser is expanding causing the MX bending moment.

If we could add some flexibility in to the area where the pipe is expanding we can absorb some of this expansion, and so reduce the bending moment. We have the top leg which is flexible, but the bottom leg is not flexible enough.

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CAESAR II Statics Training Pipe 1

If we can transfer some of the flexibility in A to B then we may solve the problem. To do this, increase the length of B by 1m and so consequently reduce the length of A by 1m. This should give us more flexibility at the bottom, hopefully without removing too much flexibility at the top. Return to the input and select element 30 to 40. The DZ value here is 825mm. Edit this to 1825mm.

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CAESAR II Statics Training Pipe 1

Repeat for element 100 to 110. We will have to also consequently reduce the length of 140 to 150 by the same amount (1m). Change this from 2000mm to 1000mm.

The model should now look like the one below.

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CAESAR II Statics Training Pipe 1 Re run the analysis and check the results. The expansion case is now no longer coloured red and the highest code stress is 91% of the allowable at node 10. We have successfully reduced the stresses and the model now passes the code stress checks. Verify the sustained stress report that this is still acceptable – it should be around 37% of the allowable. Our model is now compliant with B31.3.

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CAESAR II Statics Training Supt 01

Supt 01 This exercise is designed to demonstrate adding supports in CAESAR II and demonstrate the Operating case and Restraint load reports and give an indication of what the results mean on the restraint load report, along with a short example on how to combat issues with supports, such as “lift off”.

The model shown above will also be in your hand-out. Model the piping system as per this isometric. Anchor at nodes 10 and 90.

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CAESAR II Statics Training Supt 01

Locating Supports The system is anchored at the termination points (nodes 10 and 90), but we also need to support the weight of the piping system as well. If both supports are pinned (free to rotate), standard beam theory states that the max moment is at the centre of the span, l.

This moment is:

If both ends are fixed then the max moment is at the end of the span

This has a value of

Where

As piping systems are neither one nor the other and tend to be somewhere in the middle, a compromise therefore is reached with an approximation thus;

Taking into account the maximum moment could be somewhere between the ends and the centre – i.e. anywhere along the span.

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CAESAR II Statics Training Supt 01 This deals with continuous runs of pipe, however there are of course concentrated loads sometimes in the piping system, such as valves, flanges etc. The effects of these items on the pipe stresses can be estimated as well. For pinned connections, the maximum moment is located at the point of loading (P).

This maximum moment has a value of

Where a = longer portion of span b = shorter portion of span For fixed connections:

He maximum moment here is located at the end nearer the load, and has a value of

In either case (or in some case in between) the additional stress (M/Z) due to the concentrated loads should be added to the stress from the uniform load in order to determine the total stress. Examining the formulas above, it can be seen that as the shorter span (b) approaches zero in length, the moment, and therefore the stresses approach zero as well. So, if supports are located as close as possible to concentrated loads, the effects of these loads are reduced as much as possible.

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CAESAR II Statics Training Supt 01 The information on the preceding pages provides a simple rule of thumb to design for weight loading. First support all concentrated loads in the system as closely as possible, reducing the stresses due to those loads to as close to zero as possible. Next, we can use Along with If we knew the allowable stress, we could then use this information to determine a maximum allowable length of pipe – i.e. a distance between supports. Rearranging the equations above, we can obtain √

As this calculation will need to be done often, in order to save time calculating the Manufacturer Standardisation Society of the Valve and Fitting Industry has calculated allowable piping spans for various configurations. These standard spans have been published and are shown on the next page. These spans assume:

The pipe is standard wall with insulation Maximum moment is Mmax = wl2/10 No concentrated loads are present There are no changes in direction Maximum allowable stress is taken to be approx. 10 MPa Max deflection is approx. 2.5mm SIFs are not taken into account

It is rare that piping systems are only horizontal runs with no changes in direction etc.; therefore a caveat is taken in that changes in direction reduce the allowable span to ¾ of the standard span. In addition, the standard span does not apply to risers, since no moment (thus no stress) develops, regardless of length. However it is preferable to locate supports above the centre of gravity of the riser to prevent toppling. These rules here are simply rules of thumb and can provide a good start point for support locations. Of course, supports should be located with practical considerations taken into account (locations of building steel/pipe racks etc.).

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CAESAR II Statics Training Supt 01

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CAESAR II Statics Training Supt 01 Adding Supports to Model Let us now return to our model SUPT01.

As there is an anchor at node 10, the valve here is supported. The valve at 60-70 requires supporting. We will create a new node on element 50 to 60, called 57, and locate a +Y support here. Use the Break command to split the element into two. First select element 50 to 60 and choose the break command.

We will locate this support close to the valve (node 60). Specify to break the pipe and insert the new node, number 57, 150mm from node 60:

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CAESAR II Statics Training Supt 01

The element will be broken and a new node inserted close to the valve. Locate a +Y support at this node 57.

The +Y support will support the pipe from below, and will allow movement in the +Y direction.

All the concentrated loads are now supported. We can return and run through the piping system, placing supports as per the standard span. Check the table on page 48 to determine the maximum span for 12” pipe carrying water

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CAESAR II Statics Training Supt 01 The table on page 48 indicates that the maximum span for 12” pipe in water service is 7m. As discussed previously, for horizontal changes in direction, the support span is amended to ¾ of the standard span. 0.75 x 7 = 5.25m The valve is supported at node 10. After node 10 the piping continues horizontally with a bend. The maximum span therefore is 5.25m. This places our support round the bend.

The piping after the bend is 13715mm before the riser. This can almost be split in two exactly with our 7m span spacing. Remember that the standard span does not apply to risers, and as mentioned before we will support the riser from the top, rather than trying to balance it from the bottom. As such we can locate a support near the middle of the 13715mm run, and one close to the bend (node 30). Break element 30 to 40 and locate a new node number 33. Locate this 600mm from node 30. It is possible to add a support in at the new node location. We wish to add a +Y support at node 33, exactly the same support configuration as at node 57. So typing in 57 in the “Get Support from Node” field will place the same support as at 57 at our new node 33.

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CAESAR II Statics Training Supt 01 Repeat and break element 33-40. Break this 7000mm from node 33. Call the new node 37. Place the same +Y support from 33 (or 57) at this point too.

Continue on after the riser. There is already a restraint next to the valve, so we have fulfilled the minimum span up to the valve. After the valve we have horizontal pipe with a bend again. Therefore our maximum span is 5.25m. The length of pipe is 4115mm and then 3640mm after the bend. There is an anchor at the end, so we just need one more support between the valve and the anchor at the end of the pipe.

Locate this support on element 70 to 80, close to the bend at node 80. Locate this 600mm from the bend. Break element 70 to 80 and create a new node 77, 600mm from node 80 and with a +Y support the same as before.

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CAESAR II Statics Training Supt 01

Finally the piping riser needs to be supported. The length of horizontal run at the top and bottom of the riser is less than our span of 7000mm. There is no bending in the riser so in theory we can place a single restraint near the top of the riser. Break element 40-50 and locate a +Y restraint 600mm from the tangent intersection point of the bend. Note that, although this support should satisfy our bending requirements on the horizontal sections, it may have a very large load since it will also support the whole of the riser.

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CAESAR II Statics Training Supt 01 The support located in the riser may be difficult to see, as it is probably hidden by the piping. To view the support either the size of the restraint symbol can be increased, or the pipe can be set to translucent mode.

The system is now supported as per the maximum span requirements. We can be sure that the sustained stress case therefore is acceptable, and should be in the order of approximately 10MPa. Error Check the model.

You should receive only the Centre of Gravity report, and no errors or warnings.

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CAESAR II Statics Training Supt 01

Analyse Access the Static load cases create only a single load case with weight only. We wish to check the support locations we have just placed are below the acceptable limits

Run the analysis. View the Sustained Stresses report.

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CAESAR II Statics Training Supt 01

The highest stress level is 10.7MPa, which is almost exactly at the allowable from the standard span limit (this limit is based on an allowable of 1500 psi ~10.3MPa). The system is supported from a purely weight induced stress perspective. We can also now view the restraint loads to see how the weight loads are distributed. View the Restraint Summary report.

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CAESAR II Statics Training Supt 01 Again this look OK, all restraints are taking a downwards acting load (-FY), although the restraint at node 43 is rather large compared to the others; 30,000N vs. less than half that for the remaining supports. These loads however are due to weight only. Let us run now the cases required by the piping code B31.3. Return to the Static Load cases and select the recommended cases.

Run the analysis and view the sustained stresses. These will have increased slightly due to the fact that we are now including the pressure term; however the stresses are still well within the allowables determined by the code. Similarly the Expansion Case stresses are also very low and well within the allowable – the system is flexible unlike the PIPE1 example. Now we can check the restraint loads in the real world operating case. Remember the Operating case is not required by the code, but it does represent the actual loads in a “real world” scenario, for the purpose of designing restraints. View the Operating case Restraint Summary.

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CAESAR II Statics Training Supt 01

The loads are different to before as we have included the effects of thermal expansion. The load on node 77 is 0 (in the FY). This shows that this restraint is not taking any load. What is happening here? View the displacements report to see what is happening at this point.

At node 77 the pipe is moving upwards 2.3mm. Also notice that at node 50 (the bottom of the riser) the pipe is moving down 26mm.

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CAESAR II Statics Training Supt 01 Viewing the 3D Plot can confirm this:

View the deflected shape (you may wish to increase the deflection scale to exaggerate the deflected shape)

The 3D plot shows that the thermal expansion is causing the riser to expand downwards at the bottom (node 50). This in turn is causing the pipe to pivot at node 57 – giving the large operating load at node 57. The pipe pivoting at 57 causes lift off at node 77 – so we see a 0 load. The restraint at the top of the riser (at 43) is the datum point of expansion and so all the thermal expansion is from this point. That is why there is no expansion at the top and a lot of expansion at the bottom. We need to rectify this situation.

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Fix Model As we know, the riser is expanding due to thermal expansion. The datum point for this expansion is the support located at node 43, at the top of the riser, so all the expansion is going downwards – causing the lift off issue. To rectify this we can attempt to move the datum point of the expansion, so that the expansion is more evenly distributed. Insert an additional restraint on the riser. Call this node number 45 and locate this restraint 6000mm below node 43. Insert another +Y support at this location. This should have two effects: 1. Give a better distribution of the weight loads of the riser 2. Cause less thermal expansion downwards at node 50.

Re-run the analysis, the batch run command can be used as we have only made a small change by adding a support.

Review the stresses is the SUS and EXP cases. These stresses should still be acceptable.

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CAESAR II Statics Training Supt 01 Review the restraint report for the sustained and operating cases to see how the new restraint has affected the results.

The sustained case shows that we have a better distribution of the weight of the pipe on the riser, as the new restraint is taking some load. The load on node 43 at the top of the riser is now distributed between 43 and 45 (43 has dropped from 30kN to 9kN).

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The operating case however still shows lift zero load at node 77, and now also zero load at node 43. Checking the displacements also confirms this; there is still a positive displacement at nodes 77 and now at 43. Node 50 is still moving downwards, although only 15mm now.

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CAESAR II Statics Training Supt 01 We will attempt to further distribute the thermal expansion of the riser by adding a third restraint, located near the bottom. Break element 45-50 and create node 47. Locate node 47 6000mm below node 45 and locate a +Y support at this point.

Rerun the analysis and check that the stress levels have not been adversely affected. As before, view the SUS and OPE loads on the restraints to see how the new restraint has affected the analysis.

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The sustained report shows that we have further improved the weight distribution among the restraints.

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The Operating case now shows a negative load on restraint at node 77. There is no more lift off here at 77. However the operating loads at node 43 and 45 are now zero. All the thermal expansion that was going downwards with only the one restraint at the top of the riser has now been forced upwards instead, causing the pipe to lift off at the top of the riser (43 and 45). The displacements report confirms this

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CAESAR II Statics Training Supt 01 The pipe is lifting off 22mm at the top of the riser. The 3D plot can also confirm the situation:

So we have a situation where we are supporting the weight of the system adequately in the SUS load case, but we have an issue with the thermal expansion. If we replace the rigid +Y restraints along the riser with Variable Spring Hangers (VSH), these hangers should allow thermal growth whilst also supporting the required weight for the SUS condition.

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CAESAR II Statics Training Supt 01 Place Spring Hangers Return to the input at locate element 40-43. Remove the restraint at node 43 by double clicking the restraint check box. Place a hanger here instead. Double click the Hangers check box

Select the Hanger table as Carpenter & Paterson. Carpenter & Paterson are a UK manufacturer whose database of available spring hangers is programmed into CAESAR II. CAESAR II will automatically calculate the required load and movement at the location, and then review the database to select an appropriate spring for the calculated load and movements. Notice that 2 hangers are located at this location also. The graphics will not change in CAESAR II, but this will locate 2 hangers at this location, and the selected spring will be based upon this shared load.

Error check the model. You should now notice two further notes during the error check.

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The first not simply shows the number of hangers in the job, and how many of these hangers will be designed by CAESAR II at run time. The second message states that new load case combinations are required for the hanger design. A load case for weight loads is required, so that CAESAR II knows how much weight the hanger(s) need to support. Secondly, a hanger design operating case is required. This case determines the thermal expansion at each restraint location to determine the movement at the spring hanger locations as well. The values of weight from the previous weight load case are used. These two cases together are used by CAESAR II’s spring selection algorithm to select the appropriate spring from the in-built catalogue. Access the load case editor to create these new load cases.

Click the Recommend button in the load case editor. CAESAR II knows that there are hangers present that require designing, so will recommend the correct load cases for hanger design – cases 1 and 2.

Accept these cases. Note the stress type for these cases are HGR type. The results for these hanger cases are supressed by default (theses are pre-analysis cases and the figures do not actually mean anything other than for the spring hanger selection). Case 1 W (HGR) This case performs a Weight Analysis only with all support locations as rigid restraints. This tells the spring selection algorithm how much weight needs to be supported at each location (usually in the Operating condition)

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CAESAR II Statics Training Supt 01 Case 2 W+T1+P1 (HGR) The case uses the support weight values derived from case 1 as upward forces for an Expansion analysis. That is, the values of W cancel each other out (support load versus actual weight), and the system is then subject to temperature T1 in order to establish the thermal movement at each restraint location. Given the Weight to be supported and the thermal movement at the same location, the spring and its associated stiffness values can be selected and incorporated into the subsequent load cases. Run the analysis

CAESAR II will have selected and sized a spring hanger during the analysis. Check the Hanger Table with text to view the hanger properties of the selected hanger.

As can be seen, CAESAR II has determined that the hanger will need to support a hot load (i.e. OPE) of 6723N. There are two springs at this location, so this 6723N is the total load shared between two supports (i.e. the total load is 6723N x 2). CAESAR has taken these properties and browsed the inbuilt Carpenter & Paterson database and selected a DV70 Size 11 spring. Verify the sustained and expansion stresses – these should still be acceptable (13% and 19%). Now check the OPE restraint loads.

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CAESAR II Statics Training Supt 01

The hanger at node 43 is now taking load. This load is 13447N (which is 6723N x 2), however there is still no load being taken at node 45. Return to the input and replace the rigid +Y support at node 45 with a spring hanger. As before, select the Carpenter & Paterson catalogue, and place 2 hangers at this location before re-running the analysis. As before the SUS and EXP stresses are acceptable. The OPE case Restraint summary now shows that all the restraints are taking load. The new spring hanger is taking some of the load of the riser – this is now distributed evenly.

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CAESAR II has again run the two hanger cases and used the results from these to select appropriate hangers for placing at the two hanger locations. These can be seen from the Hanger Table with text.

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CAESAR II Statics Training Turbo

Turbo This exercise will build upon knowledge we have gained so far, and introduce the following new features.

Combining Pipe Models Rigid Construction Elements CNode Connections NEMA SM23 Analysis

The model is shown above and is also supplied in the hand-out in a larger format. As can be seen, this is an inlet and exhaust on a turbine. The turbine itself is anchored to the floor at the anchor point specified. To keep modelling simple, we can model the inlet and exhaust as two separate models. These two models can be combined into a single model later – there is a common location at the turbine anchor point. We will model this common anchor point location as node number 5. However, we will come back and model this point last.

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Model Inlet Model the inlet pipework, on the first element; change 10 to 20 to 11 to 20. Begin at node 11, the flange connection to the turbine nozzle, as shown below. Note that node 11 also has an anchor attached.

Once the inlet piping is complete, return to the first element, 11 to 20. We will now insert an element before 11 to 20, numbered 5 to 10. Node 5 will be the turbine anchor location. Node 10 will be connected to the anchor at node 11. We will connect these via CNode connections. As there is an anchor at node 11, this node is fixed in all 6 degrees of freedom. However, the nozzle connection on the turbine will undergo some movement due to the thermal expansion of the turbine. Recall previously that we had a similar situation where displacements were specified to account for a similar situation in PIPE 1 for the vessel thermal expansion. In this case, we do not know what the thermal expansion is here so we cannot enter the displacements. To apply the displacements to the nozzle point we will add in an element from the nozzle to the turbine base. This will be a rigid element with zero weight, and it will have temperature applied (so it will undergo thermal expansion). This element will also be anchored at the turbine base. If however we specified this as 5-11 for example, nodes 5 and 11 are both anchored, so cannot move and all that will happen is we will obtain large forces at nodes 5 and 11. We need a way of connecting this rigid construction element to node 11 which will allow node 11 to move due to the expansion of the construction element, but still be fixed as far as the rest of the piping is concerned. This can be achieved in CAESAR II this using CNodes. A CNode will allow the anchor at node 11 to be connected to another node “indirectly”. Essentially, both these points will be at the same location, but CAESAR II will see these points as separate nodes. Therefore what will happen is that as element 5-10 expands, node 11 will act as an anchor, but as it is connected to node 10, node 11 will move to wherever node 10 moves to, while still acting as an anchor.

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Nodes 10 and 11 are the same point in space. Select element 11-20. First specify a CNode on the anchor at node 11; the CNode will be node 10.

Next use the Insert function to insert an element before this element.

Change the node numbers to 5 to 10

Fill in the DX, DY, DZ fields as shown on the isometric sketch

This is a rigid element, but leave the weight blank in this case. Also add an anchor at node 5.

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The zero weight rigid will be inserted and connected to node 11 as above. We now need to specify the temperature for the rigid, as this will undergo thermal expansion. Select element 5-10 and double click the “>>” on the temperature/pressure section to “tear off” the Operating Conditions box. Uncheck the Propagate parameters box to ensure that the data entered here is only entered on this one element, and not the whole model. Enter 200°C for T1 and make sure that no pressure is specified.

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CAESAR II Statics Training Turbo Check that this has been specified correctly, by using the Show Pressure graphical tool.

Display P1.

The rigid construction element should show as unspecified, and the rest of the model should show as 12 bars.

The inlet is now complete. Save the file and using the same concept, create a new job file for the exhaust. Start the exhaust using nodes 1011 to 1020 for the first element.

Continue on. After the reducer, there is a bend. Place a length of pipe 350mm long in the Z direction, adding a bend to this pipe. Place a corresponding pipe 350mm long in the Y direction afterwards to complete the bend.

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Complete the rest of the exhaust. Once finished, add one final element, inserted before 1011 to 1020 and numbered 5 to 1010. Set the pressure for this element to blank, and ensure that only this element has no pressure. Connect via a CNode of 1010 at the anchor at node 1011. The exhaust is now also complete. Notice that we have a node numbered 5 in both our inlet and exhaust models. This node is a common location in both files. As such we can combine the models and they will be linked at node 5.

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Combine Models Save the Turbine exhaust as Turbo_Combined.c2 Select the Include Piping Files button to bring in the Inlet piping to create one single model.

Browse for the inlet model and click OK.

The two models will be combined around node 5 – the common node in both files.

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CAESAR II Statics Training Turbo Select an element in the inlet. Notice that it can be selected, but the input screen has all fields disabled.

This is because currently the inlet is simply being “referenced” and not fully included. Return back to the combine pipe models screen. As well as the File name field, there are three other columns. RotY – allows the included file to be rotated by a specified angle about the Y axis. Inc – allows the node numbers in the new file to be incremented by a certain value. i.e. if the file included was 10-20, 20-30 etc., we could increment by 1000 so that the nodes would become 10101020, 1020-1030 etc. The final column is Include Now? This column allows users to choosing whether to reference or actually permanently include the file. This can be useful if checking that the file is correct before including, so any changes required can be done in the original separate model. If your model looks correct, change Include Now? to Y.

Selecting an element in the inlet side of the piping will now show all the fields to be enabled.

Error Check and analyse the model, use the recommended load cases. The analysis results should show that the expansion and Sustained stresses are acceptable. Check the OPE case and note the loads on the nozzles at nodes 11 and 1011.

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There is a reasonable force on these nozzles, as the anchor points are supporting some of the weight of the pipe. We will now take these forces and check them against NEMA SM23 to analyse the turbine to see if the loads on the nozzles are acceptable.

NEMA SM23 The National Electrical Manufacturers Association (NEMA) publishes and maintains a standard SM23 Steam Turbines for Mechanical Drive Service. This standard includes allowable loads that can be applied safely to our turbine nozzles. CAESAR II incorporates this standard and a separate module can be used to evaluate nozzles, using calculated loads from the piping analysis (as we have just done). Return to the CAESAR II main window. Select the Analysis menu and select the NEMA SM23 option to load the module. You may need to use the to access the whole menu.

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CAESAR II Statics Training Turbo Create a new file called pass1. If you wish, give the equipment a short description. Select the NEMA Input Data tab. The first data to enter is the direction of the equipment centreline. This must be specified as the direction Cosines.

The direction cosines are specified as the cosine of the angle of the centreline with the respective axis. For example, if the centreline was as shown above, 60° from the Z axis and 30° from the Y axis, the direction cosines would be: Z = Cos 60° = 0.5 X = Cos 30° = 0.866 Our equipment centreline is along the Z axis, so the angle between the centreline and the Z axis is 0° and the angle between the centreline and the X axis is 90° Therefore the direction cosines are: Z = Cos 0° = 1 X = Cos 90° = 0 Now we can define the nozzles. Click the Add Nozzle button

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CAESAR II Statics Training Turbo The Node number is the corresponding node number which matches the node number in the CAESAR II model. Specify the Inlet first – so this node number is 11. This is the Inlet nozzle and is 4” diameter The next box is the Distance from Resolution Point to Nozzle. NEMA SM23 is ambiguous about the point of resolution of the combined forces and moments. Select one of the three fields and hit F1 to bring up the help.

This point is the distance from the resolution point (face of the exhaust nozzle flange) to the nozzle at node 11. This is as follows: DX = +100 -150 = -50 mm DY = -300 + 500 = +200 mm DZ = +450 + 50 = 500 mm The basic nozzle information is input. The final thing to do for this nozzle is to apply the loads on this nozzle. We already have the loads in the CAESAR II job file that we have just analysed. So these loads can be imported straight into NEMA SM23 module. Click the Select Loads Job and Load Case button.

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Browse to the combined turbine model and select the operating case.

The loads will be imported from the job, these will be the loads at node 11 (as we specified the node number as 11).

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The inlet nozzle is now complete. Select to add a new nozzle and enter the Exhaust nozzle details. As before, import the loads from the OPE case in the combined job file.

Once complete, analyse the model using the “Running Man” icon.

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CAESAR II Statics Training Turbo Another tab will now be present showing the results of the analysis. The analysis fails.

The Inlet and Exhaust both fail the analysis. A closer look at the results shows that the FY and MZ moments are by far the leading causes of the failure. The FY is 214% of the allowable, while the MZ is also 182%.

Save and Close the NEMA module and return to the piping input.

Looking at the input, it can be seen that the weight of the piping causing the FY will also clearly result in the MZ moment being excessive – there is very little supporting the weight of the piping other than the nozzles themselves. The only other supports are on the headers. We need to support the weight of the pipe. Let us focus on the Exhaust first. Let us support the weight of the pipe to reduce the FY component. Locate a Y support below the elbow. This will be node 1039. We have not defined node 1039, only 1030 and 1040; so why 1039? When building the model, it is built in the following way:

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CAESAR II Statics Training Turbo Once a bend is inserted, CAESAR II moves node 1040 to the end of the bend, and inserts two intermediate nodes:

These intermediate nodes are added by default at 0° around the bend, and at the mid-point of the bend. This can be seen in the Bend auxiliary data (single click on the bend check box on element 1030 – 1040). M is used to designate the mid-point of the bend.

These nodes can be moved to the required location if needed for any reason by simply editing the angle. But we just wish to add a +Y support under the mid-point of the bend, at node 1039. Add a +Y at 1039.

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Re-run the analysis. Check the SUS and expansion stresses, these should again be OK. Now review the OPE case restraint summary to check if the load on node 1011 has reduced. The loads on node 1011 are the same. The loads on 1039 are 0. This restraint is not taking any load in the OPE case.

View the 3D plot to see the reason for this. View the deflected shape (you may need to increase the deflection scale). From a left view, it can be seen that the expansion is causing the pipe to lift off the support at node 1039.

The Operating/Displacements report confirms this, node 1039 is experiencing 0.614mm displacement upwards – lift off.

The load on node 1011 has not changed. As such there is no need to run another NEMA analysis – the results will be identical. Therefore, return to the input.

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CAESAR II Statics Training Turbo Change the design by replacing the Y restraint with a spring hanger. Select a Carpenter and Paterson spring hanger, and enter -500 in the Available Space field. The can will be shown as below.

Re-run the error check and visit the Load cases window. We have added spring hanger into our model, so we require` the hanger cases to determine the hanger size. Use the recommended load cases again and analyse.

As before, the SUS and EXP cases are well within the code allowables. Check the restraint summary for the OPE case.

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The spring hanger is taking some load now (4800N) and the load on the restraint at 1011 is much reduced. Return to the NEMA module and we will re-analyse with our new loads. Save As… on the existing NEMA file, and select Nozzle 2 of 2 – the exhaust. The Inlet has not changed so there is no need to re-import the inlet loads. Refresh the loads from the current job to import the new changed data.

Once done, rerun the analysis. The exhaust now passes at 79% of the allowable.

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CAESAR II Statics Training Turbo The Inlet of course still fails as we have not changed this. Now let us reduce the load on the inlet. To do this, break element 40-50 with a new node number 42. This node should be 300m from node 40. Locate a spring hanger at node 42. As before, select Carpenter & Paterson. Re-run the analysis and check the OPE restraint summary. The load on node 11 will be reduced.

Return to the NEMA module and Save As… this file. Re-import the loads for the inlet nozzle and rerun the NEMA analysis. The Inlet should now also pass.

The whole turbine passes

The piping system is acceptable in within the code allowables, and the loads on the turbine are also within the allowables of NEMA SM23.

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CAESAR II Statics Training Manifold

Manifold This exercise demonstrates multiple load cases can be used along with multiple operating conditions in order to evaluate various “what if” scenarios. In addition, the API 610 module is used to evaluate loads on pumps. Other features shown include naming nodes and naming load cases to make reviewing the results easier. The model below will also be on the hand-out. Notice that the three branch legs are virtually identical. The input should be setup to take advantage of this trait through the use of the element duplication facility.

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CAESAR II Statics Training Manifold Begin at node 10 and model all the way to the end anchor as shown. Note that the bend has not yet been specified at node 70.

Use the duplicate feature to create the remaining two legs for Pumps B and C. Increase the nodes by 1000 each time. You will not see the new elements initially, as they will be in the same location as run 10 to 70. Find elements 1060-1070 and change to 1060-90. Also do the same for 2060-2070 and change to 2060100 The elements will all now be connected. Finish by specifying the bend at node 70.

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CAESAR II Statics Training Manifold Now that the model is complete, we can enter the loading information. The hangers are to be designed with the entire system hot. Then, each branch line must in turn be run at ambient with the remainder of the system hot. These four conditions can be evaluated in a single run, using four different temperature and displacement vectors. First we will label the pump locations so that we can easier review these locations in the results. Select element 10-20 and double click the Name check box.

Specify that the from Node (node 10) is labelled as Pump A

Repeat this for Pumps B and C Next we wish to reduce the loads on the pumps by having the hanger support the riser weight. The hanger algorithm works by distributing the weight evenly among all supports. If we free the pump in the Y direction at node 10, this will ensure that the weight is not distributed at this point – and so is supported by the hanger. Do this by specifying the Hanger as follows:

Repeat this for Pumps B and C.

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CAESAR II Statics Training Manifold Now we need to specify the loading conditions, as mentioned before, we wish to evaluate the system in four conditions. We can do this by specifying four different temperature/pressure cases, and four different displacement vectors at the pumps. All pumps on Pump A idle Pump B idle Pump C idle

T1 T2 T3 T4

P1 P2 P3 P4

D1 D2 D3 D4

Enter the temperatures as follows. The element listing displays the value in red whenever it changes from the previous value.

Use the graphics to verify that the temperatures are correct. Note that the temperatures do not simply stop being 120°C and suddenly drop to ambient. The way we have entered the temperatures give a basic approximation of a temperature gradient.

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CAESAR II Statics Training Manifold T1 – All same temperature

T2 – Pump A idle

T3 – Pump B idle

T4 – Pump C idle

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CAESAR II Statics Training Manifold Perform a similar task with the pressure. Only this time the pressure will drop from 20 bars to 0 after the valve. It is at fill pressure right up to the valve, then it will drop. Enter the pressures as shown below:

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CAESAR II Statics Training Manifold Again the graphics can be used to verify the correct pressure has been specified P1 – All same pressure

P2 – Pump A idle

P3 – Pump B idle

P4 – Pump C idle

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CAESAR II Statics Training Manifold Finally we need to specify the pump nozzle displacement. The pump discharge nozzle vertical growth is 0.75mm, when the pump is running. Therefore we also need 4 displacements at each pump. Enter the displacements as in the table below. An example for Pump A is shown in the screenshot afterwards.

D1 D2 D3 D4

Pump A 0.75 0 0.75 0.75

Pump B 0.75 0.75 0 0.75

Pump C 0.75 0.75 0.75 0

The model is now complete. Run the error checker. You should receive 3 notes – two on the hanger design, plus the C of G report. Correct any errors or warnings you may receive. Access the Static Load cases. We require a number of load cases now – one each for SUS, OPE and EXP for each of our situations, i.e. 12 cases. Plus we require the hanger design cases. The hangers should be designed for the system when all pumps are hot. The recommended cases should satisfy these requirements.

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CAESAR II Statics Training Manifold As we have a number of load cases now, it is becoming a little confusing to work out each time which combination of loads is which case. To make this easier, we will rename the load cases. Access the Load Case Options tab and rename the load cases to reflect the situation.

Run the analysis The list of load cases will still be the CAESAR II Load Case name. To change this, go to Options > Load Case Name and select User Defined Loadcase Name instead

In addition, to make it easier to identify the pumps, choose to display the Node Name in the reports as well as the number. Again, this is accessible via Options menu > Node Name

Verify that the system is within the allowables for B31.3 in all situations, both EXP and SUS. Also check the OPE loads on the pump nozzle connection.

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API 610 Analysis The model is complete and satisfies the requirements of B31.3. We can now evaluate the pump nozzles to ensure that the nozzle connections satisfy the requirements of API 610 for the pump. A total of 12 API-610 evaluations must be made in order to find the worst case scenario. These scenarios are shown below: Pump A – All pumps on

Pump A – Pump A idle

Pump A - Pump B idle

Pump A - Pump C idle

Pump B – All pumps on

Pump B - Pump A idle

Pump B - Pump B idle

Pump B - Pump C idle

Pump C – All pumps on

Pump C - Pump A idle

Pump C - Pump B idle

Pump C - Pump C idle

Access the API-610 module from the CAESAR II main window and create a new file for the first iteration – Pump A with all pumps activated.

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Move to the Input Data tab to specify the data for the pump. Note the API coordinate system is different from the CAESAR II coordinate system, hence API My aligns with CAESAR II Mz. We are also only concerned with the Discharge nozzle; as such we do not need to enter any data into the Suction Nozzle tab or fields. We wish to evaluate the discharge nozzle. This is pump A, so the nozzle is node 10. Fill in the correct data for Node 10.

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Now we need to specify the loads on the discharge nozzle. As before, these loads can be imported from the analysis just done. Select Load Case 3 – Operating case for all pumps active.

Also, for the analysis, we will assume that the distance from the centreline to the nozzle is zero.

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All the data has been input, so the analysis can now be run.

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The results show that Pump A is OK for this condition. However, to determine the worst case, we must perform the other eleven evaluations. Repeat the above task for all the remaining pumps.

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CAESAR II Statics Training Manifold After completing all twelve iterations, you should notice that one of the iterations fails. This is Pump C with Leg B Idle.

From these results, it can be seen that the local Y moment is failing, and is 262% of the allowable. As mentioned previously, the API-610 coordinate system is different to the CAESAR II local coordinate system. The local MY translates to the MZ in CAESAR II. Return to the piping static output and review the results. View the restraint summary for all the Operating cases.

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CAESAR II Statics Training Manifold The MZ for Pump C in case 5 is the highest of any MZ moments – confirming the findings of the API 610 analysis. View the 3D plot and view the deflected shape for Operating case with Pump B idle.

The datum for the thermal expansion is the line stop at node 80. The expansion at the leg for pump C is the greatest, and so is causing the higher moment at this point. Similar to the exercise SUPT01, if we can adjust the datum for thermal expansion, we should be able to reduce the amount of expansion which is causing the moment on Pump C. This can be done by moving the line stop from node 80 to node 110. Remove the Z restraint at node 80 and add a new Z restraint at node 110, then re-run the analysis. Notice now that the restraint summary shows that Pump C has a much lower MZ now. The loads have been more evenly distributed (Pumps A and B have slightly greater loads, but these pumps were OK anyway).

Return to the API 610 module and open the file which failed previously -

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CAESAR II Statics Training Manifold Select the Discharge nozzle tab. The loads on this pump have changed, so we will have to import these new loads. Use the Refresh Loads from Current Job button to bring in the new loads and re-run the analysis.

This time the pump should pass – as we have reduced the loads sufficiently

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Tutor This exercise will develop various sequences of “run – evaluate – modify” workflow to determine the acceptability of the system. Each of the evaluations of the system will develop another aspect of CAESAR II. Once the system is acceptable, we will generate a custom report and stress isometrics.

System parameters Pipe: 8” diameter, standard wall, ASTM A-53 Gr. B Analysis temperature: 315°C Analysis pressure: 2 bar Corrosion allowance: 0.8 mm Insulation: 75 mm CaSi Fluid: 0.8SG Pipe Specification: 150 pound class components Design Code: B31.3

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CAESAR II Statics Training Tutor Node 10 is connected to a Pump and node 110 is connected to a vessel Nozzle. Their details are as follows: Pump Details: 10 inch end suction, 8 inch top discharge Suction is -380 mm in X from pump centre Discharge is 500 mm above and 300 mm in Z from pump centre Piping load on suction nozzle given as: (4450,-3550,-5340) N and (-4070,-3390,2170) N-m Nozzle Details: Fixed end is preceded by a long weld neck flange in the -Z direction: OD=247.65, wt=22.225, length=300 mm, weight=458 N and a standard, 8 inch weld neck flange and gasket

Model the system as shown in the isometric. When modelling the bypass loop, the Close Loop command can be used if required to connect node 150 to 60. Change the node numbers to 150 and 60 and click the close loop button. CAESAR II will add in an element of the required length automatically.

The completed model will look as the one below.

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CAESAR II Statics Training Tutor Boundary Conditions We now need to specify the boundary conditions for the analysis. The piping is connected to a pump and a vessel at the termination points, so we can apply the effects of these to the relevant nodes. Pump Connection – Node 10 The discharge is 500mm above (Y) and 300mm in Z from pump centre We have two options for the approach here. 1.

Calculate the thermal growth of discharge nozzle from pump base point. Alpha= 0.003832 mm/mm Displacements therefore: X=0 Y = 500 x 0.003832 = 1.916 mm Z = 300 x 0.003832 = 1.1496 mm No rotational displacements

2. Add a construction element between the nozzle node (10) and the pump base with appropriate material and temperature. For this exercise, specify the displacement set for node 10 as above.

Vessel Connection – Node 110 As before we have the same two approaches; provide the thermal growth of the nozzle, or model the vessel. The thermal growth of the vessel is X=0 Y = 8.43 Z = -2.87 RX = 0 RY = 0 RZ = 0

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CAESAR II Statics Training Tutor Support Riser We wish to unload the pump discharge nozzle as much as possible, and also support the thermal growth of the riser. To do this we will locate a spring hanger near the elbow (node 70). Place a Carpenter & Paterson hanger at node 70

Support Horizontal Runs The suggested maximum support spacing for 8” water filled pipe is 5.8m for horizontal straight runs. 75% of that spacing for horizontal spans including changes in direction would therefore be 4.35m. This will support the pipe weight and so account for the SUS case. Since we will check these SUStained stresses (and since the fluid weight is less than water-filled) we can exceed the suggested spacing. Locate a restraint on each horizontal 8” run using the Break function. 70-80 add node 75, located 1200mm before node 80 80-90 add node 85, located 3000mm after node 80 Add the following restraints: Node 75 1x (double acting) Y restraint, with a friction coefficient of 0.3 1x guide with a gap of 8mm, again with friction

Node 85 1x (double acting) Y restraint, with a friction coefficient of 0.3

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CAESAR II Statics Training Tutor The model is now complete. Error Check the model and run the Recommended load cases. Immediately it can be seen that there is an issue with the EXP case. Check the stresses for both the EXP and SUS cases. The SUS case is OK

The EXP case however is an issue:

The only issue is at node 30, where the stress is 130% of the allowable.

Node 30 is the Tee connecting the bypass. One of the easiest fixes for an overstressed component is to replace it with a stronger component. Component strength is indicated by the stress intensification factor (SIF). Here, the stub-in branches are overstressed. Their in-plane SIF is 3.96 and their out-plane SIF is 4.95. Adding a pad to these tees will strengthen them. Check the effect of adding a pad by using the Tee SIF Scratchpad. Change the unreinforced tee to a reinforced tee with a 9mm pad. Using the Recalculate button will show that the SIFs have been reduced to 2.04 and 2.38 for in-plane and out-plane respectively.

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Accept these changes and apply to node 30. Re-run the analysis and review the results. The expansion case is now ~75% rather than 130%.

The SUS case is still 14%. Hanger Sizing Review the Hanger table with text. A Carpenter & Paterson DV70 spring is selected.

Hot Load 1355N, deflection 17mmm cold load 1544N. We need to now see if this is appropriate. View the Restraint summary for the OPErating and installed (SUS) cases.

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Look at the operating load and installed load on the pump discharge nozzle (node 10). Typically, with a spring hanger above the pump, the pump will see a positive (up) load in the cold state and a negative (down) load in the hot state. Here, the piping pushes down on the pump in both states. This spring is undersized. Why? The calculated load carried by the spring is based on the overall distribution of weight between all vertical supports. The interaction of the pump nozzle (anchor), the spring and the other Y supports has very little load “assigned” to the hanger location. More weight is carried by the pump rather than the spring hanger. Deadweight that is resting on the pump must now be transferred to the hanger. The easy way to do this is to remove the load-carrying capability of the pump in the initial weight analysis when the hanger load is first calculated. To do this, CAESAR II allows the restraint to be “freed” – effectively removing this node from the hanger sizing calculation, so the load is distributed amongst the remaining support locations. Return to the input and on the hanger; free the restraint at node 10 in the Y axis:

Now reanalyse the system. Review the results again.

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CAESAR II Statics Training Tutor The EXPansion stress results are unaffected by this hanger change. The maximum SUS stress ratio is also still around 14%. Review the hanger table with text.

A Carpenter & Paterson DV70 has been selected again, but the hot load has increased to 7000N and the installed load has increased to 8000N. Review the restraint summary report to view the pump load (node 10).

The resized spring now pulls up on the pump in the cold position and unloads as the system heats up. (The riser growth drops the load supplied by the spring.) This spring is much better than in the first iteration; however it could be improved even more. The hanger data input provides for the specification of the hanger operating (hot) load:

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CAESAR II Statics Training Tutor Pump Load Review the restraint summary report for the OPE and SUS (installed) cases. The loads shown for the pump are a little high in some directions – MX is almost 30000N. However no indication is given that these loads are excessive.

American Petroleum Institute Standard 610 (API 610) sets maximum nozzle loads for pedestal supported pumps. CAESAR II provides this calculation. Run this analysis with the pump data provided above and using the discharge loads from this analysis. Since both suction and discharge nozzles are evaluated together, the Table 4 limits in API 610 can be doubled (see API 610 Annex F).

API 610 Analysis Access the API 610 module from the Analysis menu on the main window.

Create a new file and input the pump data. The pump centreline can be seen to be in along the X axis, therefore the angle between X axis and pump Centreline is 0°. The angle between the Z axis and the pump centreline is 90°. The direction cosines are therefore X Cosine = cos 0 = 1 Z Cosine = cos 90 = 0 The Base point node number can be any arbitrary node number. This node number does not have to appear in any of the piping model, but is used by API 610 as a point of reference about which to sum moments. The suction Nozzle is not defined in the piping model as we are given the loads so can input these. We also know that this is a 10” End type suction nozzle. The discharge nozzle is in our piping model, and is node 10. This is an 8” Top type suction nozzle. As mentioned, since both suction and discharge nozzles are evaluated together, the Table 4 limits in API 610 can be doubled.

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The suction nozzle loads and location have already been given: Suction is -380 mm in X from pump centre. Piping load on suction nozzle given as: (4450,-3550,-5340) N and (-4070,-3390,2170) N-m

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CAESAR II Statics Training Tutor The pump discharge nozzle is located 500 mm above (Y) and 300 mm in Z from pump centre. The loads on the discharge nozzle can be imported from the piping model. This will be the OPE case.

Now analyse the pump. The suction nozzle passes OK. But the discharge nozzle fails.

The load in the local Y direction (global Z) is excessive as are all three moment terms. The worst component is the local My (global Mz) which is almost 10 times the Table 4 limit.

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Fix Model – Part 1 We need to know what is causing this large load. Return to the piping model and again view the results. Review the Restraint summary for the OPE and SUS (installed) cases.

The large loads are present in operation but not at “installation”. Therefore these excessive loads are caused by the thermal expansion of the system. To reduce these loads we need to increase system flexibility. There are two options to do this. 1. 2.

Model existing flexibility not currently in the model Modifying the piping and/or support layout.

The most inexpensive modification would be to provide more modelling detail – modelling flexibility in the system that is not currently included. Welding Research Council Bulleting 297 provides flexibilities for cylinder – cylinder intersections. These flexibilities may be applicable to the vessel connection at node 110. Include WRC 297 flexibilities The vessel nozzle/connection is as follows:

Vertical vessel constructed of SA-516 Gr. 70 OD = 1500mm (D), wall = 4.75mm (T) Nozzle is 2200mm above skirt Skirt is 3000mm above foundation The long weld neck flange serves as the nozzle OD=247.65mm (d), wall=22.225mm (t) Nozzle pad is 4.75mm thick and 100mm wide A tray is within 600 mm of the nozzle and a stiffener ring is 1000 mm on the other side Firstly we must evaluate the vessel/nozzle to check that the WRC 297 approach is valid. We have d and t (relating to the nozzle) and D and T (relating to the vessel) described as above. Below, T is the vessel thickness plus the pad thickness. According to WRC 297: ⁄ ⁄ ⁄

⁄

⁄

⁄

We will use this data even though it is outside the acceptable range Apply the nozzle flexibility and complete the vessel/nozzle data in the Nozzles input.

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The nozzle node is at 110 (recall that the nozzle is represented by the long weld neck). A valid nozzle node has only a single element connecting to it (i.e. must have a free end) and also a nozzle node is not restrained nor does it have any displacements specified. We have displacements applied at node 110, for the vessel thermal growth. To rectify this we will specify a vessel node and apply the displacements to the vessel node. The vessel node is optional and works in a similar way to CNode described earlier. Give the vessel node a unique number. In this case ours will be 1500. In addition, change the node the displacements are acting on to 1500 as well. Fill in the remaining vessel data, including the direction cosine – the vessel is vertical (Y) so the Y direction cosine is 1.

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CAESAR II Statics Training Tutor This models the nozzle flexibility by inserting a zero length spring which is inserted between the long weld neck flange (100-110) and the displacements representing the vessel thermal growth – which we have now reassigned to node 1500. Run the error checker. The WRC nozzle flexibilities will be calculated and included in the notes.

The nozzle provides limited axial flexibility, but the longitudinal and circumferential bending flexibilities appear significant. Re-analyse the system and again review the results. Review Results These changes have not had any effect on the SUS case, and the EXP case is still below the allowable, in fact the highest stress has now dropped slightly - as we have added more flexibility in the model. The selected spring hanger is still a Carpenter & Paterson DV70, but the hot load has increased by around 40N. However, we were previously concerned with the pump loads. Review the OPE case restraint summary. The loads on the pump (node 10) have now decreased.

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CAESAR II Statics Training Tutor Run these new loads through the API 610 processor. Use the “Refresh Loads from Current Job” button to bring in the new loads.

The values have decreased slightly, but still the discharge nozzle fails.

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Fix Model – Part 2 Return to the piping results and review the OPE restraint summary once again. There is a rather large load on the guide (Z restraint) at node 75.

The thermal growth of the long Z run from 80-90 loads the guide and pushes the elbow at node 70 in the positive Z direction. This thermal growth increases both the pump load in Z and the bending moment about X. Is the structure guiding the pipe as rigid as the CAESAR II model says it is? If the guide has lower stiffness, the pump loads may reduce within their allowed limits. There may be reason, then, to model the structural steel that is interacting with this piping system. There are two structures – a frame under Node 75 and a T pole under Node 85. These structures will be included in the analysis.

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CAESAR II Statics Training Tutor Build Steel Structure CAESAR II includes a structural modeller. This module can be used as just described, to model steel structures to support the piping in order to include the flexibility in the supports, as opposed to fully rigid supports. Return to the CAESAR II main window and create a new file. Specify this as structural input.

The structural wizard will guide you through the process of setting up the structural file. First the units to be used must be specified. Ensure that the Training units (TRAIN.FIL) are selected here. Click Next

On next screen, the vertical axis should be selected for the model, either the Y or Z axis can be set to vertical. Select the Y axis as vertical and click Next

The following screen is to specify the material and material properties. Any number of materials can be specified, each identified by a Material ID. For each material ID the material properties can be specified. Within the steel modeller, each steel member is assigned a material ID. Accept the defaults for material ID number one and click Next. (The units are those from the specified *.FIL from the first step).

