Piping stress

1.

Introduction

Caesar II, Version 4.20, used in FEDO, is a PC based pipe stress analysis software program developed by COADE/ Engineering Physics Software Inc. This software package is an engineering tool used in the mechanical design and analysis of piping systems. The user creates a model of the piping system using simple beam elements and defines the loading conditions imposed on the system. With this input, the software produces results in the form of displacements, loads and stresses throughout the system. Additionally the software compares these results to limits specified by recognised codes and standards. The minimum system requirements are; •

Intel Pentium microprocessor

•

Windows 95 and above

•

32 MB RAM

•

76 MB disk space

•

800 x 600 resolution using small fonts and 1024 x 786 using big fonts.

The new features of Caesar II are listed below. •

New Input Graphics - utilizes a true 3D library, enabling graphic element selection

•

Element input or redirection via local coordinate (cosines) system

•

Completely revised material data base, including Code updates

•

Optional static output in ODBC compliant data base for static restraints is available

•

Hydrodynamic loading for offshore applications. This includes the Airy, Stokes 5th, and Stream Function wave theories, as well as Linear and Power Law current profiles.

•

Wind analysis expanded to handle up to 3 wind load cases

•

New piping codes: B31.4 Chapter IX, B31.8 Chapter VIII, and DNV (ASD)

•

A wave scratchpad - see the recommended theory graphically, or plot the particle data for the specified wave.

•

Hydra expansion joint data bases

•

A new / revised expansion joint data base is available as a result of the merger of Senior Flexonics and Pathway Bellows

•

A new hanger table (Myricks) is available.

•

Updated piping codes: B31.1, B31.3, B31.4, ASME NC, ASME ND

•

Automatic Dynamic DLF Plotting

•

PCF Interface

2.

Working in Caesar II

2.1. Invoking Caesar II Double-clicking the CAESAR II icon, which should point to the program C2.EXE in the CAESAR II installation directory, will start the CAESAR II program. Click on File-New/ Old to open the relevant file. Selecting a job name does not open the file; as noted, it simply indicates the job on which input modeling, analysis, output review, or other operations will be done. The user must still select one of these operations from the menu.

2.2. Input Piping Once the desired job name has been specified, the user can invoke the interactive model builder by selecting the Input-Piping entry of the Main Menu. The preferred method of data entry is the piping spreadsheet. Here each pipe element is described in its own sheet. The right side of the screen offers an auxiliary area, with changing data-fields that support items entered through check boxes pressing [F12] alternatively displays the various auxiliary screens). 1.

Enter the node numbers - These points are used as locations at which information may be entered or extracted. CAESAR II can generate both values if the AUTO_NODE_INCREMENT directive is set to a value other than zero using the Tools-Configure/Setup + Geometry Directives option of the Main Menu.

2.

Enter the Dx, Dy or Dz value i.e., the distance for the respective node numbers. Where the piping element is skewed, two or three entries must be made. One or more entries must be made for all elements except “zero length” expansion joints.

3.

•

Offsets can be used to modify the stiffness of the current element by adjusting its length and the orientation of its neutral axis in 3-D space.

•

This auxiliary screen is used to specify offsets to correct modeled element length and orientation to actual length and orientation. Offsets may be specified at From and/or To nodes.

Enter the pipe diameter and the thickness. Mill tolerance is automatically generated. Nominal diameters, thickness, and schedule numbers are a function of the pipe size specification. ANSI, JIS, or DIN are set via the Tools-Configure/Setup option of the Main Menu.

4.

Enter the corrosion thickness given in the specification.

5.

Enter the insulation thickness given in the specification.

6.

Enter the temperature and pressure. CAESAR II uses an ambient temperature of 70°F, (21 0C) unless changed using the Special Execution Parameters Option. Each temperature and each pressure entered creates a loading for use when building load cases. Both thermal and pressure data carries forward from one element to the next until changed.

7.

Enter the special element information. The end connection whether it is a bend, rigid element like valves, flanges etc. is to be entered. Double click the selected box, which opens an auxiliary table. Here the details of the bend are entered in another screen, which appears, on the right. The Node numbers are generated automatically. •

Bends - This auxiliary screen is used to enter information regarding bend radius, miter cuts fitting wall thickness, or attached flanges.