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The following screen is to specify the steel members to be used in the structural model. Each steel member is identified by a section ID and can be either selected from an included database of sections, or can be User defined.

In the structural modeller, each element can be assigned a section ID as well as a material ID. We will use I-Beams in our model and will select from the built in database. Choose the Select Section ID button and select the following I-Beams Section ID 1: Section ID 2:

W8 x 31 W6 x 20

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The final stage of the structural modeller wizard is to specify the method of element definition. There are two options for this. Method One - “EDIM” method, which is similar in concept to how piping elements are defined – a start node and an end node are specified, along with the distance between the two to define the structural elements. Method Two – Node/Element method is a slightly different concept. Nodes are added and are located at points in 3D space. Elements are then defined and users specify the nodes which each element connects. Select Method one and click Finish.

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CAESAR II Statics Training Tutor The steel modeller will now appear with the options selected in the wizard added to the “Card Stack”. The Card Stack is a logical list view of the structural model where all parameters are listed and can be edited.

Now we will define the structure. As we have used the wizard to define the material and section IDs, the next items we can define are the elements themselves. Use the EDim button to add a new entry to the card stack.

From the sketch we can see that starting at node 2000, there are two vertical steel members, both 2500mm in length. These two members can actually be defined in one entry into the card stack as they are identical. Expand the new row in the Card Stack and first enter the From and To node numbers as 2000 and 2010. Also enter dy as 2500. Specify the section ID and Material ID for this section also. Section ID is 1 and Material ID, as there is only 1 is 1. We now have one element, from Node 2000 to 2010, 2500mm in length in the vertical (+Y) direction. The inc, incTo and last fields can be used to duplicate this element quickly without adding a new entry into the card stack. The inc field will increment the “From” node, starting with the original “From” node. i.e. if we enter 10, the “From” node on the second element will be 2000 +10 = 2010. So in this case would connect to the first element. The incTo is the same concept, but using the “To” node. The last field is simply the “to” node on the last element to be defined. Enter inc and incTo as 10 and the last “To” node will be 2020.

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Continue and add a second Edim to the card stack. Define element 2010 – 2012. This time the section ID 2 will be used.

The model so far should look like the following

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CAESAR II Statics Training Tutor Continue with 2002 – 2012. Again, this entry in the card stack will define multiple elements

Add the finial members on the top. As these are not identical, they must be defined as separate entries in the card stack.

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CAESAR II Statics Training Tutor The final step is to anchor the steel at the base. Use the Fix icon to add a “Fix” entry into the Card Stack, and fix at node 2000 and 2002. Fix in all degrees of freedom.

The completed frame should look like the following.

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CAESAR II Statics Training Tutor Save the frame. On saving the structural modeller will check the file. The following dialogue will appear. Ensure that all three check boxes are checked.

Now create a new structural file for the T-post. As before, follow the new structural file wizard. The T Pole is similar to the Frame in that it is the same material and the same two steel sections used – W8 x 31 and W6 x 20. After completing the wizard, the Card Stack should again display as before with the same starting entries.

The first thing to note about the T Pole is that it is rotated 90°. Add in a rotation angle of 90°

Continue and add in the elements

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The remaining horizontal elements will not be rotated 90°, so add in another Angle and set this to 0

The remaining horizontal elements will also all be Section ID 2. To save having to specify Section ID 2 for all elements, a default Section ID can be set.

Set this default section ID to 2.

Continue and add the remaining elements as follows From 1005 1005 1015

To 1010 1015 1020

DX -600 300 300

Finish off by fixing node 1000.

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CAESAR II Statics Training Tutor The completed T Pole should look like the following

Save the T Pole and again ensure that all three check boxes are checked.

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CAESAR II Statics Training Tutor Combine Pipe and Steel models Return to the piping input. We will now include the Steel models in the Pipe model. Select the “Include Structural Files” button and browse to locate the two files just created.

After Clicking OK the steel members will be included in the pipe file, however as there are no common node points between the pipe and steel, the structural members are simply located at the origin. We now need to move these structural files into the correct location. A quick review of the pipe and steel model node numbers shows that pipe node number 75 will be connected to steel node number 2021 and pipe node 85 will be connected to steel node 1015. However the centrelines of the steel and pipe are not in contact, rather the bottom of the pipe is resting on the top of the structure. The pipe and steel can be connected either way; connecting the bottom of pipe with top of steel will be a more visually pleasing model, and in some cases (e.g. where friction or a guide is included on larger diameter pipe) the proper contact point will affect the results. A dummy rigid element will be built at both support points to offset the pipe above the steel. First locate element 70-75. INSERT a new element AFTER this element. The new element will be from 75 to 1075 and the distance between these nodes will be -210 mm in Y. Make this a weightless, rigid element.

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Now return to the element 70-75 and redefine the restraint at node 75 by changing the Node to 1075 and define a CNode (connecting node) of 2021. Now that the pipe to 1075 is in Y, the Guide must be replaced with a Z restraint (a Guide makes both X & Z on a Y pipe). Be sure to do this for all restraints at this point.

The frame will now be moved to connect to node 1075.

Repeat this procedure for the restraint at 85, creating a new element 85-1085 and connecting 1085 to 1015.

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The completed model will show the steel structures supporting the pipe as below.

Re Analyse the system.

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CAESAR II Statics Training Tutor Review Results The SUS case has increased very slightly, but the EXP case has dropped down to 38%. This is because further flexibility has been added to the system. Specifically the stiffness at node 75 which was a rigid guide now matches the frame stiffness. The OPE displacements report shows that the 8mm gap on the Guide (now the Z restraint) is closed, but then the guide itself shifts another 8mm in the Z direction, rather than being stationary as a rigid. Note the displacements on nodes 1075 and 2021.

The restraint summary for the OPE case shows a significant reduction on the operating loads on the pump nozzle.

As before, run these new loads through the API 610 processor (use Refresh Loads button to bring in the new loads). The discharge nozzle now shows that only the moment about the Y axis (global Z) exceeds the allowable limit.

Adding the steel effectively increased the guide’s gap. This greatly reduced the pivot action and the resulting pump load.

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Fix Model – Part 3 The only issue with the model now is that the local Y moment, global Z moment on the pump discharge nozzle (node 10) is excessive. Without changing the position of the pump or vessel nozzle, or changing the thermal strain, the only way to reduce these loads is to add flexibility to the layout. There is no inherent flexibility that was excluded from the model so an expansion loop will be introduced. How big a loop is required and where should it be placed? Expansion loop legs should be perpendicular to the thermal growth causing the load. We will focus on the Z axis bending moment. This bending moment is being caused by the +X force – the thermal growth in the X direction (element 70-75).

Therefore the loop can be added in the Y or Z direction (perpendicular to X). Which is the best loop layout?

Layout A - A loop in the Z direction at the end of the X run (node 80)

Layout B – A loop in the Y direction at the end of the X run (node 80)

Layout C – A Y loop on the opposite end of the X run (node 70)

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⁄ ∑

The bending stress at the nozzle is estimated using

= stress range in leg j (leg j is orthogonal to the direction of thermal growth to be absorbed) = Length of leg j = length of leg i (leg i represents each leg helping to absorb the thermal growth) We know that

∑ So let 6EIΔ = K Therefore solving for K using the current M (MZ Bending moment which is 5139 Nm) and Li and Lj Lj = 4200mm Li = L1 6205mm & L2 4200mm

∑ (∑

)

Keeping K as a constant, we can attempt to reduce M. To do this we will increase the length of the leg in the three layouts mentioned previously and recalculate M The following table and graph summarises this. Added Loop Leg (m)

In Z (Layout A) 0 1 2 3 4 5

5.153 3.591 2.542 1.831 1.343 1.004

In Y (Layout B) 5.153 5.120 4.902 4.395 3.657 2.865

Riser (Layout C) 5.153 5.248 4.907 4.326 3.686 3.092

Max Mz (= 2 * Table 4) 3.525 3.525 3.525 3.525 3.525 3.525

Red = above max Mz Green = below Max Mz

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Effect of Various Loops on Pump Moment - Mz

Moment (KN-m)

6

Riser (Layout C)

4

In Y (Layout B) In Z (Layout A)

2

Max Mz (= 2 * Table 4)

0

0

1

2

3

4

5

Added Loop Leg (m) As can be seen, the most effective way of reducing the MZ moment is to use layout A – an expansion loop along the Z axis. This increases Li which is cubed in the equation so will have a much larger effect of the MZ Moment.

According to the calculation, slightly over 1m run in the Z direction is required, however this simple equation does not take into account any rigid elements or elbows, nor does it consider any intermediate supports such as the guide at node 75. We could insert a loop of 1m in length and continue iterating the model until we find a suitable loop length. However this can take time and finding an efficient loop design may involve several iterations, even on a simple setup such as this. CAESAR II provides a Loop Optimisation Wizard to automatically size and create an expansion loop to get the most efficient loop for the target data.

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CAESAR II Statics Training Tutor Loop Optimisation Wizard Return to the model and use File > Save As… to create a new iteration of the model with an expansion loop. After performing the Save As… the analysis must be run once again because the Loop Optimisation Wizard uses existing results in modifying the layout. Run the analysis and return immediately back to the input. The Loop Optimisation Wizard button will now be available (if this button is ever greyed out then there are no results available for use – rerun the analysis). Select element 75-80 as this is where the loop will be placed and click the Optimisation Wizard button to access the wizard.

The Loop Design Wizard will appear and the data required can be input in order for CAESAR II can design the expansion loop. The wizard will create iterations of a loop setup in order to focus in on a specific Stress value or Restraint load. We wish to reduce the Restraint Load on node 10 to below the allowable for API 610 table 4. We will reduce the load to 3300Nm (currently the load is around 5150Nm). The loop will be located on what is currently the element 75 – 80. This will therefore be as in Loop Layout A. The final thing to define is the space allowed for locating the loop. A cube of space can be defined which the loop will fit inside. The Wizard will create the largest loop possible in the available space, and if this is below the specified target load, the wizard will continue iterating to create the most efficient loop possible, as close as possible to the target value. In the Loop Design Wizard, select the OPErating Load Case and choose the target data to be Restraint Load.

As we already have element 75-80 selected, this element will be selected anyway. The table will be filled in with the results data. Double Click in the MZ cell on the Node 10 row. This will fill in the Node and Type fields. Enter 3300 as the data in the Load field.

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Specify the Loop Type as the centre loop type – this matches the type A that we have already determined is the most efficient. The final option in the loop type section will allow the wizard to evaluate all of the Loop Types and determine the most efficient. This takes longer as 8 loop types are defined. Also in the loop type section, change the Height to Width ratio to to allow the height to vary as needed.

Finally the space available for the loop must be specified. Click the Draw Cube button. A cube of space will be shown in the model. Currently this will be facing the wrong way. Click and Drag the point labelled PT3 to reposition the cube in the correct orientation. On doing this the “Major Direction” field will change to –Z. Increase the size of the cube in the –Z direction to ensure that there is enough room to design the loop.

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Once finished, click Design. The wizard will run through a number of iterations and converge on the defined target value.

Once complete the loop will be added into the model automatically. A confirmation message of the total length of pipe and number of bends is displayed

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CAESAR II Statics Training Tutor The loop wizard has added an additional ~3070mm of pipe. Split between the two legs to the loop, each leg is now ~1535mm longer. Our quick hand calculation indicated a length of just over 1m, but as noted previously this did not take into account rigid elements or elbows, nor does it consider any intermediate supports such as the guide at node 75. In addition, we used a target value slightly lower than the Max Mz as in the hand calculation. For simplicity, round up the length of each of the two new legs to 1600mm. With even more flexibility, the MZ moment at node 10 will be lower still. Re-run the analysis.

Code Checks: SUS –Max stress is now 16% at node 68. Node 68 is the top of the riser. Recall how CAESAR II adds intermediate node points around the bends as discussed in the TURBO example. EXP – Max stress is 34% located at node 78. This node is the far end of the elbow at the start of the long Z run Hanger Sizing: Carpenter & Paterson DV70 size 11 hanger is still selected. The hot load has decreased slightly.

Pump Load: The loads on Node 10 look much better now:

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CAESAR II Statics Training Tutor Re-run these loads through the API-610 processor once again

This time all loads pass on the discharge nozzle. The local My (global Mz) is now 1.85 times the allowable (we have used the 2x table 4 approach) and so now passes.

We have reduced the load on the pump by adding flexibility into the system in the form of an expansion loop. The addition of this loop required an extra 1.6metres of space. What if this space was not available?

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Fix Model – Part 4 We will now return to the model without the expansion loop and once again attempt to reduce the load on node 10, this time assuming that there is no space available for addition of an expansion loop. In this case we will add in an expansion joint instead to add in flexibility. Open TUTOR.c2 (the file before the expansion loop was added) and save as Tutor_Expansion_Joint_Check.c2 We already know that the issue with the pump is the Mz moment. This moment as we have seen is caused by the thermal growth of 70-75. This horizontal displacement at node 70 causes the bending moment.

As such we wish to prevent this horizontal growth from being applied to node 10. We will include an expansion joint to absorb this horizontal growth. Adding the expansion joint just above the pump will best absorb this growth. What type of joint should be used? As we are only trying to absorb movement by lateral deflection only and there is no axial deflection or relative bending rotations at the joint ends, a tied expansion joint will be suitable. First of all we need to know the horizontal deflection that we have to absorb. We will use CAESAR II to determine this by breaking the system above the pump and viewing the displacements report. The value we obtain from this can be used to select the number of convolutions in the expansion joint. Select node 20 to 10 and change to 21 to 30

The system will now have two sub-systems sharing the same origin. We need to reconnect 20 and 21.

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CAESAR II Statics Training Tutor Add a Y restraint at node 20 and specify node 21 as a CNode.

We also need to prevent any rotation at this point as well. Specify three rotation restraints (RX., RY, RZ) at node 21, CNode 20

Leave the transverse directions X & Z free to move. The system near the pump connection should now look like the following:

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CAESAR II Statics Training Tutor Using the EXP case Displacements report, we need to calculate the change in position between Node 20 and Node 21. Nodes 20 and 21 will move together in Y, RX, RY, RZ because of the Node/CNode restraint definitions.

DX = 33.4mm DZ = 11.446 – 1.150 = 10.3mm This results in a relative horizontal displacement of 35mm. This also shows a Mz moment of 4900Nm. This is quite a high load – as the system is completely free to move in the X and Z direction, resulting in the largest displacement. If we were to introduce some stiffness (as would be in the expansion joint itself) this displacement would decrease. Using the Senior Flexonics/Pathway expansion Joint catalogue, we will select a 3.5kg/cm2 class 150, 8” expansion joint. The catalogue shows a 20 convolution expansion joint provides 38.8mm lateral deflection. This satisfies our requirement. However this expansion joint also adds a lateral stiffness of 6kg/mm or 58.7N/mm. If we introduce this stiffness, the deflection would reduce. Reduced deflection drops the required number of convolutions and, in turn, increases the stiffness between nodes 20 and 21. This iterative process can continue until the deflection test fails or the pump load becomes too high. Add the final two restraints (X and Z) between 20 and 21. Set stiffness to 58.7 N/mm

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CAESAR II Statics Training Tutor Re running the analysis and viewing the EXP case displacements shows the new relative lateral displacement of around 21mm. The OPE restraint loads show that the MZ has now decreased drastically and is now around 25% of the previous value.

However, the MY is excessive at over 6000Nm. This moment will also place torsion on the expansion joint and this torsion may also be excessive. If this observation did not stop the iteration, how would this process proceed? • Test 16 convolutions - 16 convolutions allow 24.8 mm lateral deflection and has K = 118 N/mm • Reset X and Z restraint stiffness to 118 and reanalyse • Check travel limits for the proposed joint and the load limits for the pump. If 16 convolutions is OK and overall joint lateral translation drops, test a shorter (i.e., fewer convolutions) joint. In conclusion, because of the large global My on the pump and the torque on the expansion joint, the proposed length and location of this joint should be reconsidered. For the purposes of this exercise, analysis of a 20 convolution, tied expansion joint will be evaluated. For this length, a tied universal joint would probably be preferred; consult manufacturer for other options.

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CAESAR II Statics Training Tutor Model the Expansion Joint Assembly The flanged expansion joint would be located between the discharge nozzle and the existing weld neck flange. To save time in this examination, the expansion joint will be placed between the flange and pipe rather than between the nozzle and flange. The error introduced will be small. Return to Tutor.c2 and rename as Tutor with Expansion Joint.c2 Select Element 20-30 and access the Expansion Joint Modeller.

Select to create an expansion joint with the following properties: Pressure Style Convolution Material # Convolutions End Type

50 pound Tied 304SS 20 Slip on (Both Ends)

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CAESAR II Statics Training Tutor After clicking OK, CAESAR II will split the selected element to fit in the expansion joint. Which end of the element to place the joint must be specified. We will split at the From end (Node 20).

The temperature of the element in question is 315°C. Apply this temperature to the joint, which will subsequently cause the stiffness to be adjusted.

The expansion joint modeller will finally confirm the creation of all the elements to be used in creation of the joint. The stiffnesses will also be displayed, along with the Allowed Movement.

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Click build and CAESAR II will attempt to define the expansion joint using the data supplied/obtained from the catalogue.

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Re analyse the system. Using the Expansion Case displacements, calculate the lateral deflection between nodes 21 and 22 – the nodes on either end of the expansion joint. DX = 20mm; DZ = approx. 12mm. The overall deflection is therefore around 23mm. The Flexonics catalogue shows that this displacement is acceptable for a 20 convolution joint. There is minimal Axial deflection (DY = approx. 0.3mm) and Angular Rotation (RX and RZ = 0mm). Torsion in the joint is 0.3 degrees. The catalogue actually shows that this torsion is excessive.

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Document the Analysis The analysis is now complete, and the model is acceptable. We will work with the model including the expansion loop, rather than the expansion joint. The stresses are all acceptable and well below the code allowables. The loads on the pump are also all acceptable and below the allowables for API 610. We can now document the analysis and produce a report which could be supplied to a client, including a plot of the system and annotated stress isometrics. Custom Reports In addition to these, custom reports can also be created.

Custom reports are created using the Report template editor.

In the report template editor, a new report can be created by adding in all the columns you require. Any column from any report section can be selected. The following sections are available. The individual columns from these reports can be added in any order as required.

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CAESAR II Statics Training Tutor In addition to setting the column order, various other properties on each individual column can be set. These properties are as follows:

As well as properties for each individual column, report wide settings can also be set.

The template can be either an individual report (one load case per report) or a summary report (multiple load cases per report). Or a Code Compliance report (detailed information on calculated values vs allowable) or a Nozzle check report (Displays nozzle loads if present).

We wish to create a custom report which shows the stresses in the EXP case and the SUS case similar to the “Stresses” report. View this report for the EXP and SUS cases. The issue here is that two reports are created, one for each case.

But we wish to view both cases in one report. This therefore would need to be a “Summary” report. View the stress summary report for both of these cases. This report displays the max stress for each case in one report, but does not display the stresses at each node, like in the stresses report. We need a summary report which shows data at each node.

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CAESAR II Statics Training Tutor Create this as a custom report. So that we can view sample data in the report, select the load cases as well before accessing the report template editor.

First of all give the report a title “Stress Summary with Detail”. The report template preview will update to show this. Also change the Report Type to Summary.

The report itself we wish to be shown in a nicer to read font that Courier. Select Calibri, 11pt text and align the column text to the centre of the column to ensure everything stays inline.

Now we can add the following columns into the report, in the following order: 1. Bending Stress 2. Torsion Stress 3. SIF in Plane 4. SIF Out Plane 5. Code Stress 6. Allowable Stress 7. Ratio % 8. Piping Code Enter in the column number next to each column required. Also tick the Show Piping Code check box.

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The report preview should show a sample of the report.

Currently there is no summary table like in the Stress Summary report showing the max stresses. Insert this into the report as well by checking the Show Highest Stresses check box.

Save the complete report. Any custom reports created can be exported and then imported on any machine so that all users have access to all reports.

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CAESAR II Statics Training Tutor Filters We have created a new customised report to show the data we are interested in. View this report for both the SUS and EXP load cases. The report will look as we expected and show all the data we require. However there is a lot of data as we have all the stresses at all nodes, in two load cases. Reviewing the data shows that a number of nodes have very low or even zero stress. We can filter this data out to display only stresses above a certain value. Admittedly, our stresses are quite low throughout (highest is only 33.5%), but we still are not concerned with stresses that are only a fraction of a per cent for example. As such we will filter the data so that any stresses 1000N was applied as a filter, this would not be applied to for example the displacements report – FY is not displayed in the Displacements report. Create a filter to display, as mentioned previously, all stresses greater than 5%.

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Click Apply and now review the Stress Summary With Detail custom report for the SUS and EXP cases. The report will not show every single element now, only those which have stresses higher than 5%. Generate Report As we have seen, there are many reports produced by the CAESAR II analysis. All these reports can be viewed on screen as we have been doing, or alternatively each report can be sent to Microsoft Word or Excel, or a text file. We can produce a full report document of the type which could be submitted along with the analysis for approval. For our report we wish to include the following information.

Input Echo Load Case Report SUStained Stresses EXPansion Stresses OPE & SUS restraint loads OPE displacements at all nodes Hanger Table with text

This is a simple procedure and is simply a matter of selecting the reports to publish which contain the data we require and including them in the “Output Viewer Wizard” section of the output processor.

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CAESAR II Statics Training Tutor Review each of the reports mentioned above in turn to verify that the data is suitable. Start with the Input Echo.

The listing options window appears prior to the report being generated, where all input data can be selected for inclusion in the input echo By default CAESAR II picks the most relevant data depending on the model input – i.e. if WRC nozzle flexibilities are included, this is ticked, if there were no WRC 297 nozzle flexibilities, tis box would be un-ticked by default.

Select these defaults and click OK. Review the Input echo to ensure that all data required is included. Once happy with the contents of the input echo, close the report and click on the Add button to add into the Output Viewer list.

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CAESAR II Statics Training Tutor Repeat this process for each of the reports shown, including for the SUS and EXP stresses; add in the custom Stress Summary with Detail report. Once complete all reports we wish to publish will be in the list. We will now send these to MS Word. Ensure that the Send to MS Word radio button is selected and click Finish.

Word will load in the background and CAESAR II will publish all the selected data. The results will be inserted as tables into the Word document.

Once complete, review the Word document. Formatting can be applied as usual within Word.

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CAESAR II Statics Training Tutor ISOGEN Stress Isometrics In addition to the Word Document report, stress isometrics can be generated and annotated with input/output data to supplement the report. Stress isometrics can be configured so that the output appears as the user requires, if you have company/client standards for isometric drawings, these can be set up and configured using the ISOGEN I-Configure module supplied with CAESAR II. We will set up I-Configure to use one of the default styles. There are many switches which are available to control the appearance and content of the isometrics. These switches are not covered in this course. However, a number of Wizards are available for configuring common parameters. I-Configure can be accessed from the CAESAR II main window, from the Tools menu.

The I-Configure window will currently be empty, as no styles will be set up.

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CAESAR II Statics Training Tutor Most of the buttons on the toolbar along the top will be greyed out.

There will however be two buttons available; the first of which we are concerned with, in that this button will be used to create a new Isometric directory. (The second button is simply to connect to an existing isometric directory). ISOGEN uses a specific file/folder structure, at the top is the isometric directory. Contained within the isometric directory is a number of Project directories. Each isometric directory can contain multiple project directories. Contained with a project directory can be many style directories. As above, each project directory can contain multiple Style directories. Within each style directory are a number of files, each of which contain various different data for the appearance and content of the isometric output (including the format of the output - *.DWG, *.DXF etc). These files are created by I-Configure. I-Configure reads an XML file on selecting the current style containing all the settings and then writes these settings to various files which ISOGEN reads when producing an output. Choose to create a new Isometric Directory.

We will create a new folder on the E:\ drive in which all the ISOGEN data will be located. Browse to E:\ and create a new folder called ISOGEN and set this as the Isometric directory. An additional button is now available which allows us to create the project directory.

Within each project directory there must also be at least one style, so the template styles are available to choose from. Name the project TRNProject (spaces are not allowed) and select the Final Basic Style as the only style to produce (Un-tick all other styles). Change the Name column to Stress-Iso as well.

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Before we produce isometrics, let’s check the output to see what an example isometric would look like. Before any style created in I-Configure can be used, it must be exported for use (as discussed above). Select the Stress-Iso style and click Export Style.

Next we can process a sample file through ISOGEN to get a preview of what the output would look like with our style. To do this, select the Preview Isogen Output button.

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A sample output will be produced. Select the Drawing preview.DXF and click View. The resulting isometric will look like the one below. This is not quite what we want. We are producing a stress isometric, so we do not need a Bill of Materials, and we also want a different drawing border.

A sample drawing border already exists; we can use this sample border and turn the bill of materials off. Copy and paste the file from E:\Training\Masters\A2StressISOBorder.dxf into the isometric style directory E:\ISOGEN\TRNPROJECT\Stress Iso.

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CAESAR II Statics Training Tutor Within I-Configure, select the current style and in the bottom left pane, select the Overview tab. Highlight the Drawing Frame entry in the tree. This will take you to the TemplateFile variable in the table in the right pane. Double click this field and browse to the new file to be used as the border.

We have now specified our custom drawing frame, as we will not require a Bill of Materials on our Isometrics, we have a little more space available for the isometric plot. Increase this space by reducing the drawing margin. Currently the drawing margin on the right hand side is 202mm. The left margin is only 10mm. Make these equal by changing the RightMargin to 10mm also. ISOGEN is now allowed to use the space that was previously taken up by the BOM as extra space for the plot.

Finally we must now turn off the Bill of Materials. Still in the Overview tab, select the Material List = True entry in the tree. Again, this will display the relevant variable in the right hand list. Change this value to False.

Save the changes and Export the style once again so that we can see the results of these changes.

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This output looks acceptable. Save and close I-Configure and return to CAESAR II. I-Configure is now set up and we can now use the ISOGEN module in CAESAR II to annotate and produce stress isometrics.

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CAESAR II Statics Training Tutor From the CAESAR II main window, access the ISOGEN isometrics module

CAESAR II will open the model for isometric production. Click OK to confirm and continue.

The model will be shown and can now be annotated

Annotating the model involves simply selecting which data to include in the annotations, and is simply a matter of ticking the required data. All input data can in included as follows.

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CAESAR II Statics Training Tutor All analysis data can also be included as well. For each load case run, the displacements, restraint loads and stresses can be specified, as well as hanger data. In addition to input and output data, custom annotations can be added to any node number or on any element. Project attributes can also be specified and placed on the resulting isometric. We will annotate our isometric with the following data: Input: Node numbers Temperature T1 Pressure P1 Output: SUS Max stress (node 68) EXP Max stress (Node 78) Nodal Annotations: Node 10 – PUMP A CONNECTION Node 110 – VESSEL D CONNECTION Elemental Annotations: Element 100 – 110 – LWN Flange as Nozzle Project Attributes Project Name Project No Client Name Area System Prepared By

TRN 001 TRAINING T1 TUTOR

Select to Eit stress annotations to bring up the annotations panel.

From the panel select Input data and choose Node Numbers from the feature drop down list. We wish to annotate all the node numbers. However, as we have discussed previously, CAESAR II automatically splits bends and inserts intermediate nodes. We do not wish to annotate these intermediate nodes. As such, select all nodes except the intermediate bend nodes. These bend nodes should be as follows: 68

69

79

81

82

83

84

118

119

148

149

Select all nodes except those listed above. If you wish, return to the input and check which nodes are the intermediate bend nodes on your model.

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Once completed, select Temperatures from the feature drop down and select T1. Do the same for Pressure P1.

We can now specify the output data. Select Output tab and pick the SUS load case. Select the Stress option. The highest stress for the SUS case is on the bend at the hanger (node 70) – the stress is actually at node 68, but this is not selectable in the list. Node 60-70 is selectable and will annotate correctly. Pick this node.

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Repeat for the stress in the EXP case. The max stress in the EXP case is at node 78

Next select the Nodal annotations. Annotate the two equipment connections as mentioned previously. Node 10 – PUMP A CONNECTION Node 110 – VESSEL D CONNECTION Perform a similar task for the elemental annotations, and annotate Element 100 – 110 – LWN Flange as Nozzle Finally enter the project attributes.

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CAESAR II Statics Training Tutor Now we have completed the annotations, we can produce the drawings. Select Create Isometric Drawing.

Select to Use Existing Style – as we have already created and configured our isometric style.

Browse to the Isometric ,Project and Stye directories as configured earlier

Once complete, click Create Drawing.

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CAESAR II Statics Training Tutor After CAESAR II passes the information to ISOGEN, the data is processed and after a few seconds, a drawing will be created. Select the drawing created and click View.

The annotations and attributes specified will be inserted into the resulting isometric. The isometric could do with a little tidying up – the attributes are not quite correctly positioned. The colours could also do with some improvement – perhaps to make the restraints/hangers stand out more. All this can be done via I-Configure if required.

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CAESAR II Statics Training Cool H20 – FRP Piping

Cool H20 – FRP Piping

This job consists of an FRP cooling water header, which decreases from 1800mm diameter to 1500mm diameter to 1200mm diameter to 1050mm diameter as a succession of 750mm diameter lines tap off it. Modelling this job provides the opportunity for the user to explore the capabilities that CAESAR II offers for analysing FRP pipe. Additionally static seismic loads will be applied to this system, illustrating methods using uniform loads and load combinations.

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Basics of Fibreglass Piping Analysis Analysis of FRP materials is different to analysis of metallic materials, due to the orthotropic properties of the FRP material. Stress analysis of Fibre Reinforced Plastic components must be viewed on many levels. These levels, or scales, have been called “Micro-Mini-Macro” levels, with analysis proceeding along the levels according to the “MMM” principle. Micro level analysis: Stress analysis on the “Micro” level refers to the detailed evaluation of the individual materials and boundary mechanisms comprising the composite material. In general, FRP pipe is manufactured from laminates, which are constructed from elongated fibres of a commercial grade of glass (called E-glass), which are coated with a coupling agent or sizing prior to being embedded in a thermosetting plastic material, typically epoxy or polyester resin. Typically, on a micro level, the following failure modes are evaluated: 1) failure of the fibre 2) failure of the plastic matrix 3) failure of the fibre-matrix interface Generally, the glass fibre is found to be much stronger in tension than is the matrix, so most tension (along the axis of the fibre) is naturally taken by the fibre, rather than the matrix.

MICRO LEVEL GRP SAMPLE – SINGLE FIBRE EMBEDDED IN SQUARE PROFILE OF MATRIX

Mini level analysis: Although feasible in concept, micro level analysis is not feasible in practice. This is due to the uncertainty of the arrangement of the glass in the composite -- the thousands of fibres which may be randomly distributed, semi-randomly oriented (although primarily in a parallel pattern), and of randomly varying lengths. This condition indicates that a sample can truly be evaluated only on a statistical basis, thus rendering detailed element analysis inappropriate. For mini-level analysis, a laminate layer is considered to act as a continuous material, with material properties and failure modes estimated by averaging them over the assumed cross-sectional distribution. The assumption regarding the distribution of the fibres can have a marked effect on the determination of the material parameters; two of the most commonly postulated distributions are the square and the hexagonal, with the latter generally considered to be a better representation of randomly distributed fibres.

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CAESAR II Statics Training Cool H20 – FRP Piping Use of these parameters permits the development of the homogenous material models which facilitate the calculation of longitudinal and transverse stresses acting on a laminate layer. Typical mini-level analysis shows that due to stress intensification and relative weakness of the matrix relative to the glass fibres, laminate layers are typically very strong only in a single direction – i.e., the direction corresponding to the predominate alignment of the glass fibres.

STRESS INTENSIFICATION IN MATRIX CROSS SECTION

Macro level analysis: Where Mini level analysis provides the means of evaluation of individual lamina layers, Macro level analysis provides the means of evaluating components made up of multiple laminate layers. It is based upon the assumption that not only the composite behaves as a continuum, but that the series of laminate layers acts as a homogenous material with properties estimated based on the properties of the layer and the winding angle, and that finally, failure criteria are functions of the level of equivalent stress.

MACRO TO MICRO STRESS CONVERSION Since individual laminate layers are usually strong only in one direction, they are wound upon each other at various angles to tailor the desired strength in various directions. Typically, for pipes, the laminate layers would be arranged in such a way that their strength in the hoop direction is approximately twice that in the axial direction.

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CAESAR II Statics Training Cool H20 – FRP Piping Total laminate properties may be estimated by summing the layer properties (adjusted for winding angle) over all layers. For example: ||

(

)∑

||

Where: ||

= Longitudinal modulus of elasticity of laminate = thickness of laminate = transformation matrix orienting axes of layer k to longitudinal laminate

axis = transformation matrix orienting axes of layer k to transverse laminate axis = thickness of laminate layer k Once composite properties are determined, the component stiffness parameters may be determined as though it were made of homogenous material – i.e., based on component crosssectional and composite material properties, and interaction formulae for normal and shear stresses can be developed.

COMBINED STRESSES σ AND τ AT FAILURE: ARALDITE CY232

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CAESAR II Statics Training Cool H20 – FRP Piping

CAESAR II’s Orthotropic Model for Piping Systems CAESAR II’s orthotropic material model is activated through the selection of Material 20 – FRP. The orthotropic material model is indicated by the changing of two fields from their previous isotropic values: "Elastic Modulus (C)" "Elastic Modulus/axial" "Poisson’s Ratio" "Ea/Eh*Vh/a". These changes are necessary due to the fact that orthotropic models require more material parameters than do isotropic. For example, there is no longer a single modulus of elasticity for the material, but now two – axial and hoop. There is no longer a single Poisson's ratio, but again two -Vh/a (Poisson's ratio relating strain in the axial direction due to stress-induced strain in the hoop direction) and Va/h (Poisson's ratio relating strain in the hoop direction due to stress-induced strain in the axial direction). Also, unlike with isotropic materials, the shear modulus does not follow the relationship G = 1 / E (1-V) as for metals, so that value must be explicitly input as well. In order to minimize input, a few of these parameters can be combined, due to their use in the program. Generally, the only time that the modulus of elasticity in the hoop direction, or the Poisson's ratios are used during flexibility analysis is when calculating piping elongation due to pressure (note that the modulus of elasticity in the hoop direction is used when determining certain stress allowables for the BS 7159 code): ⁄

Where:

⁄

= extension of piping element due to pressure = longitudinal pressure stress in the piping element = Modulus of elasticity in the axial direction = Poisson’s ratio relating strain in the axial direction due to stress induced strain in the hoop direction = Hoop pressure stress in the piping element = Modulus of elasticity in the hoop direction = Length of piping element

This equation can be rearranged, to require only a single new parameter as: ( Note that in theory, the single parameter (

(

⁄

⁄

))

) is identical to Va/h.

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Requirements of the ISO 14692 Code In light of the isotropic nature of fiberglass reinforced plastic pipe, where hoop and axial strengths are distinct, stress evaluation in ISO 14692 utilizes an idealized envelope of combinations of axial and hoop stresses which cause the equivalent stress to reach failure. This curve represents the plot of: (

)

(

)

*

+

Where: = Allowable stress, axial = Allowable stress, hoop These terms are expressed in the ISO short term failure envelope:

ISO SHORT TERM FAILURE ENVELOPE The (2:1) line indicates points where the hoop stress is twice the axial stress. This stress state occurs in the wall of a pressurized, closed cylinder. The short term axial strength, σsa(2:1), and short term hoop strength, σsh(2:1), occur where this (2:1) line intersects the failure envelope. By definition, σsh(2:1)=2*σsa(2:1). A third strength is illustrated here – σsa(0:1) – this is the axial strength of the pipe in the absence of pressure. But there are several factors which reduce this short term strength in setting allowable (hoop and axial) pipe stress: • • •

Reduced long term strength of the component [fscale] A design safety factor (based on load type) [f2] Accommodation of specific load conditions (reduced strength associated with temperature, chemical attack, and fatigue) [A1, A2, A3]

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CAESAR II Statics Training Cool H20 – FRP Piping This short term failure ellipse can be represented by a “fully measured envelope” shown below:

ISO FULLY MEASURED ENVELOPE The line set intersecting the short term failure ellipse is a straight line representation of that ellipse – labelled “short, ideal”. The manufacturer can establish σsh(2:1) from burst tests (and half of that is σsa(2:1)) and can establish σsa(0:1) from tension tests. The next smaller line set, labelled “long, ideal” reflects the long term strength of the pipe. This is the material limits usually provided by the manufacturer. Using long term pressure testing, the manufacturer can project the “end of life” strength of their components. The ISO Code reduces this material data by a system factor of safety. This is the third line set, labelled “design” here. The limits used for piping evaluation are shown in the smallest line set, “factored design”. Factored design limits account for those operating conditions that reduce long term strength of the piping material. Note also the (1:1) line in the figure above. This line represents the stress condition where the axial stress equals the hoop stress. While having no engineering design significance, this line produces a point on the failure ellipse where the axial limit will drop below σsa(2:1). The manufacturer may provide σsa(1:1) (or the equal σsh(1:1)). If not the following simplification may be necessary:

ISO SIMPLIFIED ENVELOPE

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CAESAR II Statics Training Cool H20 – FRP Piping The dotted line set shows the simplified short term strength. This envelope would then be reduced to a similar “factored (long term) design” envelope described above. This curve is also used in the UKOOA Code. ISO 14692 Annex D provides equations for effective hoop and axial stresses in piping component. These effective stresses combine structural loads (due to weight, thermal strain, etc.) with pressure. Safe design is assumed if both the hoop and axial stresses lie within the factored design boundaries. CAESAR II analysis will evaluate both hoop and axial stress. The effective hoop stress must be less than the factored design limit for hoop stress. The axial term will also be evaluated but, here, the allowed axial stress is a function of the hoop stress. CAESAR II will report the stress term (hoop or axial) that produces the largest stress/limit ratio. The strength envelopes above are for straight pipe. Other piping components such as tees, bends and joints do not have fully developed strength envelopes. Instead, manufacturers establish a qualified stress, σqs, for these components. (

)

(

)

(

)

Where: = mean diameter of matching pipe = reinforced pipe thickness of the matching pipe = Qualified pressure of the fitting This is a combination of equations (6) and (7) of the Code. Qualified stress serves as the long term design hoop assigned to pipe. This qualified stress will be adjusted by the same terms as pipe to develop a long term hoop design stress. The axial limit is established through the biaxial stress ratio, r. For pipe,

(

) (Equation (12) of the Code). The ISO Code assigns values for r for non-pipe

components in Table 4. Given r and the qualified stress, CAESAR II will calculate σsa(0:1) for the component. CAESAR II requires qualified stress and biaxial stress ratio for bends and joints. Tees have r=1 so only require a qualified stress. The stress envelope for a non-pipe component is a simple rectangle bounded by a factored design hoop (or qualified) stress and an axial stress equal to r times that hoop limit. Note that, for some piping components with relatively large axial strength, r can go as large as 2 indicating that the component is just as strong axially as it is in hoop for any hoop stress.

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CAESAR II Statics Training Cool H20 – FRP Piping

Allowable Stress Data for this Model As shown on the isometric, the material for this model is Wavin 55 material. Pipe Data: The value for long term hoop strength (shown as hl(2:1) in CAESAR II) may be obtained from vendor data. In the case of the Wavin 55 material, it is available from the graph of the combined stress failure envelope, as shown below. Note that the axes have been switched (axial stress on the horizontal axis) on this graph relative to the traditional ISO envelope format, so the desired 2:1 position is now identified as R = 0.5. Likewise, the values in this graph include the service factor f2, which can be eliminated by dividing the values on the outer curve by 0.67. This gives a f1 x LTHS value of 125 N/mm2. An alternative means of getting this value is to find the value given by the vendor for the long term Hydrostatic Design Basis; again, for this case 125 MPa. The long term axial stress at maximum hoop stress, al(2:1), is, by definition, half of hl(2:1). The axial tension-only long term strength is shown on the chart below as (41 MPa/0.67). PIPES, WINDING ANGLE ω = 55°

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CAESAR II Statics Training Cool H20 – FRP Piping HYDROSTATIC PROPERTIES

Joint & Fitting Data: Tees, bends and joints reference Qualified Stress instead of the pipe term hl(2:1). For this example, these components have a lower “pressure rating” than the matching pipe. The Qualified Stress (Qs) will also be set to 75 MPa. The axial stress limit for tees is constant but bends and joints may have a varying axial stress limit measures by r, the ratio of two times al(0:1) divided by hl(2:1). For this model, r is set to 2 for joints and 1.0 for bends. Bends also reference the hoop modulus of elasticity which is entered here as the Eh/Ea ratio of 1.7 Other factors: • A1 – factor for temperature • A2 – factor for chemical resistance • A3 – factor for cyclic service • System Design Factor – this is a CAESAR II term that is combined with the CAESAR II Occasional Load Factor (which is set or adjusted in the Load Case Options) to produce the “part factor for loading”.

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CAESAR II Statics Training Cool H20 – FRP Piping

Configuration Options for FRP Piping: In this example, the material has the properties of Wavin 55o winding FRP pipe. These parameters are: 𝐸𝑎

𝑀𝑃𝑎

𝐸

𝑀𝑃𝑎 𝐸 ⁄𝐸𝑎

𝐸 ⁄𝐸𝑎 𝑉

⁄𝑎

𝐷𝑒𝑛𝑠𝑖𝑡𝑦

𝐶𝑇𝐸

𝑘𝑔 𝑚

𝑚𝑚⁄𝑚𝑚⁄°𝐶

𝑆 𝑒𝑎𝑟 𝑀𝑜𝑑𝑢𝑙𝑢𝑠

𝑀𝑃𝑎

𝐵𝑒𝑛𝑑 𝐿𝑎𝑚𝑖𝑛𝑎𝑡𝑒 𝑇𝑦𝑝𝑒

𝐶 𝑜𝑝𝑝𝑒𝑑 𝑆𝑡𝑟𝑎𝑛𝑑 𝑚𝑎𝑡 𝑤𝑖𝑡 𝑚𝑢𝑙𝑡𝑖

𝑓𝑖𝑙𝑎𝑚𝑒𝑛𝑡 𝑟𝑜𝑣𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛

CAESAR II’s material database is not currently configured for orthotropic materials such as FRP. Therefore, CAESAR II’s orthotropic model must be triggered through use of Material 20 (FRP), with the material parameters entered explicitly. These parameters include: Axial Modulus of Elasticity (Ea) The Ratio (Ea/Eh)Vh/a Pipe Density Coefficient of Thermal Expansion Ratio of Shear Modulus (G) to Axial Modulus (Ea) FRP Bend Laminate Type

(entered on spread sheet) (entered on spread sheet) (entered on spread sheet) (entered on Special Execution Parameters) (entered on Special Execution Parameters) (entered on Special Execution Parameters)

This may become tedious, especially if the same type of FRP material is used frequently. In this case, the appropriate material parameters may be entered in the CAESAR II Configure/Setup, to be used automatically whenever Material 20 is used.

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CAESAR II Statics Training Cool H20 – FRP Piping These parameters are entered using the FRP PROPERTIES group in of Configure/Setup. The configuration items are described below: Axial Modulus of Elasticity: Self-explanatory; can be read from an FRP file. Axial Strain : Hoop Stress (Ea/Eh*Vh/a): Ratio of the FRP axial modulus of elasticity to the hoop modulus of elasticity, all multiplied by Poisson’s ratio for strain in longitudinal direction due to stress-induced strain in circumferential direction; can be read from an FRP file. FRP Alpha (x E-06): The coefficient of thermal expansion, length/length/degree, multiplied by 1,000,000; can be read from an FRP file. FRP Density: Self-explanatory; can be read from an FRP file. FRP Laminate Type: This item is considered when calculating SIFs and Flexibility Factors of bends under the BS 7159 and UKOOA codes. Choices include: Type 1 – All chopped strand mat (CSM) construction with an internal and an external surface tissue reinforced layer. Type 2 – Chopped strand mat (CSM) and woven roving (WR) construction with an internal and an external surface tissue reinforced layer. Type 3 – Chopped strand mat (CSM) and multi-filament roving construction with an internal and an external surface tissue reinforced layer. FRP Property Data File: Selecting an FRP type from one of the ones listed reads in much of the associated material data. Ratio Shear Mod : Elastic Mod: Ratio of the FRP shear modulus to the axial modulus of elasticity; can be read from an FRP file. The remaining settings are used with the other FRP codes BS 7159 and UKOOA and are unused for ISO 14962. Their uses are discussed in the help file and are displayed on pressing F1 while on the field.

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CAESAR II Statics Training Cool H20 – FRP Piping

Model the system When modelling using the orthotropic material, the very first thing that must be done, before even creating a new file, is to enter the material properties in the configuration file (remember this can be done by selecting an FRP data file). The once material 20 is selected within the job, these properties will be used. Any changes made to the FRP properties in the configuration file will only take effect when a new job is created. On the CAESAR II main window, select Tools > Configure/Setup

Select the RP properties node and specify the properties of the FRP. This FRP is Wavin55 as mentioned previously. Select this FRP property data file.

Confirm the choice

The FRP parameters will update to those set in the FRP data file. Whilst in the configuration file, also specify a default friction coefficient of 0.15 to represent plastic on steel/concrete.

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CAESAR II Statics Training Cool H20 – FRP Piping Once these FRP parameters have been set, only then can the job file be created. Create a new job file called CoolH20.

Create the first element, 10 to 20. Note that this pipe is non-standard 1800mm diameter and also has non-standard 46mm wall thickness. The 1.5mm Corrosion layer should also be entered here. This layer will always be used in the weight and thermal force calculations, but excluded from the pipe strength calculations.

Select the material number 20 – FRP.

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CAESAR II Statics Training Cool H20 – FRP Piping Upon selection of the material, the labels on the material properties change. Elastic Modulus (C) becomes Elastic Modulus/axial and Poisson’s Ratio becomes Ea/Eh*Vh/a. The values will be brought in from the FRP data file and will be as described above (as we chose the Wavin55 FRP data file). Also check the Special execution parameters for further FRP data. Again this should match the correct data coming from the FRP data file.

Enter the temperature and pressure (50°C and 2 bars). We must now also select the design code. Currently the code is the default - B31.3. Change this to ISO 14692. Now we must enter the stress envelope for the FRP material. The entries are as described previously. Recall the graph:

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CAESAR II Statics Training Cool H20 – FRP Piping

(as mentioned before, the axes have been switched, so the 2:1 position is now identified by R = 0.5), and also recall that mentioned previously the values on the graph include service factor f2, 0.67. This factor also needs removing (i.e. divide all values by 0.67). the 0.67 value will be entered as the system design factor. As shown in the graph, the reading for the hoop stress is 84 N/mm2. Therefore the hl(2:1) value is:

By definition, long term axial stress at maximum hoop stress, al(2:1), is half of hl(2:1). Therefore:

The axial tension-only long term strength is shown on the chart above as 41 MPa. Therefore

The joint and fitting data is also discussed above. The Qualified stress Qs will be set to 75 MPa and for bends r = 1.0 and for tees r = 2. Bends also reference the hoop modulus of elasticity which is entered here as the Eh/Ea ratio of 1.7.

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CAESAR II Statics Training Cool H20 – FRP Piping A1, A2, & A3 bring in environmental effects to reduce the design stress to the factored design stress. Thermal Factor (k) is the “mean temperature multiplier”, a factor by which the difference in temperature between the fluid the environment is to be multiplied (since FRP has natural insulating qualities). For liquids, the Code dictates a K value of 0.85; use 0.80 for vapour.

Note that we have not entered al(1:1) or hl(1:1) therefore the simplified envelope will be used. Complete the first element by adding an anchor at node 10 and continue into the bend. The bend is a mitred bend and has 2 mitre points. Note that the ISO Code ignores the number of mitres when calculating the bend SIF and flexibility factor.

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CAESAR II Statics Training Cool H20 – FRP Piping In addition, there is also a +Y restraint on the start of the bend (node 18). Notice the friction factor is included automatically when adding the restraint.

Continue to the next element.

The model so far should look like the one below:

Continue and complete the model. Note the following points: •

•

The branch connection at node 40 (as well as all other branches) is a tee (SIF type 1). Node 40 (along with nodes 60, 100, 120, 160, 180, 190, and 250) is supported by a +Y (weight only) support (with friction coefficient of 0.15). The restraint at node 50 (as well as those at nodes 90, 110, 150, and 170) is combination guide and +Y (weight only) restraint (with friction coefficient of 0.15).

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CAESAR II Statics Training Cool H20 – FRP Piping •

Element 70-80 is a reducer (conical section). It can be modelled as such with the exiting diameter and thickness set to 1500mm and 38mm.

Element 40-280 is a branch off of the 1800 mm line. Its diameter and thickness should be changed to 750 mm and 25 mm, respectively. (Offsets should be considered here as the actual flexible length of straight pipe [before the bend] – 3600 mm – is much smaller than the modelled length – 4500 mm – and therefore much stiffer. However, for this layout the effect is minimal [about 5% in terms of stress] and excluded for simplicity.) The bend at node 280 has 4 mitre points. After modelling the branch through node 300, that branch can be duplicated via the list processor 5 times (with the node increment set to 30, 60, 90, etc.). It is also necessary to change the branch intersection nodes to 60 (from 70), 120 (from 130), and 180 (from 190). The completed model should look as below.

Error Check the model

A warning relating to the fact that al(1:1) and hl(1:1) were not entered and so the simplified envelope will be used is shown, as is a warning about SIFs on the intersections and that the reducer Alpha was not entered so CAESAR II has calculated this value. Accept these warnings and access the load case editor.

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CAESAR II Statics Training Cool H20 – FRP Piping

Load Case Setup ISO 14692 evaluates both hoop stress and axial stress in the installed and operating conditions and also for any short duration (occasional) loads. The type of load will set the part factor, f2, used to set the design stress limits. The System Design Factor specified in the input is multiplied by the CAESAR II Occasional Load Factor in the Load Case Options tab to produce this f2. f2 = (System Design Factor)*(Occasional Load Factor). The Code provides values for f2 in Table 3. Remember that the System Design Factor in the CAESAR II input is set to 0.67.

Review Results ISO 14692 Annex D provides a method for converting torsion and bending moments into hoop and axial stress terms. These stresses, summed with their pressure counterparts, produce effective hoop stress and effective axial stress. Terms common to B31 piping – flexibility factor and stress intensification factor – are used here too. Stress evaluation will first compare effective hoop stress to the factored design hoop stress. If this check fails, the hoop stress is reported, otherwise, CAESAR II will continue with the axial check. The effective hoop stress is used with the design envelope to pick up the factored design axial stress. The effective axial stress is then compared to the factored design axial stress. If this check fails, the axial stress is reported, otherwise CAESAR II will print the cause of the largest (stress/limit) ratio – either hoop or axial. Running this analysis shows that this system stresses are satisfactory. Note the changing allowable stress from node to node. CAESAR II prints a different allowable depending upon which stress calculation controls – Hoop or Axial.

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CAESAR II Statics Training Cool H20 – FRP Piping

Solving Expansion Problems The philosophy behind solving expansion problems in a fiberglass piping application is different from that in a steel piping application. For steel piping, the preferred hierarchy for solving such a problem is 1) adding flexibility through loops and bends, 2) using expansion joints, and 3) using restraints to re-direct growth to areas where it can be better handled. For fiberglass applications, due to the relatively low modulus of elasticity of fiberglass, the lack of significant flexibility provided by FRP bends, and the potential problems involved in the joining of FRP sections, the hierarchy is exactly the opposite. The preferred method is to use axial restraint to force the thermal expansion into compression (in this case, the line must be adequately guided); the next preference is to use expansion joints; and the last resort is to use expansion loops.

Static Seismic Using the ASCE 7-05: This cooling water system is located in a seismically active region, so it must also be designed to withstand earthquake loads. For this analysis, the ASCE 7 Minimum Design Loads for Buildings and Other Structures, 2005 Edition is in effect. We will assume that this installation is located in Site Class D (Stiff soil profile), near Los Angeles, California. (For Site Class Definitions, refer to Table 11.4-1.) The structure in which this system is operating has an average roof height of 12m. Section 13.3.2 discusses Seismic Relative Displacements to which piping must be designed. It states “The effects of seismic relative displacements shall be considered in combination with displacements caused by other loads as appropriate.” – meaning that they shall be treated as “secondary” loads, rather than “primary” loads. Inertial Loads Section 1621.1.4 defines a horizontal seismic acceleration factor to be applied uniformly throughout the structural mass. This acceleration factor, aH, is defined as:

( [ But:

)

] and

Where: = Component amplification factor, from Table 13.6-1 = 2.5 for piping = Design elastic response acceleration at short period, from Section 11.4.4 = Component response modification factor, from Table 13.6-1. Use 4.5 for pipes not in accordance with B31, with bonded joints or use 12 for welded, steel B31 pipe. = 4.5 = Component importance factor, from Section 13.1.3 (1.5 for life-safety components, hazardous material containing, or piping is in a Category IV structure (essential facility); 1.0 for all others).

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CAESAR II Statics Training Cool H20 – FRP Piping = 1.0 = Height in structure at point of attachment. Here, use the average of elevation of all 8 connections = 6m = Average roof height of structure = 12m Section 13.3.1 states that a vertical acceleration be considered as well. This acceleration factor, aV, is defined as 20% of the Design elastic response acceleration at short period, or:

Determine SDS: From section 11.4.4

Where = Maximum considered earthquake spectral response accelerations for short period adjusted for site class effects And from section 11.4.3

Where: = Site Coefficient defined in Table 11.4-1 = 1.0 = Mapped spectral accelerations for short periods, from Section 11.4.1 = 1.552 g (see below) Maps of spectral acceleration are available from several sources (ASCE, IBC, NEHRP, and FEMA). Data is also available on-line at http://earthquake.usgs.gov/hazards/ using the Java Ground Motion Parameter Calculator (http://earthquake.usgs.gov/hazards/designmaps/javacalc.php). The location of this piping system on the coast near Los Angeles is 33.9083 latitude and -118.41045 longitude. Below is a screen capture from the USGS software. SS for the location of interest is shown; SS=1.552g.

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CAESAR II Statics Training Cool H20 – FRP Piping

Therefore:

So the appropriate seismic acceleration is:

( [

)

] ](

[

)

Checking the limits on aH:

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CAESAR II Statics Training Cool H20 – FRP Piping Seismic load adjustment: The building codes are based on strength design where components (such as reinforced concrete structures) are evaluated on their load-carrying capacity rather than stress. Piping codes are based on allowable stress design and, while the calculated seismic load provides a good estimate of the internal loads and deflections of the piping system, these seismic loads over predict the resulting stress used here. Section 13.1.7 states “The earthquake loads determined in accordance with Section 13.3.1 shall be multiplied by a factor of 0.7.” Therefore the adjusted seismic loads for allowable stress design are:

Relative Seismic Displacements: Section 1621.1.5 discusses the means of addressing relative displacements due to “story drift” – this should be calculated via a structural analysis of the enclosing building. Assume this analysis yields the following displacements (with attachment points near building columns, no vertical drift is included):

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CAESAR II Statics Training Cool H20 – FRP Piping Node 10 18 40 50 60 90 100 110 120 150 160 170 180 190 240 270 300 330 360 390 420 450

Function Anchor +Y +Y X, +Y +Y X, +Y +Y X, +Y, Z +Y X, +Y +Y X, +Y +Y +Y +Y Anchor Anchor Anchor Anchor Anchor Anchor Anchor

Approx Elev (m) 4.6 4.6 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 28 0 7.3 7.3 7.3 7.3 7.3 7.3

X-Disp (mm) 26 26 16 16 16 16 16 16 16 16 16 16 16 16 16 0 42 42 42 42 42 42

Z-Disp (mm) 9 9 5 5 5 5 5 5 5 5 5 5 5 5 5 0 14 14 14 14 14 14

Note: Displacements need only be placed on +Y supports if friction loads are considered to be significant.

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CAESAR II Statics Training Cool H20 – FRP Piping Seismic Data Input We have already calculated the Seismic data and could build uniform loads to model the load in the X Y and Z directions from what we have just calculated. Alternatively, CAESAR II includes a static seismic wizard which can be used to perform all the calculations automatically, and build the uniform loads and incorporate into the model. We will use the static seismic wizard, and see that the values match up to our hand calculations. The Static Seismic Wizard is available from the same toolbar as the Loop design wizard used previously.

The static seismic wizard provides input for the various data we have discussed previously. Recall the following values: = Component amplification factor, from Table 13.6-1 = 2.5 for piping = Component response modification factor, from Table 13.6-1. Use 4.5 for pipes not in accordance with B31, with bonded joints or use 12 for welded, steel B31 pipe. = 4.5 = Component importance factor, from Section 13.1.3 (1.5 for life-safety components, hazardous material containing, or piping is in a Category IV structure (essential facility); 1.0 for all others). = 1.0 = Height in structure at point of attachment. Here, use the average of elevation of all 8 connections = 6m = Average roof height of structure = 12m In addition, we have the SS value obtained from the USGS utility = 1.552 Input the data into the Seismic Wizard

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CAESAR II Statics Training Cool H20 – FRP Piping On clicking OK, the values will be calculated for aH and aV as we have done manually above. These will be included as Uniform Loads. (The uniform load will act on following elments until removed or set to zero).

Note that the Uniform loads are also in g’s. Next we also need to apply the displacements due to “Storey-shift” as detailed previously. These displacements can be modeled as vector D1 (for X-direction) and vector D3 (for Z-direction). They should be applied to CNODEs attached to the restraints (increment each restraint by 1000). To save inputting effort, all restraints at a common level could be connected to a single CNODE. In this case, displacements need only be entered at three locations. Add the displacements only at nodes 10, 40 and 300. Node 10

Node 40

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CAESAR II Statics Training Cool H20 – FRP Piping Node 300

We now have the restraints defined, but currently they are defined as displacements at nodes 1010, 1040 and 1300. These nodes do not exist in the model. We will use these node numbers as cNodes and connect all the restraints to the relevant displacement at the correct elevation. All restraint nodes at 4.6m elevation must be connected via Cnode to displacement node 1010. (These are nodes 10 and 18).

Similarly, restraint nodes at 2.8m must connect to 1040 (Nodes 40 – 240) and nodes at 7.3m elevation must be connected to 1300 (nodes 300 – 450). This is easier to perform using the Restraint List view.

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CAESAR II Statics Training Cool H20 – FRP Piping

You will notice that the graphic plot now looks a little odd. The reason for this is, that by default, CAESAR II displays the system with Nodes and CNodes at the same point in space. This is fine for connecting pipe nodes to structure CNodes (like in Tutor) or nozzle nodes to vessel/pump CNodes (like in Turbo). But in this model, where several restraints reference the same CNode, the display will still attempt to join all these Nodes and CNodes together, resulting in a ‘nonsense’ plot. To clean up the plot and avoid the associated coordinate mismatch error during Error Check, change the Configuration/Setup parameter “Connect Geometry through CNODEs” to False.

The plot will not update automatically, so must be done manually. Click the Reset plot button to refresh the graphics.

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CAESAR II Statics Training Cool H20 – FRP Piping The plot will once again look correct.

Re-run the eror check – there should be no errors and no new warnings or messages.

Load Case Setup Access the Load Case editor – you will receive a message stating that the individual loads for the job have changed. This message is due to the fact we now have displacement loads in the model D1 and D3 and the uniform loads U1, U2 and U3. These must be incorporated into our load cases. Section 1621.1.4 discusses the combination method for the various loading directions. It states that the load along each horizontal axis shall be applied independently, but in conjunction with the vertical load. Since ISO 14692 only looks at a single stress type (OPE), this leads to the following seismic load cases (since boundary conditions are non-linear): Note the +/- signs in the various cases

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Note that even though results only need be retained from two load cases (the last two), we are electing to keep results from all load cases in order to help us “debug” in the event of an overstress. Load Cases L10 and L11 are not combined algebraically, rather they are included to compare the displacements, forces and stresses. Hence why they ar enot added or subtracted, just listed. We wish to find the worst case load case, so we can get CAESAR II to compare the resluts from each load case and report the maximum and minimum values. Select the Load Case Options tab and select SignMin and SignMax for the Combination method for L10 and L11.

SignMax compares the displacements, forces and stresses and uses the maximum force and maximum stress value of the cases (i.e. sign is considered in the comparison). Displacements are the maximum Signed valued of all displacements from each case included in the combination. Similarly

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CAESAR II Statics Training Cool H20 – FRP Piping for forces and stresses, these are the maximum Signed forces/stresses from each case included in the combination. SignMin is the opposite of this – the minimum signed values of the stresses/forces/displacements are included. Using SignMin and SignMax we can get the enveope of restraint loads for all cases. Also for the static seismic cases, enter in the Occasional Load factor of 1.33.

Analyse the model.

Review Results It can be seen straight away that there is an issue with Cases 4 and 5.

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CAESAR II Statics Training Cool H20 – FRP Piping Reviewing the Load Case 11 confirms that the maximum stress fails the code stress check, and is at 103.8% of the code allowable at node 180. In order to solve this, it is necessary to know which of the seismic combination cases caused the failure. We can see straight away that it is either case 4 or 5. Reviewing the code compliance report for all cases 2 to 9 shows that cases 4 and 5 are very similar alhough case 5 is fractionally higher.

Cases 4 and 5 represent the-X,+Y and –X,-Y seismic loadings. Now we need to find out which component of the seismic loadings caused the failure – the interial or the displacement. Stress due to force-based load is a primary load, stress due to strain is a secondary load. Once we find out the cause we can take the appropriate action to resolve the overstress situation. An easy way to determine which is the worst cause is to run the components of the load case individually to see wihich gives the greatest stress. Return to the load case editor. Load cases 4 and 5 both consist of W, D1, T1, P1, U1 and U2.

We know that W+D1+T1+P1 is not the cause as the OPE case is perfectly fine. So the culprit must be one of eiether D1, U1 or U2. Therefore, create three new load cases and assign D1 ,U1 and U2 respectively to each load case.

After re-running the analysis review the code compliance report for the three new cases.

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CAESAR II Statics Training Cool H20 – FRP Piping

This shows that clearly the D1 components is the largest contributer to the overstress, by a long way. This is a secondary loading, so the solution is to add more flexibility. In this case the fix is actually very simple and involves simply removing the guide just before node 180 located at node 170. The system will now pass the stress check.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Gas Transmission Pipeline - Buried Pipe

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe This model of a gas transmission pipeline will introduce the buried pipe modeller, and also introduce fatigue analysis. We will also explore the requirements of the B31.8 Design Code. This job consists of a 36” header, an 8” branch, and a 2” bypass, in the vicinity of a natural gas compressor station. The lines immediately go underground, from where they continue indefinitely for a very long distance.

B31.8 Design Code Gas transmission pipelines are covered by the B31.8 Code – Gas Transmission and Distribution Piping Systems. The philosophy of this code is to use high strength steel and custom, optimized wall thicknesses wherever possible, in order to minimize the amount of steel used in the long crosscountry pipelines. Stress analysis-wise, the code seeks to prevent yielding under any set of load cases. This prevents catastrophic failure under primary loads, and prevents plastic deformation under secondary loads. There are no requirements for reducing allowables for cyclic reduction factors (i.e., fatigue requirements). B31.8 is one of the few codes in which the OPErating case is a Code case and the EXPansion case is not Requirements of the different design codes are listed here in the table:-

OPE SUS EXP

B31.1 NO YES YES

B31.3 NO YES YES

B31.4 YES YES YES

B31.8 YES YES NO

B31.4 CH IX YES YES NO

B31.8 CH VIII YES YES NO

Modelling the system Model the system as shown in the isometric sketches. The following issues are of specific interest during the modelling phase. Element 10-20 originates at (and is anchored at) the compressor connection, with a flange (250 mm long, 5780 N weight). The pipeline is 36” diameter, with a non-standard 18 mm wall thickness. Enter two temperatures to model the extremes of the operating range, which represents the expectations due to winter lows and summer solar gain: Ambient = 21 C (set in Config) T1 = 50 C, T2 = -5 C above ground ON THE FIRST ELEMENT T1 = 30 C, T2 = 10 C underground (we will use these temperatures later) The material is API-5L X65 (material no 306), high strength steel. Its parameters can be found in the CAESAR II material database. The applicable code is B31.8 For natural gas, fluid density may be neglected. The branch connection at node 30 (as well as all other branches) is a Weldolet (SIF type 5).

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe The restraint at node 40 (as well as those at nodes 80, 110, 320, 360, 420, and 450) is a +Y (weight only) restraint. Specify a coefficient of friction of 0.3 for steel-on-steel contact. The bends at nodes 60 and 70 are 3-diameter bends (radius = 1370 mm). Element 60-70 goes underground 685 mm below node 60. Therefore we will need a node to indicate where the above ground/underground transition takes place. The entire element 60-70 can be entered first, and then the Break command can be used to insert a node 65 one-third of the way along the element length.

The element can be determined to be 5405 mm long (by clicking the local cosine “…” button) so onethird of that length is 1802.

The temperatures on 65-70 should be changed to T1 = 30 C, T2 = 10 C. The valve at element 90 - 100 (as well as that at element 430-440) is supported within an accessible valve pit (covered, but not buried). Node 75 (as well as nodes 115, 405, and 445) represents the buried/non-buried transition, and will be used later. Element 115-120 extends indefinitely, in a straight run, underground. Obviously, we need not model it forever – at some point, the cumulative restraining effect of the soil acts as an anchor. We will determine the required modelling length later; for now we can put in a dummy length of 10,000 mm. The model of the main pipe will look like the one shown below:

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Now move on to the branch, starting with element 30-310. This is an 8” standard schedule pipe. The temperatures on this element should be restored to T1 = 50 C, T2 = -5 C. The bends on this line are standard Long Radius. This pipe is now A53 Gr B low carbon steel. Element 30-310, modelled as is, is deceptively flexible, with a modelled length of 2440 mm, and an actual length of 1980 mm (since the element really originates at the surface of the 36” header, not at the centreline). So in reality, its flexibility should only be (1980/2440)3, or roughly 50%, of that calculated. We could correct this by modelling a weightless rigid from the centreline of the header to surface of the header (i.e., element 30-305), and then begin modelling the 8” line from that point (i.e., element 305-310). This approach has the following problems: 1. Placing the weldolet at node 30, causes no stress intensification on the 8” line (since there is no stress calculated on the rigid, and no weldolet at node 305). 2. Alternatively placing the weldolet at node 305 intensifies the stress on the 8” line, but doesn’t intensify the stress on the 36” line. Furthermore, the SIF would be both miscalculated (since CAESAR II would think the header size would be that of the rigid element) and misapplied (CAESAR II would not be able to determine in-plane from out-plane since the SIF would be at applied to two co-linear elements). One solution to this modelling dilemma is to use an OFFSET, in this case modelling a From Offset of 457 mm in the Z-direction. This internally models element 30-310 as a 457 mm long rigid element connected to a 1980 mm pipe, and transfers all stress calculations out to the true start of the 2440 mm pipe. (Note Offsets may not be entered on bend elements, so in this case, it is first necessary to break element 30-310 into two elements. Be careful that no elements, after applying Offsets, are reduced to zero-length. So in this case, enter two elements, 30-305 (DZ = 1000 mm, From Offset Z = 457 mm) and 305-310 (DZ = 1440 mm, long radius bend).

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Element 370-380 goes underground 685 mm below node 370, so we need a node to indicate where the above ground/underground transition takes place. The entire element 370-380 can be entered first, and then the Break command can be used to insert a node 375, 685 mm along the element length. The temperatures at node 375 should be changed to T1 = 30C, T2 = 10C. The valve at element 430-440 is supported within a valve pit. Nodes 405 and 445 represent the buried/non-buried transition. Element 445-450 (like element 115-120) extends indefinitely, in a straight run, underground. We will determine the required modelling length later; and use a dummy length of 10,000 mm for now. The completed model will look like the one shown below:

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Next model the bypass. Create this model in a new file before combining the two files.

Combine the models and run the error check. Two errors will appear. Both errors relate to the temperature for case 2, at elements 10-20 and 30305. The temperature for case 2 at these locations is -5°C. The error message is showing that there is no material data available for either of the two materials we have selected for a temperature this low, in the B31.8 code.

We cannot analyse until this has been corrected. To correct, we can edit the material database to include properties for the material down to the correct temperature.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Material Database Close the piping input to return to the main window. Access the material database form the Tools menu.

Choose to edit a material

Search for material 102 (A53 B) (you can search on either term). Notice that there are a number of entries for A53 B for the various different codes, including for B31.8. Select the B31.8 entry

The lowest temperature for which an expansion coefficient is entered is 0°C. The next row down is 73.3°C, which has no expansion coefficient. As our temperature in the model is -5°, we can see where we have incomplete data. We could enter in the data here for the missing expansion coefficient.

Alternatively, using engineering judgement, we can take the material properties for A53 B from another code where the data is filled in sufficiently and use this in B31.8 code.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Search again for the material A53 B. This time, select the All Codes data. This information is more complete than the B31.8 specific data for A53 B. If we are confident that this data will be suitable for B31.8 then we can use this data in place of the default B31.8 data.

The material database is stored in two files. One file is CMAT.bin. This stores all the default data and is read only. Any changes to the material are stored in a separate file called UMAT.UMD. This file stores any material information which is different to that in CMAT.bin. CAESAR II then uses the UMAT.UMD file first, and reads any further data from CMAT.bin. Materials from CMAT.bin cannot be deleted, only those from UMAT.UMD. If we save the A53 B B31.3 material data for use with B31.8, this will be written to the UMAT database. The CMAT database will be still the same as it currently is, however the UMAT will be read in preference to this, and it will act as though the data has been “overwritten”. To make this change, simply select the Applicable piping code drop down, and change from B31.3 to B31.8 and save the material.

Return to the input. You should see a warning stating that the properties for the material A53 B, code B31.8 have changed in the material database, and given the option to use these new properties or keep the existing. Select to update the material properties via the “No – Update” button.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Select part of the bypass (or any part that is material A53 B that we have just changed) and double click on the chevron in the temperature/pressure area. Notice that the expansion coefficient is now filled in for both temperatures (whereas it was 0.000 for T2 previously). Re-running the error check will show that the error is no longer present, for material A 53B but still present for API-5L X65. We now need to update the material database for this material. Repeat the exercise from before and update the material properties for API-5L X65.

Run the error check again – the material errors will no longer appear. The error checler should show only the Centre of Gravity report.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Buried Pipe Modeller The piping system beyond nodes 65 and 375 is mostly buried. The effect of this is (1) It will be continually supported, causing the weight stresses to be negligible, (2) It will be continually restrained against axial growth and bending by the adjacent soil. The former effect can be best modelled by zeroing the density of any pipe, fluid, and insulation; the latter can best be modelled by meshing the pipe and adding restraints, with mesh spacing, restraint stiffness, etc. based upon the soil properties. CAESAR II provides an underground pipe modeller which simplifies this process, performing the following functions:

Allows for the direct input of soil properties. These properties are used to generate first the stiffnesses on a per length of pipe basis, and then the restraints that simulate the discrete buried pipe restraint. (Note that any existing restraints in the underground area are deleted during this process.) CAESAR II supports three different soil modellers – one based upon the published work of Mr. L. C. Peng, plus two others (for clay and granular soils) from the American Lifelines Alliance. Automatically breaks down straight and curved lengths of pipe. CAESAR II uses a three Zone concept to break down straight and curved sections. Those ends of pipe identified as “transverse bearing lengths” are broken down into Zone 1 lengths (the smallest element lengths selected to properly distribute the lateral forces to the soil). At distances far away from Zone 1 are Zone 3 lengths (long lengths of pipe selected to transmit axial loads). Between Zone 1 and Zone 3 is Zone 2 (transition lengths which vary linearly from the Zone 1 end to the Zone 3 end). Allows for the direct input of user’s soil stiffnesses on a per-length of pipe basis. Input parameters include axial, transverse, upward, and downward stiffnesses, as well as ultimate loads. The user can specify user-defined stiffnesses separately, or in conjunction with CAESAR II’s automatically generated soil stiffnesses.

Restraint Parameters The Underground Pipe Modeller allows the use of any of three different soil modelling algorithms. The first two are based upon the work of the American Lifelines Alliance, as published in their document “Guidelines for the Design of Buried Steel Pipe”, dated July, 2001 (with addenda through February 2005); this document offers different models for clay soils and granular (sand/gravel). The third model is based on the soil restraint modelling algorithm presented by L.C. Peng in his two-part paper entitled “Stress Analysis Methods for Underground Pipelines,” published in 1978 in Pipeline Industry. Soil supports are modelled as bilinear restraints having an initial stiffness, an ultimate load, and a yield stiffness. The yield stiffness is typically set close to zero, i.e. once the ultimate load on the soil is reached there is no further increase in load even though the displacement may continue. The basic ultimate loads that must be calculated to analyse buried pipe are the axial and three bearing (transverse, upward, and downward) ultimate loads. (Note that for the Peng model, all three bearing ultimate loads are considered to be identical.) Once the axial and bearing ultimate loads are known, the stiffness in these directions can be determined by dividing the ultimate load by the yield displacement. (Researchers have found that the yield displacement is typically related to the buried depth, the pipe diameter, the soil type, and the load type.) The ultimate loads and stiffnesses

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe computed are on a force per unit length of pipe basis; the restraint ultimate loads and stiffnesses are then based upon tributary lengths of the adjacent piping elements.

The restraint equations use these soil properties to generate ultimate loads and stiffnesses using the following equations. Initial restraint stiffness is estimated by assuming that the Ultimate Load is developed over a “Yield Displacement” (YD). Axial Stiffness (KAX) on a per-length of pipe basis:

Transverse stiffness (KTR) on a per-length of pipe basis:

American Lifelines Alliance Clay Model Lateral Ultimate Load (FAX) per unit length

inches (stiff clay) or 0.4 inches (soft clay) Where: = Pipe diameter = soil adhesion factor (dimensionless) = = soil cohesion representative of soil backfill

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Transverse Ultimate Load (FTR) per unit length

(

)

Where: = = = 6.752 = 0.065 = -11.063 = 7.119 = height of soil cover (measured to centre of pipe, note CAESAR II requests distance to top of pipe) Downward Ultimate Load (FD), per unit length

Where: = 5.14 = 1.0 (for clay) = defective density of soil (taking buoyancy into account) Upward Ultimate Load (FU), per unit length

Where:

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe American Lifelines Alliance sand model: Axial Ultimate Load (FAX), per unit length

Where: = coefficient of pressure at rest (dimensionless) = 1 – sin φ = interface angle of friction for pipe and soil = f φ φ

= soil angle of internal friction, typical values are: 27 – 45° for sand 26 – 35° for silt

F = coating dependant factor (dimensionless), typical values are: Pipe Coating

f

Concrete

1.0

Coal Tar

0.9

Rough Steel

0.8

Smooth Steel

0.7

Fusion Bonded Epoxy

0.6

Polyethylene

0.5

Transverse Ultimate Load (FTR), per unit length

(

)

Where: = A, B, C, D, E based on φ, according to the following table: φ 20° 25°

A 2.399 3.332

B 0.439 0.839

C -0.30 -0.090

D 1.059E-3 5.606E-3

E -1.754E-5 -1.319E-4

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe 30° 35° 40° 45°

4.565 6.816 10.959 17.658

1.234 2.019 1.783 3.309

-0.089 -0.146 -0.045 -0.048

4.275E-3 7.651E-3 5.425E-3 6.44E-3

-9.159E-5 -1.683E-4 -1.153E-4 -1.299E-4

Downward Ultimate Load (FD), per unit length

Where: = = = density of dry soil Upward Ultimate Load (FU), per unit length

dense sand

loose sand

Where: =

Meshing Parameters Typical buried pipe displacements are considerably different than similar above ground displacements. Buried pipe deforms laterally in areas immediately adjacent to changes in directions (i.e. bends and tees); in areas far removed from bends and tees the deformation is primarily axial. The optimal size of an element (i.e., the distance between a single FROM and a TO node) is very dependent on which of these deformation patterns is to be modelled. Where the deformation is “lateral” smaller elements are needed to properly distribute the forces from the pipe to the soil. The length over which the pipe deflects laterally is termed the “lateral bearing length” (Lb) and can be calculated by the equation: (

)

Where: = Pipe modulus of elasticity = Pipe moment of inertia

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe CAESAR II places three elements in the vicinity of a bearing span to properly model this load distribution. The bearing span lengths in a piping system are called the Zone 1 lengths. The axial displacement lengths in a piping system are called the Zone 3 lengths, and the intermediate lengths in a piping system are called the Zone 2 lengths. Zone 3 element lengths (to properly transmit axial loads) are computed by 100*Do , where Do is the outside diameter of the piping. The Zone 2 mesh is comprised of elements that are 1.5 times the length of a Zone 1 element at its Zone 1 end, and that are 50*Do long at the Zone 3 end. A typical piping system and how CAESAR II views this zone mesh distribution is illustrated below:

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Virtual Anchor Length (VAL): Since soil restraint capacity is a function of piping length, after a certain length, the soil restraints will fully counteract the piping loads, acting as a “virtual anchor”. The piping need not be modelled beyond this length. This length can be calculated as that length where the axial pipe force equals the ultimate axial restraint load. Axial pipe force consists of three types: 1. Thermal Load = 2. Poisson effect (longitudinal shrinkage due to hoop strain) = 3. Longitudinal pressure load =

Using the (ALA Sand Model), the Axial Ultimate Load (FAX) per unit length is:

The ultimate restraint load therefore is the VAL * Fax ,or: *

Ultimate restraint load

+

*

+

Simplifying this gives: [

(

)

] *

+

This value can be used to determine how long we must model elements 130-140 and 460-470 of the GASTRANS model. This pipeline is in sandy soil – the soil parameters are as follows. Soil Parameters Soil Type Coating Factor (rough steel) Dry soil density, 𝑦 Effective Soil density, 𝑦′ Buried Depth, H Angle of internal friction, φ Coefficient of Pressure at rest, K0 Yield Displacement Factor, Axial dT Yield Displacement Factor, Lat, dP (mult of D): Yield Displacement Factor, Up, dQu (mult of H): Yield Displacement Factor, Up, dQu (max mult of D): Yield Displacement Factor, Down, dQd (mult of D):

Dense Sand 0.8 1909 kg/cm3 1190 kg/cm3 915mm (36” pipe) 610mm (8” pipe) 35° 0.426 2.5mm 0.1 0.01 0.1 0.1

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

° (coldest temp underground is 10 so delta from ambient of 21.11 is about 12 ) (36" pipe) (8" pipe) pipe) , Working this out give the following Virtual Anchor Lengths: VAL36 = 206400mm VAL8 = 127600mm Unlike the perfectly rigid/perfectly plastic response due to friction alone, the CAESAR II soil modeller inserts elastic/plastic springs to model some initial “give” in the soil. The program, therefore, may require more pipe length to fully develop this virtual anchor along a straight run. Since an even longer straight run is just as quick to enter and analyse, a more generous VAL length can always be used in the model. For this example we will change the place-holder lengths originally entered for elements 115-120 and 445- 450 to 300000mm and 200000mm, respectively.

Bury Pipe We will now bury the pipe. Close the piping input and return to the main window. Access the Buried pipe modeller

As soon as the buried pipe modeller is opened, the job file is saved as a copy with the same name with suffix “B”

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe In the underground modeller the soil underground conditions can be defined. This is done in two parts: 1. Enter the soil model 2. Define where/how the system is buried First let us define the soil model. We must define two soil models for our job – one for 915mm depth, one for 610mm depth. Access the soil model entry dialog.

We will use the American Lifelines Alliance Sand method. Notice that this is soil model number 2. Soil model number 1 is reserved for a completely user defined stiffness which can be entered in the main spread sheet.

Enter the soil properties as detailed above.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Add a second soil model, model no 3 and enter the properties for the second model. Only the depth op of pipe (H) is different.

Now that the soil models have been created, we must specify where/how the system is buried. This is done in the main Buried Element description Spread sheet.

This spread sheet is used to indicate where the pipe is buried, under which soil type, which mesh type should be used, as well as any user-defined stiffnesses. A critical part of the modelling of an underground piping system is the proper definition of Zone 1 (or lateral) bearing regions. These regions primarily occur: • • •

On either side of a change in direction For all pipes framing into an intersection At points where the pipe enters or leaves the soil

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe CAESAR II automatically puts a Zone 1 mesh gradient at each side of the pipe framing into an elbow, it is the user’s responsibility to force it to do so in other areas. This is done using the FROM/TO end mesh columns in the spread sheet. A tick in either of these columns places a “zone 1” mesh at the corresponding element end (either From or To end). This should be done where the soil enters or leaves the soil, in the vicinity of tees, or in “problem areas”. The soil model number is used to specify whether the soil is buried Complete the spread sheet using the following information. The pipe enters the soil into soil model 2 at node 65, then leaves again at node 75. Enter soil model 2 on element 65-70. On the ‘from end’ of this element (i.e. node 65) place a Zone 1 mesh by checking the box – this is where the pipe enters the soil. The soil model will propagate through the spread sheet, so enter 0 on element 75-80 (the pipe is now in the valve pit, out of the soil). On the previous element, place a zone 1 mesh on the from end (i.e. node 75) – where the pipe exits the soil.

Continuing on, the pipe re-enters the soil at node 115 through to the VAL at node 120.

Next moving on to the 8” pipe line, the pipe enters the soil at node 375, into soil model 3 and remains in the soil until it exits at node 405 at the next valve pit. The one 1 meshes at the bends will be automatically added, we only need to define these at the entry and exit points.

The pipe re-enters the soil at node 445 through to the VAL at node 450. Nodes 50 through to the end are the bypass, and so are above ground.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

After completing the spread sheet, the model can be buried using the Convert Input function.

You will receive a warning during the conversion stating that any user defined intermediate nodes n bends will be deleted – CAESAR II will re-specify these as per the soil meshing algorithm during conversion. Accept this message.

The model will finish converting and will confirm that there were warnings – we only had the one which is OK. Clicking OK will close the buried pipe modeller. The currently selected c2 job file is now the buried pipe model - GASTRANSB. This is identical to any other c2 job file, the only difference between this model and the “unburied” model is the inclusion of a number of restraints with the correct stiffness added as per the soil models input. Return to the piping input to view the updated buried model.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Load Case Setup In order to get the true Expansion Stress in a non-linear system, it is necessary to evaluate the following load cases: Extreme hot operating condition Extreme cold operating condition For this example, this can be implemented as: W+P1+T1 (OPE) HOT W+P1+T2 (OPE) COLD W+P1 (SUS) L1 - L2 (EXP) L3 + L4 (OPE) CAESAR II recommends the following set of load cases to perform these analyses.

This load case setup requires some minor modification. We need to add a third expansion check on the stress range between operating case 1 and 2, along with a baseline for these expansion cases, of the weight no contents of the pipe, which will be used rather than the sustained case. Add the following load cases: L3 L7

WNC L1 – L2

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Also give the load cases meaningful names in the Load Case Options tab

We can now run the analysis

Results Review The results show that there are failures in the expansion case 6. A review of the code compliance report shows that the shakedown stresses on the weld-o-lets branch runs at 30 and 50 are overstressed. The sustained stress is also quite high at these outlets. The range from operating case 1 to operating case 2 is insignificant. Turning on the stress filter to display only nodes greater than 90 per cent of the allowable reduces this report to only the branches at nodes 30 and 50: Reducing these stresses will be left as a follow-up exercise. Now move on to the fatigue evaluation.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Fatigue Due to the danger of gas leaks, and the presence of cyclic loading (pressure fluctuations and solar heat/cooling cycles) this system is being evaluated for fatigue failures. Since B31.8 does not offer any specific guidance on fatigue analysis, our best course of action is to calculate the cyclic stresses according to the Stress Intensity equation, and compare them to ASME Section VIII Division 2 fatigue curves (Figure 5.110.1), using an appropriate factor of safety. This system should be evaluated for the following load cases: Design life: 40 years Temperature variations: Ambient temperature: 21C Summer maximum temperature, above ground: 50C (for 40 years) (T1) Summer maximum temperature, below ground: 30C (for 40 years) (T1) Winter minimum temperature, above ground: -5C (for 40 years) (T2) Winter minimum temperature, below ground: 10C (for 40 years) (T2) Daily temperature variation, above ground: 20C from extreme (14,600 days) (T3=T1-Δ, T4=T2+Δ) Daily temperature variation, below ground: 10C from extreme (14,600 days) (T3=T1-Δ, T4=T2+Δ) Pressure variations: Maximum pressure: 80 bar (P1) Annual shutdown: 0 bar (40 times) Minimum operating pressure: 63 bar, varies between 63 and 80 (1,000 occurrences) (P2) Daily fluctuation: 5 bar drop (14,600 days) (P3=P1-Δ) Setting up the Fatigue Load cases Fatigue loads are incurred by transitioning between two or more different operating cases. It is usually best to model the two extreme load cases, and set up all fatigue load cases to be a variation from one of these. For example: Operating Case A: Shutdown, winter minimum (extreme stress condition) Operating Case B: Full pressure, summer maximum (extreme stress condition) Operating Case C: Full pressure, winter minimum (enveloped in A-B cycle) Operating Case D: Compressor operation, winter minimum Operating Case E: Compressor operation, summer minimum fluctuation Operating Case F: Pressure fluctuation, winter minimum Operating Case G: Pressure fluctuation, summer minimum fluctuation Operating Case H: Full pressure, winter maximum fluctuation This translates into operating conditions of: T1 = 50 AG, 30 BG (summer maximum) T2 = -5 AG, 10 BG (winter minimum) T3 = 30 AG, 20 BG (summer minimum) T4 = 15 AG, 20 BG (winter maximum)

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe P1 = 80 bar (maximum) P2 = 63 bar (minimum pressure; compressor setting) P3 = 75 bar (daily minimum) Load Cases (including those required earlier): 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

W+T1+P1 (OPE) Hot operating, also Operating Case B W+T2+P1 (OPE) Cold operating, Operating Case C WNC (SUS) Shakedown Baseline W+P1 (SUS) Sustained W+T2 (OPE) Operating Case A W+T2+P2 (OPE) Operating Case D W+T3+P2 (OPE) Operating Case E W+T2+P3 (OPE) Operating Case F W+T3+P3 (OPE) Operating Case G W+T4+P1 (OPE) Operating Case H L1-L3 (EXP) Expansion Hot L2-L3 (EXP) Expansion Cold L1-L5 (FAT) 40 cycles (Algebraic) -- B-A (Summer MAX > Winter MIN) L2-L6 (FAT) 500 cycles (Algebraic) – C-D (Winter MAX > Winter MIN (P1-P2)) L1-L7 (FAT) 500 cycles (Algebraic) -- B-E (Summer MAX > Summer MIN) L2-L8 (FAT) 7300 cycles (Algebraic) – C-F L1-L9 (FAT) 7300 cycles (Algebraic) – B-G L10-L2 (FAT) 7300 cycles (Algebraic) – H-C

Before fatigue stresses can be checked, the allowable limits must be defined in the input. Return to the first element and click on the Fatigue Curves button at the bottom of the Auxiliary Data Area for Allowable Stress. Fatigue data may be typed in by hand but it may also be read from data files supplied with CAESAR II or built and stored on the hard drive. Select the 5-110-1B.FAT file to use the steel fatigue data for B31.8.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Also enter in the correct temperatures and pressures as listed above, changing when the pipe is below/above ground as necessary. Once complete, create the load cases as described

Run the analysis. After reanalyzing the system, select all fatigue loads and the cumulative usage report to evaluate the system loads. It is apparent that fatigue stresses and their associated cycles are quite low. Only the shakedown stresses at the weld-o-lets need be addressed.

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CAESAR II Statics Training Riser

Riser

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CAESAR II Statics Training Riser This job is an offshore jacketed production riser. The job shows how to use the offshore capabilities of CAESAR II. In addition to covering the hydrodynamic analysis techniques, this job also covers model construction, element duplication, and problem resolution. For this system, the piping details are defined in the table below Item

Diameter

Thickness

Temperature

Pressure

Fluid

Riser Jacket Product Core Injection Core

18” 6” 4”

Standard Standard Standard

15°C 80°C 95°C

0 bar 5 bar 10 bar

0 0.85 SG 1.025 SG

Marine Growth 50mm 0 0

The 4" injection line is used to inject water into the well to assist in product recovery. The oil is recovered and pumped to the surface in the 6" product line. The 18" jacket pipe is used to house the riser tubes, offering protection and support. This system is installed in shallow water, and subjected to a specified wave train. The objective of the analysis is to determine the loads and stresses on the system in accordance with ASME B31.4 Chapter IX. The wave parameters are defined in the table below: Item Height Period Depth Wave Theory

Value 5700mm 7.72 sec 9000mm Stokes 5th

Modelling The first thing you may notice on the sketch is that the node increment in this model is 5 rather than 10 as in all the previous models. As such we will adjust the node increment for this model. This change affects this model only. Alternatively the configuration file can be changed if all models should have a different node increment.

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CAESAR II Statics Training Riser This jacketed riser will be modelled in stages, where each stage represents a continuous run of piping from the bottom to the surface. The two core pipes (6" and 4") are enclosed in the jacket pipe (18"). The core pipes are positioned in the jacket through the use of internal spiders (braces). In CAESAR II, these spiders can be modelled using dummy rigid elements, connected to the jacket through the use of CNODES. For the 4" pipe, these dummy rigid elements must be (114.3 mm / 2 + 25 mm = 85 mm), while for the 6" pipe, the dummies are (168.275 mm / 2 + 25 mm = 110 mm). This will provide a clearance of 50 mm between the core pipes. When constructing a model, the first element piping spread sheet is extremely important, since much of its data is duplicated forward throughout the job. Injection Line Set the parameters as follows. Note the node numbering begins at 405 – 410. The “400” series nodes will be for the 4” line Material: A 106 B Diameter: 4” = 114.3mm Wt/Sch: S = 6.0198mm Fluid Density: 1.025 SG = 1024.5 kg/m3 Temp 1: 95°C Pressure 1: 10 bar Design Code: B31.4 Chapter IX Fac: 0.6 Fac is F1, Hoop Stress Design Factor, as per Table A402.3.5(a) of B31.4. Appropriate values are 0.72 for Pipelines or 0.60 for Platform piping and Risers. DZ = -1800mm ANC at 405 Locate a bend at node 410. Specify a bend radius of 203mm Finally, we need to reset the elevation of the system, so that node 405 lies on the sea bottom. (This is important for the wave and wind loading later. While wave loading allows a relative definition of position of the piping in the water, wind does not. Therefore, zero elevation must be properly specified on the system so that the correct wind loads calculated.) Use the global coordinate button to reset the origin, node 405, from (0,0,0) to (0,-9000,0).

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CAESAR II Statics Training Riser Continue to the next element – 410 -415 This is 1500mm in the Y direction, and has two restraints at node 415, an X and a Z. Both the restraints will have a CNODE to 414. Node 414 will be the spider connection as discussed above.

Continue to the next element. As the isometric shows, the riser continues in 1500mm sections, right the way up to node 470 at the top. We can create this all in one element, and break to split up into the 1500mm sections. Change the node numbers to 415 – 470. The pipe travels 16500mm in the Y direction overall.

Now we can break this element with a node increment of 5. Use the break command as before, but this time, select the Insert Multiple Nodes radio button.

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Enter in a node step of 5 – the Total Number and Length fields will be calculated automatically. Also specify the support configuration as at node 415. Checking the system coordinates in the list processor shows that node 440 is at the surface (elevation 0), and there are 12 vertical elements - 6 above the surface and 6 below the surface.

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Add a bend at node 470 and change the radius to 203mm as before. Return to element 410 – 415 (the bottom element on the riser) and add in a +Y support at node 415 with a CNODE to 414. This is done now because this vertical support should not be duplicated to all the spider connections. Complete the riser by adding in the final element (470 – 475). This is 1500mm in the –Z direction and an anchor is located at node 475. The injection line is now complete.

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CAESAR II Statics Training Riser Product Line For the product line, duplicate the injection line, this is essentially duplicating the entire model at this point. This duplication will use a node increment of 200, followed by a modification to the temperature, pressure, diameter, thickness, and fluid specific gravity. Select the entire model and duplicate as follows:

Change the properties of element 605-610 so that they are correct for the 6” line: Diameter: T1: Fluid Density:

6” 80°C 0.85SG

Wt/Sch: P1:

STD 5 bar

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Jacket Important Notes When Duplicating Core / Jacket Piping The diameter is changed after the duplication. Typically, the core pipe uses long radius elbows, and the jacket uses short radius elbows. This allows the radii of both the core and the jacket to be the same. If the jacket contains fluid, its density must be computed such that the unit weight across the entire jacket inner diameter yields the same weight as the real fluid in the annulus between the jacket and core pipes. Core pipes do not see environmental loads. This is important to check after building the model. Continue after the last element (670-675) and change the node numbers again. This time for the 18” pipe – so use node numbers 1810 to 1870. This element is 18000mm long Diameter: T1: P1 Fluid density: Restraints:

18” 15°C zero zero X Y Z RY Marine Growth:50mm

Next break this element, using the multiple break function again, and a node increment of 5. This will split the element into 12 sections, each 1500mm in length.