8.

9.

•

Rigid Elements - This auxiliary screen is used to enter the weight of a rigid element. If no weight is entered CAESAR II models the element as a weightless construction element.

•

This auxiliary screen is used to enter the expansion joint stiffness parameters and effective diameter. For a non-zero length expansion joint, either the transverse or bending stiffness must be omitted. Setting the effective diameter to zero de-activates the pressure thrust load. This method may be used (in conjunction with setting a large axial stiffness) to simulate the effect of axial tie-rods.

Enter the details of the boundary conditions, like restraint, hangers, nozzles, displacements, etc., at the respective node number. Double click the selected box, which opens an auxiliary table. •

This auxiliary screen is used to enter data up to four restraints per spreadsheet.

•

This auxiliary screen is used to enter imposed displacements at up to two nodes per spreadsheet.

•

This auxiliary screen is used to describe flexible nozzle connections. When entered in this way, CAESAR II automatically calculates the flexibilities and inserts them at this location. CAESAR II calculates nozzle loads according to WRC 297, API 650 or BS 5500 criteria.

•

This auxiliary screen is used to describe hanger installations. Hanger data may be fully completed by the user, or the hanger may be designed by CAESAR II.

Enter the details of the loading conditions, like forces/ moments, uniform loads, wind/ wave loads, etc., at the respective node number. Double click the selected box, which opens an auxiliary table. •

This auxiliary screen is used to enter imposed forces and/or moments at up to two nodes per spreadsheet.

•

This auxiliary screen is used to enter up to three uniform load vectors (load components U1, U2 and U3).

•

This auxiliary screen is used to specify whether this portion of the pipe is exposed to wind or wave loading. This screen is also used to enter the Wind Shape Factor (when Wind is specified) and various wave coefficients (if left blank they will be program-computed) when Wave Loading is specified.

10.

The piping material is selected next from the drop list. The program provides a database containing the parameters for many common piping materials. Caesar II requires the pipe material’s elastic modulus, Poisson’s ratio, density, and (in most cases) expansion coefficient. The coefficient of expansion does not appear on the input screen, but it can be reviewed during error checking.

11.

Double click the allowable stress box and select the code. •

This auxiliary screen is used to select the piping code (from a drop list) and to enter any data required for the code check. Allowable stresses are automatically updated for material, temperature and code if available in the material database.

•

Material Fatigue Curve data may be entered by clicking on the Fatigue Curve button. This brings up a dialog where stress vs. cycle data (up to 8 points per curve) may be entered for Butt Weld and Fillet Weld components.

•

12.

Enter the fluid density as specific gravity, which, is automatically converted, into density. Density of the pipe is automatically generated. The densities of the insulation, and fluid contents can also be specified in this block. •

13.

The Fatigue Curve data may also be read in from a COADE-supplied or usercreated file. Access these file by pressing the Read from Files button on the Fatigue Curve Dialog.

This auxiliary screen is used to enter stress intensification factors, or fitting types at up to two nodes per spreadsheet. If components are selected from the drop list, CAESAR II automatically calculates the SIF values as per the applicable code

Press Cntrl C to continue.

Once the model is completed, the job can be analyzed by exiting the piping preprocessor and starting error checking. This can be done using the File-Start Run menu option, the Start Run toolbar, or the Start Run option from the Quit Menu (invoked upon closing the input processor with the [Esc] key). The preferred method for leaving the input preprocessor is via option Start Run. This option saves the data file and invokes the Piping Error Checker. The Batch Run option saves the data, invokes the error checker, and then continues with the analysis, all without user interaction.

2.3. Error Checking The Model There are two main functions for the error checker; 1.

To verify the user’s input data

2.

To build the execution data files utilized by the remainder of the CAESAR II program.