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CAESAR II Statics Training Riser At node 1870, define a GUIDE restraint. With this element vertical, the program will create an X and a Z restraint at node 1870. The Wind/Wave settings will propgate through the model until changed or turned off, even though on subsequent elements will not have the Wind/Wave check box ticked. On element 1840-1845 (the first pipe out of the water and a t zero elevation), turn off the wave and set a wind shape factor of 0.65. This is a typical value for cylindrical bodies. The model at this point shows the three lines, but they are not properly located in space. A series of construction elements will place these lines properly in space and also provide the right structural connectivity. The idea here is to run a dummy rigid element from the restraint CNODEs of the injection line, to the nodes on the jacket and, on to the restraint CNODEs of the product line. Navigate to the end of the model and define a new element from 414 to 1815. This element will be 85mm long in the X direction, and will connect the restraint at 415 (with CNODE 414) to the jacket at 1815. Define this as a rigid element with zero weight.

Turn off the wind.

Follow with another dummy rigid element from 1815 to 614; 110 mm in X. This will join the product line through the restraint at 615 with its CNODE at 614. The graphics should now display the model correct.

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CAESAR II Statics Training Riser Using the Elements listing, duplicate these last two elements, with a node increment of 5 to place the spider on the next restraint. Continue this duplication so that the spiders are placed all the way up the riser.

Once complete, and all restraints along the riser are defined, run the error checker. There will be a number of warnings concerning "zero weight" rigid elements and "four elements framing into a node". These are all acceptable in this instance. Note that the Centre of Gravity Report shows a combined weight of about 33,000 N. Recall that the riser is supported only at its base, with a pin connection. In reality, risers are supported by top-side tensioners, exerting a force sufficient to ensure the riser is always in tension. For this job, return to the input and at node 1870 (the top of the riser), define a hanger to apply a constant vertical force of 45,000 N. Re-run the error checker. The model should now be ready for analysis.

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CAESAR II Statics Training Riser

Hydrodynamic Theory A basic discussion of hydrodynamic theory can be found in the CAESAR II documentation (Technical Reference Guide, Chapter 6). There are a variety of different wave theories, used to compute the water particle velocities and accelerations resulting from a wave train. CAESAR II includes solutions to the three most commonly used wave theories; Airy, Stokes 5th, and Stream Function. The latter two theories are non-linear, but provide a better description of the water particle behaviour. CAESAR II also includes modified versions of these three theories, which allow consideration of the fluid above the mean sea level. The basic procedure is to solve for the wave length, based on a selected wave theory. Once the wave length is known, the velocities and accelerations can be determined at any position in the water column. Based on these values, drag (Cd), inertia (Cm), and lift (Cl) coefficients are determined for each pipe element. These coefficients, along with the velocity and acceleration are used to compute the force applied to the piping elements, using Morrison's equation: | | Where: = fluid density = drag coefficient = pipe diameter = particle velocity = inertial coefficient = particle acceleration The particle velocities and accelerations are vector quantities which include the effects of any applied waves or currents. In addition to the force imposed by Morrison’s equation, piping elements are also subjected to a lift force and a buoyancy force. The lift force is defined as the force acting normal to the plane formed by the velocity vector and the element’s axis. The lift force is defined as:

Where: = fluid density = lift coefficient = pipe diameter = particle velocity The buoyancy force acts upward, and is equal to the weight of the fluid volume displaced by the element. Once the force on a particular element is available, it is placed in the system load vector just as any other load is. A standard finite element solution is performed on the system of equations which describe the piping system. For this particular model, a sample hand computation will be used to estimate the applied wave load. This will be used as a verification of the loading, to ensure we are making the correct assumptions and modelling correctly.

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CAESAR II Statics Training Riser

B31.4 Code Requirements The B31.4 piping code includes Chapter IX, for "Offshore Liquid Pipeline Systems". The scope of this chapter states: "For the purposes of this Chapter, offshore pipeline systems include offshore liquid pipelines, pipeline risers, offshore liquid pumping stations, pipeline appurtenances, pipe supports, connectors, and other components as addressed specifically in the Code." In Section A401.10.1, this Code states: "All parts of the offshore pipeline system shall be designed for the most critical combinations of operational and environmental loads, acting concurrently, to which the system may be subjected." This means that operating loads are to be combined with wind, wave, and current! In Section A402, this Code states that: - Hoop Stress is limited as defined by: Note that the pressure term used in the hoop stress equation is the difference between internal and external pressure. - Longitudinal Stress is limited as defined by: The longitudinal stress is defined as the axial stress plus or minus the bending stress, whichever results in the larger stress value. - Combined Stress is limited as defined by: Here, Scomb is defined by the Tresca Combined Stress Equation. To satisfy these requirements, a single load case can be defined. This load case should include all loads defined in the input (weight, pressure, temperature, wave, wind, etc). CAESAR II will compute the above stresses for each element and report the maximum stress value with its corresponding allowable. The factors F1, F2, and F3 are defined in the code in Table A402.3.5 (a) as: Location Pipeline Riser

Hoop F1 0.72 0.60

Longitudinal F2 0.80 0.80

Combined F3 0.90 0.90

The B31.4 piping code states that the environmental loads used in the analysis correspond to the "100 year" storm. This is equivalent to the largest storm that occurs every 100 years.

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Hydrodynamic Input The hydrodynamic input specification in CAESAR II is relatively simple. Up to four different loading conditions can be defined. These different conditions could be different waves, currents, or directions. For each of these loading conditions the data is defined as shown below

This particular load definition is specifies only a wave. However, either a standard current profile or a current table can also be defined. The particular wave used in this example is a well-publicised wave, used as the example in the paper by Skjelbreia and Hendricson for the solution to Stokes 5th Order Gravity Waves. Note this does not correspond to a "100 year storm". This wave is being used because it has published results. The wave data consists of the water depth (9 m), the wave height (5.7 m), the wave period (7.72 seconds). The wave kinematics factor is a factor used for Stream Function and Stokes 5th solutions to account for the spreading of the wave energy in a real sea state. Values typically range from 0.85 to 1.0, and serve to reduce the particle velocities. The "Phase Data" defines how the wave is imposed on the piping system. Since the wave moves over the piping system, every element of the system is exposed to every phase of the wave. At one particular position (phase) of the wave the piping system will experience the maximum environmental load. Performing 360 solutions to find this maximum is not practical, given the other factors involved (combination with current, non-uniform sea state, directionality, and spreading). Typically drag governs the loading on (small) piping system, so the wave is positioned so that most of the piping system sees a zero phase angle. Alternatively, the input can be set so that the entire system sees a zero phase angle.

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Wave Solution The hydrodynamic parameters as defined in the input are used by the Stokes 5th wave theory to determine the water particle data. This solution can be evaluated numerically (by reviewing data tables) or graphically (through the use of plots). A brief evaluation is shown below. First, two dimensionless parameters are computed and used to determine the "suggested" wave theory. This evaluation is performed by plotting these dimensionless parameters on a chart, found in a number of publications. This chart, with the location of the specified wave for this job is shown in the figure below. This chart (and the remainder of the wave solution) can be obtained using the “Chart Current Results” button on the Load Case Editor.

For this particular wave, the chart shows that the recommended wave theory is Stream Function 9th Order. (This job will still employ the Stokes 5th solution, for illustrative purposes.) Each region of the chart corresponds to a different wave theory, as detailed in the key at the bottom. The Drop down list at the top of the dialog box allows other graph representations to be shown. Select the “Surface Elevation vs Phase” option

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This results in the following graph.

This figure shows that the wave crest is at a phase of zero, with the trough at a phase of 180 degrees, as expected. Notice also that the wave profile is not symmetric about the mean water level. For this 5.7 m wave, the crest is 4 m above the still water level while the trough is 1.5 m below the still water level. Only the Airy wave theory produces a symmetric wave profile.

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CAESAR II Statics Training Riser Changing the plot to "Horizontal Velocity versus Depth at Zero Phase" results in the figure shown below. This figure shows that the velocity decreases with depth, as expected. Note however that there is still an appreciable velocity, even at the bottom for this particular wave.

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CAESAR II Statics Training Riser Selecting the plot "Horizontal Velocity versus Phase at Zero Depth" results in the figure below. This figure shows that velocities are positive in the wave crest, and negative in the wave trough, again as expected. This is why there is a mean mass transport in the direction of the wave train.

Note that in this plot, the velocity in the trough is shown as zero. This is because the plot is showing the data at a depth of zero, the still water level. In the trough region, the water is below this level. At a lower depth, the velocities do go negative, which can be seen by reviewing the actual data tables.

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CAESAR II Statics Training Riser Selecting the plot "Horizontal Acceleration versus Phase at Zero Depth" results in the figure below. This figure shows that the water particles are accelerating in front of the wave crest, and decelerating behind the wave crest. Again, in the trough area, the plot shows values of zero because the water level is below the "zero" elevation.

Plots such as these are typical of wave solutions. The wave solution produces data for the entire water depth over the entire wave phase. Horizontal and vertical velocities and accelerations can be studied as a function of depth or phase. In addition to plotting the data, the actual numerical values can be reviewed by clicking the View Data Table button. This file is called .WV1 and is a text file – so opens in Notepad.

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CAESAR II Statics Training Riser At the top of this file, the wave length and speed are reported. (The corresponding values from Skjelbreia and Hendricson's paper are 76.2 m (250.0 ft) and 9.87 m/sec (32.39 ft/sec). The difference here is due to a correction to the Stokes solution published in 1985.) This set of tables shows the free surface as a function of phase angle. If the water depth (9 m) is added to these values, the result is the row of values labelled "Surface Elevation". The "Horizontal Velocity" table (for the Z direction) is also shown. The first row (zero depth) and first column (zero phase) were used to produce the velocity plots shown above. Hydrodynamic Coefficients The water particle data can be used directly in Morrison's equation to determine the force acting on the pipe elements. However, in order to employ Morrison's equation, several hydrodynamic coefficients must be determined. These coefficients are a function of the Reynold's and KeuleganCarpenter numbers, and are typically presented in graphical form, as shown in the figure below. These coefficients have been determined through testing.

Cd versus Re and K

Cl versus Re and K

The Keulegan-Carpenter Number, K, is defined as Where: = maximum fluid particle velocity = wave period = characteristic diameter of the element The Reynolds number Re is defined as Where = maximum fluid particle velocity = characteristic diameter of the element = kinematic viscosity of the fluid (1.17 mm2/sec for sea water).

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CAESAR II Statics Training Riser Note that these parameters depend on the water particle velocity as well as the diameter of the pipe element. Therefore, these parameters typically vary over the piping model. For this reason, it is best to leave the entry for these coefficients blank in the input. This will allow CAESAR II to determine the coefficients on an element by element basis during the solution phase of the job. A rough hand computation should be made to ensure that the applied environmental loads are as expected. To assist in this check, a stand-alone load case with only wave loading will be setup to check against these hand computations. The hand computations are shown below. Wave Solution Data Elevation Velocity Elevations are measured from the sea bottom (m) (m/sec) 0 2.3 All data for a phase angle of 0.0° 1.5 2.370 3 2.440 4.5 2.615 6 2.870 7.5 3.235 9 3.710 Hydrodynamic Coefficient Computation Node

Elevation (m)

Velocity (mm/sec)

1810 0 2300 1815 1.5 2370 1820 3 2440 1825 4.5 2615 1830 6 2870 1835 7.5 3235 1840 9 3710 Element Force Computation Element

1810-1815 1815-1820 1820-1825 1825-1830 1830-1835 1835-1840

Avg. Velocity (m/sec) 2.335 2.405 2.528 2.743 3.053 3.473

Acceleration (m/sec2) 0.00 0.00 0.00 0.00 0.00 0.00 0.00

KeuleganCarpenter Number 31.87 32.84 33.81 36.23 39.76 44.82 51.40

Reynolds Number

Cd

Cm

Cl

1.08 E +6 1.11 E +6 1.14 E +6 1.22 E +6 1.34 E +6 1.51 E +6 1.74 E +6

0.661 0.656 0.651 0.639 0.621 0.625 0.631

1.746 1.749 1.751 1.759 1.769 1.765 1.759

0.257 0.250 0.243 0.226 0.202 0.200 0.200

Avg. Cd

Avg. Cl

Diameter (mm)

Density (kg/cm3)

0.658 0.653 0.645 0.630 0.623 0.628

0.254 0.247 0.235 0.214 0.201 0.200

557.2 557.2 557.2 557.2 557.2 557.2

0.001025 0.001025 0.001025 0.001025 0.001025 0.001025

Drag Force (Fd) (N/mm) 1.025 1.079 1.176 1.353 1.658 2.163

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Lift Force (Fl) (N/mm) 0.395 0.408 0.428 0.460 0.534 0.689

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Element 1810-1815 1815-1820 1820-1825 1825-1830 1830-1835 1835-1840

Length (mm) 1500.00 1500.00 1500.00 1500.00 1500.00 1500.00

Fd (N) 1537.29 1618.83 1764.72 2029.74 2468.55 3244.27

Fl (N) 592.13 611.34 642.70 689.51 801.55 1033.02

Total Drag force = 12681.40 N Total Lift Force = 4370.25 N

Notice for these computations, that "average" values are being used for the element velocities and hydrodynamic coefficients. The CAESAR II program actually computes the exact values at integration points on each element, from which the "fixed end forces and moments" are determined.

Wind Loading The default ASCE 95 wind loading procedures will be used on this riser. (This standard states that the minimum wind pressure is 10 lb/sq.ft. or 0.479 KN/sq.m.) The basic procedure to compute the wind load on each pipe element is as follows: Obtain the wind speed (V). From ASCE 95, the Gulf Coast of the U.S. can experience winds of up to 225 km/hr (140 m/hr). API-RP2A recommends a wind velocity of 175 km/hr (109 m/hr) for the Gulf of Mexico. Assume a wind speed of 55m/sec (123 m/hr) for this job. Determine the applicable structural category from ASCE 95, Table 1.1. From this table, select category II (2). Determine the Importance Factor (I) from ASCE 95, Table 6.2. Based on the selected category, the Importance factor is 1.0. Determine the Exposure Category from ASCE 95, Section 6.5.3. For this job, select exposure category D (flat, unobstructed terrain). From ASCE 95, Commentary Section 6.5, determine Kz. This term varies by elevation and therefore may vary from element to element. Constants used in the equations to determine Kz can be obtained from Table C6-2, based on the exposure category. Determine Kzt, which is the wind speed-up over hills. For this job, there are no hills, so Kzt is 1.0. Based on these parameters, compute the velocity pressure as defined in ASCE 95, Section 6.5.1. This is: qz = 0.613 * Kz * Kzt * V2 * I, where all terms are defined above. For this equation, V is expressed in meters per second and qz in newton per square meter. (If V is in mph and qz in lbf/ft2, the constant becomes 0.00256.) Once qz is known, the force on the element can be determined from: F = qz * Gf * Cf * A, where: - Gf is the gust response factor - Cf is the shape factor for the element (defined in the piping input) - A is the projected wind area of the element (including insulation if specified)

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CAESAR II Statics Training Riser The gust response factor Gf can be determined analytically as defined in the ASCE Commentary. However, this procedure requires the first natural frequency of the piping system, which can be obtained through a modal analysis. This dynamic procedure is not addressed in this seminar. If the natural frequency input is left blank, CAESAR II will use a gust response factor of 0.85 as defined in ASCE 95, Section 6.6.1. For this system, the wind load can be defined for the analysis as shown below.

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CAESAR II Statics Training Riser For this system, the applied wind loads can be approximated as shown below. Wind Solution Data (per ASCE 7) Element Mid-Point Alpha elevation (z) (m) 1840-1845 0.75 11.50 1845-1850 2.25 11.50 1850-1855 3.75 11.50 1855-1860 5.25 11.50 1860-1865 6.75 11.50 1865-1870 8.25 11.50 ( )

2/alp ha

4.6/zg

213.36 213.36 213.36 213.36 213.36 213.36

0.174 0.174 0.174 0.174 0.174 0.174

0.0216 0.0216 0.0216

⁄

z/zg

Kz

0.513 0.513 0.513 0.525 0.548 0.568

0.0246 0.0316 0.0387

1.031 1.031 1.031 1.055 1.102 1.142

⁄

where x = max (4.6 or z)

Velocity Pressures Element Kz 1840-1845 1.031 1845-1850 1.031 1850-1855 1.031 1855-1860 1.055 1860-1865 1.102 1865-1870 1.142

V (m/s) 55 55 55 55 55 55

Wind Force Element 1840-1845 1845-1850 1850-1855 1855-1860 1860-1865 1865-1870

G 0.85 0.85 0.85 0.85 0.85 0.85

qz 1912 1912 1912 1957 2044 2117

Zg (m)

I 1 1 1 1 1 1

Cf 0.65 0.65 0.65 0.65 0.65 0.65

qz 1912 1912 1912 1957 2044 2117

Af (m2) 0.686 0.686 0.686 0.686 0.686 0.686

𝑞𝑧

𝐾𝑧

𝐾𝑧𝑡

𝐼

𝑉

𝑞𝑧

𝐺

𝐶𝑓

𝐾𝑧𝑡 = 1.0

Force (N) 725 725 725 741 775 802

𝐹𝑜𝑟𝑐𝑒

Total Applied Force = 4492 N

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𝐴𝑓

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Load Case Setup The load cases required are as below: We require for our code stress check, an operating case for each wind and wave direction. In this case we have a Z direction wind load and wave load Therefore we will create cases for operating conditions PLUS the wind and wave loads and MINUS the wind and wave loads

These load cases can be given more meaningful names in the Load Case options tab

The results for all load cases will be available at the output level, but for the "environmental only" load cases, only displacements and forces will be presented by the output processor. Load cases #4 and #5 are the Code compliance cases necessary for the stress check. The output status for load case #1 could have been set to "discard", since in this instance its results are not significant on their own. However, it may be necessary to evaluate the results of this load case in the event of overloads or over stressed elements. Therefore the output status is left as "keep".)

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Analysis Once the load cases are defined (and the loading data has been checked), the analysis can proceed as usual. At the output level, the results of the "environmental" load cases should be reviewed to ensure they agree with the hand computations. For this job, the environmental loads act on the riser body and are resolved about nodes 1810 and 1870. The restraint summary report details this loading resolution.

For load cases #2 and #3, summing the FZ loads at nodes 405, 475, 605, 675, 1810 and 1870 yields the applied environmental loads. These loads are summarised in the table below. Applied Load Summation (from CAESAR II) Node 405 475 605 675 1810 1870

Wave Drag Fz (N) 539 380 1697 1145 6749 2030

Total Load: 12540

Lift Fx (N) 78 85 287 299 2769 810

Wind Fz (N) 105 200 347 589 631 2620

4328

4492

These loads can be compared to the hand computed results of 12681 N, 4370 N , and 4492 N. This is an acceptable comparison, given the approximations made in the hand computations.

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CAESAR II Statics Training Riser The code compliance report shows that there is a failure in one of the operating cases. This is located around the bottom of the riser on the elbow. Reviewing the Stress Report shows that the bending stress is dominating the behaviour of the system at these points.

One solution here is to reduce the thermal component of the stress by extending the bottom-side piping, from 1800 mm to 3000 mm. This drops the stress level to 86.5% of the allowable. (This job is not intended to be an example of good riser design. The riser tension was arbitrarily selected to be simply larger than the "air weight" of the riser. Additional vertical supports may be used along the length of the riser to assist in supporting the core piping. For larger (longer) risers, external buoyancy chambers are used to offer additional vertical support along the riser body. None of these concepts are addressed in this example.) (Fatigue has not been addressed in this example, but is typically a required consideration. For this job, the fatigue (FAT) case would be defined as "L4-L5" with a specified number of cycles and a corresponding material fatigue curve.)

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CAESAR II Statics Training SUPT01 – Water Hammer

SUPT01 – Water Hammer

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CAESAR II Statics Training SUPT01 – Water Hammer This exercise introduces the Occasional stress evaluation in B31.3. We will return to the model produced previously SUPT01 and simulate a fluid hammer event acting when the valve slams shut. This force will be applied to the model and defined as a shock load case and evaluated according to the Occasional stress requirements of B31.3. For Occasional stress evaluation, B31.3 requires: Long. Sustained Stresses + Long. Occasional Stresses ≤ k Sh, where k = 1.33 In CAESAR II, this equates to a SCALAR summation of the SUS case with the OCC case, using the OCC stress type. Note: The OCC stress type serves two purposes: (1) it directs that stresses be calculated according to the “occasional equation”, and (2) it activates (i.e., locks) any snubbers in the model.

Edit the Model Open the file created previously SUPT01. Using File > Save As… create a new file called SUPT01 fluid Hammer.c2 There are some slight changes to the support configuration in this file compared to our analysis done previously. Edit the support configuration as shown in the isometric sketch, and as detailed below. Element 20-30 o Break this element o Create a new node number 22, located 1400mm from node 20. o Add a +Y restraint at node 22 Element 30-33 o Change the “to node” from 33 to 34 o Edit the length of this element and change to 6000mm o Add a +Y restraint at node 34 Element 33-37 o o o o o

Change the “from node” from 33 to 34 Change the “to node” from 37 to 36 Edit the length of this element to be 6000mm Remove the +Y restraint Add a spring Hanger at node 36. Carpenter & Paterson hanger table

Element 37-40 o Change the “from node” from 37 to 36 o Edit the length of this element to 1715mm Node 43 o

Remove the Spring hanger

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CAESAR II Statics Training SUPT01 – Water Hammer Element 50-57 o o o o

Break this element Create a new node number 55, located 3250mm from node 50 Remove the +Y support at node 57 Add a Carpenter Spring Hanger at node 55

Element 70-77 o Change the “to node” to be 72 o Edit the length to be 2000mm o Edit the support node number to be 72 Element 77-80 o Change the from “node” to be 72 o Edit the length to be 2115mm Element 80-90 o Break this element o Create a new node number 85, located 1000mm from node 80 o Insert a +Y at this location

Determine the Load Consider water hammer acting when the valve at node 70 slams shut. This creates an unbalanced force due to the propagation of a pressure wave. The water hammer load can be estimated using Joukowski’s equation:

Where:

D t

= force acting on valve seat = dynamic load factor (use 2.0) = pressure change = = internal area of pipe (0.073 m2 for 12” std pipe) = density of fluid (1000kg/m3 for water) = speed of sound in the fluid (typ. 1000 – 2000 m/sec in water based on D/t) = change of fluid velocity (typically 1.5 – 3m/sec for water) = mean pipe diameter = pipe wall thickness

Wave speed & pressure change for water in steel pipe (ΔP/ΔV= ρ·c): D/t C (m/sec) ΔP/ΔV (bar/(m/sec)) 20 1310 13.1 40 1210 12.1 60 1130 11.3 80 1065 10.65 Using D / t = 314 / 9.5 = 33, ΔP/ ΔV = approximately 12.45 bar / (m/sec); assume ΔV = 2 m/sec; so:

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CAESAR II Statics Training SUPT01 – Water Hammer Define the Occasion Load Model a Z-direction force at node 70, equal to 364,000 N, as calculated previously.

Load Case Setup Build the shock load case(s). The hammer load may be reversing, so build both a +F1 case and a –F1 case. Then build a SCALAR combination case combining the SUS and OCC load cases:

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CAESAR II Statics Training SUPT01 – Water Hammer

Check the Results Immediately it can be seen that there are issues with the OCCasional load cases. What is causing these issues? Is this an accurate simulation? Viewing the restraint summary shows that the loads on the restraints at nodes 22 and particularly 85 – both show zero load – an immediate uplift – for at least one of the hammer cases. If a +Y restraint actually lifted off, it would first have to overcome the pre-existing downward load present during the operating case. So what we have here is not an accurate simulation

Reset the Load Cases This points out the danger when modelling occasional loads on non-linear systems: load stepping must be considered, i.e., first apply the operating loads, then apply the occasional loads, then isolate the occasional loads by subtracting the former from the latter. This accurately models the effects of the pre-existing restraint status. This can be done using the following load cases:

Remember to change the load case combination method to Scalar for the OCC load cases in the load case options tab.

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CAESAR II Statics Training SUPT01 – Water Hammer

Check Results There are still issues in the OCC load cases, but Note that even though the pipe lifts off of the restraint at node 22, the “occasional only” load, Load Case 7, does overcome the pre-existing operating load first, for an accurate simulation of events:

The Code Compliance Evaluation shows that the system is still highly overstressed under this OCC load. This problem can be resolved by adding restraint (since the water hammer is a primary load). We can use a rigid Z-restraint to contain the water hammer if we can find a point in the vicinity of the load (run 50-80) where the Z-operating displacement is negligible (so the previous expansion and sustained analyses will be relatively unaffected). A good candidate is at node 78 as the OPErating displacement report shows.

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CAESAR II Statics Training SUPT01 – Water Hammer

Correct model Return to the input and select element 72-80. Node 78 is on the 0 angle of the bend at the “to” end of this element.

Place a Z restraint at this location

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CAESAR II Statics Training SUPT01 – Water Hammer With a Z-restraint at node 78, the stresses have decreased significantly

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CAESAR II Version 2011 - Statics Training

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CAESAR II Statics Training Introduction

Contents Introduction ..................................................................................................................... 6 Interface .............................................................................................................................................. 6 Default Data Directory .................................................................................................................... 6 Units .................................................................................................................................................... 7 Create Custom Units File................................................................................................................. 7 F = Kx Example .................................................................................................................................... 9 Model Input .................................................................................................................................. 12 Load Case Editor............................................................................................................................ 16 Hand Calculation ........................................................................................................................... 18 Output Processor .......................................................................................................................... 19 Axial ............................................................................................................................................... 21

Theory and Development of Pipe Stress Requirements ................................................... 25 Basic Stress Concepts ........................................................................................................................ 25 Example ......................................................................................................................................... 30 3D State of Stress in the Pipe Wall.................................................................................................... 33 Failure Theories................................................................................................................................. 36 Maximum Stress Intensity Criterion ................................................................................................. 38 Code Stress Equations....................................................................................................................... 40 B31.1 Power Piping ....................................................................................................................... 40

Pipe 1 ............................................................................................................................. 42 Input Model ...................................................................................................................................... 43 Error Checking ................................................................................................................................... 52 Review Load Cases ............................................................................................................................ 54 Review Results .................................................................................................................................. 55

Supt 01 ........................................................................................................................... 64 Locating Supports ............................................................................................................................. 65 Adding Supports to Model ............................................................................................................ 69 Analyse .............................................................................................................................................. 75 Fix Model........................................................................................................................................... 80 Place Spring Hangers..................................................................................................................... 87

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CAESAR II Statics Training Introduction

Turbo ............................................................................................................................. 92 Model Inlet ........................................................................................................................................ 93 Combine Models ............................................................................................................................... 98 NEMA SM23 .................................................................................................................................... 100

Manifold ...................................................................................................................... 111 API 610 Analysis .............................................................................................................................. 120

Tutor ............................................................................................................................ 128 Boundary Conditions................................................................................................................... 130 API 610 Analysis .............................................................................................................................. 136 Fix Model – Part 1 ........................................................................................................................... 139 Include WRC 297 flexibilities....................................................................................................... 139 Review Results ............................................................................................................................ 141 Fix Model – Part 2 ........................................................................................................................... 143 Build Steel Structure ................................................................................................................... 144 Combine Pipe and Steel models ................................................................................................. 154 Review Results ............................................................................................................................ 157 Fix Model – Part 3 ........................................................................................................................... 158 Loop Optimisation Wizard .......................................................................................................... 161 Fix Model – Part 4 ........................................................................................................................... 166 Model the Expansion Joint Assembly ......................................................................................... 170 Document the Analysis ................................................................................................................... 174 Custom Reports........................................................................................................................... 174 Filters........................................................................................................................................... 178 Generate Report ......................................................................................................................... 179 ISOGEN Stress Isometrics ............................................................................................................ 182

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CAESAR II Statics Training Introduction

Cool H20 – FRP Piping.................................................................................................... 194 Basics of Fibreglass Piping Analysis ................................................................................................. 195 CAESAR II’s Orthotropic Model for Piping Systems ........................................................................ 198 Requirements of the ISO 14692 Code............................................................................................. 199 Allowable Stress Data for this Model.............................................................................................. 202 Configuration Options for FRP Piping: ............................................................................................ 204 Model the system ........................................................................................................................... 206 Load Case Setup .............................................................................................................................. 213 Review Results ................................................................................................................................ 213 Solving Expansion Problems ........................................................................................................... 214 Static Seismic Using the ASCE 7-05: ................................................................................................ 214 Inertial Loads ............................................................................................................................... 214 Seismic Data Input ...................................................................................................................... 219 Load Case Setup .......................................................................................................................... 223 Review Results ............................................................................................................................ 225

Gas Transmission Pipeline - Buried Pipe ........................................................................ 228 B31.8 Design Code .......................................................................................................................... 229 Modelling the system ..................................................................................................................... 229 Material Database........................................................................................................................... 234 Buried Pipe Modeller ...................................................................................................................... 237 Restraint Parameters .................................................................................................................. 237 American Lifelines Alliance Clay Model ...................................................................................... 238 American Lifelines Alliance sand model: .................................................................................... 240 Meshing Parameters ................................................................................................................... 241 Virtual Anchor Length (VAL):....................................................................................................... 243 Bury Pipe ..................................................................................................................................... 244 Load Case Setup .............................................................................................................................. 249 Results Review ................................................................................................................................ 250 Fatigue ............................................................................................................................................ 251 Setting up the Fatigue Load cases............................................................................................... 251

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CAESAR II Statics Training Introduction

Riser ............................................................................................................................. 254 Modelling ........................................................................................................................................ 255 Injection Line ............................................................................................................................... 256 Product Line ................................................................................................................................ 260 Jacket .............................................................................................................................................. 261 Hydrodynamic Theory..................................................................................................................... 264 B31.4 Code Requirements .............................................................................................................. 265 Hydrodynamic Input ....................................................................................................................... 266 Wave Solution ................................................................................................................................. 267 Hydrodynamic Coefficients ......................................................................................................... 272 Wind Loading .................................................................................................................................. 274 Load Case Setup .............................................................................................................................. 277 Analysis ........................................................................................................................................... 278

SUPT01 – Water Hammer ............................................................................................. 280 Edit the Model ................................................................................................................................ 281 Determine the Load ........................................................................................................................ 282 Define the Occasion Load ........................................................................................................... 283 Load Case Setup .............................................................................................................................. 283 Check the Results ............................................................................................................................ 284 Reset the Load Cases ...................................................................................................................... 284 Check Results .................................................................................................................................. 285 Correct model ................................................................................................................................. 286

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CAESAR II Statics Training Introduction

Introduction CAESAR II is pipe stress analysis software which uses beam theory to evaluate piping systems to numerous international standards. CAESAR II is not Finite Element Analysis (FEA) software, but instead uses a stick model built up of elements connected by nodes. This course will introduce CAESAR II and demonstrate various modelling and analysis methods in order to evaluate and correct piping systems.

Interface When starting CAESAR II, the Main Window appears. This is the window where all tasks are started from. This includes opening/creating an input file, reviewing Load Cases, reviewing results or accessing any auxiliary modules such as WRC 107/297 processor or the ISOGEN stress isometrics module. All modules open up in their own separate window.

When opening a new file, the file will open, but you will return to the Main Window. You can then choose to go to the Input processor, Output processor or the results for this file. These modules (and other auxiliary modules) and their interfaces will be introduced as they occur throughout the training. Default Data Directory CAESAR II has the option to specify the default working directory – that is all files working with will be saved/opened from this default location. Of course it is still possible to navigate using windows explorer functions, this setting is just the default location when selecting New/Open. Select File > Set Default Data Directory from the CAESAR II Main window

Click on the ellipsis button at the end of the text field and browse to E:\Training\CAESAR II\Exercises

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CAESAR II Statics Training Introduction

Units CAESAR II performs all internal calculations in English units. To enable the entry and review of data in alternative units (such as SI), units files are used by CAESAR II. These units files simply convert the internal CAESAR II English units to the user’s preferred unit. Each CAESAR II file (referred to as a “Job File”) uses a particular units file which is specified on creation of the job. Files can be converted from one units file to another if required. The units files have the extension *.FIL and are located in the CAESAR II System directory, or in the same directory as the job file. The file to use is specified in the Configuration file. Create Custom Units File Throughout this course, we wish to use specific units for various parameters such as Pressure, Density etc. As such we require a units file which is different to the supplied default files. So we will create our own CAESAR II units file. Select Tool > Make Units Files from the Main Window

This allows the creation of new units files, or the review of existing units files, useful if you receive a units file from a colleague and wish to check the units in use in the file. Choose to Create New Units File and for the template file to use as a start point, select *MM.FIL. Give the new file a name and click View/Edit file.

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CAESAR II Statics Training Introduction

In the Units File dialogue box, change the following units from the MM defaults: Stress Pressure Elastic Modulus Pipe Density Insul. Density Fluid density Transl. Stiffness Uniform Load

N/sq.mm. bars N/sq.mm. kg/cu.m. kg/cu.m. kg/cu.m. N/mm N/mm

Ensure Nominals is set to ON. This allows the entry of pipe nominal sizes and schedules into the input, which will be converted to actual diameters and wall thicknesses (e.g. enter 4 into the diameter field and CAESAR II will convert this to 114.3mm). Give the file a label as well to easily identify the file.

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CAESAR II Statics Training Introduction

F = Kx Example As CAESAR II uses a stick model, and beam theory, it is easy to prove this using a simple cantilever example. This example will introduce the basic modelling methods in CAESAR II and introduce the Input Spread Sheet, Load Case editor and the Output Processor. In addition, we can check the CAESAR II results against some simple hand calculations. CAESAR II calculates forces using . Using the example below, we will create a simple cantilever model, fixed at one end, and apply a displacement of 2mm at the other end. We can then calculate the force required to generate this 2mm displacement – and see this in the results.

First we will create the model in CAESAR II. Create a new file in CAESAR II, called FKLateral

After creating the new job file, the first time it has opened, the units will be displayed to the user for confirmation. You will notice that the units file displayed here for our file is English (CAESAR II default units) not the units file we have just created. By default, CAESAR II uses the units file set in the Configuration/Setup as the default file for new jobs (and also as the units to use to display the output results).

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CAESAR II Statics Training Introduction

Click OK on the units review screen and the input spread sheet will open. To confirm/check the units, hover over any field in the input – the units used in this field will be displayed in the tooltips. For example, we changed the pressure units to bars, but the pressure field displays the units as lb./sq.in.

Close the input screen – we will change the units and return to the input with the correct units displayed. In the CAESAR II main window select Tools > Configure/Setup

In the window which appears, select Database Definitions from the categories tree on the left.

Now change the Units File Name setting to the units file just created.

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CAESAR II Statics Training Introduction

Save and exit.

Return to the Piping Input. Again, the units file to be used will be displayed – this should now be your custom units file.

Verify that the correct units are in use via the tooltips

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CAESAR II Statics Training Introduction Model Input We will now create the simple cantilever model and apply a 2mm displacement at the free end. The model will be as follows: One element 10m in length going from node 10 to node 20 in the X direction, anchored at one end. 8” pipe with Standard wall thickness.

The input spread sheet will have defaulted to nodes 10 to 20, so simply enter 10000 in the DX field. We are in mm units already. Enter the pipe diameter and wall thickness – this is 8” NS and STD wall thickness. As we have “nominals” set to ON, simply type in 8 in the diameter and hit enter. The actual OD for 8” pipe will be inserted. Repeat for the wall thickness, simply type in “S” and press enter.

Now we must fill in the pipe properties. We need to know the material properties to carry out the analysis. Select A106 – B from the list of materials. Notice that all materials have a number to identify it, you can simply type in the material number here - in the case of A106-B this is 106. Selecting the material will fill in the Elastic modulus and Poisson ratio and various material allowables under the Allowable Stress area, depending on the design code selected (B31.3 default).

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CAESAR II Statics Training Introduction

That is our pipe itself. We now need to anchor it at one end (node 10) and apply a displacement at the other end (node 20). Place the anchor by double clicking the Restraints check box. All the check boxes shown in the middle column on the spread sheet must be double clicked to check/uncheck.

To define a restraint you must specify a minimum of the node that the restraint will be attached to, plus the type of restraint. Press F1 for more information on the different restraint types. We need an anchor, so select ANC and locate it at node 10.

Now we will apply the 2mm displacement at the opposite end. Double click the Displacements check box to apply a displacement.

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CAESAR II Statics Training Introduction Specify the displacement at node 20, and specify a 2mm displacement downwards in the Y direction – i.e. enter -2 in the DY row. Leave the remaining rows empty – do not specify 0. Specifying 0 fixes the node in the specified direction. Entering 0 in each row would be the same as an anchor. Leaving the values blank leaves the remaining directions free.

Finally to complete the analysis we must specify a design temperature and pressure. In our case these are not really relevant as we are only concerned with displacement, so just enter 21°C in T1 and 1bar in P1 fields.

The file can now be analysed. Before analysis the input must be error checked in order to identify any issues which may prevent the analysis running (such as specifying both an anchor and an applied displacement at the same point), or anything which may provide incorrect results (such as Stress Intensification factors not present at a geometric intersection). Run the error checker to check the model.

You should see only one note in the error checker report – the C of G. This can be useful for identifying problems such as incorrect densities applied – giving an incorrect weight for example.

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CAESAR II Statics Training Introduction

If you receive anything other than this C of G, review the model for any issues. A common error on this exercise is the following:

This indicates that the displacement and the anchor have been specified at the same location. Check that the Anchor is specified at Node 10 and the displacement is specified at Node 20.

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CAESAR II Statics Training Introduction Load Case Editor Once the error check is successful, we can create load cases to analyse the system. Access the load case editor. This button is only available after a successful error check.

The load case editor will be shown.

The default load cases are the Operating, Sustained and Expansion cases, as required by the design codes such as B31.3. Remove all these load cases, as we are only concerned with the displacement.

Add one new row.

Into the load case we can add any of the loads defined in the input into the load case. As we are only concerned with the displacement, drag in D1 – Displacement Case #1 into the L1 row.

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CAESAR II Statics Training Introduction

Also select the stress type as SUS(tained).

The analysis will now take into account only the displacement reaction. Before we analyse the piping system, let us first perform the hand calculation in order to check.

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CAESAR II Statics Training Introduction Hand Calculation As we know,

The stiffness K is

; Where D = Pipe OD and d = Pipe ID E being Modulus of Elasticity and L being the length. So if we wish to know what force is required to displace the cantilever 2mm, we can calculate this quite easily.

So for a 2mm displacement, the force required is

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CAESAR II Statics Training Introduction Output Processor Back in CAESAR II, run the analysis by clicking on the “Running Man” icon from within the load case editor.

You will see the following message explaining that certain loads have been defined in the model but are not included in any of the load cases to be analysed – this is OK in our case, but can serve as a useful warning if you have may loads/load cases defined. Select OK as is…Continue and click OK to analyse.

Once the analysis is complete, the Output Processor will be shown. We can view various results for any load case from here, plus general model reports such as the Input Echo. These reports can be viewed on screen, or output to Word/Excel/Text or straight to a printer. In addition Custom report templates can be created, and any available report can be selected and added to the Output viewer Wizard, and exported/viewed to create/view a comprehensive report very quickly. For now we will just check the displacement at node 20 to verify that it is 2mm, and the force at node 20 to check against out hand calculation. Select the load case (SUS) D1 and the Displacements standard report and click to show on screen:

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CAESAR II Statics Training Introduction The DY at Node 20 is -2mm, as we specified.

Now to check the force at node 20; view the Global Element Forces report.

37 N as we calculated.

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CAESAR II Statics Training Introduction Axial We can repeat this exercise for axial forces. This is a simple change in the model changing the displacement from the Y to the X direction.

The analysis can be quickly re-run in cases where a change such as this has been made by using the Batch Run “Double Running Man” icon. This will run the error checker followed immediately by the analysis (providing there are no Errors).

The force should be as follows: We are still using F = Kx, but we are using the Axial stiffness.

Therefore:

110,021 N/mm So for an axial extension of 2mm, the force required is

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CAESAR II Statics Training Introduction

The CAESAR II results, Global Element forces report should verify this:

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CAESAR II Statics Training Introduction The forces calculated such as in the previous example produce bending moments throughout the piping system. Bending moment is produced when a Force is applied at a distance – MB = F x L Once the bending moment has been calculated, beam theory is used in order to calculate the stress at this point.

rearranges to is the section modulus Z. So this reduces further to

The stresses are calculated using this basic theory and compared to the allowable stresses in the design codes. CAESAR II has many design codes available, all of which have evolved separately over time, thus the way the stresses are calculated for each specific code are slightly different. However, looking at one of the most common piping codes – B31.3 – it can be seen that the equations used are based on the basic bending as detailed above. B31.3 Chemical Plant and Petroleum Refinery Piping Sustained:

Expansion:

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CAESAR II Statics Training Introduction As can be seen, the equations essentially use bending stress M/Z. The equations are a little more complicated than the basic cantilever example for the following reasons:

To address piping systems in 3 dimensions To address areas in a piping system where particular geometry/components, such as at a branch connection or a bend, can increase the stress, and therefore the likelihood of failure. At these points, the stress is increased by a Stress Intensification Factor (SIF) known as i. The design codes contain formulae to calculate these SIFs. Stresses can also be caused by Pressure and Axial Forces The Stresses are categorised into Sustained, Expansion and Occasional, as detailed below.

Sustained Stress: This is primary stresses caused by primary loadings such as the weight and pressure of the piping system. Expansion Stress: Expansion stresses are secondary stresses caused by secondary loadings such as the thermal expansion and applied displacements. Occasional Stress: Combines sustained stresses with those produced by an occasional loading such as earthquake of relief valve operation. As these are occasional loads, the allowable can be increased by a scalability factor, k. k is usually dependant of the duration or frequency of the occasional load.

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Theory and Development of Pipe Stress Requirements Basic Stress Concepts Normal Stresses: Normal stresses are those acting in a direction normal to the face of the crystal structure of the material, and may either be tensile or compressive in nature. In fact in piping, normal stresses tend more to be in tension due to the predominant nature of internal pressure as a load case. Normal stresses may be applied in more than one direction, and may develop from a number of different types of loads. For a piping system these are: Longitudinal Stress: Longitudinal or axial stress is the normal stress acting along the axis of the pipe. This may be caused by an internal force acting axially in the pipe.

Where: Longitudinal Stress Internal axial force acting on cross section Cross sectional area of pipe (

) Outer diameter Inner diameter

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements A specific instance of longitudinal stress is that due to internal pressure:

⁄ Design pressure Internal area of pipe ⁄ Replacing the terms for the internal and metal areas of the pipe, the previous equation may be written as ⁄

Or:

⁄ For convenience the longitudinal pressure stress is often conservatively approximated as

Bending Stress: Another component of axial normal stress is bending stress. Bending stress is zero at the neutral axis of the pipe and varies linearly across the cross-section from the maximum compressive outer fibre to the maximum tensile outer fibre. Calculating the stress as linearly proportional to the distance from the neutral axis:

⁄ Where: Bending moment acting on cross section Distance of point of interest from neutral axis of cross section Moment of inertial of cross section

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements The maximum bending stress occurs where c is highest – the maximum value c can be is equal to the radius of the pipe. ⁄

=

Where: Outer radius of pipe. Section modulus of pipe

Summing all components of longitudinal normal stress (for axial and bending):

Hoop Stress: Hoop stress is another of the normal stresses present in the pipe and is caused by internal pressure. This stress acts in a direction parallel to the pipe circumference.

The magnitude of the hoop stress varies through the pipe wall and can be calculated by Lame’s equation as: (

)

Where: Hoop stress due to pressure Inner radius of pipe Outer Radius of pipe Radial position where stress is being considered The hoop stress can be approximated conservatively for thin-wall cylinders by assuming that the pressure force applied over an arbitrary length of pipe, l is resisted uniformly by the pipe wall over that same arbitrary length.

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Or conservatively

Radial Stress: Radial Stress is the third normal stress present in the pipe wall. It acts in the third orthogonal direction – parallel to the pipe radius. Radial stress is caused by internal pressure and varies between a stress equal to the internal pressure at the pipe’s inner surface, and a stress equal the atmospheric pressure at the pipe’s external surface. Assuming that there is no external pressure, radial stress is calculated as:

Where Radial stress due to pressure Note that radial stress is zero at the outer radius of the pipe, where the bending stresses are maximised. For this reason, this stress component has traditionally been ignored during the stress calculations. Shear Stresses: Shear Stresses are applied in a direction parallel to the face of the plane of the crystal structure of the material and tend to cause adjacent planes of the crystal to slip against each other. Shear stresses may be caused by more than one type of applied load. For example, shear stress may be caused by shear forces acting on the cross section.

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Where: Maximum shear stress shear force shear form factor. Dimensionless quantity (1.333 for solid circular section) These shear stresses are distributed such that they are at the maximum at the neutral axis of the pipe and zero at the maximum distance from the neutral axis. Since this is the opposite of the case with bending stresses and since these Shear stresses are usually small, shear stresses due to forces are traditionally neglected during pipe stress analysis. Shear Stresses may also be caused by torsional loads.

⁄ Where: Internal torsional moment acting on cross-section distance of point of interest from torsional centre (intersection of neutral axes) or cross section torsional resistance of cross section

(

)

Maximum torsional stress occurs where c is maximised. Again at the outer radius. ⁄ Summing the individual components of the shear stress, the maximum shear stress acting on the pipe cross section is:

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements As noted above, a number of the stress components described above have been neglected for convenience during calculation of pipe stresses. Most piping codes require stresses to be calculated using some form of the following equations: Longitudinal Stress: Shear Stress: Hoop Stress: Example This example calculation illustrates for a 6” nominal diameter, standard schedule pipe (assuming the piping loads are known): Cross sectional properties Outside diameter Mean thickness Inside diameter 154.076mm Cross sectional Area

–

(

–

(

Moment of Inertia

–

(

)

) –

(

Section Modulus

)

)

⁄

⁄

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Piping loads Bending Moment Axial Force Internal Pressure Torsional Moment

Stresses Longitudinal Stress

Shear Stress

Hoop Stress

Bending Component of Longitudinal stress is the radius where the stress is being considered. This will be at a maximum value at the outer surface where ⁄ (

)

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Torsional Stress

The maximum torsional stress occurs at the outer radius where again

– at the outer surface

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

3D State of Stress in the Pipe Wall During operation, pipes are subject to all these types of stresses. Examining a small cube of metal form the most highly stressed point of the pipe wall, the stresses are distributed as so:

There are an infinite number of orientations in which this cube could have been selected, each with a different combination of normal and shear stresses on the faces. For example, there is one orientation of the orthogonal stress axes for which one normal stress is maximised and another for which one normal stress is minimised – in both cases; all shear stress components are zero. In orientation in which the shear stress is zero, the resulting normal components of the stress are termed the principal stresses. For 3-dimensional analyses, there are three of them and they are designated S1 (the maximum), S2 and S3 (the minimum). Note that regardless of the orientation of the stress axes, the sum of the orthogonal stress components is always equal, i.e.:

The converse of these orientations is that in which the shear stress component is maximised (there is also an orientation in which the shear stress is minimised, but this is ignored since the magnitudes of the minimum and maximum shear stresses are the same); this is appropriately called the orientation of maximum shear stress. The maximum shear stress in a three dimensional state of stress is equal to ½ the difference between the largest and smallest of the principal stresses (S1 and S3). The values of the principal and maximum shear stress can be determined through the use of Mohr’s circle. The Mohr’s circle analysis can be simplified by neglecting the radial stress component, therefore considering a less complex (i.e. 2D) state of stress. A Mohr’s circle can be developed by plotting the normal vs. shear stresses for the two known orientations (i.e. longitudinal stress vs. shear and hoop stress vs. shear), and constructing a circle through the two points. The infinite combinations of normal and shear stresses around the circle represent the combinations present in the infinite number of possible orientations of the local stress axes. A differential element at the outer radius of the pipe (where bending and torsional stresses are maximised and the radial normal and force-induced shear stresses are usually zero) is subject to 2D plane stress and thus the principal stress terms can be computed from the following Mohr’s circle:

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

The centre of the circle is at

and the radius is equal to(*

+

)

. Therefore

the principal stresses S1 and S2 are equal to the centre of the circle, plus or minus the radius respectively. The principal stresses are calculated as: *(

)

+

*(

)

+

and

As noted above, the maximum shear stress present in any orientation is equal to

Continuing our example: Mohr’s Circle of Stress Centre of circle

Radius of Circle

√( √(

) )

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or :

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Maximum Principal Stress S1 √(

√(

)

)

Or from the Mohr’s circle above, S1 = 78.07 + 50.59 = 128.66 MPa Maximum Principal Stresses S2 and S3 √(

√(

)

)

Or from the Mohr’s circle, S2 = 78.07 – 50.59 = 27.48 MPa S3 = S2

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Failure Theories The calculated stresses are not much use on their own, until they are compared to material allowables. Material allowable stresses are related to strengths as determined by material uniaxial tests, therefore calculated stresses must also be related to the uniaxial tensile test. This relationship can be developed by looking at available failure theories.

There are three generally accepted failure theories which may be used to predict the onset of yielding in a material:

Octahedral Shear or Von Mises theory Maximum Shear or Tresca Theory Maximum Stress or Rankine Theory

These theories relate failure in an arbitrary 3D stress state in a material to failure in the stress state found in a uniaxial tensile test specimen, since it is that test that is most commonly used to determine the allowable strength of commonly used materials. Failure of a uniaxial tensile test specimen is deemed to occur when plastic deformation occurs, i.e. when the specimen yields; that is, release of the load does not result in the specimen returning to its original state. The three failure theories state: Von Mises:

“Failure occurs when the octahedral shear stress in a body is equal to the octahedral shear stress at yield in a uniaxial tension test”

The octahedral shear stress is calculated as: √ In a uniaxial tensile test specimen at the point of yield:

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Therefore the octahedral shear stress in a uniaxial tensile test specimen at failure is calculated as: √(

)

(

)

√ Therefore under the Von Mises theory: Plastic deformation occurs in a 3-Dimensional stress state whenever the octahedral shear stress 𝑆𝑦𝑖𝑒𝑙𝑑

exceeds √

Tresca:

“Failure occurs when the maximum shear stress in a body is equal to the maximum shear stress at yield in a uniaxial tension test.

The maximum shear stress is calculated as:

In a uniaxial tensile test specimen at the point of yield:

Therefore

Therefore, under Tresca theory Plastic deformation occurs in a 3-Dimensional stress state whenever the maximum shear stress exceeds

𝑆𝑦𝑖𝑒𝑙𝑑

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Rankine:

“Failure occurs when the maximum tensile stress in a body is equal to the maximum tensile stress at yield in a uniaxial tension test”

The maximum tensile stress is the largest, positive principal stress, S1 (by definition, S1 is always the largest of the principal stresses.) In a uniaxial tensile test specimen at the point of yield:

Therefore, under Rankine theory: Plastic deformation occurs in a 3-Dimensional stress state whenever the maximum shear stress exceeds 𝑆𝑦𝑖𝑒𝑙𝑑

Maximum Stress Intensity Criterion Most of the piping codes use a slight modification of the maximum shear stress theory for flexibility related failures. Repeating, the maximum shear stress theory predicts that failure occurs when the maximum shear stress in a body equals

, the maximum shear stress existing at failure during

the uniaxial tensile test. Recapping, the maximum shear stress in a body is given by:

For a differential element at the outer surface of the pipe, the principal stresses were computed earlier as: √(

)

√(

)

As seen previously, the maximum shear stress theory states that during the uniaxial tensile test the maximum shear stress at failure is equal to one-half of the yield stress, so the following requirement is necessary: √

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Multiplying both sides by 2 creates the stress intensity, which is an artificial parameter defined simply as twice the maximum shear stress. Therefore the Maximum Stress Intensity Criterion, as adopted by most piping codes, dictates the following requirement: √ Note that when calculating only the varying stresses for fatigue evaluation purposes, the pressure components drop out of the equation. If an allowable stress based upon a suitable factor of safety is used, the Maximum Stress Intensity criterion yields an expression very similar to that specified by the B31.3 code: √ Where: longitudinal normal stress due to bending shear stress due to torsion allowable stress for loading case Continuing our example for the 6” diameter, standard wall pipe, in which longitudinal, shear and hoop stresses were calculated:

Assuming that the yield stress of the pipe material is 206 MPa (30,000 psi) at operating temperature, and a factor of safely of 2/3 is to be used, the following calculations must be made: √ √

The 101.185 MPa is the calculated stress intensity in the pipe wall, while the 137.33 MPa is the allowable stress intensity for the material at the specified temperature. In this case, the pipe would appear to be safely loaded under these conditions.

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements

Code Stress Equations The piping code stress equations are a direct outgrowth of the theoretical and investigative work discussed above, with specific limitations established by Markl in his 1955 paper. The stress equations were quite similar throughout the piping codes (i.e. between B31.1 and B31.3) until the winter of 1974 when the power codes having observed that Markl was incorrect in neglecting intensification of the torsional moment in a manner analogous to the bending component, combined the bending and torsional stress terms, thus intensifying torsion. It should be noted that the piping codes calculate exactly the stress intensity (twice the maximum shear stress) only for the expansion stress, since this load case contains no hoop or radial components and thus becomes an easy calculation. Including hoop and radial stresses (present in sustained loadings only) in the stress intensity calculation makes the calculation much more difficult. When considering the hoop and radial stresses, it is no longer clear which of the principal stresses is largest and which is the smallest. Additionally the subtraction of S1 – S3 does not produce a simple expression for the stress intensity. As it turns out the inclusion of the pressure term can be simplified by adding only the longitudinal component of the pressure stress directly to the stress intensity produced moment loading only. This provides an equally easy to use equation and sacrifices little as far as accuracy is concerned. The explicit stress requirements for the B31.1 piping code addressed by CAESAR II follows. Note that most codes allow for the exact expression for pressure stress

to be using in place of

in

the sustained stress calculations. Note also that there are many additional piping codes addressed by CAESAR II. B31.1 Power Piping The B31.1 code requires that the engineer calculate sustained, expansion and occasional stresses, exactly defined as below: Sustained

Where: = sustained stress = intensification factor = resultant moment due to sustained (primary) loads √ = basic allowable material stress at the hot (operating) temperature, as per Appendix A of B31.1 Code. Sh is roughly defined as the minimum of: 1. ¼ of the ultimate tensile strength of the material at operating temperature 2. ¼ of the ultimate tensile strength of the material at room temperature 3. 5/8 of the yield strength of the material at operating temperature (90% of the yield stress for austenitic stainless steels) 4. 5/8 of the yield strength of the material at room temperature (90% of the yield stress for austenitic stainless steels) 5. 100% of the average stress for a 0.01% creep rate per 1000 hours

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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Expansion

Where: = expansion stress range = resultant range of moments due to expansion (secondary) loads =√ = Allowable expansion stress = basic allowable material stress at the cold (installation) temperature, as per Appendix A of B31.1 Code

Occasional:

Where: = Occasional Stresses = resultant moment due to occasional loads =√ = occasional load factor = 1.2 for loads occurring less than 1% of the time = 1.15 for loads occurring less than 10% of the time.

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CAESAR II Statics Training Pipe 1

Pipe 1 This exercise will provide further practise with the piping input, and introduce alternative editing tools which may increase productivity in creating models. We will also investigate and review the results to see what to look for and see how the piping system is behaving, and how to correct any issues which may arise during the design. The first stage of this exercise is to input the model. The model is below; you will also have the same isometric printed on a separate hand-out in a larger format. As before with the cantilever example, the model will be input using the node numbering system. Each section between two nodes is called an element. i.e. node 10 to node 20 are linked together by an element, referred to by ‘element 10 to 20’. Prior to entering geometry, it can be very useful and is a good idea to mark up the isometric drawing with the intended node number sequence.

We will use a slightly different method of inputting the data, which will allow us to maximise the graphics area during input. In the main “Classic Piping Input”, on each area, notice the “>>” symbol in the top right corner:

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CAESAR II Statics Training Pipe 1 Double click this symbol to “tear off” the particular section of the input spread sheet. This will allow the Classic window to be minimised for the most part thus maximising the graphics. Tear off the Node Numbers, Dimension Deltas and Pipe Sizes areas. As the material temperatures and pressures do not change throughout the model we can enter these on the first element and then we will not need them again.

Input Model Enter A106-B as the material, 330°C as the temperature and 17 bars as the pressure

In this model we also require insulation; 65mm thick Calcium Silicate.

The rest of the information we will need to enter for our model can be done via the three windows we have “torn off”. Minimise the Classic piping input (of course this can always be maximised at any point if needed).

Finally we can enter the pipe size and schedule, along with the densities and corrosion allowance, as per the isometric. The fluid density can be entered as 0.72SG and CAESAR II will convert this specific gravity to the correct units. As before the pipe size can be entered as 10 for 10” and S for STD schedule piping.

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CAESAR II Statics Training Pipe 1

We will begin at the bottom “right” pipe where it is connected to a pump. This will be node 10. Note that this is an anchor, a fixed point in our system. Element 10 to 20 is 400mm in length, in the -Z direction. Enter DZ as -400mm

Node 10 is also fixed so we need to specify an anchor. Use the toolbar on the left hand side of the graphics window (default location) to specify a restraint.

The Auxiliary Data – Restraints window will appear. Specify that the anchor is at node 10. The auxiliary data window can now be closed.

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CAESAR II Statics Training Pipe 1

Our first element is complete, and should look like the one below:

Use the Continue button to create a new element:

This next element is a 300# flanged gate valve. We could enter this in a number of ways. The valve will be rigid relative to the surrounding piping, so must be specified as a “rigid element” with a weight. This can be done either as 3 separate elements (flange – valve – flange), or as one overall element with the total length and combined weight specified. This can be done manually or by using the valve flange database to obtain the length/weight automatically from CAESAR II’s catalogue, which we will do. Select the Valve flange database button and select a gate valve with flanged ends, class 300.

The Flange – Valve – Flange check box can be used to split the component into 3 elements ifrequired.

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CAESAR II Statics Training Pipe 1

The element will appear in node 20 to 30.

The correct length will be inserted (and the element will continue in the same direction as the previous element). Also note that the Rigid check box is checked and the rigid weight has been entered with the relevant weight for a 300# gate valve and flanges. (Hover briefly over the Classic piping input where it is docked).

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CAESAR II Statics Training Pipe 1 Continue to the next element

.

Enter the DZ as -825mm. This element also leads into a bend, so press the Bend button on the right hand toolbar. If using the classic piping input we could check the bend check box to achieve the same result.

The bend auxiliary data window will appear.

The default bend type is a long radius (1.5D) bend This radius can be changed. Common bend radii are available in the drop down, alternatively any radius required can simply be typed in here.

In addition, further data can also be entered such as if the bend is flanged or mitred etc. Accept the default long radius bend. The graphics will not display the bend yet, as there is no following element.

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CAESAR II Statics Training Pipe 1 Continue to the next element

.

This time we are now continuing in the –X direction. DX is -1050. The bend will now be visible in the graphics. Continue to the next element

.

This element is a 10”x12” concentric reducer and is 203mm in length. Enter DX as -203mm and specify that this is a reducer.

The Reducer Auxiliary will appear and we can specify further data, including the second end size. A s before, entering a nominal size in here will be converted to the actual OD. Enter 12 in the diameter 2 and S in the thickness 2 fields, which will be converted to the actual values. Continue to the next element

.

Finally continue from the end of the reducer to the centre of the tee, 254mm as shown on the isometric. DX is -254mm The model at this point should now resemble the image below, note the node numbers in the image:

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CAESAR II Statics Training Pipe 1 We can now take advantage of the fact that the model is symmetrical and use the functions in CAESAR II to mirror the piping to create the opposite leg. Use the Select group function to activate the graphical selection mode and draw a window around the model.

All elements will turn yellow to indicate that they are currently selected. Ensure all components are selected. The Duplicate function can be used to copy, and mirror if required, selected elements.

Duplicate the selected elements and choose to mirror about the Y-Z plane.

We also need to increment the node numbers so that we do not have duplicate nodes. Currently our model goes from node 10 through to node 70. If we increase the node numbers by 70, node 10 will become node 80, 20 becomes 90 and so on. Therefore the second leg will be node 80 through to node 140. The only issue with this is that there are no common nodes, so the piping will not actually be connected. This can easily be fixed by chaging node 140 (the centre of the tee on the second leg) to become node 70 (the node at the centre of the tee on the first leg). This will connect up the piping at the common node, 70 – the centre of the tee.

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CAESAR II Statics Training Pipe 1

Click OK and the pipe will be duplicated, but as already stated there is no common node so CAESAR II does not know where to place the pipe. As such it locates it at the origin. The resulting model looks like the following.

All we need to do is connect element 130 – 140 to element 60 – 70. This can be done by changing 140 to become node 70. Select element 140. There are various ways of doing this – either double click in the graphics area, or user the navigation buttons to navigate to the correct element (as this is the last element the end button will quickly take you to the correct element).

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CAESAR II Statics Training Pipe 1 The Edit Node numbers window should now read 13 to 140 and the element will be highlighted in the model.

Simply change the “To” node from 140 to 70. The model will now be connected as should look like the one below:

We can now complete the model by adding the vertical leg and connection to the vessel. Skip to the last element. This can be done by again using the Last Element navigation button or using the Ctrl + End buttons on the keyboard. Click “Continue” to move to the next element need to change this to 70 to 140.

. The node numbers will default to 70 to 80. We

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CAESAR II Statics Training Pipe 1 This element is the vertical leg, and is 7m in the Y direction. DY is therefore 7000. This also leads into a bend so select the Bend icon as well.

.

Click “continue” and place the final element 140 to 150 in the –Z direction, 2000mm. The final element connects to the vessel, so we will place an anchor at this point. Click the retsraint button and specify an anchor at node 150 Notice in the isometric that at the vessel connection, there are DY and DZ displacements. These are due to the thermal expansion of the vessel.

Select the Displacements button and enter in the required values 3mm in DZ and 12mm in DY.

Error Checking The model is now complete, so run the error checker.

We will receive a fatal error and three warnings. We must correct the errors before we can analyse the model. The warnings may be acceptable but we should check to confirm that the input is as intended.

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CAESAR II Statics Training Pipe 1 So our error is mentioning that we have both an anchor and displacements speciified at node 150. This cannot be possible as the anchor fixes the point, but the displacements move the same point. We cannot have both at the same time. Remove the anchor and edit the displacements. Double click the error message to go straight to the area of concern. Now click the restraints button to remove restraints. Click OK in the message which appears. Now edit the displacements and fill in 0 in all other field (DX,RX,RY,RZ). A displacement of zero will fix the node in that direction, so now our node is fixed in all directions, except for DY and DZ where the relevant displacements are applied.

Re run the error checker and investigate the warnings. The second two warnings are regarding the reducer alpha angle which is not specified. CAESAR II is therefore using a default computed value. This is acceptable here for us. The first warning is stating that there is a geomtric intersectaion at node 70 (the tee) but we have not specified a type of tee, and therefore a SIF. This can sometimes be correct but is most often the result of an oversight, as in this case. Return to the input and locate node 70. The Find tool can be used to do this:

The Zoom to Node if found check box will also zoom into that node/element if it is found, useful on larger models.

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CAESAR II Statics Training Pipe 1 On node 70 use the SIFs/Tees button to specify a SIF at this point. This only needs to be done on one of the elements connecting to node 70, it is not necessary to do this on all three.

Select an unreinforced tee.

Re-run the error checker. All should now be OK, only the reducer alpha warnings will remain, plus the C of G report.

Review Load Cases Access the load case editor

Recall from earlier the design code (we are using B31.3) addresses the stresses produced by the various loads. In our model we have the following loads applied: Weight Pressure Temperature Displacement B31.3 requires that two checks are performed – Sustained and Expansion Sustained – Weight and Pressure Expansion – Temperature and Displacement

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CAESAR II Statics Training Pipe 1 These load cases are defined by CAESAR II as the default (recommended) load cases, shown in rows L2 and L3.

Row L1 is an operating case (OPE) and is the “Hot” case consisting of the ‘real world’ loads. This case is not required by B31.3 (although some codes do require this case also). However as this case is a “real world” scenario it is used to estalish restraint loads and loads on equipment conections. In addition, it is used to derive the Expansion case. The expansion case is the algebraic difference between L1 and L2 (L1 – L2). Accept these load cases and run the analysis by clicking the “Running Man” icon.

Review Results After the analysis has run, the output processor will appear. The first thing to notice is that the EXP case is coloured red. This indicates that this case has failed to code stress check. That is, the computed stresses in the system at some point are greater than the allowables published in the code. We need to fix this. Select the Expansion case and view the results for the Stresses report.

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CAESAR II Statics Training Pipe 1

The report shows that the code stress check failed and highlights in red where the check failed. Double clikcing on any column will order the report by that coluumn. Double click on the Code Stress column header to order by highest stress.

The overstress points are at nodes 70, 10 and 80.

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CAESAR II Statics Training Pipe 1 First we will check node 70. This is the tee. Look at the SIFs here. The in-plane SIF is 4.625 and the Out-Plane is 5.833. The stresses at this point are therefore being multipled by 4 and 5 times. If we can reduce these SIFs then the stress will reduce and can easily be reduced below the code allowable.

Return to the input and return back to node 70. Pick the Intersection SIF scratchpad and choose node 70.

Change the unreinforced tee to a reinforced tee. Specify a pad thickness of 10mm

Click the Recalculate button and notice the SIFs reduce dramatically. Now the stresses will be multplied by 2.887 and 2.415 rather than 4 and 5.

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CAESAR II Statics Training Pipe 1 Re-run the analysis using the batch run feature. The Expansion case is still shown in red, indicating the system is still overstressed. But check the Stress report for the Expansion case and notice that only nodes 10 and 80 are overstressed.

So what is happening at nodes 10 and 80? Nodes 10 and 80 are the initial anchor locations, so we need to find out what is causing the overstress. This is in the expansion case, so if we recall the code equation for the expansion case:

From this equation it can be seen that the dominant factor in the code equation is the bending moment – it is the only factor in the expansion case. So which bending moment is this, Mi, Mo or Mt? Mt is torsion, Mz and Mi and Mo are inplane and outplane – so vary dependant on the location. What we can see from the results though, is which bending moment is the highest in terms of our axes. View the Expansion case, Restraint Summary report.

We can see from this report that at nodes 10 and 80, the highest bending moment is the MY moment, at 116 kN.m. The MX is also rather high at 88 kN.m.

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CAESAR II Statics Training Pipe 1

So we know what is causing the overstress, but how do we correct this and reduce the bending moment (and therefore the stress)? Let us look at the 3D plot to view what is causing the bending moment. Close the report and view the 3D plot

In the 3D plot window which appears, ensure that the Load case we are viewing is the expansion case and select to Show the deflected shape. You may need to Adjust the deflection scale to get a more exaggerated deflected shape.

View the pipe from the bottom, using the standard views available

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CAESAR II Statics Training Pipe 1

We are looking upwards at the pipe from below. The Y axis is pointing upwards (away from us). The pipe is undergoing thermal expansion and causing the pipe to bend at the anchor points. Looking at the model from the side view will also explain the MX moment. As can be seen, the riser is expanding causing the MX bending moment.

If we could add some flexibility in to the area where the pipe is expanding we can absorb some of this expansion, and so reduce the bending moment. We have the top leg which is flexible, but the bottom leg is not flexible enough.

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CAESAR II Statics Training Pipe 1

If we can transfer some of the flexibility in A to B then we may solve the problem. To do this, increase the length of B by 1m and so consequently reduce the length of A by 1m. This should give us more flexibility at the bottom, hopefully without removing too much flexibility at the top. Return to the input and select element 30 to 40. The DZ value here is 825mm. Edit this to 1825mm.

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CAESAR II Statics Training Pipe 1

Repeat for element 100 to 110. We will have to also consequently reduce the length of 140 to 150 by the same amount (1m). Change this from 2000mm to 1000mm.

The model should now look like the one below.

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CAESAR II Statics Training Pipe 1 Re run the analysis and check the results. The expansion case is now no longer coloured red and the highest code stress is 91% of the allowable at node 10. We have successfully reduced the stresses and the model now passes the code stress checks. Verify the sustained stress report that this is still acceptable – it should be around 37% of the allowable. Our model is now compliant with B31.3.

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CAESAR II Statics Training Supt 01

Supt 01 This exercise is designed to demonstrate adding supports in CAESAR II and demonstrate the Operating case and Restraint load reports and give an indication of what the results mean on the restraint load report, along with a short example on how to combat issues with supports, such as “lift off”.

The model shown above will also be in your hand-out. Model the piping system as per this isometric. Anchor at nodes 10 and 90.

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CAESAR II Statics Training Supt 01

Locating Supports The system is anchored at the termination points (nodes 10 and 90), but we also need to support the weight of the piping system as well. If both supports are pinned (free to rotate), standard beam theory states that the max moment is at the centre of the span, l.

This moment is:

If both ends are fixed then the max moment is at the end of the span

This has a value of

Where

As piping systems are neither one nor the other and tend to be somewhere in the middle, a compromise therefore is reached with an approximation thus;

Taking into account the maximum moment could be somewhere between the ends and the centre – i.e. anywhere along the span.

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CAESAR II Statics Training Supt 01 This deals with continuous runs of pipe, however there are of course concentrated loads sometimes in the piping system, such as valves, flanges etc. The effects of these items on the pipe stresses can be estimated as well. For pinned connections, the maximum moment is located at the point of loading (P).

This maximum moment has a value of

Where a = longer portion of span b = shorter portion of span For fixed connections:

He maximum moment here is located at the end nearer the load, and has a value of

In either case (or in some case in between) the additional stress (M/Z) due to the concentrated loads should be added to the stress from the uniform load in order to determine the total stress. Examining the formulas above, it can be seen that as the shorter span (b) approaches zero in length, the moment, and therefore the stresses approach zero as well. So, if supports are located as close as possible to concentrated loads, the effects of these loads are reduced as much as possible.

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CAESAR II Statics Training Supt 01 The information on the preceding pages provides a simple rule of thumb to design for weight loading. First support all concentrated loads in the system as closely as possible, reducing the stresses due to those loads to as close to zero as possible. Next, we can use Along with If we knew the allowable stress, we could then use this information to determine a maximum allowable length of pipe – i.e. a distance between supports. Rearranging the equations above, we can obtain √

As this calculation will need to be done often, in order to save time calculating the Manufacturer Standardisation Society of the Valve and Fitting Industry has calculated allowable piping spans for various configurations. These standard spans have been published and are shown on the next page. These spans assume:

The pipe is standard wall with insulation Maximum moment is Mmax = wl2/10 No concentrated loads are present There are no changes in direction Maximum allowable stress is taken to be approx. 10 MPa Max deflection is approx. 2.5mm SIFs are not taken into account

It is rare that piping systems are only horizontal runs with no changes in direction etc.; therefore a caveat is taken in that changes in direction reduce the allowable span to ¾ of the standard span. In addition, the standard span does not apply to risers, since no moment (thus no stress) develops, regardless of length. However it is preferable to locate supports above the centre of gravity of the riser to prevent toppling. These rules here are simply rules of thumb and can provide a good start point for support locations. Of course, supports should be located with practical considerations taken into account (locations of building steel/pipe racks etc.).

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CAESAR II Statics Training Supt 01

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CAESAR II Statics Training Supt 01 Adding Supports to Model Let us now return to our model SUPT01.

As there is an anchor at node 10, the valve here is supported. The valve at 60-70 requires supporting. We will create a new node on element 50 to 60, called 57, and locate a +Y support here. Use the Break command to split the element into two. First select element 50 to 60 and choose the break command.

We will locate this support close to the valve (node 60). Specify to break the pipe and insert the new node, number 57, 150mm from node 60:

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CAESAR II Statics Training Supt 01

The element will be broken and a new node inserted close to the valve. Locate a +Y support at this node 57.

The +Y support will support the pipe from below, and will allow movement in the +Y direction.

All the concentrated loads are now supported. We can return and run through the piping system, placing supports as per the standard span. Check the table on page 48 to determine the maximum span for 12” pipe carrying water

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CAESAR II Statics Training Supt 01 The table on page 48 indicates that the maximum span for 12” pipe in water service is 7m. As discussed previously, for horizontal changes in direction, the support span is amended to ¾ of the standard span. 0.75 x 7 = 5.25m The valve is supported at node 10. After node 10 the piping continues horizontally with a bend. The maximum span therefore is 5.25m. This places our support round the bend.

The piping after the bend is 13715mm before the riser. This can almost be split in two exactly with our 7m span spacing. Remember that the standard span does not apply to risers, and as mentioned before we will support the riser from the top, rather than trying to balance it from the bottom. As such we can locate a support near the middle of the 13715mm run, and one close to the bend (node 30). Break element 30 to 40 and locate a new node number 33. Locate this 600mm from node 30. It is possible to add a support in at the new node location. We wish to add a +Y support at node 33, exactly the same support configuration as at node 57. So typing in 57 in the “Get Support from Node” field will place the same support as at 57 at our new node 33.

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CAESAR II Statics Training Supt 01 Repeat and break element 33-40. Break this 7000mm from node 33. Call the new node 37. Place the same +Y support from 33 (or 57) at this point too.

Continue on after the riser. There is already a restraint next to the valve, so we have fulfilled the minimum span up to the valve. After the valve we have horizontal pipe with a bend again. Therefore our maximum span is 5.25m. The length of pipe is 4115mm and then 3640mm after the bend. There is an anchor at the end, so we just need one more support between the valve and the anchor at the end of the pipe.

Locate this support on element 70 to 80, close to the bend at node 80. Locate this 600mm from the bend. Break element 70 to 80 and create a new node 77, 600mm from node 80 and with a +Y support the same as before.

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CAESAR II Statics Training Supt 01

Finally the piping riser needs to be supported. The length of horizontal run at the top and bottom of the riser is less than our span of 7000mm. There is no bending in the riser so in theory we can place a single restraint near the top of the riser. Break element 40-50 and locate a +Y restraint 600mm from the tangent intersection point of the bend. Note that, although this support should satisfy our bending requirements on the horizontal sections, it may have a very large load since it will also support the whole of the riser.

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CAESAR II Statics Training Supt 01 The support located in the riser may be difficult to see, as it is probably hidden by the piping. To view the support either the size of the restraint symbol can be increased, or the pipe can be set to translucent mode.

The system is now supported as per the maximum span requirements. We can be sure that the sustained stress case therefore is acceptable, and should be in the order of approximately 10MPa. Error Check the model.

You should receive only the Centre of Gravity report, and no errors or warnings.

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Analyse Access the Static load cases create only a single load case with weight only. We wish to check the support locations we have just placed are below the acceptable limits

Run the analysis. View the Sustained Stresses report.

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The highest stress level is 10.7MPa, which is almost exactly at the allowable from the standard span limit (this limit is based on an allowable of 1500 psi ~10.3MPa). The system is supported from a purely weight induced stress perspective. We can also now view the restraint loads to see how the weight loads are distributed. View the Restraint Summary report.

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CAESAR II Statics Training Supt 01 Again this look OK, all restraints are taking a downwards acting load (-FY), although the restraint at node 43 is rather large compared to the others; 30,000N vs. less than half that for the remaining supports. These loads however are due to weight only. Let us run now the cases required by the piping code B31.3. Return to the Static Load cases and select the recommended cases.

Run the analysis and view the sustained stresses. These will have increased slightly due to the fact that we are now including the pressure term; however the stresses are still well within the allowables determined by the code. Similarly the Expansion Case stresses are also very low and well within the allowable – the system is flexible unlike the PIPE1 example. Now we can check the restraint loads in the real world operating case. Remember the Operating case is not required by the code, but it does represent the actual loads in a “real world” scenario, for the purpose of designing restraints. View the Operating case Restraint Summary.

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The loads are different to before as we have included the effects of thermal expansion. The load on node 77 is 0 (in the FY). This shows that this restraint is not taking any load. What is happening here? View the displacements report to see what is happening at this point.

At node 77 the pipe is moving upwards 2.3mm. Also notice that at node 50 (the bottom of the riser) the pipe is moving down 26mm.

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CAESAR II Statics Training Supt 01 Viewing the 3D Plot can confirm this:

View the deflected shape (you may wish to increase the deflection scale to exaggerate the deflected shape)

The 3D plot shows that the thermal expansion is causing the riser to expand downwards at the bottom (node 50). This in turn is causing the pipe to pivot at node 57 – giving the large operating load at node 57. The pipe pivoting at 57 causes lift off at node 77 – so we see a 0 load. The restraint at the top of the riser (at 43) is the datum point of expansion and so all the thermal expansion is from this point. That is why there is no expansion at the top and a lot of expansion at the bottom. We need to rectify this situation.

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Fix Model As we know, the riser is expanding due to thermal expansion. The datum point for this expansion is the support located at node 43, at the top of the riser, so all the expansion is going downwards – causing the lift off issue. To rectify this we can attempt to move the datum point of the expansion, so that the expansion is more evenly distributed. Insert an additional restraint on the riser. Call this node number 45 and locate this restraint 6000mm below node 43. Insert another +Y support at this location. This should have two effects: 1. Give a better distribution of the weight loads of the riser 2. Cause less thermal expansion downwards at node 50.

Re-run the analysis, the batch run command can be used as we have only made a small change by adding a support.

Review the stresses is the SUS and EXP cases. These stresses should still be acceptable.

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CAESAR II Statics Training Supt 01 Review the restraint report for the sustained and operating cases to see how the new restraint has affected the results.

The sustained case shows that we have a better distribution of the weight of the pipe on the riser, as the new restraint is taking some load. The load on node 43 at the top of the riser is now distributed between 43 and 45 (43 has dropped from 30kN to 9kN).

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The operating case however still shows lift zero load at node 77, and now also zero load at node 43. Checking the displacements also confirms this; there is still a positive displacement at nodes 77 and now at 43. Node 50 is still moving downwards, although only 15mm now.

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CAESAR II Statics Training Supt 01 We will attempt to further distribute the thermal expansion of the riser by adding a third restraint, located near the bottom. Break element 45-50 and create node 47. Locate node 47 6000mm below node 45 and locate a +Y support at this point.

Rerun the analysis and check that the stress levels have not been adversely affected. As before, view the SUS and OPE loads on the restraints to see how the new restraint has affected the analysis.

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The sustained report shows that we have further improved the weight distribution among the restraints.

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The Operating case now shows a negative load on restraint at node 77. There is no more lift off here at 77. However the operating loads at node 43 and 45 are now zero. All the thermal expansion that was going downwards with only the one restraint at the top of the riser has now been forced upwards instead, causing the pipe to lift off at the top of the riser (43 and 45). The displacements report confirms this

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CAESAR II Statics Training Supt 01 The pipe is lifting off 22mm at the top of the riser. The 3D plot can also confirm the situation:

So we have a situation where we are supporting the weight of the system adequately in the SUS load case, but we have an issue with the thermal expansion. If we replace the rigid +Y restraints along the riser with Variable Spring Hangers (VSH), these hangers should allow thermal growth whilst also supporting the required weight for the SUS condition.

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CAESAR II Statics Training Supt 01 Place Spring Hangers Return to the input at locate element 40-43. Remove the restraint at node 43 by double clicking the restraint check box. Place a hanger here instead. Double click the Hangers check box

Select the Hanger table as Carpenter & Paterson. Carpenter & Paterson are a UK manufacturer whose database of available spring hangers is programmed into CAESAR II. CAESAR II will automatically calculate the required load and movement at the location, and then review the database to select an appropriate spring for the calculated load and movements. Notice that 2 hangers are located at this location also. The graphics will not change in CAESAR II, but this will locate 2 hangers at this location, and the selected spring will be based upon this shared load.

Error check the model. You should now notice two further notes during the error check.

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The first not simply shows the number of hangers in the job, and how many of these hangers will be designed by CAESAR II at run time. The second message states that new load case combinations are required for the hanger design. A load case for weight loads is required, so that CAESAR II knows how much weight the hanger(s) need to support. Secondly, a hanger design operating case is required. This case determines the thermal expansion at each restraint location to determine the movement at the spring hanger locations as well. The values of weight from the previous weight load case are used. These two cases together are used by CAESAR II’s spring selection algorithm to select the appropriate spring from the in-built catalogue. Access the load case editor to create these new load cases.

Click the Recommend button in the load case editor. CAESAR II knows that there are hangers present that require designing, so will recommend the correct load cases for hanger design – cases 1 and 2.

Accept these cases. Note the stress type for these cases are HGR type. The results for these hanger cases are supressed by default (theses are pre-analysis cases and the figures do not actually mean anything other than for the spring hanger selection). Case 1 W (HGR) This case performs a Weight Analysis only with all support locations as rigid restraints. This tells the spring selection algorithm how much weight needs to be supported at each location (usually in the Operating condition)

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CAESAR II Statics Training Supt 01 Case 2 W+T1+P1 (HGR) The case uses the support weight values derived from case 1 as upward forces for an Expansion analysis. That is, the values of W cancel each other out (support load versus actual weight), and the system is then subject to temperature T1 in order to establish the thermal movement at each restraint location. Given the Weight to be supported and the thermal movement at the same location, the spring and its associated stiffness values can be selected and incorporated into the subsequent load cases. Run the analysis

CAESAR II will have selected and sized a spring hanger during the analysis. Check the Hanger Table with text to view the hanger properties of the selected hanger.

As can be seen, CAESAR II has determined that the hanger will need to support a hot load (i.e. OPE) of 6723N. There are two springs at this location, so this 6723N is the total load shared between two supports (i.e. the total load is 6723N x 2). CAESAR has taken these properties and browsed the inbuilt Carpenter & Paterson database and selected a DV70 Size 11 spring. Verify the sustained and expansion stresses – these should still be acceptable (13% and 19%). Now check the OPE restraint loads.

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CAESAR II Statics Training Supt 01

The hanger at node 43 is now taking load. This load is 13447N (which is 6723N x 2), however there is still no load being taken at node 45. Return to the input and replace the rigid +Y support at node 45 with a spring hanger. As before, select the Carpenter & Paterson catalogue, and place 2 hangers at this location before re-running the analysis. As before the SUS and EXP stresses are acceptable. The OPE case Restraint summary now shows that all the restraints are taking load. The new spring hanger is taking some of the load of the riser – this is now distributed evenly.

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CAESAR II has again run the two hanger cases and used the results from these to select appropriate hangers for placing at the two hanger locations. These can be seen from the Hanger Table with text.

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CAESAR II Statics Training Turbo

Turbo This exercise will build upon knowledge we have gained so far, and introduce the following new features.

Combining Pipe Models Rigid Construction Elements CNode Connections NEMA SM23 Analysis

The model is shown above and is also supplied in the hand-out in a larger format. As can be seen, this is an inlet and exhaust on a turbine. The turbine itself is anchored to the floor at the anchor point specified. To keep modelling simple, we can model the inlet and exhaust as two separate models. These two models can be combined into a single model later – there is a common location at the turbine anchor point. We will model this common anchor point location as node number 5. However, we will come back and model this point last.

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Model Inlet Model the inlet pipework, on the first element; change 10 to 20 to 11 to 20. Begin at node 11, the flange connection to the turbine nozzle, as shown below. Note that node 11 also has an anchor attached.

Once the inlet piping is complete, return to the first element, 11 to 20. We will now insert an element before 11 to 20, numbered 5 to 10. Node 5 will be the turbine anchor location. Node 10 will be connected to the anchor at node 11. We will connect these via CNode connections. As there is an anchor at node 11, this node is fixed in all 6 degrees of freedom. However, the nozzle connection on the turbine will undergo some movement due to the thermal expansion of the turbine. Recall previously that we had a similar situation where displacements were specified to account for a similar situation in PIPE 1 for the vessel thermal expansion. In this case, we do not know what the thermal expansion is here so we cannot enter the displacements. To apply the displacements to the nozzle point we will add in an element from the nozzle to the turbine base. This will be a rigid element with zero weight, and it will have temperature applied (so it will undergo thermal expansion). This element will also be anchored at the turbine base. If however we specified this as 5-11 for example, nodes 5 and 11 are both anchored, so cannot move and all that will happen is we will obtain large forces at nodes 5 and 11. We need a way of connecting this rigid construction element to node 11 which will allow node 11 to move due to the expansion of the construction element, but still be fixed as far as the rest of the piping is concerned. This can be achieved in CAESAR II this using CNodes. A CNode will allow the anchor at node 11 to be connected to another node “indirectly”. Essentially, both these points will be at the same location, but CAESAR II will see these points as separate nodes. Therefore what will happen is that as element 5-10 expands, node 11 will act as an anchor, but as it is connected to node 10, node 11 will move to wherever node 10 moves to, while still acting as an anchor.

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Nodes 10 and 11 are the same point in space. Select element 11-20. First specify a CNode on the anchor at node 11; the CNode will be node 10.

Next use the Insert function to insert an element before this element.

Change the node numbers to 5 to 10

Fill in the DX, DY, DZ fields as shown on the isometric sketch

This is a rigid element, but leave the weight blank in this case. Also add an anchor at node 5.

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The zero weight rigid will be inserted and connected to node 11 as above. We now need to specify the temperature for the rigid, as this will undergo thermal expansion. Select element 5-10 and double click the “>>” on the temperature/pressure section to “tear off” the Operating Conditions box. Uncheck the Propagate parameters box to ensure that the data entered here is only entered on this one element, and not the whole model. Enter 200°C for T1 and make sure that no pressure is specified.

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CAESAR II Statics Training Turbo Check that this has been specified correctly, by using the Show Pressure graphical tool.

Display P1.

The rigid construction element should show as unspecified, and the rest of the model should show as 12 bars.

The inlet is now complete. Save the file and using the same concept, create a new job file for the exhaust. Start the exhaust using nodes 1011 to 1020 for the first element.

Continue on. After the reducer, there is a bend. Place a length of pipe 350mm long in the Z direction, adding a bend to this pipe. Place a corresponding pipe 350mm long in the Y direction afterwards to complete the bend.

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Complete the rest of the exhaust. Once finished, add one final element, inserted before 1011 to 1020 and numbered 5 to 1010. Set the pressure for this element to blank, and ensure that only this element has no pressure. Connect via a CNode of 1010 at the anchor at node 1011. The exhaust is now also complete. Notice that we have a node numbered 5 in both our inlet and exhaust models. This node is a common location in both files. As such we can combine the models and they will be linked at node 5.

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Combine Models Save the Turbine exhaust as Turbo_Combined.c2 Select the Include Piping Files button to bring in the Inlet piping to create one single model.

Browse for the inlet model and click OK.

The two models will be combined around node 5 – the common node in both files.

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CAESAR II Statics Training Turbo Select an element in the inlet. Notice that it can be selected, but the input screen has all fields disabled.

This is because currently the inlet is simply being “referenced” and not fully included. Return back to the combine pipe models screen. As well as the File name field, there are three other columns. RotY – allows the included file to be rotated by a specified angle about the Y axis. Inc – allows the node numbers in the new file to be incremented by a certain value. i.e. if the file included was 10-20, 20-30 etc., we could increment by 1000 so that the nodes would become 10101020, 1020-1030 etc. The final column is Include Now? This column allows users to choosing whether to reference or actually permanently include the file. This can be useful if checking that the file is correct before including, so any changes required can be done in the original separate model. If your model looks correct, change Include Now? to Y.

Selecting an element in the inlet side of the piping will now show all the fields to be enabled.

Error Check and analyse the model, use the recommended load cases. The analysis results should show that the expansion and Sustained stresses are acceptable. Check the OPE case and note the loads on the nozzles at nodes 11 and 1011.

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There is a reasonable force on these nozzles, as the anchor points are supporting some of the weight of the pipe. We will now take these forces and check them against NEMA SM23 to analyse the turbine to see if the loads on the nozzles are acceptable.

NEMA SM23 The National Electrical Manufacturers Association (NEMA) publishes and maintains a standard SM23 Steam Turbines for Mechanical Drive Service. This standard includes allowable loads that can be applied safely to our turbine nozzles. CAESAR II incorporates this standard and a separate module can be used to evaluate nozzles, using calculated loads from the piping analysis (as we have just done). Return to the CAESAR II main window. Select the Analysis menu and select the NEMA SM23 option to load the module. You may need to use the to access the whole menu.

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CAESAR II Statics Training Turbo Create a new file called pass1. If you wish, give the equipment a short description. Select the NEMA Input Data tab. The first data to enter is the direction of the equipment centreline. This must be specified as the direction Cosines.

The direction cosines are specified as the cosine of the angle of the centreline with the respective axis. For example, if the centreline was as shown above, 60° from the Z axis and 30° from the Y axis, the direction cosines would be: Z = Cos 60° = 0.5 X = Cos 30° = 0.866 Our equipment centreline is along the Z axis, so the angle between the centreline and the Z axis is 0° and the angle between the centreline and the X axis is 90° Therefore the direction cosines are: Z = Cos 0° = 1 X = Cos 90° = 0 Now we can define the nozzles. Click the Add Nozzle button

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CAESAR II Statics Training Turbo The Node number is the corresponding node number which matches the node number in the CAESAR II model. Specify the Inlet first – so this node number is 11. This is the Inlet nozzle and is 4” diameter The next box is the Distance from Resolution Point to Nozzle. NEMA SM23 is ambiguous about the point of resolution of the combined forces and moments. Select one of the three fields and hit F1 to bring up the help.

This point is the distance from the resolution point (face of the exhaust nozzle flange) to the nozzle at node 11. This is as follows: DX = +100 -150 = -50 mm DY = -300 + 500 = +200 mm DZ = +450 + 50 = 500 mm The basic nozzle information is input. The final thing to do for this nozzle is to apply the loads on this nozzle. We already have the loads in the CAESAR II job file that we have just analysed. So these loads can be imported straight into NEMA SM23 module. Click the Select Loads Job and Load Case button.

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Browse to the combined turbine model and select the operating case.

The loads will be imported from the job, these will be the loads at node 11 (as we specified the node number as 11).

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The inlet nozzle is now complete. Select to add a new nozzle and enter the Exhaust nozzle details. As before, import the loads from the OPE case in the combined job file.

Once complete, analyse the model using the “Running Man” icon.

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CAESAR II Statics Training Turbo Another tab will now be present showing the results of the analysis. The analysis fails.

The Inlet and Exhaust both fail the analysis. A closer look at the results shows that the FY and MZ moments are by far the leading causes of the failure. The FY is 214% of the allowable, while the MZ is also 182%.

Save and Close the NEMA module and return to the piping input.

Looking at the input, it can be seen that the weight of the piping causing the FY will also clearly result in the MZ moment being excessive – there is very little supporting the weight of the piping other than the nozzles themselves. The only other supports are on the headers. We need to support the weight of the pipe. Let us focus on the Exhaust first. Let us support the weight of the pipe to reduce the FY component. Locate a Y support below the elbow. This will be node 1039. We have not defined node 1039, only 1030 and 1040; so why 1039? When building the model, it is built in the following way:

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CAESAR II Statics Training Turbo Once a bend is inserted, CAESAR II moves node 1040 to the end of the bend, and inserts two intermediate nodes:

These intermediate nodes are added by default at 0° around the bend, and at the mid-point of the bend. This can be seen in the Bend auxiliary data (single click on the bend check box on element 1030 – 1040). M is used to designate the mid-point of the bend.

These nodes can be moved to the required location if needed for any reason by simply editing the angle. But we just wish to add a +Y support under the mid-point of the bend, at node 1039. Add a +Y at 1039.

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Re-run the analysis. Check the SUS and expansion stresses, these should again be OK. Now review the OPE case restraint summary to check if the load on node 1011 has reduced. The loads on node 1011 are the same. The loads on 1039 are 0. This restraint is not taking any load in the OPE case.

View the 3D plot to see the reason for this. View the deflected shape (you may need to increase the deflection scale). From a left view, it can be seen that the expansion is causing the pipe to lift off the support at node 1039.

The Operating/Displacements report confirms this, node 1039 is experiencing 0.614mm displacement upwards – lift off.

The load on node 1011 has not changed. As such there is no need to run another NEMA analysis – the results will be identical. Therefore, return to the input.

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CAESAR II Statics Training Turbo Change the design by replacing the Y restraint with a spring hanger. Select a Carpenter and Paterson spring hanger, and enter -500 in the Available Space field. The can will be shown as below.

Re-run the error check and visit the Load cases window. We have added spring hanger into our model, so we require` the hanger cases to determine the hanger size. Use the recommended load cases again and analyse.