The verification of the user’s input data consists of checking each individual piping element for consistency. Once invoked, the error checker reviews the CAESAR II model and alerts the user to any possible errors, inconsistencies, or noteworthy items. These items are presented to the user as Errors, Warnings, or Notes. •

Errors are flagged when there is a problem with the model due to which analysis cannot continue. An example of this would be if no length is defined for a piping element. These errors are also called fatal errors, since they are fatal to the analysis, and must be corrected before continuing.

•

Warnings are flagged whenever there is a problem with a model, which can be overcome using some assumptions. An example of this would be if an element’s wall thickness is insufficient to meet the minimum wall thickness for the given pressure (hoop stress). Warnings need not be corrected in order to get a successful analysis.

•

Notes simply inform the user of some noteworthy fact related to the model. An example of a note may be a message informing the user of the number of hangers to be designed by the CAESAR II pro-gram.

If the error check process completes without fatal errors, a center of gravity report is presented and the analysis data files can be generated and the solution phase can commence. Upon successful completion of the error checking routines, the user is, by default, returned to the main CAESAR II menu.

2.4. Building static Load Cases A static analysis can be started from the Main Menu once the error checker has generated the analysis data files. The first stage of a static analysis is the setup of the load cases. In CAESAR II terms, a load case is a group of piping system loads that are analyzed together, i.e., that are assumed to be occurring at the same time. An example of a load case is an operating analysis composed of the thermal, deadweight, and pressure loads together. Another is an as-installed analysis of deadweight loads alone. A load case may also be composed of the combinations of the results of other load cases; for example, the difference in displacements between the operating and installed cases. No matter what the contents of the load case, it always produces a set of reports in the output, which list restraint loads, displacements and rotations, internal forces, moments, and stresses. Because of piping code definitions of calculation methods and/or allowable stresses, the load cases are also tagged with a stress category. For example, the combination mentioned above might be tagged as an expansion stress case. Available piping system loads are displayed on the left hand side of the Static Load Case screen. Available stress types are displayed in the lower left hand side of the Static Load Case screen. 1.

The Load Case Builder is invoked by selecting the Analysis + Statics option of the Main Menu.

2.

For new jobs (no previous solution files available), the static analysis module recommends load cases to the user based on the load types encountered in the input file. These recommended load cases are usually sufficient to satisfy the piping code requirements for the Sustained and Expansion load cases. This can be invoked by clicking the recommend button. If the job has been run previously, the loads shown are those saved during the last session. •

The user can define up to ninety-nine load cases. Load cases may be edited by clicking on a line in the Load List area.

•

Only the load components listed in the upper left-hand portion of the screen may be specified in the load cases. Available stress types are also specified. Stress type determines the stress calculation method and the allowable stress to use (if any).

3.

The basic Load cases may be built through drag and drop actions. Dragging a load component from the Loads Defined in Input list to a line on the load list automatically adds the load component to the load case, if it is not already included. Dragging a stress type from the Available Stress Type list to a load case in the list changes the stress type for that case.

4.

Combination cases, if present, must always follow the basic cases. They are built by selecting (one or more), dragging, and dropping basic load cases from earlier in the load list to combination cases (or blank load cases) later in the load list.

5.

Up to four different wind load cases may be specified for any one job. The only wind load information that is specified in the piping input is the shape factor that causes load cases WIN1, WIN2, WIN3, and WIN4 to be listed as an available load to be analyzed. When wind loads are used in the model, CAESAR II makes available the screen to define the extra wind load data. Once defined, this input is stored and may be changed on subsequent entries into the static analysis processor.

6.

Up to four different hydrodynamic load cases may be specified for any one job. Several hydrodynamic coefficients are defined on the element spreadsheet. The inclusion of hydrodynamic coefficients causes the loads WAV1, WAV2, WAV3, and WAV4 to be available in the load case editor.