As before, the SUS and EXP cases are well within the code allowables. Check the restraint summary for the OPE case.

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The spring hanger is taking some load now (4800N) and the load on the restraint at 1011 is much reduced. Return to the NEMA module and we will re-analyse with our new loads. Save As… on the existing NEMA file, and select Nozzle 2 of 2 – the exhaust. The Inlet has not changed so there is no need to re-import the inlet loads. Refresh the loads from the current job to import the new changed data.

Once done, rerun the analysis. The exhaust now passes at 79% of the allowable.

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CAESAR II Statics Training Turbo The Inlet of course still fails as we have not changed this. Now let us reduce the load on the inlet. To do this, break element 40-50 with a new node number 42. This node should be 300m from node 40. Locate a spring hanger at node 42. As before, select Carpenter & Paterson. Re-run the analysis and check the OPE restraint summary. The load on node 11 will be reduced.

Return to the NEMA module and Save As… this file. Re-import the loads for the inlet nozzle and rerun the NEMA analysis. The Inlet should now also pass.

The whole turbine passes

The piping system is acceptable in within the code allowables, and the loads on the turbine are also within the allowables of NEMA SM23.

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CAESAR II Statics Training Manifold

Manifold This exercise demonstrates multiple load cases can be used along with multiple operating conditions in order to evaluate various “what if” scenarios. In addition, the API 610 module is used to evaluate loads on pumps. Other features shown include naming nodes and naming load cases to make reviewing the results easier. The model below will also be on the hand-out. Notice that the three branch legs are virtually identical. The input should be setup to take advantage of this trait through the use of the element duplication facility.

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CAESAR II Statics Training Manifold Begin at node 10 and model all the way to the end anchor as shown. Note that the bend has not yet been specified at node 70.

Use the duplicate feature to create the remaining two legs for Pumps B and C. Increase the nodes by 1000 each time. You will not see the new elements initially, as they will be in the same location as run 10 to 70. Find elements 1060-1070 and change to 1060-90. Also do the same for 2060-2070 and change to 2060100 The elements will all now be connected. Finish by specifying the bend at node 70.

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CAESAR II Statics Training Manifold Now that the model is complete, we can enter the loading information. The hangers are to be designed with the entire system hot. Then, each branch line must in turn be run at ambient with the remainder of the system hot. These four conditions can be evaluated in a single run, using four different temperature and displacement vectors. First we will label the pump locations so that we can easier review these locations in the results. Select element 10-20 and double click the Name check box.

Specify that the from Node (node 10) is labelled as Pump A

Repeat this for Pumps B and C Next we wish to reduce the loads on the pumps by having the hanger support the riser weight. The hanger algorithm works by distributing the weight evenly among all supports. If we free the pump in the Y direction at node 10, this will ensure that the weight is not distributed at this point – and so is supported by the hanger. Do this by specifying the Hanger as follows:

Repeat this for Pumps B and C.

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CAESAR II Statics Training Manifold Now we need to specify the loading conditions, as mentioned before, we wish to evaluate the system in four conditions. We can do this by specifying four different temperature/pressure cases, and four different displacement vectors at the pumps. All pumps on Pump A idle Pump B idle Pump C idle

T1 T2 T3 T4

P1 P2 P3 P4

D1 D2 D3 D4

Enter the temperatures as follows. The element listing displays the value in red whenever it changes from the previous value.

Use the graphics to verify that the temperatures are correct. Note that the temperatures do not simply stop being 120°C and suddenly drop to ambient. The way we have entered the temperatures give a basic approximation of a temperature gradient.

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CAESAR II Statics Training Manifold T1 – All same temperature

T2 – Pump A idle

T3 – Pump B idle

T4 – Pump C idle

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CAESAR II Statics Training Manifold Perform a similar task with the pressure. Only this time the pressure will drop from 20 bars to 0 after the valve. It is at fill pressure right up to the valve, then it will drop. Enter the pressures as shown below:

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CAESAR II Statics Training Manifold Again the graphics can be used to verify the correct pressure has been specified P1 – All same pressure

P2 – Pump A idle

P3 – Pump B idle

P4 – Pump C idle

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CAESAR II Statics Training Manifold Finally we need to specify the pump nozzle displacement. The pump discharge nozzle vertical growth is 0.75mm, when the pump is running. Therefore we also need 4 displacements at each pump. Enter the displacements as in the table below. An example for Pump A is shown in the screenshot afterwards.

D1 D2 D3 D4

Pump A 0.75 0 0.75 0.75

Pump B 0.75 0.75 0 0.75

Pump C 0.75 0.75 0.75 0

The model is now complete. Run the error checker. You should receive 3 notes – two on the hanger design, plus the C of G report. Correct any errors or warnings you may receive. Access the Static Load cases. We require a number of load cases now – one each for SUS, OPE and EXP for each of our situations, i.e. 12 cases. Plus we require the hanger design cases. The hangers should be designed for the system when all pumps are hot. The recommended cases should satisfy these requirements.

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CAESAR II Statics Training Manifold As we have a number of load cases now, it is becoming a little confusing to work out each time which combination of loads is which case. To make this easier, we will rename the load cases. Access the Load Case Options tab and rename the load cases to reflect the situation.

Run the analysis The list of load cases will still be the CAESAR II Load Case name. To change this, go to Options > Load Case Name and select User Defined Loadcase Name instead

In addition, to make it easier to identify the pumps, choose to display the Node Name in the reports as well as the number. Again, this is accessible via Options menu > Node Name

Verify that the system is within the allowables for B31.3 in all situations, both EXP and SUS. Also check the OPE loads on the pump nozzle connection.

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CAESAR II Statics Training Manifold

API 610 Analysis The model is complete and satisfies the requirements of B31.3. We can now evaluate the pump nozzles to ensure that the nozzle connections satisfy the requirements of API 610 for the pump. A total of 12 API-610 evaluations must be made in order to find the worst case scenario. These scenarios are shown below: Pump A – All pumps on

Pump A – Pump A idle

Pump A - Pump B idle

Pump A - Pump C idle

Pump B – All pumps on

Pump B - Pump A idle

Pump B - Pump B idle

Pump B - Pump C idle

Pump C – All pumps on

Pump C - Pump A idle

Pump C - Pump B idle

Pump C - Pump C idle

Access the API-610 module from the CAESAR II main window and create a new file for the first iteration – Pump A with all pumps activated.

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Move to the Input Data tab to specify the data for the pump. Note the API coordinate system is different from the CAESAR II coordinate system, hence API My aligns with CAESAR II Mz. We are also only concerned with the Discharge nozzle; as such we do not need to enter any data into the Suction Nozzle tab or fields. We wish to evaluate the discharge nozzle. This is pump A, so the nozzle is node 10. Fill in the correct data for Node 10.

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Now we need to specify the loads on the discharge nozzle. As before, these loads can be imported from the analysis just done. Select Load Case 3 – Operating case for all pumps active.

Also, for the analysis, we will assume that the distance from the centreline to the nozzle is zero.

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All the data has been input, so the analysis can now be run.

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The results show that Pump A is OK for this condition. However, to determine the worst case, we must perform the other eleven evaluations. Repeat the above task for all the remaining pumps.

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CAESAR II Statics Training Manifold After completing all twelve iterations, you should notice that one of the iterations fails. This is Pump C with Leg B Idle.

From these results, it can be seen that the local Y moment is failing, and is 262% of the allowable. As mentioned previously, the API-610 coordinate system is different to the CAESAR II local coordinate system. The local MY translates to the MZ in CAESAR II. Return to the piping static output and review the results. View the restraint summary for all the Operating cases.

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CAESAR II Statics Training Manifold The MZ for Pump C in case 5 is the highest of any MZ moments – confirming the findings of the API 610 analysis. View the 3D plot and view the deflected shape for Operating case with Pump B idle.

The datum for the thermal expansion is the line stop at node 80. The expansion at the leg for pump C is the greatest, and so is causing the higher moment at this point. Similar to the exercise SUPT01, if we can adjust the datum for thermal expansion, we should be able to reduce the amount of expansion which is causing the moment on Pump C. This can be done by moving the line stop from node 80 to node 110. Remove the Z restraint at node 80 and add a new Z restraint at node 110, then re-run the analysis. Notice now that the restraint summary shows that Pump C has a much lower MZ now. The loads have been more evenly distributed (Pumps A and B have slightly greater loads, but these pumps were OK anyway).

Return to the API 610 module and open the file which failed previously -

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CAESAR II Statics Training Manifold Select the Discharge nozzle tab. The loads on this pump have changed, so we will have to import these new loads. Use the Refresh Loads from Current Job button to bring in the new loads and re-run the analysis.

This time the pump should pass – as we have reduced the loads sufficiently

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Tutor This exercise will develop various sequences of “run – evaluate – modify” workflow to determine the acceptability of the system. Each of the evaluations of the system will develop another aspect of CAESAR II. Once the system is acceptable, we will generate a custom report and stress isometrics.

System parameters Pipe: 8” diameter, standard wall, ASTM A-53 Gr. B Analysis temperature: 315°C Analysis pressure: 2 bar Corrosion allowance: 0.8 mm Insulation: 75 mm CaSi Fluid: 0.8SG Pipe Specification: 150 pound class components Design Code: B31.3

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CAESAR II Statics Training Tutor Node 10 is connected to a Pump and node 110 is connected to a vessel Nozzle. Their details are as follows: Pump Details: 10 inch end suction, 8 inch top discharge Suction is -380 mm in X from pump centre Discharge is 500 mm above and 300 mm in Z from pump centre Piping load on suction nozzle given as: (4450,-3550,-5340) N and (-4070,-3390,2170) N-m Nozzle Details: Fixed end is preceded by a long weld neck flange in the -Z direction: OD=247.65, wt=22.225, length=300 mm, weight=458 N and a standard, 8 inch weld neck flange and gasket

Model the system as shown in the isometric. When modelling the bypass loop, the Close Loop command can be used if required to connect node 150 to 60. Change the node numbers to 150 and 60 and click the close loop button. CAESAR II will add in an element of the required length automatically.

The completed model will look as the one below.

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CAESAR II Statics Training Tutor Boundary Conditions We now need to specify the boundary conditions for the analysis. The piping is connected to a pump and a vessel at the termination points, so we can apply the effects of these to the relevant nodes. Pump Connection – Node 10 The discharge is 500mm above (Y) and 300mm in Z from pump centre We have two options for the approach here. 1.

Calculate the thermal growth of discharge nozzle from pump base point. Alpha= 0.003832 mm/mm Displacements therefore: X=0 Y = 500 x 0.003832 = 1.916 mm Z = 300 x 0.003832 = 1.1496 mm No rotational displacements

2. Add a construction element between the nozzle node (10) and the pump base with appropriate material and temperature. For this exercise, specify the displacement set for node 10 as above.

Vessel Connection – Node 110 As before we have the same two approaches; provide the thermal growth of the nozzle, or model the vessel. The thermal growth of the vessel is X=0 Y = 8.43 Z = -2.87 RX = 0 RY = 0 RZ = 0

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CAESAR II Statics Training Tutor Support Riser We wish to unload the pump discharge nozzle as much as possible, and also support the thermal growth of the riser. To do this we will locate a spring hanger near the elbow (node 70). Place a Carpenter & Paterson hanger at node 70

Support Horizontal Runs The suggested maximum support spacing for 8” water filled pipe is 5.8m for horizontal straight runs. 75% of that spacing for horizontal spans including changes in direction would therefore be 4.35m. This will support the pipe weight and so account for the SUS case. Since we will check these SUStained stresses (and since the fluid weight is less than water-filled) we can exceed the suggested spacing. Locate a restraint on each horizontal 8” run using the Break function. 70-80 add node 75, located 1200mm before node 80 80-90 add node 85, located 3000mm after node 80 Add the following restraints: Node 75 1x (double acting) Y restraint, with a friction coefficient of 0.3 1x guide with a gap of 8mm, again with friction

Node 85 1x (double acting) Y restraint, with a friction coefficient of 0.3

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CAESAR II Statics Training Tutor The model is now complete. Error Check the model and run the Recommended load cases. Immediately it can be seen that there is an issue with the EXP case. Check the stresses for both the EXP and SUS cases. The SUS case is OK

The EXP case however is an issue:

The only issue is at node 30, where the stress is 130% of the allowable.

Node 30 is the Tee connecting the bypass. One of the easiest fixes for an overstressed component is to replace it with a stronger component. Component strength is indicated by the stress intensification factor (SIF). Here, the stub-in branches are overstressed. Their in-plane SIF is 3.96 and their out-plane SIF is 4.95. Adding a pad to these tees will strengthen them. Check the effect of adding a pad by using the Tee SIF Scratchpad. Change the unreinforced tee to a reinforced tee with a 9mm pad. Using the Recalculate button will show that the SIFs have been reduced to 2.04 and 2.38 for in-plane and out-plane respectively.

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Accept these changes and apply to node 30. Re-run the analysis and review the results. The expansion case is now ~75% rather than 130%.

The SUS case is still 14%. Hanger Sizing Review the Hanger table with text. A Carpenter & Paterson DV70 spring is selected.

Hot Load 1355N, deflection 17mmm cold load 1544N. We need to now see if this is appropriate. View the Restraint summary for the OPErating and installed (SUS) cases.

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Look at the operating load and installed load on the pump discharge nozzle (node 10). Typically, with a spring hanger above the pump, the pump will see a positive (up) load in the cold state and a negative (down) load in the hot state. Here, the piping pushes down on the pump in both states. This spring is undersized. Why? The calculated load carried by the spring is based on the overall distribution of weight between all vertical supports. The interaction of the pump nozzle (anchor), the spring and the other Y supports has very little load “assigned” to the hanger location. More weight is carried by the pump rather than the spring hanger. Deadweight that is resting on the pump must now be transferred to the hanger. The easy way to do this is to remove the load-carrying capability of the pump in the initial weight analysis when the hanger load is first calculated. To do this, CAESAR II allows the restraint to be “freed” – effectively removing this node from the hanger sizing calculation, so the load is distributed amongst the remaining support locations. Return to the input and on the hanger; free the restraint at node 10 in the Y axis:

Now reanalyse the system. Review the results again.

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CAESAR II Statics Training Tutor The EXPansion stress results are unaffected by this hanger change. The maximum SUS stress ratio is also still around 14%. Review the hanger table with text.

A Carpenter & Paterson DV70 has been selected again, but the hot load has increased to 7000N and the installed load has increased to 8000N. Review the restraint summary report to view the pump load (node 10).

The resized spring now pulls up on the pump in the cold position and unloads as the system heats up. (The riser growth drops the load supplied by the spring.) This spring is much better than in the first iteration; however it could be improved even more. The hanger data input provides for the specification of the hanger operating (hot) load:

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CAESAR II Statics Training Tutor Pump Load Review the restraint summary report for the OPE and SUS (installed) cases. The loads shown for the pump are a little high in some directions – MX is almost 30000N. However no indication is given that these loads are excessive.

American Petroleum Institute Standard 610 (API 610) sets maximum nozzle loads for pedestal supported pumps. CAESAR II provides this calculation. Run this analysis with the pump data provided above and using the discharge loads from this analysis. Since both suction and discharge nozzles are evaluated together, the Table 4 limits in API 610 can be doubled (see API 610 Annex F).

API 610 Analysis Access the API 610 module from the Analysis menu on the main window.

Create a new file and input the pump data. The pump centreline can be seen to be in along the X axis, therefore the angle between X axis and pump Centreline is 0°. The angle between the Z axis and the pump centreline is 90°. The direction cosines are therefore X Cosine = cos 0 = 1 Z Cosine = cos 90 = 0 The Base point node number can be any arbitrary node number. This node number does not have to appear in any of the piping model, but is used by API 610 as a point of reference about which to sum moments. The suction Nozzle is not defined in the piping model as we are given the loads so can input these. We also know that this is a 10” End type suction nozzle. The discharge nozzle is in our piping model, and is node 10. This is an 8” Top type suction nozzle. As mentioned, since both suction and discharge nozzles are evaluated together, the Table 4 limits in API 610 can be doubled.

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The suction nozzle loads and location have already been given: Suction is -380 mm in X from pump centre. Piping load on suction nozzle given as: (4450,-3550,-5340) N and (-4070,-3390,2170) N-m

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CAESAR II Statics Training Tutor The pump discharge nozzle is located 500 mm above (Y) and 300 mm in Z from pump centre. The loads on the discharge nozzle can be imported from the piping model. This will be the OPE case.

Now analyse the pump. The suction nozzle passes OK. But the discharge nozzle fails.

The load in the local Y direction (global Z) is excessive as are all three moment terms. The worst component is the local My (global Mz) which is almost 10 times the Table 4 limit.

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Fix Model – Part 1 We need to know what is causing this large load. Return to the piping model and again view the results. Review the Restraint summary for the OPE and SUS (installed) cases.

The large loads are present in operation but not at “installation”. Therefore these excessive loads are caused by the thermal expansion of the system. To reduce these loads we need to increase system flexibility. There are two options to do this. 1. 2.

Model existing flexibility not currently in the model Modifying the piping and/or support layout.

The most inexpensive modification would be to provide more modelling detail – modelling flexibility in the system that is not currently included. Welding Research Council Bulleting 297 provides flexibilities for cylinder – cylinder intersections. These flexibilities may be applicable to the vessel connection at node 110. Include WRC 297 flexibilities The vessel nozzle/connection is as follows:

Vertical vessel constructed of SA-516 Gr. 70 OD = 1500mm (D), wall = 4.75mm (T) Nozzle is 2200mm above skirt Skirt is 3000mm above foundation The long weld neck flange serves as the nozzle OD=247.65mm (d), wall=22.225mm (t) Nozzle pad is 4.75mm thick and 100mm wide A tray is within 600 mm of the nozzle and a stiffener ring is 1000 mm on the other side Firstly we must evaluate the vessel/nozzle to check that the WRC 297 approach is valid. We have d and t (relating to the nozzle) and D and T (relating to the vessel) described as above. Below, T is the vessel thickness plus the pad thickness. According to WRC 297: ⁄ ⁄ ⁄

⁄

⁄

⁄

We will use this data even though it is outside the acceptable range Apply the nozzle flexibility and complete the vessel/nozzle data in the Nozzles input.

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The nozzle node is at 110 (recall that the nozzle is represented by the long weld neck). A valid nozzle node has only a single element connecting to it (i.e. must have a free end) and also a nozzle node is not restrained nor does it have any displacements specified. We have displacements applied at node 110, for the vessel thermal growth. To rectify this we will specify a vessel node and apply the displacements to the vessel node. The vessel node is optional and works in a similar way to CNode described earlier. Give the vessel node a unique number. In this case ours will be 1500. In addition, change the node the displacements are acting on to 1500 as well. Fill in the remaining vessel data, including the direction cosine – the vessel is vertical (Y) so the Y direction cosine is 1.

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CAESAR II Statics Training Tutor This models the nozzle flexibility by inserting a zero length spring which is inserted between the long weld neck flange (100-110) and the displacements representing the vessel thermal growth – which we have now reassigned to node 1500. Run the error checker. The WRC nozzle flexibilities will be calculated and included in the notes.

The nozzle provides limited axial flexibility, but the longitudinal and circumferential bending flexibilities appear significant. Re-analyse the system and again review the results. Review Results These changes have not had any effect on the SUS case, and the EXP case is still below the allowable, in fact the highest stress has now dropped slightly - as we have added more flexibility in the model. The selected spring hanger is still a Carpenter & Paterson DV70, but the hot load has increased by around 40N. However, we were previously concerned with the pump loads. Review the OPE case restraint summary. The loads on the pump (node 10) have now decreased.

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CAESAR II Statics Training Tutor Run these new loads through the API 610 processor. Use the “Refresh Loads from Current Job” button to bring in the new loads.

The values have decreased slightly, but still the discharge nozzle fails.

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Fix Model – Part 2 Return to the piping results and review the OPE restraint summary once again. There is a rather large load on the guide (Z restraint) at node 75.

The thermal growth of the long Z run from 80-90 loads the guide and pushes the elbow at node 70 in the positive Z direction. This thermal growth increases both the pump load in Z and the bending moment about X. Is the structure guiding the pipe as rigid as the CAESAR II model says it is? If the guide has lower stiffness, the pump loads may reduce within their allowed limits. There may be reason, then, to model the structural steel that is interacting with this piping system. There are two structures – a frame under Node 75 and a T pole under Node 85. These structures will be included in the analysis.

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CAESAR II Statics Training Tutor Build Steel Structure CAESAR II includes a structural modeller. This module can be used as just described, to model steel structures to support the piping in order to include the flexibility in the supports, as opposed to fully rigid supports. Return to the CAESAR II main window and create a new file. Specify this as structural input.

The structural wizard will guide you through the process of setting up the structural file. First the units to be used must be specified. Ensure that the Training units (TRAIN.FIL) are selected here. Click Next

On next screen, the vertical axis should be selected for the model, either the Y or Z axis can be set to vertical. Select the Y axis as vertical and click Next

The following screen is to specify the material and material properties. Any number of materials can be specified, each identified by a Material ID. For each material ID the material properties can be specified. Within the steel modeller, each steel member is assigned a material ID. Accept the defaults for material ID number one and click Next. (The units are those from the specified *.FIL from the first step).

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The following screen is to specify the steel members to be used in the structural model. Each steel member is identified by a section ID and can be either selected from an included database of sections, or can be User defined.

In the structural modeller, each element can be assigned a section ID as well as a material ID. We will use I-Beams in our model and will select from the built in database. Choose the Select Section ID button and select the following I-Beams Section ID 1: Section ID 2:

W8 x 31 W6 x 20

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The final stage of the structural modeller wizard is to specify the method of element definition. There are two options for this. Method One - “EDIM” method, which is similar in concept to how piping elements are defined – a start node and an end node are specified, along with the distance between the two to define the structural elements. Method Two – Node/Element method is a slightly different concept. Nodes are added and are located at points in 3D space. Elements are then defined and users specify the nodes which each element connects. Select Method one and click Finish.

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CAESAR II Statics Training Tutor The steel modeller will now appear with the options selected in the wizard added to the “Card Stack”. The Card Stack is a logical list view of the structural model where all parameters are listed and can be edited.

Now we will define the structure. As we have used the wizard to define the material and section IDs, the next items we can define are the elements themselves. Use the EDim button to add a new entry to the card stack.

From the sketch we can see that starting at node 2000, there are two vertical steel members, both 2500mm in length. These two members can actually be defined in one entry into the card stack as they are identical. Expand the new row in the Card Stack and first enter the From and To node numbers as 2000 and 2010. Also enter dy as 2500. Specify the section ID and Material ID for this section also. Section ID is 1 and Material ID, as there is only 1 is 1. We now have one element, from Node 2000 to 2010, 2500mm in length in the vertical (+Y) direction. The inc, incTo and last fields can be used to duplicate this element quickly without adding a new entry into the card stack. The inc field will increment the “From” node, starting with the original “From” node. i.e. if we enter 10, the “From” node on the second element will be 2000 +10 = 2010. So in this case would connect to the first element. The incTo is the same concept, but using the “To” node. The last field is simply the “to” node on the last element to be defined. Enter inc and incTo as 10 and the last “To” node will be 2020.

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Continue and add a second Edim to the card stack. Define element 2010 – 2012. This time the section ID 2 will be used.

The model so far should look like the following

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CAESAR II Statics Training Tutor Continue with 2002 – 2012. Again, this entry in the card stack will define multiple elements

Add the finial members on the top. As these are not identical, they must be defined as separate entries in the card stack.

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CAESAR II Statics Training Tutor The final step is to anchor the steel at the base. Use the Fix icon to add a “Fix” entry into the Card Stack, and fix at node 2000 and 2002. Fix in all degrees of freedom.

The completed frame should look like the following.

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CAESAR II Statics Training Tutor Save the frame. On saving the structural modeller will check the file. The following dialogue will appear. Ensure that all three check boxes are checked.

Now create a new structural file for the T-post. As before, follow the new structural file wizard. The T Pole is similar to the Frame in that it is the same material and the same two steel sections used – W8 x 31 and W6 x 20. After completing the wizard, the Card Stack should again display as before with the same starting entries.

The first thing to note about the T Pole is that it is rotated 90°. Add in a rotation angle of 90°

Continue and add in the elements

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The remaining horizontal elements will not be rotated 90°, so add in another Angle and set this to 0

The remaining horizontal elements will also all be Section ID 2. To save having to specify Section ID 2 for all elements, a default Section ID can be set.

Set this default section ID to 2.

Continue and add the remaining elements as follows From 1005 1005 1015

To 1010 1015 1020

DX -600 300 300

Finish off by fixing node 1000.

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CAESAR II Statics Training Tutor The completed T Pole should look like the following

Save the T Pole and again ensure that all three check boxes are checked.

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CAESAR II Statics Training Tutor Combine Pipe and Steel models Return to the piping input. We will now include the Steel models in the Pipe model. Select the “Include Structural Files” button and browse to locate the two files just created.

After Clicking OK the steel members will be included in the pipe file, however as there are no common node points between the pipe and steel, the structural members are simply located at the origin. We now need to move these structural files into the correct location. A quick review of the pipe and steel model node numbers shows that pipe node number 75 will be connected to steel node number 2021 and pipe node 85 will be connected to steel node 1015. However the centrelines of the steel and pipe are not in contact, rather the bottom of the pipe is resting on the top of the structure. The pipe and steel can be connected either way; connecting the bottom of pipe with top of steel will be a more visually pleasing model, and in some cases (e.g. where friction or a guide is included on larger diameter pipe) the proper contact point will affect the results. A dummy rigid element will be built at both support points to offset the pipe above the steel. First locate element 70-75. INSERT a new element AFTER this element. The new element will be from 75 to 1075 and the distance between these nodes will be -210 mm in Y. Make this a weightless, rigid element.

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Now return to the element 70-75 and redefine the restraint at node 75 by changing the Node to 1075 and define a CNode (connecting node) of 2021. Now that the pipe to 1075 is in Y, the Guide must be replaced with a Z restraint (a Guide makes both X & Z on a Y pipe). Be sure to do this for all restraints at this point.

The frame will now be moved to connect to node 1075.

Repeat this procedure for the restraint at 85, creating a new element 85-1085 and connecting 1085 to 1015.

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The completed model will show the steel structures supporting the pipe as below.

Re Analyse the system.

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CAESAR II Statics Training Tutor Review Results The SUS case has increased very slightly, but the EXP case has dropped down to 38%. This is because further flexibility has been added to the system. Specifically the stiffness at node 75 which was a rigid guide now matches the frame stiffness. The OPE displacements report shows that the 8mm gap on the Guide (now the Z restraint) is closed, but then the guide itself shifts another 8mm in the Z direction, rather than being stationary as a rigid. Note the displacements on nodes 1075 and 2021.

The restraint summary for the OPE case shows a significant reduction on the operating loads on the pump nozzle.

As before, run these new loads through the API 610 processor (use Refresh Loads button to bring in the new loads). The discharge nozzle now shows that only the moment about the Y axis (global Z) exceeds the allowable limit.

Adding the steel effectively increased the guide’s gap. This greatly reduced the pivot action and the resulting pump load.

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Fix Model – Part 3 The only issue with the model now is that the local Y moment, global Z moment on the pump discharge nozzle (node 10) is excessive. Without changing the position of the pump or vessel nozzle, or changing the thermal strain, the only way to reduce these loads is to add flexibility to the layout. There is no inherent flexibility that was excluded from the model so an expansion loop will be introduced. How big a loop is required and where should it be placed? Expansion loop legs should be perpendicular to the thermal growth causing the load. We will focus on the Z axis bending moment. This bending moment is being caused by the +X force – the thermal growth in the X direction (element 70-75).

Therefore the loop can be added in the Y or Z direction (perpendicular to X). Which is the best loop layout?

Layout A - A loop in the Z direction at the end of the X run (node 80)

Layout B – A loop in the Y direction at the end of the X run (node 80)

Layout C – A Y loop on the opposite end of the X run (node 70)

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⁄ ∑

The bending stress at the nozzle is estimated using

= stress range in leg j (leg j is orthogonal to the direction of thermal growth to be absorbed) = Length of leg j = length of leg i (leg i represents each leg helping to absorb the thermal growth) We know that

∑ So let 6EIΔ = K Therefore solving for K using the current M (MZ Bending moment which is 5139 Nm) and Li and Lj Lj = 4200mm Li = L1 6205mm & L2 4200mm

∑ (∑

)

Keeping K as a constant, we can attempt to reduce M. To do this we will increase the length of the leg in the three layouts mentioned previously and recalculate M The following table and graph summarises this. Added Loop Leg (m)

In Z (Layout A) 0 1 2 3 4 5

5.153 3.591 2.542 1.831 1.343 1.004

In Y (Layout B) 5.153 5.120 4.902 4.395 3.657 2.865

Riser (Layout C) 5.153 5.248 4.907 4.326 3.686 3.092

Max Mz (= 2 * Table 4) 3.525 3.525 3.525 3.525 3.525 3.525

Red = above max Mz Green = below Max Mz

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Effect of Various Loops on Pump Moment - Mz

Moment (KN-m)

6

Riser (Layout C)

4

In Y (Layout B) In Z (Layout A)

2

Max Mz (= 2 * Table 4)

0

0

1

2

3

4

5

Added Loop Leg (m) As can be seen, the most effective way of reducing the MZ moment is to use layout A – an expansion loop along the Z axis. This increases Li which is cubed in the equation so will have a much larger effect of the MZ Moment.

According to the calculation, slightly over 1m run in the Z direction is required, however this simple equation does not take into account any rigid elements or elbows, nor does it consider any intermediate supports such as the guide at node 75. We could insert a loop of 1m in length and continue iterating the model until we find a suitable loop length. However this can take time and finding an efficient loop design may involve several iterations, even on a simple setup such as this. CAESAR II provides a Loop Optimisation Wizard to automatically size and create an expansion loop to get the most efficient loop for the target data.

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CAESAR II Statics Training Tutor Loop Optimisation Wizard Return to the model and use File > Save As… to create a new iteration of the model with an expansion loop. After performing the Save As… the analysis must be run once again because the Loop Optimisation Wizard uses existing results in modifying the layout. Run the analysis and return immediately back to the input. The Loop Optimisation Wizard button will now be available (if this button is ever greyed out then there are no results available for use – rerun the analysis). Select element 75-80 as this is where the loop will be placed and click the Optimisation Wizard button to access the wizard.

The Loop Design Wizard will appear and the data required can be input in order for CAESAR II can design the expansion loop. The wizard will create iterations of a loop setup in order to focus in on a specific Stress value or Restraint load. We wish to reduce the Restraint Load on node 10 to below the allowable for API 610 table 4. We will reduce the load to 3300Nm (currently the load is around 5150Nm). The loop will be located on what is currently the element 75 – 80. This will therefore be as in Loop Layout A. The final thing to define is the space allowed for locating the loop. A cube of space can be defined which the loop will fit inside. The Wizard will create the largest loop possible in the available space, and if this is below the specified target load, the wizard will continue iterating to create the most efficient loop possible, as close as possible to the target value. In the Loop Design Wizard, select the OPErating Load Case and choose the target data to be Restraint Load.

As we already have element 75-80 selected, this element will be selected anyway. The table will be filled in with the results data. Double Click in the MZ cell on the Node 10 row. This will fill in the Node and Type fields. Enter 3300 as the data in the Load field.

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Specify the Loop Type as the centre loop type – this matches the type A that we have already determined is the most efficient. The final option in the loop type section will allow the wizard to evaluate all of the Loop Types and determine the most efficient. This takes longer as 8 loop types are defined. Also in the loop type section, change the Height to Width ratio to to allow the height to vary as needed.

Finally the space available for the loop must be specified. Click the Draw Cube button. A cube of space will be shown in the model. Currently this will be facing the wrong way. Click and Drag the point labelled PT3 to reposition the cube in the correct orientation. On doing this the “Major Direction” field will change to –Z. Increase the size of the cube in the –Z direction to ensure that there is enough room to design the loop.

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Once finished, click Design. The wizard will run through a number of iterations and converge on the defined target value.

Once complete the loop will be added into the model automatically. A confirmation message of the total length of pipe and number of bends is displayed

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CAESAR II Statics Training Tutor The loop wizard has added an additional ~3070mm of pipe. Split between the two legs to the loop, each leg is now ~1535mm longer. Our quick hand calculation indicated a length of just over 1m, but as noted previously this did not take into account rigid elements or elbows, nor does it consider any intermediate supports such as the guide at node 75. In addition, we used a target value slightly lower than the Max Mz as in the hand calculation. For simplicity, round up the length of each of the two new legs to 1600mm. With even more flexibility, the MZ moment at node 10 will be lower still. Re-run the analysis.

Code Checks: SUS –Max stress is now 16% at node 68. Node 68 is the top of the riser. Recall how CAESAR II adds intermediate node points around the bends as discussed in the TURBO example. EXP – Max stress is 34% located at node 78. This node is the far end of the elbow at the start of the long Z run Hanger Sizing: Carpenter & Paterson DV70 size 11 hanger is still selected. The hot load has decreased slightly.

Pump Load: The loads on Node 10 look much better now:

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CAESAR II Statics Training Tutor Re-run these loads through the API-610 processor once again

This time all loads pass on the discharge nozzle. The local My (global Mz) is now 1.85 times the allowable (we have used the 2x table 4 approach) and so now passes.

We have reduced the load on the pump by adding flexibility into the system in the form of an expansion loop. The addition of this loop required an extra 1.6metres of space. What if this space was not available?

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Fix Model – Part 4 We will now return to the model without the expansion loop and once again attempt to reduce the load on node 10, this time assuming that there is no space available for addition of an expansion loop. In this case we will add in an expansion joint instead to add in flexibility. Open TUTOR.c2 (the file before the expansion loop was added) and save as Tutor_Expansion_Joint_Check.c2 We already know that the issue with the pump is the Mz moment. This moment as we have seen is caused by the thermal growth of 70-75. This horizontal displacement at node 70 causes the bending moment.

As such we wish to prevent this horizontal growth from being applied to node 10. We will include an expansion joint to absorb this horizontal growth. Adding the expansion joint just above the pump will best absorb this growth. What type of joint should be used? As we are only trying to absorb movement by lateral deflection only and there is no axial deflection or relative bending rotations at the joint ends, a tied expansion joint will be suitable. First of all we need to know the horizontal deflection that we have to absorb. We will use CAESAR II to determine this by breaking the system above the pump and viewing the displacements report. The value we obtain from this can be used to select the number of convolutions in the expansion joint. Select node 20 to 10 and change to 21 to 30

The system will now have two sub-systems sharing the same origin. We need to reconnect 20 and 21.

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CAESAR II Statics Training Tutor Add a Y restraint at node 20 and specify node 21 as a CNode.

We also need to prevent any rotation at this point as well. Specify three rotation restraints (RX., RY, RZ) at node 21, CNode 20

Leave the transverse directions X & Z free to move. The system near the pump connection should now look like the following:

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CAESAR II Statics Training Tutor Using the EXP case Displacements report, we need to calculate the change in position between Node 20 and Node 21. Nodes 20 and 21 will move together in Y, RX, RY, RZ because of the Node/CNode restraint definitions.

DX = 33.4mm DZ = 11.446 – 1.150 = 10.3mm This results in a relative horizontal displacement of 35mm. This also shows a Mz moment of 4900Nm. This is quite a high load – as the system is completely free to move in the X and Z direction, resulting in the largest displacement. If we were to introduce some stiffness (as would be in the expansion joint itself) this displacement would decrease. Using the Senior Flexonics/Pathway expansion Joint catalogue, we will select a 3.5kg/cm2 class 150, 8” expansion joint. The catalogue shows a 20 convolution expansion joint provides 38.8mm lateral deflection. This satisfies our requirement. However this expansion joint also adds a lateral stiffness of 6kg/mm or 58.7N/mm. If we introduce this stiffness, the deflection would reduce. Reduced deflection drops the required number of convolutions and, in turn, increases the stiffness between nodes 20 and 21. This iterative process can continue until the deflection test fails or the pump load becomes too high. Add the final two restraints (X and Z) between 20 and 21. Set stiffness to 58.7 N/mm

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CAESAR II Statics Training Tutor Re running the analysis and viewing the EXP case displacements shows the new relative lateral displacement of around 21mm. The OPE restraint loads show that the MZ has now decreased drastically and is now around 25% of the previous value.

However, the MY is excessive at over 6000Nm. This moment will also place torsion on the expansion joint and this torsion may also be excessive. If this observation did not stop the iteration, how would this process proceed? • Test 16 convolutions - 16 convolutions allow 24.8 mm lateral deflection and has K = 118 N/mm • Reset X and Z restraint stiffness to 118 and reanalyse • Check travel limits for the proposed joint and the load limits for the pump. If 16 convolutions is OK and overall joint lateral translation drops, test a shorter (i.e., fewer convolutions) joint. In conclusion, because of the large global My on the pump and the torque on the expansion joint, the proposed length and location of this joint should be reconsidered. For the purposes of this exercise, analysis of a 20 convolution, tied expansion joint will be evaluated. For this length, a tied universal joint would probably be preferred; consult manufacturer for other options.

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CAESAR II Statics Training Tutor Model the Expansion Joint Assembly The flanged expansion joint would be located between the discharge nozzle and the existing weld neck flange. To save time in this examination, the expansion joint will be placed between the flange and pipe rather than between the nozzle and flange. The error introduced will be small. Return to Tutor.c2 and rename as Tutor with Expansion Joint.c2 Select Element 20-30 and access the Expansion Joint Modeller.

Select to create an expansion joint with the following properties: Pressure Style Convolution Material # Convolutions End Type

50 pound Tied 304SS 20 Slip on (Both Ends)

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CAESAR II Statics Training Tutor After clicking OK, CAESAR II will split the selected element to fit in the expansion joint. Which end of the element to place the joint must be specified. We will split at the From end (Node 20).

The temperature of the element in question is 315°C. Apply this temperature to the joint, which will subsequently cause the stiffness to be adjusted.

The expansion joint modeller will finally confirm the creation of all the elements to be used in creation of the joint. The stiffnesses will also be displayed, along with the Allowed Movement.

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Click build and CAESAR II will attempt to define the expansion joint using the data supplied/obtained from the catalogue.

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Re analyse the system. Using the Expansion Case displacements, calculate the lateral deflection between nodes 21 and 22 – the nodes on either end of the expansion joint. DX = 20mm; DZ = approx. 12mm. The overall deflection is therefore around 23mm. The Flexonics catalogue shows that this displacement is acceptable for a 20 convolution joint. There is minimal Axial deflection (DY = approx. 0.3mm) and Angular Rotation (RX and RZ = 0mm). Torsion in the joint is 0.3 degrees. The catalogue actually shows that this torsion is excessive.

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Document the Analysis The analysis is now complete, and the model is acceptable. We will work with the model including the expansion loop, rather than the expansion joint. The stresses are all acceptable and well below the code allowables. The loads on the pump are also all acceptable and below the allowables for API 610. We can now document the analysis and produce a report which could be supplied to a client, including a plot of the system and annotated stress isometrics. Custom Reports In addition to these, custom reports can also be created.

Custom reports are created using the Report template editor.

In the report template editor, a new report can be created by adding in all the columns you require. Any column from any report section can be selected. The following sections are available. The individual columns from these reports can be added in any order as required.

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CAESAR II Statics Training Tutor In addition to setting the column order, various other properties on each individual column can be set. These properties are as follows:

As well as properties for each individual column, report wide settings can also be set.

The template can be either an individual report (one load case per report) or a summary report (multiple load cases per report). Or a Code Compliance report (detailed information on calculated values vs allowable) or a Nozzle check report (Displays nozzle loads if present).

We wish to create a custom report which shows the stresses in the EXP case and the SUS case similar to the “Stresses” report. View this report for the EXP and SUS cases. The issue here is that two reports are created, one for each case.

But we wish to view both cases in one report. This therefore would need to be a “Summary” report. View the stress summary report for both of these cases. This report displays the max stress for each case in one report, but does not display the stresses at each node, like in the stresses report. We need a summary report which shows data at each node.

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CAESAR II Statics Training Tutor Create this as a custom report. So that we can view sample data in the report, select the load cases as well before accessing the report template editor.

First of all give the report a title “Stress Summary with Detail”. The report template preview will update to show this. Also change the Report Type to Summary.

The report itself we wish to be shown in a nicer to read font that Courier. Select Calibri, 11pt text and align the column text to the centre of the column to ensure everything stays inline.

Now we can add the following columns into the report, in the following order: 1. Bending Stress 2. Torsion Stress 3. SIF in Plane 4. SIF Out Plane 5. Code Stress 6. Allowable Stress 7. Ratio % 8. Piping Code Enter in the column number next to each column required. Also tick the Show Piping Code check box.

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The report preview should show a sample of the report.

Currently there is no summary table like in the Stress Summary report showing the max stresses. Insert this into the report as well by checking the Show Highest Stresses check box.

Save the complete report. Any custom reports created can be exported and then imported on any machine so that all users have access to all reports.

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CAESAR II Statics Training Tutor Filters We have created a new customised report to show the data we are interested in. View this report for both the SUS and EXP load cases. The report will look as we expected and show all the data we require. However there is a lot of data as we have all the stresses at all nodes, in two load cases. Reviewing the data shows that a number of nodes have very low or even zero stress. We can filter this data out to display only stresses above a certain value. Admittedly, our stresses are quite low throughout (highest is only 33.5%), but we still are not concerned with stresses that are only a fraction of a per cent for example. As such we will filter the data so that any stresses 1000N was applied as a filter, this would not be applied to for example the displacements report – FY is not displayed in the Displacements report. Create a filter to display, as mentioned previously, all stresses greater than 5%.

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Click Apply and now review the Stress Summary With Detail custom report for the SUS and EXP cases. The report will not show every single element now, only those which have stresses higher than 5%. Generate Report As we have seen, there are many reports produced by the CAESAR II analysis. All these reports can be viewed on screen as we have been doing, or alternatively each report can be sent to Microsoft Word or Excel, or a text file. We can produce a full report document of the type which could be submitted along with the analysis for approval. For our report we wish to include the following information.

Input Echo Load Case Report SUStained Stresses EXPansion Stresses OPE & SUS restraint loads OPE displacements at all nodes Hanger Table with text

This is a simple procedure and is simply a matter of selecting the reports to publish which contain the data we require and including them in the “Output Viewer Wizard” section of the output processor.

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CAESAR II Statics Training Tutor Review each of the reports mentioned above in turn to verify that the data is suitable. Start with the Input Echo.

The listing options window appears prior to the report being generated, where all input data can be selected for inclusion in the input echo By default CAESAR II picks the most relevant data depending on the model input – i.e. if WRC nozzle flexibilities are included, this is ticked, if there were no WRC 297 nozzle flexibilities, tis box would be un-ticked by default.

Select these defaults and click OK. Review the Input echo to ensure that all data required is included. Once happy with the contents of the input echo, close the report and click on the Add button to add into the Output Viewer list.

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CAESAR II Statics Training Tutor Repeat this process for each of the reports shown, including for the SUS and EXP stresses; add in the custom Stress Summary with Detail report. Once complete all reports we wish to publish will be in the list. We will now send these to MS Word. Ensure that the Send to MS Word radio button is selected and click Finish.

Word will load in the background and CAESAR II will publish all the selected data. The results will be inserted as tables into the Word document.

Once complete, review the Word document. Formatting can be applied as usual within Word.

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CAESAR II Statics Training Tutor ISOGEN Stress Isometrics In addition to the Word Document report, stress isometrics can be generated and annotated with input/output data to supplement the report. Stress isometrics can be configured so that the output appears as the user requires, if you have company/client standards for isometric drawings, these can be set up and configured using the ISOGEN I-Configure module supplied with CAESAR II. We will set up I-Configure to use one of the default styles. There are many switches which are available to control the appearance and content of the isometrics. These switches are not covered in this course. However, a number of Wizards are available for configuring common parameters. I-Configure can be accessed from the CAESAR II main window, from the Tools menu.

The I-Configure window will currently be empty, as no styles will be set up.

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CAESAR II Statics Training Tutor Most of the buttons on the toolbar along the top will be greyed out.

There will however be two buttons available; the first of which we are concerned with, in that this button will be used to create a new Isometric directory. (The second button is simply to connect to an existing isometric directory). ISOGEN uses a specific file/folder structure, at the top is the isometric directory. Contained within the isometric directory is a number of Project directories. Each isometric directory can contain multiple project directories. Contained with a project directory can be many style directories. As above, each project directory can contain multiple Style directories. Within each style directory are a number of files, each of which contain various different data for the appearance and content of the isometric output (including the format of the output - *.DWG, *.DXF etc). These files are created by I-Configure. I-Configure reads an XML file on selecting the current style containing all the settings and then writes these settings to various files which ISOGEN reads when producing an output. Choose to create a new Isometric Directory.

We will create a new folder on the E:\ drive in which all the ISOGEN data will be located. Browse to E:\ and create a new folder called ISOGEN and set this as the Isometric directory. An additional button is now available which allows us to create the project directory.

Within each project directory there must also be at least one style, so the template styles are available to choose from. Name the project TRNProject (spaces are not allowed) and select the Final Basic Style as the only style to produce (Un-tick all other styles). Change the Name column to Stress-Iso as well.

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Before we produce isometrics, let’s check the output to see what an example isometric would look like. Before any style created in I-Configure can be used, it must be exported for use (as discussed above). Select the Stress-Iso style and click Export Style.

Next we can process a sample file through ISOGEN to get a preview of what the output would look like with our style. To do this, select the Preview Isogen Output button.

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A sample output will be produced. Select the Drawing preview.DXF and click View. The resulting isometric will look like the one below. This is not quite what we want. We are producing a stress isometric, so we do not need a Bill of Materials, and we also want a different drawing border.

A sample drawing border already exists; we can use this sample border and turn the bill of materials off. Copy and paste the file from E:\Training\Masters\A2StressISOBorder.dxf into the isometric style directory E:\ISOGEN\TRNPROJECT\Stress Iso.

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CAESAR II Statics Training Tutor Within I-Configure, select the current style and in the bottom left pane, select the Overview tab. Highlight the Drawing Frame entry in the tree. This will take you to the TemplateFile variable in the table in the right pane. Double click this field and browse to the new file to be used as the border.

We have now specified our custom drawing frame, as we will not require a Bill of Materials on our Isometrics, we have a little more space available for the isometric plot. Increase this space by reducing the drawing margin. Currently the drawing margin on the right hand side is 202mm. The left margin is only 10mm. Make these equal by changing the RightMargin to 10mm also. ISOGEN is now allowed to use the space that was previously taken up by the BOM as extra space for the plot.

Finally we must now turn off the Bill of Materials. Still in the Overview tab, select the Material List = True entry in the tree. Again, this will display the relevant variable in the right hand list. Change this value to False.

Save the changes and Export the style once again so that we can see the results of these changes.

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This output looks acceptable. Save and close I-Configure and return to CAESAR II. I-Configure is now set up and we can now use the ISOGEN module in CAESAR II to annotate and produce stress isometrics.

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CAESAR II Statics Training Tutor From the CAESAR II main window, access the ISOGEN isometrics module

CAESAR II will open the model for isometric production. Click OK to confirm and continue.

The model will be shown and can now be annotated

Annotating the model involves simply selecting which data to include in the annotations, and is simply a matter of ticking the required data. All input data can in included as follows.

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CAESAR II Statics Training Tutor All analysis data can also be included as well. For each load case run, the displacements, restraint loads and stresses can be specified, as well as hanger data. In addition to input and output data, custom annotations can be added to any node number or on any element. Project attributes can also be specified and placed on the resulting isometric. We will annotate our isometric with the following data: Input: Node numbers Temperature T1 Pressure P1 Output: SUS Max stress (node 68) EXP Max stress (Node 78) Nodal Annotations: Node 10 – PUMP A CONNECTION Node 110 – VESSEL D CONNECTION Elemental Annotations: Element 100 – 110 – LWN Flange as Nozzle Project Attributes Project Name Project No Client Name Area System Prepared By

TRN 001 TRAINING T1 TUTOR

Select to Eit stress annotations to bring up the annotations panel.

From the panel select Input data and choose Node Numbers from the feature drop down list. We wish to annotate all the node numbers. However, as we have discussed previously, CAESAR II automatically splits bends and inserts intermediate nodes. We do not wish to annotate these intermediate nodes. As such, select all nodes except the intermediate bend nodes. These bend nodes should be as follows: 68

69

79

81

82

83

84

118

119

148

149

Select all nodes except those listed above. If you wish, return to the input and check which nodes are the intermediate bend nodes on your model.

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Once completed, select Temperatures from the feature drop down and select T1. Do the same for Pressure P1.

We can now specify the output data. Select Output tab and pick the SUS load case. Select the Stress option. The highest stress for the SUS case is on the bend at the hanger (node 70) – the stress is actually at node 68, but this is not selectable in the list. Node 60-70 is selectable and will annotate correctly. Pick this node.

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Repeat for the stress in the EXP case. The max stress in the EXP case is at node 78

Next select the Nodal annotations. Annotate the two equipment connections as mentioned previously. Node 10 – PUMP A CONNECTION Node 110 – VESSEL D CONNECTION Perform a similar task for the elemental annotations, and annotate Element 100 – 110 – LWN Flange as Nozzle Finally enter the project attributes.

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CAESAR II Statics Training Tutor Now we have completed the annotations, we can produce the drawings. Select Create Isometric Drawing.

Select to Use Existing Style – as we have already created and configured our isometric style.

Browse to the Isometric ,Project and Stye directories as configured earlier

Once complete, click Create Drawing.

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CAESAR II Statics Training Tutor After CAESAR II passes the information to ISOGEN, the data is processed and after a few seconds, a drawing will be created. Select the drawing created and click View.

The annotations and attributes specified will be inserted into the resulting isometric. The isometric could do with a little tidying up – the attributes are not quite correctly positioned. The colours could also do with some improvement – perhaps to make the restraints/hangers stand out more. All this can be done via I-Configure if required.

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CAESAR II Statics Training Cool H20 – FRP Piping

Cool H20 – FRP Piping

This job consists of an FRP cooling water header, which decreases from 1800mm diameter to 1500mm diameter to 1200mm diameter to 1050mm diameter as a succession of 750mm diameter lines tap off it. Modelling this job provides the opportunity for the user to explore the capabilities that CAESAR II offers for analysing FRP pipe. Additionally static seismic loads will be applied to this system, illustrating methods using uniform loads and load combinations.

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Basics of Fibreglass Piping Analysis Analysis of FRP materials is different to analysis of metallic materials, due to the orthotropic properties of the FRP material. Stress analysis of Fibre Reinforced Plastic components must be viewed on many levels. These levels, or scales, have been called “Micro-Mini-Macro” levels, with analysis proceeding along the levels according to the “MMM” principle. Micro level analysis: Stress analysis on the “Micro” level refers to the detailed evaluation of the individual materials and boundary mechanisms comprising the composite material. In general, FRP pipe is manufactured from laminates, which are constructed from elongated fibres of a commercial grade of glass (called E-glass), which are coated with a coupling agent or sizing prior to being embedded in a thermosetting plastic material, typically epoxy or polyester resin. Typically, on a micro level, the following failure modes are evaluated: 1) failure of the fibre 2) failure of the plastic matrix 3) failure of the fibre-matrix interface Generally, the glass fibre is found to be much stronger in tension than is the matrix, so most tension (along the axis of the fibre) is naturally taken by the fibre, rather than the matrix.

MICRO LEVEL GRP SAMPLE – SINGLE FIBRE EMBEDDED IN SQUARE PROFILE OF MATRIX

Mini level analysis: Although feasible in concept, micro level analysis is not feasible in practice. This is due to the uncertainty of the arrangement of the glass in the composite -- the thousands of fibres which may be randomly distributed, semi-randomly oriented (although primarily in a parallel pattern), and of randomly varying lengths. This condition indicates that a sample can truly be evaluated only on a statistical basis, thus rendering detailed element analysis inappropriate. For mini-level analysis, a laminate layer is considered to act as a continuous material, with material properties and failure modes estimated by averaging them over the assumed cross-sectional distribution. The assumption regarding the distribution of the fibres can have a marked effect on the determination of the material parameters; two of the most commonly postulated distributions are the square and the hexagonal, with the latter generally considered to be a better representation of randomly distributed fibres.

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CAESAR II Statics Training Cool H20 – FRP Piping Use of these parameters permits the development of the homogenous material models which facilitate the calculation of longitudinal and transverse stresses acting on a laminate layer. Typical mini-level analysis shows that due to stress intensification and relative weakness of the matrix relative to the glass fibres, laminate layers are typically very strong only in a single direction – i.e., the direction corresponding to the predominate alignment of the glass fibres.

STRESS INTENSIFICATION IN MATRIX CROSS SECTION

Macro level analysis: Where Mini level analysis provides the means of evaluation of individual lamina layers, Macro level analysis provides the means of evaluating components made up of multiple laminate layers. It is based upon the assumption that not only the composite behaves as a continuum, but that the series of laminate layers acts as a homogenous material with properties estimated based on the properties of the layer and the winding angle, and that finally, failure criteria are functions of the level of equivalent stress.

MACRO TO MICRO STRESS CONVERSION Since individual laminate layers are usually strong only in one direction, they are wound upon each other at various angles to tailor the desired strength in various directions. Typically, for pipes, the laminate layers would be arranged in such a way that their strength in the hoop direction is approximately twice that in the axial direction.

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CAESAR II Statics Training Cool H20 – FRP Piping Total laminate properties may be estimated by summing the layer properties (adjusted for winding angle) over all layers. For example: ||

(

)∑

||

Where: ||

= Longitudinal modulus of elasticity of laminate = thickness of laminate = transformation matrix orienting axes of layer k to longitudinal laminate

axis = transformation matrix orienting axes of layer k to transverse laminate axis = thickness of laminate layer k Once composite properties are determined, the component stiffness parameters may be determined as though it were made of homogenous material – i.e., based on component crosssectional and composite material properties, and interaction formulae for normal and shear stresses can be developed.

COMBINED STRESSES σ AND τ AT FAILURE: ARALDITE CY232

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CAESAR II Statics Training Cool H20 – FRP Piping

CAESAR II’s Orthotropic Model for Piping Systems CAESAR II’s orthotropic material model is activated through the selection of Material 20 – FRP. The orthotropic material model is indicated by the changing of two fields from their previous isotropic values: "Elastic Modulus (C)" "Elastic Modulus/axial" "Poisson’s Ratio" "Ea/Eh*Vh/a". These changes are necessary due to the fact that orthotropic models require more material parameters than do isotropic. For example, there is no longer a single modulus of elasticity for the material, but now two – axial and hoop. There is no longer a single Poisson's ratio, but again two -Vh/a (Poisson's ratio relating strain in the axial direction due to stress-induced strain in the hoop direction) and Va/h (Poisson's ratio relating strain in the hoop direction due to stress-induced strain in the axial direction). Also, unlike with isotropic materials, the shear modulus does not follow the relationship G = 1 / E (1-V) as for metals, so that value must be explicitly input as well. In order to minimize input, a few of these parameters can be combined, due to their use in the program. Generally, the only time that the modulus of elasticity in the hoop direction, or the Poisson's ratios are used during flexibility analysis is when calculating piping elongation due to pressure (note that the modulus of elasticity in the hoop direction is used when determining certain stress allowables for the BS 7159 code): ⁄

Where:

⁄

= extension of piping element due to pressure = longitudinal pressure stress in the piping element = Modulus of elasticity in the axial direction = Poisson’s ratio relating strain in the axial direction due to stress induced strain in the hoop direction = Hoop pressure stress in the piping element = Modulus of elasticity in the hoop direction = Length of piping element

This equation can be rearranged, to require only a single new parameter as: ( Note that in theory, the single parameter (

(

⁄

⁄

))

) is identical to Va/h.

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Requirements of the ISO 14692 Code In light of the isotropic nature of fiberglass reinforced plastic pipe, where hoop and axial strengths are distinct, stress evaluation in ISO 14692 utilizes an idealized envelope of combinations of axial and hoop stresses which cause the equivalent stress to reach failure. This curve represents the plot of: (

)

(

)

*

+

Where: = Allowable stress, axial = Allowable stress, hoop These terms are expressed in the ISO short term failure envelope:

ISO SHORT TERM FAILURE ENVELOPE The (2:1) line indicates points where the hoop stress is twice the axial stress. This stress state occurs in the wall of a pressurized, closed cylinder. The short term axial strength, σsa(2:1), and short term hoop strength, σsh(2:1), occur where this (2:1) line intersects the failure envelope. By definition, σsh(2:1)=2*σsa(2:1). A third strength is illustrated here – σsa(0:1) – this is the axial strength of the pipe in the absence of pressure. But there are several factors which reduce this short term strength in setting allowable (hoop and axial) pipe stress: • • •

Reduced long term strength of the component [fscale] A design safety factor (based on load type) [f2] Accommodation of specific load conditions (reduced strength associated with temperature, chemical attack, and fatigue) [A1, A2, A3]

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CAESAR II Statics Training Cool H20 – FRP Piping This short term failure ellipse can be represented by a “fully measured envelope” shown below:

ISO FULLY MEASURED ENVELOPE The line set intersecting the short term failure ellipse is a straight line representation of that ellipse – labelled “short, ideal”. The manufacturer can establish σsh(2:1) from burst tests (and half of that is σsa(2:1)) and can establish σsa(0:1) from tension tests. The next smaller line set, labelled “long, ideal” reflects the long term strength of the pipe. This is the material limits usually provided by the manufacturer. Using long term pressure testing, the manufacturer can project the “end of life” strength of their components. The ISO Code reduces this material data by a system factor of safety. This is the third line set, labelled “design” here. The limits used for piping evaluation are shown in the smallest line set, “factored design”. Factored design limits account for those operating conditions that reduce long term strength of the piping material. Note also the (1:1) line in the figure above. This line represents the stress condition where the axial stress equals the hoop stress. While having no engineering design significance, this line produces a point on the failure ellipse where the axial limit will drop below σsa(2:1). The manufacturer may provide σsa(1:1) (or the equal σsh(1:1)). If not the following simplification may be necessary:

ISO SIMPLIFIED ENVELOPE

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CAESAR II Statics Training Cool H20 – FRP Piping The dotted line set shows the simplified short term strength. This envelope would then be reduced to a similar “factored (long term) design” envelope described above. This curve is also used in the UKOOA Code. ISO 14692 Annex D provides equations for effective hoop and axial stresses in piping component. These effective stresses combine structural loads (due to weight, thermal strain, etc.) with pressure. Safe design is assumed if both the hoop and axial stresses lie within the factored design boundaries. CAESAR II analysis will evaluate both hoop and axial stress. The effective hoop stress must be less than the factored design limit for hoop stress. The axial term will also be evaluated but, here, the allowed axial stress is a function of the hoop stress. CAESAR II will report the stress term (hoop or axial) that produces the largest stress/limit ratio. The strength envelopes above are for straight pipe. Other piping components such as tees, bends and joints do not have fully developed strength envelopes. Instead, manufacturers establish a qualified stress, σqs, for these components. (

)

(

)

(

)

Where: = mean diameter of matching pipe = reinforced pipe thickness of the matching pipe = Qualified pressure of the fitting This is a combination of equations (6) and (7) of the Code. Qualified stress serves as the long term design hoop assigned to pipe. This qualified stress will be adjusted by the same terms as pipe to develop a long term hoop design stress. The axial limit is established through the biaxial stress ratio, r. For pipe,

(

) (Equation (12) of the Code). The ISO Code assigns values for r for non-pipe

components in Table 4. Given r and the qualified stress, CAESAR II will calculate σsa(0:1) for the component. CAESAR II requires qualified stress and biaxial stress ratio for bends and joints. Tees have r=1 so only require a qualified stress. The stress envelope for a non-pipe component is a simple rectangle bounded by a factored design hoop (or qualified) stress and an axial stress equal to r times that hoop limit. Note that, for some piping components with relatively large axial strength, r can go as large as 2 indicating that the component is just as strong axially as it is in hoop for any hoop stress.

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CAESAR II Statics Training Cool H20 – FRP Piping

Allowable Stress Data for this Model As shown on the isometric, the material for this model is Wavin 55 material. Pipe Data: The value for long term hoop strength (shown as hl(2:1) in CAESAR II) may be obtained from vendor data. In the case of the Wavin 55 material, it is available from the graph of the combined stress failure envelope, as shown below. Note that the axes have been switched (axial stress on the horizontal axis) on this graph relative to the traditional ISO envelope format, so the desired 2:1 position is now identified as R = 0.5. Likewise, the values in this graph include the service factor f2, which can be eliminated by dividing the values on the outer curve by 0.67. This gives a f1 x LTHS value of 125 N/mm2. An alternative means of getting this value is to find the value given by the vendor for the long term Hydrostatic Design Basis; again, for this case 125 MPa. The long term axial stress at maximum hoop stress, al(2:1), is, by definition, half of hl(2:1). The axial tension-only long term strength is shown on the chart below as (41 MPa/0.67). PIPES, WINDING ANGLE ω = 55°

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CAESAR II Statics Training Cool H20 – FRP Piping HYDROSTATIC PROPERTIES

Joint & Fitting Data: Tees, bends and joints reference Qualified Stress instead of the pipe term hl(2:1). For this example, these components have a lower “pressure rating” than the matching pipe. The Qualified Stress (Qs) will also be set to 75 MPa. The axial stress limit for tees is constant but bends and joints may have a varying axial stress limit measures by r, the ratio of two times al(0:1) divided by hl(2:1). For this model, r is set to 2 for joints and 1.0 for bends. Bends also reference the hoop modulus of elasticity which is entered here as the Eh/Ea ratio of 1.7 Other factors: • A1 – factor for temperature • A2 – factor for chemical resistance • A3 – factor for cyclic service • System Design Factor – this is a CAESAR II term that is combined with the CAESAR II Occasional Load Factor (which is set or adjusted in the Load Case Options) to produce the “part factor for loading”.

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CAESAR II Statics Training Cool H20 – FRP Piping

Configuration Options for FRP Piping: In this example, the material has the properties of Wavin 55o winding FRP pipe. These parameters are: 𝐸𝑎

𝑀𝑃𝑎

𝐸

𝑀𝑃𝑎 𝐸 ⁄𝐸𝑎

𝐸 ⁄𝐸𝑎 𝑉

⁄𝑎

𝐷𝑒𝑛𝑠𝑖𝑡𝑦

𝐶𝑇𝐸

𝑘𝑔 𝑚

𝑚𝑚⁄𝑚𝑚⁄°𝐶

𝑆 𝑒𝑎𝑟 𝑀𝑜𝑑𝑢𝑙𝑢𝑠

𝑀𝑃𝑎

𝐵𝑒𝑛𝑑 𝐿𝑎𝑚𝑖𝑛𝑎𝑡𝑒 𝑇𝑦𝑝𝑒

𝐶 𝑜𝑝𝑝𝑒𝑑 𝑆𝑡𝑟𝑎𝑛𝑑 𝑚𝑎𝑡 𝑤𝑖𝑡 𝑚𝑢𝑙𝑡𝑖

𝑓𝑖𝑙𝑎𝑚𝑒𝑛𝑡 𝑟𝑜𝑣𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛

CAESAR II’s material database is not currently configured for orthotropic materials such as FRP. Therefore, CAESAR II’s orthotropic model must be triggered through use of Material 20 (FRP), with the material parameters entered explicitly. These parameters include: Axial Modulus of Elasticity (Ea) The Ratio (Ea/Eh)Vh/a Pipe Density Coefficient of Thermal Expansion Ratio of Shear Modulus (G) to Axial Modulus (Ea) FRP Bend Laminate Type

(entered on spread sheet) (entered on spread sheet) (entered on spread sheet) (entered on Special Execution Parameters) (entered on Special Execution Parameters) (entered on Special Execution Parameters)

This may become tedious, especially if the same type of FRP material is used frequently. In this case, the appropriate material parameters may be entered in the CAESAR II Configure/Setup, to be used automatically whenever Material 20 is used.

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CAESAR II Statics Training Cool H20 – FRP Piping These parameters are entered using the FRP PROPERTIES group in of Configure/Setup. The configuration items are described below: Axial Modulus of Elasticity: Self-explanatory; can be read from an FRP file. Axial Strain : Hoop Stress (Ea/Eh*Vh/a): Ratio of the FRP axial modulus of elasticity to the hoop modulus of elasticity, all multiplied by Poisson’s ratio for strain in longitudinal direction due to stress-induced strain in circumferential direction; can be read from an FRP file. FRP Alpha (x E-06): The coefficient of thermal expansion, length/length/degree, multiplied by 1,000,000; can be read from an FRP file. FRP Density: Self-explanatory; can be read from an FRP file. FRP Laminate Type: This item is considered when calculating SIFs and Flexibility Factors of bends under the BS 7159 and UKOOA codes. Choices include: Type 1 – All chopped strand mat (CSM) construction with an internal and an external surface tissue reinforced layer. Type 2 – Chopped strand mat (CSM) and woven roving (WR) construction with an internal and an external surface tissue reinforced layer. Type 3 – Chopped strand mat (CSM) and multi-filament roving construction with an internal and an external surface tissue reinforced layer. FRP Property Data File: Selecting an FRP type from one of the ones listed reads in much of the associated material data. Ratio Shear Mod : Elastic Mod: Ratio of the FRP shear modulus to the axial modulus of elasticity; can be read from an FRP file. The remaining settings are used with the other FRP codes BS 7159 and UKOOA and are unused for ISO 14962. Their uses are discussed in the help file and are displayed on pressing F1 while on the field.

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CAESAR II Statics Training Cool H20 – FRP Piping

Model the system When modelling using the orthotropic material, the very first thing that must be done, before even creating a new file, is to enter the material properties in the configuration file (remember this can be done by selecting an FRP data file). The once material 20 is selected within the job, these properties will be used. Any changes made to the FRP properties in the configuration file will only take effect when a new job is created. On the CAESAR II main window, select Tools > Configure/Setup

Select the RP properties node and specify the properties of the FRP. This FRP is Wavin55 as mentioned previously. Select this FRP property data file.

Confirm the choice

The FRP parameters will update to those set in the FRP data file. Whilst in the configuration file, also specify a default friction coefficient of 0.15 to represent plastic on steel/concrete.

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CAESAR II Statics Training Cool H20 – FRP Piping Once these FRP parameters have been set, only then can the job file be created. Create a new job file called CoolH20.

Create the first element, 10 to 20. Note that this pipe is non-standard 1800mm diameter and also has non-standard 46mm wall thickness. The 1.5mm Corrosion layer should also be entered here. This layer will always be used in the weight and thermal force calculations, but excluded from the pipe strength calculations.

Select the material number 20 – FRP.

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CAESAR II Statics Training Cool H20 – FRP Piping Upon selection of the material, the labels on the material properties change. Elastic Modulus (C) becomes Elastic Modulus/axial and Poisson’s Ratio becomes Ea/Eh*Vh/a. The values will be brought in from the FRP data file and will be as described above (as we chose the Wavin55 FRP data file). Also check the Special execution parameters for further FRP data. Again this should match the correct data coming from the FRP data file.

Enter the temperature and pressure (50°C and 2 bars). We must now also select the design code. Currently the code is the default - B31.3. Change this to ISO 14692. Now we must enter the stress envelope for the FRP material. The entries are as described previously. Recall the graph:

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CAESAR II Statics Training Cool H20 – FRP Piping

(as mentioned before, the axes have been switched, so the 2:1 position is now identified by R = 0.5), and also recall that mentioned previously the values on the graph include service factor f2, 0.67. This factor also needs removing (i.e. divide all values by 0.67). the 0.67 value will be entered as the system design factor. As shown in the graph, the reading for the hoop stress is 84 N/mm2. Therefore the hl(2:1) value is:

By definition, long term axial stress at maximum hoop stress, al(2:1), is half of hl(2:1). Therefore:

The axial tension-only long term strength is shown on the chart above as 41 MPa. Therefore

The joint and fitting data is also discussed above. The Qualified stress Qs will be set to 75 MPa and for bends r = 1.0 and for tees r = 2. Bends also reference the hoop modulus of elasticity which is entered here as the Eh/Ea ratio of 1.7.

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CAESAR II Statics Training Cool H20 – FRP Piping A1, A2, & A3 bring in environmental effects to reduce the design stress to the factored design stress. Thermal Factor (k) is the “mean temperature multiplier”, a factor by which the difference in temperature between the fluid the environment is to be multiplied (since FRP has natural insulating qualities). For liquids, the Code dictates a K value of 0.85; use 0.80 for vapour.

Note that we have not entered al(1:1) or hl(1:1) therefore the simplified envelope will be used. Complete the first element by adding an anchor at node 10 and continue into the bend. The bend is a mitred bend and has 2 mitre points. Note that the ISO Code ignores the number of mitres when calculating the bend SIF and flexibility factor.

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CAESAR II Statics Training Cool H20 – FRP Piping In addition, there is also a +Y restraint on the start of the bend (node 18). Notice the friction factor is included automatically when adding the restraint.

Continue to the next element.

The model so far should look like the one below:

Continue and complete the model. Note the following points: •

•

The branch connection at node 40 (as well as all other branches) is a tee (SIF type 1). Node 40 (along with nodes 60, 100, 120, 160, 180, 190, and 250) is supported by a +Y (weight only) support (with friction coefficient of 0.15). The restraint at node 50 (as well as those at nodes 90, 110, 150, and 170) is combination guide and +Y (weight only) restraint (with friction coefficient of 0.15).

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CAESAR II Statics Training Cool H20 – FRP Piping •

Element 70-80 is a reducer (conical section). It can be modelled as such with the exiting diameter and thickness set to 1500mm and 38mm.

Element 40-280 is a branch off of the 1800 mm line. Its diameter and thickness should be changed to 750 mm and 25 mm, respectively. (Offsets should be considered here as the actual flexible length of straight pipe [before the bend] – 3600 mm – is much smaller than the modelled length – 4500 mm – and therefore much stiffer. However, for this layout the effect is minimal [about 5% in terms of stress] and excluded for simplicity.) The bend at node 280 has 4 mitre points. After modelling the branch through node 300, that branch can be duplicated via the list processor 5 times (with the node increment set to 30, 60, 90, etc.). It is also necessary to change the branch intersection nodes to 60 (from 70), 120 (from 130), and 180 (from 190). The completed model should look as below.

Error Check the model

A warning relating to the fact that al(1:1) and hl(1:1) were not entered and so the simplified envelope will be used is shown, as is a warning about SIFs on the intersections and that the reducer Alpha was not entered so CAESAR II has calculated this value. Accept these warnings and access the load case editor.

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CAESAR II Statics Training Cool H20 – FRP Piping

Load Case Setup ISO 14692 evaluates both hoop stress and axial stress in the installed and operating conditions and also for any short duration (occasional) loads. The type of load will set the part factor, f2, used to set the design stress limits. The System Design Factor specified in the input is multiplied by the CAESAR II Occasional Load Factor in the Load Case Options tab to produce this f2. f2 = (System Design Factor)*(Occasional Load Factor). The Code provides values for f2 in Table 3. Remember that the System Design Factor in the CAESAR II input is set to 0.67.

Review Results ISO 14692 Annex D provides a method for converting torsion and bending moments into hoop and axial stress terms. These stresses, summed with their pressure counterparts, produce effective hoop stress and effective axial stress. Terms common to B31 piping – flexibility factor and stress intensification factor – are used here too. Stress evaluation will first compare effective hoop stress to the factored design hoop stress. If this check fails, the hoop stress is reported, otherwise, CAESAR II will continue with the axial check. The effective hoop stress is used with the design envelope to pick up the factored design axial stress. The effective axial stress is then compared to the factored design axial stress. If this check fails, the axial stress is reported, otherwise CAESAR II will print the cause of the largest (stress/limit) ratio – either hoop or axial. Running this analysis shows that this system stresses are satisfactory. Note the changing allowable stress from node to node. CAESAR II prints a different allowable depending upon which stress calculation controls – Hoop or Axial.

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CAESAR II Statics Training Cool H20 – FRP Piping

Solving Expansion Problems The philosophy behind solving expansion problems in a fiberglass piping application is different from that in a steel piping application. For steel piping, the preferred hierarchy for solving such a problem is 1) adding flexibility through loops and bends, 2) using expansion joints, and 3) using restraints to re-direct growth to areas where it can be better handled. For fiberglass applications, due to the relatively low modulus of elasticity of fiberglass, the lack of significant flexibility provided by FRP bends, and the potential problems involved in the joining of FRP sections, the hierarchy is exactly the opposite. The preferred method is to use axial restraint to force the thermal expansion into compression (in this case, the line must be adequately guided); the next preference is to use expansion joints; and the last resort is to use expansion loops.

Static Seismic Using the ASCE 7-05: This cooling water system is located in a seismically active region, so it must also be designed to withstand earthquake loads. For this analysis, the ASCE 7 Minimum Design Loads for Buildings and Other Structures, 2005 Edition is in effect. We will assume that this installation is located in Site Class D (Stiff soil profile), near Los Angeles, California. (For Site Class Definitions, refer to Table 11.4-1.) The structure in which this system is operating has an average roof height of 12m. Section 13.3.2 discusses Seismic Relative Displacements to which piping must be designed. It states “The effects of seismic relative displacements shall be considered in combination with displacements caused by other loads as appropriate.” – meaning that they shall be treated as “secondary” loads, rather than “primary” loads. Inertial Loads Section 1621.1.4 defines a horizontal seismic acceleration factor to be applied uniformly throughout the structural mass. This acceleration factor, aH, is defined as:

( [ But:

)

] and

Where: = Component amplification factor, from Table 13.6-1 = 2.5 for piping = Design elastic response acceleration at short period, from Section 11.4.4 = Component response modification factor, from Table 13.6-1. Use 4.5 for pipes not in accordance with B31, with bonded joints or use 12 for welded, steel B31 pipe. = 4.5 = Component importance factor, from Section 13.1.3 (1.5 for life-safety components, hazardous material containing, or piping is in a Category IV structure (essential facility); 1.0 for all others).

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CAESAR II Statics Training Cool H20 – FRP Piping = 1.0 = Height in structure at point of attachment. Here, use the average of elevation of all 8 connections = 6m = Average roof height of structure = 12m Section 13.3.1 states that a vertical acceleration be considered as well. This acceleration factor, aV, is defined as 20% of the Design elastic response acceleration at short period, or:

Determine SDS: From section 11.4.4

Where = Maximum considered earthquake spectral response accelerations for short period adjusted for site class effects And from section 11.4.3

Where: = Site Coefficient defined in Table 11.4-1 = 1.0 = Mapped spectral accelerations for short periods, from Section 11.4.1 = 1.552 g (see below) Maps of spectral acceleration are available from several sources (ASCE, IBC, NEHRP, and FEMA). Data is also available on-line at http://earthquake.usgs.gov/hazards/ using the Java Ground Motion Parameter Calculator (http://earthquake.usgs.gov/hazards/designmaps/javacalc.php). The location of this piping system on the coast near Los Angeles is 33.9083 latitude and -118.41045 longitude. Below is a screen capture from the USGS software. SS for the location of interest is shown; SS=1.552g.

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CAESAR II Statics Training Cool H20 – FRP Piping

Therefore:

So the appropriate seismic acceleration is:

( [

)

] ](

[

)

Checking the limits on aH:

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CAESAR II Statics Training Cool H20 – FRP Piping Seismic load adjustment: The building codes are based on strength design where components (such as reinforced concrete structures) are evaluated on their load-carrying capacity rather than stress. Piping codes are based on allowable stress design and, while the calculated seismic load provides a good estimate of the internal loads and deflections of the piping system, these seismic loads over predict the resulting stress used here. Section 13.1.7 states “The earthquake loads determined in accordance with Section 13.3.1 shall be multiplied by a factor of 0.7.” Therefore the adjusted seismic loads for allowable stress design are:

Relative Seismic Displacements: Section 1621.1.5 discusses the means of addressing relative displacements due to “story drift” – this should be calculated via a structural analysis of the enclosing building. Assume this analysis yields the following displacements (with attachment points near building columns, no vertical drift is included):

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CAESAR II Statics Training Cool H20 – FRP Piping Node 10 18 40 50 60 90 100 110 120 150 160 170 180 190 240 270 300 330 360 390 420 450

Function Anchor +Y +Y X, +Y +Y X, +Y +Y X, +Y, Z +Y X, +Y +Y X, +Y +Y +Y +Y Anchor Anchor Anchor Anchor Anchor Anchor Anchor

Approx Elev (m) 4.6 4.6 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 28 0 7.3 7.3 7.3 7.3 7.3 7.3

X-Disp (mm) 26 26 16 16 16 16 16 16 16 16 16 16 16 16 16 0 42 42 42 42 42 42

Z-Disp (mm) 9 9 5 5 5 5 5 5 5 5 5 5 5 5 5 0 14 14 14 14 14 14

Note: Displacements need only be placed on +Y supports if friction loads are considered to be significant.

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CAESAR II Statics Training Cool H20 – FRP Piping Seismic Data Input We have already calculated the Seismic data and could build uniform loads to model the load in the X Y and Z directions from what we have just calculated. Alternatively, CAESAR II includes a static seismic wizard which can be used to perform all the calculations automatically, and build the uniform loads and incorporate into the model. We will use the static seismic wizard, and see that the values match up to our hand calculations. The Static Seismic Wizard is available from the same toolbar as the Loop design wizard used previously.

The static seismic wizard provides input for the various data we have discussed previously. Recall the following values: = Component amplification factor, from Table 13.6-1 = 2.5 for piping = Component response modification factor, from Table 13.6-1. Use 4.5 for pipes not in accordance with B31, with bonded joints or use 12 for welded, steel B31 pipe. = 4.5 = Component importance factor, from Section 13.1.3 (1.5 for life-safety components, hazardous material containing, or piping is in a Category IV structure (essential facility); 1.0 for all others). = 1.0 = Height in structure at point of attachment. Here, use the average of elevation of all 8 connections = 6m = Average roof height of structure = 12m In addition, we have the SS value obtained from the USGS utility = 1.552 Input the data into the Seismic Wizard

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CAESAR II Statics Training Cool H20 – FRP Piping On clicking OK, the values will be calculated for aH and aV as we have done manually above. These will be included as Uniform Loads. (The uniform load will act on following elments until removed or set to zero).

Note that the Uniform loads are also in g’s. Next we also need to apply the displacements due to “Storey-shift” as detailed previously. These displacements can be modeled as vector D1 (for X-direction) and vector D3 (for Z-direction). They should be applied to CNODEs attached to the restraints (increment each restraint by 1000). To save inputting effort, all restraints at a common level could be connected to a single CNODE. In this case, displacements need only be entered at three locations. Add the displacements only at nodes 10, 40 and 300. Node 10

Node 40

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CAESAR II Statics Training Cool H20 – FRP Piping Node 300

We now have the restraints defined, but currently they are defined as displacements at nodes 1010, 1040 and 1300. These nodes do not exist in the model. We will use these node numbers as cNodes and connect all the restraints to the relevant displacement at the correct elevation. All restraint nodes at 4.6m elevation must be connected via Cnode to displacement node 1010. (These are nodes 10 and 18).

Similarly, restraint nodes at 2.8m must connect to 1040 (Nodes 40 – 240) and nodes at 7.3m elevation must be connected to 1300 (nodes 300 – 450). This is easier to perform using the Restraint List view.

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CAESAR II Statics Training Cool H20 – FRP Piping

You will notice that the graphic plot now looks a little odd. The reason for this is, that by default, CAESAR II displays the system with Nodes and CNodes at the same point in space. This is fine for connecting pipe nodes to structure CNodes (like in Tutor) or nozzle nodes to vessel/pump CNodes (like in Turbo). But in this model, where several restraints reference the same CNode, the display will still attempt to join all these Nodes and CNodes together, resulting in a ‘nonsense’ plot. To clean up the plot and avoid the associated coordinate mismatch error during Error Check, change the Configuration/Setup parameter “Connect Geometry through CNODEs” to False.

The plot will not update automatically, so must be done manually. Click the Reset plot button to refresh the graphics.

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CAESAR II Statics Training Cool H20 – FRP Piping The plot will once again look correct.

Re-run the eror check – there should be no errors and no new warnings or messages.

Load Case Setup Access the Load Case editor – you will receive a message stating that the individual loads for the job have changed. This message is due to the fact we now have displacement loads in the model D1 and D3 and the uniform loads U1, U2 and U3. These must be incorporated into our load cases. Section 1621.1.4 discusses the combination method for the various loading directions. It states that the load along each horizontal axis shall be applied independently, but in conjunction with the vertical load. Since ISO 14692 only looks at a single stress type (OPE), this leads to the following seismic load cases (since boundary conditions are non-linear): Note the +/- signs in the various cases

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Note that even though results only need be retained from two load cases (the last two), we are electing to keep results from all load cases in order to help us “debug” in the event of an overstress. Load Cases L10 and L11 are not combined algebraically, rather they are included to compare the displacements, forces and stresses. Hence why they ar enot added or subtracted, just listed. We wish to find the worst case load case, so we can get CAESAR II to compare the resluts from each load case and report the maximum and minimum values. Select the Load Case Options tab and select SignMin and SignMax for the Combination method for L10 and L11.

SignMax compares the displacements, forces and stresses and uses the maximum force and maximum stress value of the cases (i.e. sign is considered in the comparison). Displacements are the maximum Signed valued of all displacements from each case included in the combination. Similarly

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CAESAR II Statics Training Cool H20 – FRP Piping for forces and stresses, these are the maximum Signed forces/stresses from each case included in the combination. SignMin is the opposite of this – the minimum signed values of the stresses/forces/displacements are included. Using SignMin and SignMax we can get the enveope of restraint loads for all cases. Also for the static seismic cases, enter in the Occasional Load factor of 1.33.

Analyse the model.

Review Results It can be seen straight away that there is an issue with Cases 4 and 5.

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CAESAR II Statics Training Cool H20 – FRP Piping Reviewing the Load Case 11 confirms that the maximum stress fails the code stress check, and is at 103.8% of the code allowable at node 180. In order to solve this, it is necessary to know which of the seismic combination cases caused the failure. We can see straight away that it is either case 4 or 5. Reviewing the code compliance report for all cases 2 to 9 shows that cases 4 and 5 are very similar alhough case 5 is fractionally higher.

Cases 4 and 5 represent the-X,+Y and –X,-Y seismic loadings. Now we need to find out which component of the seismic loadings caused the failure – the interial or the displacement. Stress due to force-based load is a primary load, stress due to strain is a secondary load. Once we find out the cause we can take the appropriate action to resolve the overstress situation. An easy way to determine which is the worst cause is to run the components of the load case individually to see wihich gives the greatest stress. Return to the load case editor. Load cases 4 and 5 both consist of W, D1, T1, P1, U1 and U2.

We know that W+D1+T1+P1 is not the cause as the OPE case is perfectly fine. So the culprit must be one of eiether D1, U1 or U2. Therefore, create three new load cases and assign D1 ,U1 and U2 respectively to each load case.

After re-running the analysis review the code compliance report for the three new cases.

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CAESAR II Statics Training Cool H20 – FRP Piping

This shows that clearly the D1 components is the largest contributer to the overstress, by a long way. This is a secondary loading, so the solution is to add more flexibility. In this case the fix is actually very simple and involves simply removing the guide just before node 180 located at node 170. The system will now pass the stress check.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Gas Transmission Pipeline - Buried Pipe

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe This model of a gas transmission pipeline will introduce the buried pipe modeller, and also introduce fatigue analysis. We will also explore the requirements of the B31.8 Design Code. This job consists of a 36” header, an 8” branch, and a 2” bypass, in the vicinity of a natural gas compressor station. The lines immediately go underground, from where they continue indefinitely for a very long distance.

B31.8 Design Code Gas transmission pipelines are covered by the B31.8 Code – Gas Transmission and Distribution Piping Systems. The philosophy of this code is to use high strength steel and custom, optimized wall thicknesses wherever possible, in order to minimize the amount of steel used in the long crosscountry pipelines. Stress analysis-wise, the code seeks to prevent yielding under any set of load cases. This prevents catastrophic failure under primary loads, and prevents plastic deformation under secondary loads. There are no requirements for reducing allowables for cyclic reduction factors (i.e., fatigue requirements). B31.8 is one of the few codes in which the OPErating case is a Code case and the EXPansion case is not Requirements of the different design codes are listed here in the table:-

OPE SUS EXP

B31.1 NO YES YES

B31.3 NO YES YES

B31.4 YES YES YES

B31.8 YES YES NO

B31.4 CH IX YES YES NO

B31.8 CH VIII YES YES NO

Modelling the system Model the system as shown in the isometric sketches. The following issues are of specific interest during the modelling phase. Element 10-20 originates at (and is anchored at) the compressor connection, with a flange (250 mm long, 5780 N weight). The pipeline is 36” diameter, with a non-standard 18 mm wall thickness. Enter two temperatures to model the extremes of the operating range, which represents the expectations due to winter lows and summer solar gain: Ambient = 21 C (set in Config) T1 = 50 C, T2 = -5 C above ground ON THE FIRST ELEMENT T1 = 30 C, T2 = 10 C underground (we will use these temperatures later) The material is API-5L X65 (material no 306), high strength steel. Its parameters can be found in the CAESAR II material database. The applicable code is B31.8 For natural gas, fluid density may be neglected. The branch connection at node 30 (as well as all other branches) is a Weldolet (SIF type 5).

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe The restraint at node 40 (as well as those at nodes 80, 110, 320, 360, 420, and 450) is a +Y (weight only) restraint. Specify a coefficient of friction of 0.3 for steel-on-steel contact. The bends at nodes 60 and 70 are 3-diameter bends (radius = 1370 mm). Element 60-70 goes underground 685 mm below node 60. Therefore we will need a node to indicate where the above ground/underground transition takes place. The entire element 60-70 can be entered first, and then the Break command can be used to insert a node 65 one-third of the way along the element length.

The element can be determined to be 5405 mm long (by clicking the local cosine “…” button) so onethird of that length is 1802.

The temperatures on 65-70 should be changed to T1 = 30 C, T2 = 10 C. The valve at element 90 - 100 (as well as that at element 430-440) is supported within an accessible valve pit (covered, but not buried). Node 75 (as well as nodes 115, 405, and 445) represents the buried/non-buried transition, and will be used later. Element 115-120 extends indefinitely, in a straight run, underground. Obviously, we need not model it forever – at some point, the cumulative restraining effect of the soil acts as an anchor. We will determine the required modelling length later; for now we can put in a dummy length of 10,000 mm. The model of the main pipe will look like the one shown below:

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Now move on to the branch, starting with element 30-310. This is an 8” standard schedule pipe. The temperatures on this element should be restored to T1 = 50 C, T2 = -5 C. The bends on this line are standard Long Radius. This pipe is now A53 Gr B low carbon steel. Element 30-310, modelled as is, is deceptively flexible, with a modelled length of 2440 mm, and an actual length of 1980 mm (since the element really originates at the surface of the 36” header, not at the centreline). So in reality, its flexibility should only be (1980/2440)3, or roughly 50%, of that calculated. We could correct this by modelling a weightless rigid from the centreline of the header to surface of the header (i.e., element 30-305), and then begin modelling the 8” line from that point (i.e., element 305-310). This approach has the following problems: 1. Placing the weldolet at node 30, causes no stress intensification on the 8” line (since there is no stress calculated on the rigid, and no weldolet at node 305). 2. Alternatively placing the weldolet at node 305 intensifies the stress on the 8” line, but doesn’t intensify the stress on the 36” line. Furthermore, the SIF would be both miscalculated (since CAESAR II would think the header size would be that of the rigid element) and misapplied (CAESAR II would not be able to determine in-plane from out-plane since the SIF would be at applied to two co-linear elements). One solution to this modelling dilemma is to use an OFFSET, in this case modelling a From Offset of 457 mm in the Z-direction. This internally models element 30-310 as a 457 mm long rigid element connected to a 1980 mm pipe, and transfers all stress calculations out to the true start of the 2440 mm pipe. (Note Offsets may not be entered on bend elements, so in this case, it is first necessary to break element 30-310 into two elements. Be careful that no elements, after applying Offsets, are reduced to zero-length. So in this case, enter two elements, 30-305 (DZ = 1000 mm, From Offset Z = 457 mm) and 305-310 (DZ = 1440 mm, long radius bend).

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Element 370-380 goes underground 685 mm below node 370, so we need a node to indicate where the above ground/underground transition takes place. The entire element 370-380 can be entered first, and then the Break command can be used to insert a node 375, 685 mm along the element length. The temperatures at node 375 should be changed to T1 = 30C, T2 = 10C. The valve at element 430-440 is supported within a valve pit. Nodes 405 and 445 represent the buried/non-buried transition. Element 445-450 (like element 115-120) extends indefinitely, in a straight run, underground. We will determine the required modelling length later; and use a dummy length of 10,000 mm for now. The completed model will look like the one shown below:

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Next model the bypass. Create this model in a new file before combining the two files.

Combine the models and run the error check. Two errors will appear. Both errors relate to the temperature for case 2, at elements 10-20 and 30305. The temperature for case 2 at these locations is -5°C. The error message is showing that there is no material data available for either of the two materials we have selected for a temperature this low, in the B31.8 code.

We cannot analyse until this has been corrected. To correct, we can edit the material database to include properties for the material down to the correct temperature.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Material Database Close the piping input to return to the main window. Access the material database form the Tools menu.

Choose to edit a material

Search for material 102 (A53 B) (you can search on either term). Notice that there are a number of entries for A53 B for the various different codes, including for B31.8. Select the B31.8 entry

The lowest temperature for which an expansion coefficient is entered is 0°C. The next row down is 73.3°C, which has no expansion coefficient. As our temperature in the model is -5°, we can see where we have incomplete data. We could enter in the data here for the missing expansion coefficient.

Alternatively, using engineering judgement, we can take the material properties for A53 B from another code where the data is filled in sufficiently and use this in B31.8 code.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Search again for the material A53 B. This time, select the All Codes data. This information is more complete than the B31.8 specific data for A53 B. If we are confident that this data will be suitable for B31.8 then we can use this data in place of the default B31.8 data.

The material database is stored in two files. One file is CMAT.bin. This stores all the default data and is read only. Any changes to the material are stored in a separate file called UMAT.UMD. This file stores any material information which is different to that in CMAT.bin. CAESAR II then uses the UMAT.UMD file first, and reads any further data from CMAT.bin. Materials from CMAT.bin cannot be deleted, only those from UMAT.UMD. If we save the A53 B B31.3 material data for use with B31.8, this will be written to the UMAT database. The CMAT database will be still the same as it currently is, however the UMAT will be read in preference to this, and it will act as though the data has been “overwritten”. To make this change, simply select the Applicable piping code drop down, and change from B31.3 to B31.8 and save the material.

Return to the input. You should see a warning stating that the properties for the material A53 B, code B31.8 have changed in the material database, and given the option to use these new properties or keep the existing. Select to update the material properties via the “No – Update” button.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Select part of the bypass (or any part that is material A53 B that we have just changed) and double click on the chevron in the temperature/pressure area. Notice that the expansion coefficient is now filled in for both temperatures (whereas it was 0.000 for T2 previously). Re-running the error check will show that the error is no longer present, for material A 53B but still present for API-5L X65. We now need to update the material database for this material. Repeat the exercise from before and update the material properties for API-5L X65.

Run the error check again – the material errors will no longer appear. The error checler should show only the Centre of Gravity report.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Buried Pipe Modeller The piping system beyond nodes 65 and 375 is mostly buried. The effect of this is (1) It will be continually supported, causing the weight stresses to be negligible, (2) It will be continually restrained against axial growth and bending by the adjacent soil. The former effect can be best modelled by zeroing the density of any pipe, fluid, and insulation; the latter can best be modelled by meshing the pipe and adding restraints, with mesh spacing, restraint stiffness, etc. based upon the soil properties. CAESAR II provides an underground pipe modeller which simplifies this process, performing the following functions:

Allows for the direct input of soil properties. These properties are used to generate first the stiffnesses on a per length of pipe basis, and then the restraints that simulate the discrete buried pipe restraint. (Note that any existing restraints in the underground area are deleted during this process.) CAESAR II supports three different soil modellers – one based upon the published work of Mr. L. C. Peng, plus two others (for clay and granular soils) from the American Lifelines Alliance. Automatically breaks down straight and curved lengths of pipe. CAESAR II uses a three Zone concept to break down straight and curved sections. Those ends of pipe identified as “transverse bearing lengths” are broken down into Zone 1 lengths (the smallest element lengths selected to properly distribute the lateral forces to the soil). At distances far away from Zone 1 are Zone 3 lengths (long lengths of pipe selected to transmit axial loads). Between Zone 1 and Zone 3 is Zone 2 (transition lengths which vary linearly from the Zone 1 end to the Zone 3 end). Allows for the direct input of user’s soil stiffnesses on a per-length of pipe basis. Input parameters include axial, transverse, upward, and downward stiffnesses, as well as ultimate loads. The user can specify user-defined stiffnesses separately, or in conjunction with CAESAR II’s automatically generated soil stiffnesses.