2.4.1 Recommended Load Cases For Hanger selection If spring hangers are to be designed by the program, two additional load cases must first be analyzed in order to obtain the data required to select a variable support. The two basic requirements for sizing hangers are 1. The deadweight carried by the hanger (hot load) 2. The range of vertical travel to be accommodated. The first load case (traditionally called “Restrained Weight”) consists of only deadweight and applied forces (W+F1). For this analysis CAESAR II includes a rigid restraint in the vertical direction at every location where a hanger is to be sized. The load on the restraint from this analysis is the deadweight that must be carried by the support in the hot condition. For the second load case, the hanger is replaced with an upward force equal to the calculated hot load, and an operating load case is run. This load case (traditionally called “Free Thermal”) includes the dead weight and thermal effects, the first pressure set (if defined), any displacements, and the applied forces (W+D1+T1+P1+F1). The vertical displacements of the hanger locations, along with the previously calculated deadweights are then passed on to the hanger selection routine. Once the hangers are sized, the added forces are removed and replaced with the selected supports along with their pre-loads (cold loads). CAESAR II then continues with the load case recommendations as defined above. A typical set of recommended load cases for a single operating load case spring hanger design appears as follows: Case # 1

-

W+F1

-

WEIGHT FOR HANGER LOADS

Case # 2

-

W+D1+T1+P1+F1

-

OPERATING FOR HANGER TRAVEL

Case # 3

-

W+D1+T1+P1+F1 (OPE)

-

OPERATING (HGRS. INCLUDED)

Case # 4

-

W+P1+F1 (SUS)

-

SUSTAINED LOAD CASE

Case # 5

-

DS3-DS4 (EXP)

-

EXPANSION LOAD CASE

These hangers sizing load cases (#1 & #2) supply no information to the output reports other than the data found in the hanger tables. Note how cases 3, 4, & 5 match the recommended load cases for a standard analysis with one thermal and one pressure defined. Also notice how the displacement combination numbers in case 5 have changed to reflect the new order. If multiple temperatures and pressures existed in the input, they too would appear in this set after the second spring hanger design load case. Two other hanger design criteria also affect the recommended load cases. 1. If the “actual cold loads” for selected springs are to be calculated, one additional load case (WNC+F1) would appear before case #3 above. 2. If the piping system’s hanger design criteria is set so that the proposed springs must accommodate more than one operating condition, other load cases must additionally appear before the case #3 above. An extra hanger design operating load case must be performed for each additional operating load case used to design springs.

2.5. Executing Static Analysis

Once the load cases have been defined, the user begins the actual finite element solution through the use of the File-Analyze command on the Static Analysis screen toolbar/ menu. The solution phase commences with the generation of the element stiffness matrices and load vectors, and solves for displacements, forces and moments, reactions, and stresses. This solution phase also performs the design and selection of spring hangers, and iterative stiffness matrix modifications for nonlinear restraints. The user is kept appraised of the solution status throughout the calculation. The static analysis performed by CAESAR II follows the regular finite element solution routine. •

Element stiffness is combined to form a global system stiffness matrix.

•

Each basic load case defines a set of loads for the ends of all the elements. These elemental load sets are combined into system load vectors.

•

Using the relationship of force equals stiffness times displacement (F=KX), the unknown system deflections and rotations can be calculated.

•

The known, however, may change during the analysis as hanger sizing, nonlinear supports, and friction all affect both the stiffness matrix and load vectors.

•

The root solution from this equation, the system-wide deflections and rotations, is used with the element stiffness to determine the global (X, Y, Z) forces and moments at the end of each element.

•

These forces and moments are translated into a local coordinate system for the element from which the code-defined stresses are calculated.

•

Forces and moments on anchors, restraints, and fixed displacement points are summed to balance all global forces and moments entering the node.

•

Algebraic combinations of the basic load cases pick up this process where appropriate at the displacement, force & moment, or stress level.

2.6. Static Output Processor A review of the static analysis results is possible immediately after a static solution, or at a later time by selecting the Output-Static option of the CAESAR II Main Menu. The static output processor presents the user with an interactive selection menu from which load cases analyzed (left hand column), report options (center column) and general computed results (left hand column) (which show reports such as input listings or hanger selection reports that are not associated with load cases) can be selected. Results can be reviewed by selecting one or more load cases along with one or more reports (selection is done by clicking and ctrl-clicking the mouse). The results can be reviewed on the terminal, printed, or sent to a file, by using the View Reports, FileSave/ Save As, or File-Print menu commands and/or toolbars. The user can also use the View-Plot menu command or the Plot toolbar to review the analytic results in graphics mode, which can produce displaced shapes, stress distributions, and restraint actions. Various commands are available in File, View Filters, Options and Show menus in the menu bar. For most load cases (except hanger design and fatigue) there are seven different report options that can be selected for review. They are 1. Displacements - Translations and rotations for each degree of freedom are reported at each node in the model. 2. Restraints - Forces and moments on each restraint in the model are reported. There is a separate report generated for each load case selected.