Restraint Parameters The Underground Pipe Modeller allows the use of any of three different soil modelling algorithms. The first two are based upon the work of the American Lifelines Alliance, as published in their document “Guidelines for the Design of Buried Steel Pipe”, dated July, 2001 (with addenda through February 2005); this document offers different models for clay soils and granular (sand/gravel). The third model is based on the soil restraint modelling algorithm presented by L.C. Peng in his two-part paper entitled “Stress Analysis Methods for Underground Pipelines,” published in 1978 in Pipeline Industry. Soil supports are modelled as bilinear restraints having an initial stiffness, an ultimate load, and a yield stiffness. The yield stiffness is typically set close to zero, i.e. once the ultimate load on the soil is reached there is no further increase in load even though the displacement may continue. The basic ultimate loads that must be calculated to analyse buried pipe are the axial and three bearing (transverse, upward, and downward) ultimate loads. (Note that for the Peng model, all three bearing ultimate loads are considered to be identical.) Once the axial and bearing ultimate loads are known, the stiffness in these directions can be determined by dividing the ultimate load by the yield displacement. (Researchers have found that the yield displacement is typically related to the buried depth, the pipe diameter, the soil type, and the load type.) The ultimate loads and stiffnesses

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe computed are on a force per unit length of pipe basis; the restraint ultimate loads and stiffnesses are then based upon tributary lengths of the adjacent piping elements.

The restraint equations use these soil properties to generate ultimate loads and stiffnesses using the following equations. Initial restraint stiffness is estimated by assuming that the Ultimate Load is developed over a “Yield Displacement” (YD). Axial Stiffness (KAX) on a per-length of pipe basis:

Transverse stiffness (KTR) on a per-length of pipe basis:

American Lifelines Alliance Clay Model Lateral Ultimate Load (FAX) per unit length

inches (stiff clay) or 0.4 inches (soft clay) Where: = Pipe diameter = soil adhesion factor (dimensionless) = = soil cohesion representative of soil backfill

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Transverse Ultimate Load (FTR) per unit length

(

)

Where: = = = 6.752 = 0.065 = -11.063 = 7.119 = height of soil cover (measured to centre of pipe, note CAESAR II requests distance to top of pipe) Downward Ultimate Load (FD), per unit length

Where: = 5.14 = 1.0 (for clay) = defective density of soil (taking buoyancy into account) Upward Ultimate Load (FU), per unit length

Where:

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe American Lifelines Alliance sand model: Axial Ultimate Load (FAX), per unit length

Where: = coefficient of pressure at rest (dimensionless) = 1 – sin φ = interface angle of friction for pipe and soil = f φ φ

= soil angle of internal friction, typical values are: 27 – 45° for sand 26 – 35° for silt

F = coating dependant factor (dimensionless), typical values are: Pipe Coating

f

Concrete

1.0

Coal Tar

0.9

Rough Steel

0.8

Smooth Steel

0.7

Fusion Bonded Epoxy

0.6

Polyethylene

0.5

Transverse Ultimate Load (FTR), per unit length

(

)

Where: = A, B, C, D, E based on φ, according to the following table: φ 20° 25°

A 2.399 3.332

B 0.439 0.839

C -0.30 -0.090

D 1.059E-3 5.606E-3

E -1.754E-5 -1.319E-4

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe 30° 35° 40° 45°

4.565 6.816 10.959 17.658

1.234 2.019 1.783 3.309

-0.089 -0.146 -0.045 -0.048

4.275E-3 7.651E-3 5.425E-3 6.44E-3

-9.159E-5 -1.683E-4 -1.153E-4 -1.299E-4

Downward Ultimate Load (FD), per unit length

Where: = = = density of dry soil Upward Ultimate Load (FU), per unit length

dense sand

loose sand

Where: =

Meshing Parameters Typical buried pipe displacements are considerably different than similar above ground displacements. Buried pipe deforms laterally in areas immediately adjacent to changes in directions (i.e. bends and tees); in areas far removed from bends and tees the deformation is primarily axial. The optimal size of an element (i.e., the distance between a single FROM and a TO node) is very dependent on which of these deformation patterns is to be modelled. Where the deformation is “lateral” smaller elements are needed to properly distribute the forces from the pipe to the soil. The length over which the pipe deflects laterally is termed the “lateral bearing length” (Lb) and can be calculated by the equation: (

)

Where: = Pipe modulus of elasticity = Pipe moment of inertia

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe CAESAR II places three elements in the vicinity of a bearing span to properly model this load distribution. The bearing span lengths in a piping system are called the Zone 1 lengths. The axial displacement lengths in a piping system are called the Zone 3 lengths, and the intermediate lengths in a piping system are called the Zone 2 lengths. Zone 3 element lengths (to properly transmit axial loads) are computed by 100*Do , where Do is the outside diameter of the piping. The Zone 2 mesh is comprised of elements that are 1.5 times the length of a Zone 1 element at its Zone 1 end, and that are 50*Do long at the Zone 3 end. A typical piping system and how CAESAR II views this zone mesh distribution is illustrated below:

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Virtual Anchor Length (VAL): Since soil restraint capacity is a function of piping length, after a certain length, the soil restraints will fully counteract the piping loads, acting as a “virtual anchor”. The piping need not be modelled beyond this length. This length can be calculated as that length where the axial pipe force equals the ultimate axial restraint load. Axial pipe force consists of three types: 1. Thermal Load = 2. Poisson effect (longitudinal shrinkage due to hoop strain) = 3. Longitudinal pressure load =

Using the (ALA Sand Model), the Axial Ultimate Load (FAX) per unit length is:

The ultimate restraint load therefore is the VAL * Fax ,or: *

Ultimate restraint load

+

*

+

Simplifying this gives: [

(

)

] *

+

This value can be used to determine how long we must model elements 130-140 and 460-470 of the GASTRANS model. This pipeline is in sandy soil – the soil parameters are as follows. Soil Parameters Soil Type Coating Factor (rough steel) Dry soil density, 𝑦 Effective Soil density, 𝑦′ Buried Depth, H Angle of internal friction, φ Coefficient of Pressure at rest, K0 Yield Displacement Factor, Axial dT Yield Displacement Factor, Lat, dP (mult of D): Yield Displacement Factor, Up, dQu (mult of H): Yield Displacement Factor, Up, dQu (max mult of D): Yield Displacement Factor, Down, dQd (mult of D):

Dense Sand 0.8 1909 kg/cm3 1190 kg/cm3 915mm (36” pipe) 610mm (8” pipe) 35° 0.426 2.5mm 0.1 0.01 0.1 0.1

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

° (coldest temp underground is 10 so delta from ambient of 21.11 is about 12 ) (36" pipe) (8" pipe) pipe) , Working this out give the following Virtual Anchor Lengths: VAL36 = 206400mm VAL8 = 127600mm Unlike the perfectly rigid/perfectly plastic response due to friction alone, the CAESAR II soil modeller inserts elastic/plastic springs to model some initial “give” in the soil. The program, therefore, may require more pipe length to fully develop this virtual anchor along a straight run. Since an even longer straight run is just as quick to enter and analyse, a more generous VAL length can always be used in the model. For this example we will change the place-holder lengths originally entered for elements 115-120 and 445- 450 to 300000mm and 200000mm, respectively.

Bury Pipe We will now bury the pipe. Close the piping input and return to the main window. Access the Buried pipe modeller

As soon as the buried pipe modeller is opened, the job file is saved as a copy with the same name with suffix “B”

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe In the underground modeller the soil underground conditions can be defined. This is done in two parts: 1. Enter the soil model 2. Define where/how the system is buried First let us define the soil model. We must define two soil models for our job – one for 915mm depth, one for 610mm depth. Access the soil model entry dialog.

We will use the American Lifelines Alliance Sand method. Notice that this is soil model number 2. Soil model number 1 is reserved for a completely user defined stiffness which can be entered in the main spread sheet.

Enter the soil properties as detailed above.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Add a second soil model, model no 3 and enter the properties for the second model. Only the depth op of pipe (H) is different.

Now that the soil models have been created, we must specify where/how the system is buried. This is done in the main Buried Element description Spread sheet.

This spread sheet is used to indicate where the pipe is buried, under which soil type, which mesh type should be used, as well as any user-defined stiffnesses. A critical part of the modelling of an underground piping system is the proper definition of Zone 1 (or lateral) bearing regions. These regions primarily occur: • • •

On either side of a change in direction For all pipes framing into an intersection At points where the pipe enters or leaves the soil

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe CAESAR II automatically puts a Zone 1 mesh gradient at each side of the pipe framing into an elbow, it is the user’s responsibility to force it to do so in other areas. This is done using the FROM/TO end mesh columns in the spread sheet. A tick in either of these columns places a “zone 1” mesh at the corresponding element end (either From or To end). This should be done where the soil enters or leaves the soil, in the vicinity of tees, or in “problem areas”. The soil model number is used to specify whether the soil is buried Complete the spread sheet using the following information. The pipe enters the soil into soil model 2 at node 65, then leaves again at node 75. Enter soil model 2 on element 65-70. On the ‘from end’ of this element (i.e. node 65) place a Zone 1 mesh by checking the box – this is where the pipe enters the soil. The soil model will propagate through the spread sheet, so enter 0 on element 75-80 (the pipe is now in the valve pit, out of the soil). On the previous element, place a zone 1 mesh on the from end (i.e. node 75) – where the pipe exits the soil.

Continuing on, the pipe re-enters the soil at node 115 through to the VAL at node 120.

Next moving on to the 8” pipe line, the pipe enters the soil at node 375, into soil model 3 and remains in the soil until it exits at node 405 at the next valve pit. The one 1 meshes at the bends will be automatically added, we only need to define these at the entry and exit points.

The pipe re-enters the soil at node 445 through to the VAL at node 450. Nodes 50 through to the end are the bypass, and so are above ground.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

After completing the spread sheet, the model can be buried using the Convert Input function.

You will receive a warning during the conversion stating that any user defined intermediate nodes n bends will be deleted – CAESAR II will re-specify these as per the soil meshing algorithm during conversion. Accept this message.

The model will finish converting and will confirm that there were warnings – we only had the one which is OK. Clicking OK will close the buried pipe modeller. The currently selected c2 job file is now the buried pipe model - GASTRANSB. This is identical to any other c2 job file, the only difference between this model and the “unburied” model is the inclusion of a number of restraints with the correct stiffness added as per the soil models input. Return to the piping input to view the updated buried model.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Load Case Setup In order to get the true Expansion Stress in a non-linear system, it is necessary to evaluate the following load cases: Extreme hot operating condition Extreme cold operating condition For this example, this can be implemented as: W+P1+T1 (OPE) HOT W+P1+T2 (OPE) COLD W+P1 (SUS) L1 - L2 (EXP) L3 + L4 (OPE) CAESAR II recommends the following set of load cases to perform these analyses.

This load case setup requires some minor modification. We need to add a third expansion check on the stress range between operating case 1 and 2, along with a baseline for these expansion cases, of the weight no contents of the pipe, which will be used rather than the sustained case. Add the following load cases: L3 L7

WNC L1 – L2

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Also give the load cases meaningful names in the Load Case Options tab

We can now run the analysis

Results Review The results show that there are failures in the expansion case 6. A review of the code compliance report shows that the shakedown stresses on the weld-o-lets branch runs at 30 and 50 are overstressed. The sustained stress is also quite high at these outlets. The range from operating case 1 to operating case 2 is insignificant. Turning on the stress filter to display only nodes greater than 90 per cent of the allowable reduces this report to only the branches at nodes 30 and 50: Reducing these stresses will be left as a follow-up exercise. Now move on to the fatigue evaluation.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe

Fatigue Due to the danger of gas leaks, and the presence of cyclic loading (pressure fluctuations and solar heat/cooling cycles) this system is being evaluated for fatigue failures. Since B31.8 does not offer any specific guidance on fatigue analysis, our best course of action is to calculate the cyclic stresses according to the Stress Intensity equation, and compare them to ASME Section VIII Division 2 fatigue curves (Figure 5.110.1), using an appropriate factor of safety. This system should be evaluated for the following load cases: Design life: 40 years Temperature variations: Ambient temperature: 21C Summer maximum temperature, above ground: 50C (for 40 years) (T1) Summer maximum temperature, below ground: 30C (for 40 years) (T1) Winter minimum temperature, above ground: -5C (for 40 years) (T2) Winter minimum temperature, below ground: 10C (for 40 years) (T2) Daily temperature variation, above ground: 20C from extreme (14,600 days) (T3=T1-Δ, T4=T2+Δ) Daily temperature variation, below ground: 10C from extreme (14,600 days) (T3=T1-Δ, T4=T2+Δ) Pressure variations: Maximum pressure: 80 bar (P1) Annual shutdown: 0 bar (40 times) Minimum operating pressure: 63 bar, varies between 63 and 80 (1,000 occurrences) (P2) Daily fluctuation: 5 bar drop (14,600 days) (P3=P1-Δ) Setting up the Fatigue Load cases Fatigue loads are incurred by transitioning between two or more different operating cases. It is usually best to model the two extreme load cases, and set up all fatigue load cases to be a variation from one of these. For example: Operating Case A: Shutdown, winter minimum (extreme stress condition) Operating Case B: Full pressure, summer maximum (extreme stress condition) Operating Case C: Full pressure, winter minimum (enveloped in A-B cycle) Operating Case D: Compressor operation, winter minimum Operating Case E: Compressor operation, summer minimum fluctuation Operating Case F: Pressure fluctuation, winter minimum Operating Case G: Pressure fluctuation, summer minimum fluctuation Operating Case H: Full pressure, winter maximum fluctuation This translates into operating conditions of: T1 = 50 AG, 30 BG (summer maximum) T2 = -5 AG, 10 BG (winter minimum) T3 = 30 AG, 20 BG (summer minimum) T4 = 15 AG, 20 BG (winter maximum)

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe P1 = 80 bar (maximum) P2 = 63 bar (minimum pressure; compressor setting) P3 = 75 bar (daily minimum) Load Cases (including those required earlier): 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

W+T1+P1 (OPE) Hot operating, also Operating Case B W+T2+P1 (OPE) Cold operating, Operating Case C WNC (SUS) Shakedown Baseline W+P1 (SUS) Sustained W+T2 (OPE) Operating Case A W+T2+P2 (OPE) Operating Case D W+T3+P2 (OPE) Operating Case E W+T2+P3 (OPE) Operating Case F W+T3+P3 (OPE) Operating Case G W+T4+P1 (OPE) Operating Case H L1-L3 (EXP) Expansion Hot L2-L3 (EXP) Expansion Cold L1-L5 (FAT) 40 cycles (Algebraic) -- B-A (Summer MAX > Winter MIN) L2-L6 (FAT) 500 cycles (Algebraic) – C-D (Winter MAX > Winter MIN (P1-P2)) L1-L7 (FAT) 500 cycles (Algebraic) -- B-E (Summer MAX > Summer MIN) L2-L8 (FAT) 7300 cycles (Algebraic) – C-F L1-L9 (FAT) 7300 cycles (Algebraic) – B-G L10-L2 (FAT) 7300 cycles (Algebraic) – H-C

Before fatigue stresses can be checked, the allowable limits must be defined in the input. Return to the first element and click on the Fatigue Curves button at the bottom of the Auxiliary Data Area for Allowable Stress. Fatigue data may be typed in by hand but it may also be read from data files supplied with CAESAR II or built and stored on the hard drive. Select the 5-110-1B.FAT file to use the steel fatigue data for B31.8.

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CAESAR II Statics Training Gas Transmission Pipeline - Buried Pipe Also enter in the correct temperatures and pressures as listed above, changing when the pipe is below/above ground as necessary. Once complete, create the load cases as described

Run the analysis. After reanalyzing the system, select all fatigue loads and the cumulative usage report to evaluate the system loads. It is apparent that fatigue stresses and their associated cycles are quite low. Only the shakedown stresses at the weld-o-lets need be addressed.

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CAESAR II Statics Training Riser

Riser

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CAESAR II Statics Training Riser This job is an offshore jacketed production riser. The job shows how to use the offshore capabilities of CAESAR II. In addition to covering the hydrodynamic analysis techniques, this job also covers model construction, element duplication, and problem resolution. For this system, the piping details are defined in the table below Item

Diameter

Thickness

Temperature

Pressure

Fluid

Riser Jacket Product Core Injection Core

18” 6” 4”

Standard Standard Standard

15°C 80°C 95°C

0 bar 5 bar 10 bar

0 0.85 SG 1.025 SG

Marine Growth 50mm 0 0

The 4" injection line is used to inject water into the well to assist in product recovery. The oil is recovered and pumped to the surface in the 6" product line. The 18" jacket pipe is used to house the riser tubes, offering protection and support. This system is installed in shallow water, and subjected to a specified wave train. The objective of the analysis is to determine the loads and stresses on the system in accordance with ASME B31.4 Chapter IX. The wave parameters are defined in the table below: Item Height Period Depth Wave Theory

Value 5700mm 7.72 sec 9000mm Stokes 5th

Modelling The first thing you may notice on the sketch is that the node increment in this model is 5 rather than 10 as in all the previous models. As such we will adjust the node increment for this model. This change affects this model only. Alternatively the configuration file can be changed if all models should have a different node increment.

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CAESAR II Statics Training Riser This jacketed riser will be modelled in stages, where each stage represents a continuous run of piping from the bottom to the surface. The two core pipes (6" and 4") are enclosed in the jacket pipe (18"). The core pipes are positioned in the jacket through the use of internal spiders (braces). In CAESAR II, these spiders can be modelled using dummy rigid elements, connected to the jacket through the use of CNODES. For the 4" pipe, these dummy rigid elements must be (114.3 mm / 2 + 25 mm = 85 mm), while for the 6" pipe, the dummies are (168.275 mm / 2 + 25 mm = 110 mm). This will provide a clearance of 50 mm between the core pipes. When constructing a model, the first element piping spread sheet is extremely important, since much of its data is duplicated forward throughout the job. Injection Line Set the parameters as follows. Note the node numbering begins at 405 – 410. The “400” series nodes will be for the 4” line Material: A 106 B Diameter: 4” = 114.3mm Wt/Sch: S = 6.0198mm Fluid Density: 1.025 SG = 1024.5 kg/m3 Temp 1: 95°C Pressure 1: 10 bar Design Code: B31.4 Chapter IX Fac: 0.6 Fac is F1, Hoop Stress Design Factor, as per Table A402.3.5(a) of B31.4. Appropriate values are 0.72 for Pipelines or 0.60 for Platform piping and Risers. DZ = -1800mm ANC at 405 Locate a bend at node 410. Specify a bend radius of 203mm Finally, we need to reset the elevation of the system, so that node 405 lies on the sea bottom. (This is important for the wave and wind loading later. While wave loading allows a relative definition of position of the piping in the water, wind does not. Therefore, zero elevation must be properly specified on the system so that the correct wind loads calculated.) Use the global coordinate button to reset the origin, node 405, from (0,0,0) to (0,-9000,0).

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CAESAR II Statics Training Riser Continue to the next element – 410 -415 This is 1500mm in the Y direction, and has two restraints at node 415, an X and a Z. Both the restraints will have a CNODE to 414. Node 414 will be the spider connection as discussed above.

Continue to the next element. As the isometric shows, the riser continues in 1500mm sections, right the way up to node 470 at the top. We can create this all in one element, and break to split up into the 1500mm sections. Change the node numbers to 415 – 470. The pipe travels 16500mm in the Y direction overall.

Now we can break this element with a node increment of 5. Use the break command as before, but this time, select the Insert Multiple Nodes radio button.

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Enter in a node step of 5 – the Total Number and Length fields will be calculated automatically. Also specify the support configuration as at node 415. Checking the system coordinates in the list processor shows that node 440 is at the surface (elevation 0), and there are 12 vertical elements - 6 above the surface and 6 below the surface.

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Add a bend at node 470 and change the radius to 203mm as before. Return to element 410 – 415 (the bottom element on the riser) and add in a +Y support at node 415 with a CNODE to 414. This is done now because this vertical support should not be duplicated to all the spider connections. Complete the riser by adding in the final element (470 – 475). This is 1500mm in the –Z direction and an anchor is located at node 475. The injection line is now complete.

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CAESAR II Statics Training Riser Product Line For the product line, duplicate the injection line, this is essentially duplicating the entire model at this point. This duplication will use a node increment of 200, followed by a modification to the temperature, pressure, diameter, thickness, and fluid specific gravity. Select the entire model and duplicate as follows:

Change the properties of element 605-610 so that they are correct for the 6” line: Diameter: T1: Fluid Density:

6” 80°C 0.85SG

Wt/Sch: P1:

STD 5 bar

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Jacket Important Notes When Duplicating Core / Jacket Piping The diameter is changed after the duplication. Typically, the core pipe uses long radius elbows, and the jacket uses short radius elbows. This allows the radii of both the core and the jacket to be the same. If the jacket contains fluid, its density must be computed such that the unit weight across the entire jacket inner diameter yields the same weight as the real fluid in the annulus between the jacket and core pipes. Core pipes do not see environmental loads. This is important to check after building the model. Continue after the last element (670-675) and change the node numbers again. This time for the 18” pipe – so use node numbers 1810 to 1870. This element is 18000mm long Diameter: T1: P1 Fluid density: Restraints:

18” 15°C zero zero X Y Z RY Marine Growth:50mm

Next break this element, using the multiple break function again, and a node increment of 5. This will split the element into 12 sections, each 1500mm in length.

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CAESAR II Statics Training Riser At node 1870, define a GUIDE restraint. With this element vertical, the program will create an X and a Z restraint at node 1870. The Wind/Wave settings will propgate through the model until changed or turned off, even though on subsequent elements will not have the Wind/Wave check box ticked. On element 1840-1845 (the first pipe out of the water and a t zero elevation), turn off the wave and set a wind shape factor of 0.65. This is a typical value for cylindrical bodies. The model at this point shows the three lines, but they are not properly located in space. A series of construction elements will place these lines properly in space and also provide the right structural connectivity. The idea here is to run a dummy rigid element from the restraint CNODEs of the injection line, to the nodes on the jacket and, on to the restraint CNODEs of the product line. Navigate to the end of the model and define a new element from 414 to 1815. This element will be 85mm long in the X direction, and will connect the restraint at 415 (with CNODE 414) to the jacket at 1815. Define this as a rigid element with zero weight.

Turn off the wind.

Follow with another dummy rigid element from 1815 to 614; 110 mm in X. This will join the product line through the restraint at 615 with its CNODE at 614. The graphics should now display the model correct.

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CAESAR II Statics Training Riser Using the Elements listing, duplicate these last two elements, with a node increment of 5 to place the spider on the next restraint. Continue this duplication so that the spiders are placed all the way up the riser.

Once complete, and all restraints along the riser are defined, run the error checker. There will be a number of warnings concerning "zero weight" rigid elements and "four elements framing into a node". These are all acceptable in this instance. Note that the Centre of Gravity Report shows a combined weight of about 33,000 N. Recall that the riser is supported only at its base, with a pin connection. In reality, risers are supported by top-side tensioners, exerting a force sufficient to ensure the riser is always in tension. For this job, return to the input and at node 1870 (the top of the riser), define a hanger to apply a constant vertical force of 45,000 N. Re-run the error checker. The model should now be ready for analysis.

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Hydrodynamic Theory A basic discussion of hydrodynamic theory can be found in the CAESAR II documentation (Technical Reference Guide, Chapter 6). There are a variety of different wave theories, used to compute the water particle velocities and accelerations resulting from a wave train. CAESAR II includes solutions to the three most commonly used wave theories; Airy, Stokes 5th, and Stream Function. The latter two theories are non-linear, but provide a better description of the water particle behaviour. CAESAR II also includes modified versions of these three theories, which allow consideration of the fluid above the mean sea level. The basic procedure is to solve for the wave length, based on a selected wave theory. Once the wave length is known, the velocities and accelerations can be determined at any position in the water column. Based on these values, drag (Cd), inertia (Cm), and lift (Cl) coefficients are determined for each pipe element. These coefficients, along with the velocity and acceleration are used to compute the force applied to the piping elements, using Morrison's equation: | | Where: = fluid density = drag coefficient = pipe diameter = particle velocity = inertial coefficient = particle acceleration The particle velocities and accelerations are vector quantities which include the effects of any applied waves or currents. In addition to the force imposed by Morrison’s equation, piping elements are also subjected to a lift force and a buoyancy force. The lift force is defined as the force acting normal to the plane formed by the velocity vector and the element’s axis. The lift force is defined as:

Where: = fluid density = lift coefficient = pipe diameter = particle velocity The buoyancy force acts upward, and is equal to the weight of the fluid volume displaced by the element. Once the force on a particular element is available, it is placed in the system load vector just as any other load is. A standard finite element solution is performed on the system of equations which describe the piping system. For this particular model, a sample hand computation will be used to estimate the applied wave load. This will be used as a verification of the loading, to ensure we are making the correct assumptions and modelling correctly.

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B31.4 Code Requirements The B31.4 piping code includes Chapter IX, for "Offshore Liquid Pipeline Systems". The scope of this chapter states: "For the purposes of this Chapter, offshore pipeline systems include offshore liquid pipelines, pipeline risers, offshore liquid pumping stations, pipeline appurtenances, pipe supports, connectors, and other components as addressed specifically in the Code." In Section A401.10.1, this Code states: "All parts of the offshore pipeline system shall be designed for the most critical combinations of operational and environmental loads, acting concurrently, to which the system may be subjected." This means that operating loads are to be combined with wind, wave, and current! In Section A402, this Code states that: - Hoop Stress is limited as defined by: Note that the pressure term used in the hoop stress equation is the difference between internal and external pressure. - Longitudinal Stress is limited as defined by: The longitudinal stress is defined as the axial stress plus or minus the bending stress, whichever results in the larger stress value. - Combined Stress is limited as defined by: Here, Scomb is defined by the Tresca Combined Stress Equation. To satisfy these requirements, a single load case can be defined. This load case should include all loads defined in the input (weight, pressure, temperature, wave, wind, etc). CAESAR II will compute the above stresses for each element and report the maximum stress value with its corresponding allowable. The factors F1, F2, and F3 are defined in the code in Table A402.3.5 (a) as: Location Pipeline Riser

Hoop F1 0.72 0.60

Longitudinal F2 0.80 0.80

Combined F3 0.90 0.90

The B31.4 piping code states that the environmental loads used in the analysis correspond to the "100 year" storm. This is equivalent to the largest storm that occurs every 100 years.

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Hydrodynamic Input The hydrodynamic input specification in CAESAR II is relatively simple. Up to four different loading conditions can be defined. These different conditions could be different waves, currents, or directions. For each of these loading conditions the data is defined as shown below

This particular load definition is specifies only a wave. However, either a standard current profile or a current table can also be defined. The particular wave used in this example is a well-publicised wave, used as the example in the paper by Skjelbreia and Hendricson for the solution to Stokes 5th Order Gravity Waves. Note this does not correspond to a "100 year storm". This wave is being used because it has published results. The wave data consists of the water depth (9 m), the wave height (5.7 m), the wave period (7.72 seconds). The wave kinematics factor is a factor used for Stream Function and Stokes 5th solutions to account for the spreading of the wave energy in a real sea state. Values typically range from 0.85 to 1.0, and serve to reduce the particle velocities. The "Phase Data" defines how the wave is imposed on the piping system. Since the wave moves over the piping system, every element of the system is exposed to every phase of the wave. At one particular position (phase) of the wave the piping system will experience the maximum environmental load. Performing 360 solutions to find this maximum is not practical, given the other factors involved (combination with current, non-uniform sea state, directionality, and spreading). Typically drag governs the loading on (small) piping system, so the wave is positioned so that most of the piping system sees a zero phase angle. Alternatively, the input can be set so that the entire system sees a zero phase angle.

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Wave Solution The hydrodynamic parameters as defined in the input are used by the Stokes 5th wave theory to determine the water particle data. This solution can be evaluated numerically (by reviewing data tables) or graphically (through the use of plots). A brief evaluation is shown below. First, two dimensionless parameters are computed and used to determine the "suggested" wave theory. This evaluation is performed by plotting these dimensionless parameters on a chart, found in a number of publications. This chart, with the location of the specified wave for this job is shown in the figure below. This chart (and the remainder of the wave solution) can be obtained using the “Chart Current Results” button on the Load Case Editor.

For this particular wave, the chart shows that the recommended wave theory is Stream Function 9th Order. (This job will still employ the Stokes 5th solution, for illustrative purposes.) Each region of the chart corresponds to a different wave theory, as detailed in the key at the bottom. The Drop down list at the top of the dialog box allows other graph representations to be shown. Select the “Surface Elevation vs Phase” option

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This results in the following graph.

This figure shows that the wave crest is at a phase of zero, with the trough at a phase of 180 degrees, as expected. Notice also that the wave profile is not symmetric about the mean water level. For this 5.7 m wave, the crest is 4 m above the still water level while the trough is 1.5 m below the still water level. Only the Airy wave theory produces a symmetric wave profile.

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CAESAR II Statics Training Riser Changing the plot to "Horizontal Velocity versus Depth at Zero Phase" results in the figure shown below. This figure shows that the velocity decreases with depth, as expected. Note however that there is still an appreciable velocity, even at the bottom for this particular wave.

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CAESAR II Statics Training Riser Selecting the plot "Horizontal Velocity versus Phase at Zero Depth" results in the figure below. This figure shows that velocities are positive in the wave crest, and negative in the wave trough, again as expected. This is why there is a mean mass transport in the direction of the wave train.

Note that in this plot, the velocity in the trough is shown as zero. This is because the plot is showing the data at a depth of zero, the still water level. In the trough region, the water is below this level. At a lower depth, the velocities do go negative, which can be seen by reviewing the actual data tables.

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CAESAR II Statics Training Riser Selecting the plot "Horizontal Acceleration versus Phase at Zero Depth" results in the figure below. This figure shows that the water particles are accelerating in front of the wave crest, and decelerating behind the wave crest. Again, in the trough area, the plot shows values of zero because the water level is below the "zero" elevation.

Plots such as these are typical of wave solutions. The wave solution produces data for the entire water depth over the entire wave phase. Horizontal and vertical velocities and accelerations can be studied as a function of depth or phase. In addition to plotting the data, the actual numerical values can be reviewed by clicking the View Data Table button. This file is called .WV1 and is a text file – so opens in Notepad.

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CAESAR II Statics Training Riser At the top of this file, the wave length and speed are reported. (The corresponding values from Skjelbreia and Hendricson's paper are 76.2 m (250.0 ft) and 9.87 m/sec (32.39 ft/sec). The difference here is due to a correction to the Stokes solution published in 1985.) This set of tables shows the free surface as a function of phase angle. If the water depth (9 m) is added to these values, the result is the row of values labelled "Surface Elevation". The "Horizontal Velocity" table (for the Z direction) is also shown. The first row (zero depth) and first column (zero phase) were used to produce the velocity plots shown above. Hydrodynamic Coefficients The water particle data can be used directly in Morrison's equation to determine the force acting on the pipe elements. However, in order to employ Morrison's equation, several hydrodynamic coefficients must be determined. These coefficients are a function of the Reynold's and KeuleganCarpenter numbers, and are typically presented in graphical form, as shown in the figure below. These coefficients have been determined through testing.

Cd versus Re and K

Cl versus Re and K

The Keulegan-Carpenter Number, K, is defined as Where: = maximum fluid particle velocity = wave period = characteristic diameter of the element The Reynolds number Re is defined as Where = maximum fluid particle velocity = characteristic diameter of the element = kinematic viscosity of the fluid (1.17 mm2/sec for sea water).

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CAESAR II Statics Training Riser Note that these parameters depend on the water particle velocity as well as the diameter of the pipe element. Therefore, these parameters typically vary over the piping model. For this reason, it is best to leave the entry for these coefficients blank in the input. This will allow CAESAR II to determine the coefficients on an element by element basis during the solution phase of the job. A rough hand computation should be made to ensure that the applied environmental loads are as expected. To assist in this check, a stand-alone load case with only wave loading will be setup to check against these hand computations. The hand computations are shown below. Wave Solution Data Elevation Velocity Elevations are measured from the sea bottom (m) (m/sec) 0 2.3 All data for a phase angle of 0.0° 1.5 2.370 3 2.440 4.5 2.615 6 2.870 7.5 3.235 9 3.710 Hydrodynamic Coefficient Computation Node

Elevation (m)

Velocity (mm/sec)

1810 0 2300 1815 1.5 2370 1820 3 2440 1825 4.5 2615 1830 6 2870 1835 7.5 3235 1840 9 3710 Element Force Computation Element

1810-1815 1815-1820 1820-1825 1825-1830 1830-1835 1835-1840

Avg. Velocity (m/sec) 2.335 2.405 2.528 2.743 3.053 3.473

Acceleration (m/sec2) 0.00 0.00 0.00 0.00 0.00 0.00 0.00

KeuleganCarpenter Number 31.87 32.84 33.81 36.23 39.76 44.82 51.40

Reynolds Number

Cd

Cm

Cl

1.08 E +6 1.11 E +6 1.14 E +6 1.22 E +6 1.34 E +6 1.51 E +6 1.74 E +6

0.661 0.656 0.651 0.639 0.621 0.625 0.631

1.746 1.749 1.751 1.759 1.769 1.765 1.759

0.257 0.250 0.243 0.226 0.202 0.200 0.200

Avg. Cd

Avg. Cl

Diameter (mm)

Density (kg/cm3)

0.658 0.653 0.645 0.630 0.623 0.628

0.254 0.247 0.235 0.214 0.201 0.200

557.2 557.2 557.2 557.2 557.2 557.2

0.001025 0.001025 0.001025 0.001025 0.001025 0.001025

Drag Force (Fd) (N/mm) 1.025 1.079 1.176 1.353 1.658 2.163

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Lift Force (Fl) (N/mm) 0.395 0.408 0.428 0.460 0.534 0.689

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Element 1810-1815 1815-1820 1820-1825 1825-1830 1830-1835 1835-1840

Length (mm) 1500.00 1500.00 1500.00 1500.00 1500.00 1500.00

Fd (N) 1537.29 1618.83 1764.72 2029.74 2468.55 3244.27

Fl (N) 592.13 611.34 642.70 689.51 801.55 1033.02

Total Drag force = 12681.40 N Total Lift Force = 4370.25 N

Notice for these computations, that "average" values are being used for the element velocities and hydrodynamic coefficients. The CAESAR II program actually computes the exact values at integration points on each element, from which the "fixed end forces and moments" are determined.

Wind Loading The default ASCE 95 wind loading procedures will be used on this riser. (This standard states that the minimum wind pressure is 10 lb/sq.ft. or 0.479 KN/sq.m.) The basic procedure to compute the wind load on each pipe element is as follows: Obtain the wind speed (V). From ASCE 95, the Gulf Coast of the U.S. can experience winds of up to 225 km/hr (140 m/hr). API-RP2A recommends a wind velocity of 175 km/hr (109 m/hr) for the Gulf of Mexico. Assume a wind speed of 55m/sec (123 m/hr) for this job. Determine the applicable structural category from ASCE 95, Table 1.1. From this table, select category II (2). Determine the Importance Factor (I) from ASCE 95, Table 6.2. Based on the selected category, the Importance factor is 1.0. Determine the Exposure Category from ASCE 95, Section 6.5.3. For this job, select exposure category D (flat, unobstructed terrain). From ASCE 95, Commentary Section 6.5, determine Kz. This term varies by elevation and therefore may vary from element to element. Constants used in the equations to determine Kz can be obtained from Table C6-2, based on the exposure category. Determine Kzt, which is the wind speed-up over hills. For this job, there are no hills, so Kzt is 1.0. Based on these parameters, compute the velocity pressure as defined in ASCE 95, Section 6.5.1. This is: qz = 0.613 * Kz * Kzt * V2 * I, where all terms are defined above. For this equation, V is expressed in meters per second and qz in newton per square meter. (If V is in mph and qz in lbf/ft2, the constant becomes 0.00256.) Once qz is known, the force on the element can be determined from: F = qz * Gf * Cf * A, where: - Gf is the gust response factor - Cf is the shape factor for the element (defined in the piping input) - A is the projected wind area of the element (including insulation if specified)

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CAESAR II Statics Training Riser The gust response factor Gf can be determined analytically as defined in the ASCE Commentary. However, this procedure requires the first natural frequency of the piping system, which can be obtained through a modal analysis. This dynamic procedure is not addressed in this seminar. If the natural frequency input is left blank, CAESAR II will use a gust response factor of 0.85 as defined in ASCE 95, Section 6.6.1. For this system, the wind load can be defined for the analysis as shown below.

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CAESAR II Statics Training Riser For this system, the applied wind loads can be approximated as shown below. Wind Solution Data (per ASCE 7) Element Mid-Point Alpha elevation (z) (m) 1840-1845 0.75 11.50 1845-1850 2.25 11.50 1850-1855 3.75 11.50 1855-1860 5.25 11.50 1860-1865 6.75 11.50 1865-1870 8.25 11.50 ( )

2/alp ha

4.6/zg

213.36 213.36 213.36 213.36 213.36 213.36

0.174 0.174 0.174 0.174 0.174 0.174

0.0216 0.0216 0.0216

⁄

z/zg

Kz

0.513 0.513 0.513 0.525 0.548 0.568

0.0246 0.0316 0.0387

1.031 1.031 1.031 1.055 1.102 1.142

⁄

where x = max (4.6 or z)

Velocity Pressures Element Kz 1840-1845 1.031 1845-1850 1.031 1850-1855 1.031 1855-1860 1.055 1860-1865 1.102 1865-1870 1.142

V (m/s) 55 55 55 55 55 55

Wind Force Element 1840-1845 1845-1850 1850-1855 1855-1860 1860-1865 1865-1870

G 0.85 0.85 0.85 0.85 0.85 0.85

qz 1912 1912 1912 1957 2044 2117

Zg (m)

I 1 1 1 1 1 1

Cf 0.65 0.65 0.65 0.65 0.65 0.65

qz 1912 1912 1912 1957 2044 2117

Af (m2) 0.686 0.686 0.686 0.686 0.686 0.686

𝑞𝑧

𝐾𝑧

𝐾𝑧𝑡

𝐼

𝑉

𝑞𝑧

𝐺

𝐶𝑓

𝐾𝑧𝑡 = 1.0

Force (N) 725 725 725 741 775 802

𝐹𝑜𝑟𝑐𝑒

Total Applied Force = 4492 N

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𝐴𝑓

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Load Case Setup The load cases required are as below: We require for our code stress check, an operating case for each wind and wave direction. In this case we have a Z direction wind load and wave load Therefore we will create cases for operating conditions PLUS the wind and wave loads and MINUS the wind and wave loads

These load cases can be given more meaningful names in the Load Case options tab

The results for all load cases will be available at the output level, but for the "environmental only" load cases, only displacements and forces will be presented by the output processor. Load cases #4 and #5 are the Code compliance cases necessary for the stress check. The output status for load case #1 could have been set to "discard", since in this instance its results are not significant on their own. However, it may be necessary to evaluate the results of this load case in the event of overloads or over stressed elements. Therefore the output status is left as "keep".)

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Analysis Once the load cases are defined (and the loading data has been checked), the analysis can proceed as usual. At the output level, the results of the "environmental" load cases should be reviewed to ensure they agree with the hand computations. For this job, the environmental loads act on the riser body and are resolved about nodes 1810 and 1870. The restraint summary report details this loading resolution.

For load cases #2 and #3, summing the FZ loads at nodes 405, 475, 605, 675, 1810 and 1870 yields the applied environmental loads. These loads are summarised in the table below. Applied Load Summation (from CAESAR II) Node 405 475 605 675 1810 1870

Wave Drag Fz (N) 539 380 1697 1145 6749 2030

Total Load: 12540

Lift Fx (N) 78 85 287 299 2769 810

Wind Fz (N) 105 200 347 589 631 2620

4328

4492

These loads can be compared to the hand computed results of 12681 N, 4370 N , and 4492 N. This is an acceptable comparison, given the approximations made in the hand computations.

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CAESAR II Statics Training Riser The code compliance report shows that there is a failure in one of the operating cases. This is located around the bottom of the riser on the elbow. Reviewing the Stress Report shows that the bending stress is dominating the behaviour of the system at these points.

One solution here is to reduce the thermal component of the stress by extending the bottom-side piping, from 1800 mm to 3000 mm. This drops the stress level to 86.5% of the allowable. (This job is not intended to be an example of good riser design. The riser tension was arbitrarily selected to be simply larger than the "air weight" of the riser. Additional vertical supports may be used along the length of the riser to assist in supporting the core piping. For larger (longer) risers, external buoyancy chambers are used to offer additional vertical support along the riser body. None of these concepts are addressed in this example.) (Fatigue has not been addressed in this example, but is typically a required consideration. For this job, the fatigue (FAT) case would be defined as "L4-L5" with a specified number of cycles and a corresponding material fatigue curve.)

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CAESAR II Statics Training SUPT01 – Water Hammer

SUPT01 – Water Hammer

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CAESAR II Statics Training SUPT01 – Water Hammer This exercise introduces the Occasional stress evaluation in B31.3. We will return to the model produced previously SUPT01 and simulate a fluid hammer event acting when the valve slams shut. This force will be applied to the model and defined as a shock load case and evaluated according to the Occasional stress requirements of B31.3. For Occasional stress evaluation, B31.3 requires: Long. Sustained Stresses + Long. Occasional Stresses ≤ k Sh, where k = 1.33 In CAESAR II, this equates to a SCALAR summation of the SUS case with the OCC case, using the OCC stress type. Note: The OCC stress type serves two purposes: (1) it directs that stresses be calculated according to the “occasional equation”, and (2) it activates (i.e., locks) any snubbers in the model.

Edit the Model Open the file created previously SUPT01. Using File > Save As… create a new file called SUPT01 fluid Hammer.c2 There are some slight changes to the support configuration in this file compared to our analysis done previously. Edit the support configuration as shown in the isometric sketch, and as detailed below. Element 20-30 o Break this element o Create a new node number 22, located 1400mm from node 20. o Add a +Y restraint at node 22 Element 30-33 o Change the “to node” from 33 to 34 o Edit the length of this element and change to 6000mm o Add a +Y restraint at node 34 Element 33-37 o o o o o

Change the “from node” from 33 to 34 Change the “to node” from 37 to 36 Edit the length of this element to be 6000mm Remove the +Y restraint Add a spring Hanger at node 36. Carpenter & Paterson hanger table

Element 37-40 o Change the “from node” from 37 to 36 o Edit the length of this element to 1715mm Node 43 o

Remove the Spring hanger

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CAESAR II Statics Training SUPT01 – Water Hammer Element 50-57 o o o o

Break this element Create a new node number 55, located 3250mm from node 50 Remove the +Y support at node 57 Add a Carpenter Spring Hanger at node 55

Element 70-77 o Change the “to node” to be 72 o Edit the length to be 2000mm o Edit the support node number to be 72 Element 77-80 o Change the from “node” to be 72 o Edit the length to be 2115mm Element 80-90 o Break this element o Create a new node number 85, located 1000mm from node 80 o Insert a +Y at this location

Determine the Load Consider water hammer acting when the valve at node 70 slams shut. This creates an unbalanced force due to the propagation of a pressure wave. The water hammer load can be estimated using Joukowski’s equation:

Where:

D t

= force acting on valve seat = dynamic load factor (use 2.0) = pressure change = = internal area of pipe (0.073 m2 for 12” std pipe) = density of fluid (1000kg/m3 for water) = speed of sound in the fluid (typ. 1000 – 2000 m/sec in water based on D/t) = change of fluid velocity (typically 1.5 – 3m/sec for water) = mean pipe diameter = pipe wall thickness

Wave speed & pressure change for water in steel pipe (ΔP/ΔV= ρ·c): D/t C (m/sec) ΔP/ΔV (bar/(m/sec)) 20 1310 13.1 40 1210 12.1 60 1130 11.3 80 1065 10.65 Using D / t = 314 / 9.5 = 33, ΔP/ ΔV = approximately 12.45 bar / (m/sec); assume ΔV = 2 m/sec; so:

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CAESAR II Statics Training SUPT01 – Water Hammer Define the Occasion Load Model a Z-direction force at node 70, equal to 364,000 N, as calculated previously.

Load Case Setup Build the shock load case(s). The hammer load may be reversing, so build both a +F1 case and a –F1 case. Then build a SCALAR combination case combining the SUS and OCC load cases:

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CAESAR II Statics Training SUPT01 – Water Hammer

Check the Results Immediately it can be seen that there are issues with the OCCasional load cases. What is causing these issues? Is this an accurate simulation? Viewing the restraint summary shows that the loads on the restraints at nodes 22 and particularly 85 – both show zero load – an immediate uplift – for at least one of the hammer cases. If a +Y restraint actually lifted off, it would first have to overcome the pre-existing downward load present during the operating case. So what we have here is not an accurate simulation

Reset the Load Cases This points out the danger when modelling occasional loads on non-linear systems: load stepping must be considered, i.e., first apply the operating loads, then apply the occasional loads, then isolate the occasional loads by subtracting the former from the latter. This accurately models the effects of the pre-existing restraint status. This can be done using the following load cases:

Remember to change the load case combination method to Scalar for the OCC load cases in the load case options tab.

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CAESAR II Statics Training SUPT01 – Water Hammer

Check Results There are still issues in the OCC load cases, but Note that even though the pipe lifts off of the restraint at node 22, the “occasional only” load, Load Case 7, does overcome the pre-existing operating load first, for an accurate simulation of events:

The Code Compliance Evaluation shows that the system is still highly overstressed under this OCC load. This problem can be resolved by adding restraint (since the water hammer is a primary load). We can use a rigid Z-restraint to contain the water hammer if we can find a point in the vicinity of the load (run 50-80) where the Z-operating displacement is negligible (so the previous expansion and sustained analyses will be relatively unaffected). A good candidate is at node 78 as the OPErating displacement report shows.

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CAESAR II Statics Training SUPT01 – Water Hammer

Correct model Return to the input and select element 72-80. Node 78 is on the 0 angle of the bend at the “to” end of this element.

Place a Z restraint at this location

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CAESAR II Statics Training SUPT01 – Water Hammer With a Z-restraint at node 78, the stresses have decreased significantly

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