3. Restraint Summary - Similar to the restraint report, this option provides force and moment data for all valid selected load cases together on one report. 4. Global Element Forces - Forces and moments on the piping are reported for each node in the model. 5. Local Element Forces - These forces and moments have been transferring into the CAESAR II local coordinate system. 6. Stresses – SIF’s and Code Stresses are reported for each node in the model. The code stresses are compared to the Allowable stress at each node as a percentage. Note that stresses are not computed at nodes on rigid elements. 7. Sorted Stresses – Bending, Torsion, and Code Stress each are sorted from highest to lowest value with corresponding node numbers.

2.6.1 Notes on Printing Reports and Plots Typically, the set of output reports that a user might wish to print out for documentation purposes might be: Load Case

Report

Purpose

SUSTAINED

STRESS

Code compliance

EXPANSION

STRESS

Code compliance

OPERATING

DISPLACEMENTS

Interference checks

OPERATING

RESTRAINTS

Hot restraint, equipment loads

SUSTAINED

RESTRAINTS

As installed restraint, equipment loads

The Cumulative Usage report is available only when there are one or more fatigue-type load cases present. One Cumulative Usage report is generated, regardless of the number of load cases selected, showing the combined impact of simulating selected fatigue loadings. All reports that are to be saved in the output file need not be declared at one time. Subsequent reports sent to the file during the session are appended to the file started in the session. (These output files are only closed and overwritten when a new output device, such as a printer, or another file, is defined.) Upon closing a series of reports, either to the printer or a file, a Table of Contents is printed. The static results may be reviewed graphically by executing the plot commands with any active load case selected. The CAESAR II output plotting is quite comprehensive. Options + Graphical output invokes the graphical mode. Only then do the Plot Options Plot view and the show buttons come alive. The show menu can be used to output a wide variety of outputs. CAESAR II allows the user to view the piping system as it moves to the displaced position of the basic load cases. To animate the static results, execute the ViewAnimate command. The animated plot menu has several plot selections. Motion and Volume Motion are the commands to activate the animation. Motion uses centerline representation while Volume Motion produces volume graphics. The desired load case may be selected from the drop down list. Animations may be sped up or slowed down or stopped using the toolbars.

3.

The Caesar II Main Menu

3.1. File Menu All CAESAR II analyses require a job name for identification purposes— subsequent input, analysis, or output review references the job name specified. The job name is selected using the File menu, using one of three methods. Whenever the user wishes to begin a new job, selecting File-New (or clicking the New toolbar) invites the user to enter a job name and data directory. •

Set Default Data Directory – The selection of the data directory is very important since any configuration, units, or other data files found in that directory are considered to be “local” to that job.

•

New

• •

Open Clean Up (Delete) Files - Use this directive to delete unwanted scratch files, listing files, input, and output files to retain more hard disk space.

•

Recent Piping Files

•

Recent Structural Files

•

Exit

3.2. Input The user can invoke the interactive model builder by selecting the Input-Piping entry of the Main Menu. The input generation of the model consists of describing the piping elements, as well as any external influences (boundary conditions or loads) acting on those elements. •

Piping

-

Input Screen appears

•

Underground

-

Convert existing pipeline to underground

•

Structural Steel

-

Structural Model

Each pipe element is identified by two node numbers, and requires the specification of geometric, cross sectional, and material data. The preferred method of data entry is the piping spreadsheet. Each pipe element is described on its own spreadsheet. •

Node Numbers

-

•

Element Lengths -

Dx, Dy, Dz.

•

Offsets

To adjust modelled pipe to actual

•

Diameter

•

Schedule

•

Mill Tolerance %

•

Corrosion

•

Insulation Thickness

•

Temperature

-

(9, default ambient. temp. 70o F)

•

Pressure

-

(9 Pressures, operating & Hydro test)

•

Special Element Information

•

Bend

-

Radius, Angle

•

Rigid

-

Weight of rigid element

•

Expansion Joints -

-

They are generated automatically.

Jt. stiffness and effective dia.

•

Reducer

•

SIF’s and Tees

•

Structural

•

Restraints

•

Hangers

•

Nozzles

•

Displacements

•

Equipment

•

Forces/ Moments

•

Uniform Loads

•

Winds and Wave

•

Thermal Blowing

•

Pitch & Roll

•

Piping Material

•

Allowable Stress

•

Material Elastic Properties

•

Elastic Modulus (C)

•

Poisson’s Ratio

•

Pipe Density

•

Fluid Density

•

Refractory Density

•

Insulation Density

•

Auxiliary data Area

•

Allowable Stress (SC, SH, F, Eff, Fac, Sy, PVar)

•

Fatigue Curves Butt Weld & Fillet Weld, Cycles, Stress)

-

Maximum 4 Restraints

3.2.1 File The File menu is used to perform actions associated with opening, closing and running the job file. •

New

•

Open

•

Save

•

Save As

•

Archive

-

Allows password protection for files

•

Start Run

-

Sends model through interactive error check

This command exits the input processor, starts the error checking procedure, and returns the user to the Main Menu for further action. •

Batch Run -

Halts only for fatal errors

This command causes the program to check the input data, analyze the system, and present the results without any user interaction. •

Print

•

Print Preview

•

Print Setup

•

Recent Files

•

Exit

Once the model is completed, the job can be analysed by exiting the piping pre processor and starting error checking. This can be done using the File-Start Run menu option, the Start Run toolbar, or the Start Run option from the Quit Menu (invoked upon closing the input processor with the [Esc] key). The preferred method for leaving the input pre processor is via option Start Run. This option saves the data file and invokes the Piping Error Checker. The Batch Run option saves the data, invokes the error checker, and then continues with the analysis, all without user interaction.

3.2.2 Edit The edit menu provides commands for cutting and pasting, navigating through the spread sheets, and performing a few small utilities. •

Cut

-

•

Copy

-

•

Paste

-

•

Continue

-

Moves the spreadsheet to the next element

•

Insert

-

Inserts before or after current element

•

Delete

-

Deletes current element

•

Find

-

find an element containing one or more named nodes

•

Global

-

Prompts for global co-ordinates

•

Close Loop -

Closes loop by filling in delta cord. bet. 2 nodes

•

Increment -

Changes automatic node increment

•

Distance

-

Calculates distance bet. Origin and a node

•

List

-

Alternative format

•

Next Element

•

Previous Element

•

First Element

•

Last Element

Unlike the Continue command, [Pg Dn] does not create a new element once the end of the model is reached.

3.2.3 Model The Model menu contains modeling aids, as well as means for entering associated, system wide information. •

Break

-

Breaks nodes into multiple nodes

•

Valve

-

Model a valve or flange from database

•

Expansion Joint

-

•

Title

-

•

Hanger Design Control Data – System wide hanger design criteria

Activates expansion joint modeller

3.2.4 KAux •

Review SIF’s at Intersection Nodes - What if tests on SIF’s at intersections

•

Review SIF’s at Bend Nodes

•

Special Execution Parameters- Options affecting analysis of current jobs

•

Include Piping Input Files model.

•

Include Structural Input Files

•

Show Informational Messages

- What if tests on SIF’s at bends - Allows other piping models in the current

3.2.5 Plot •

Standard Graphics

•

3D Modeller

- File, Edit, Options, View

Icons on the tool bar and the drop list of the menu, permits many other functions like pan, zoom render etc. in the plot menu. CAESAR II graphics screen can be displayed with the Plot menu command or toolbar.

3.2.6 Help •

Press F1 or? For Help

3.3. Analysis A static analysis can be started from the Main Menu once the error checker has generated the analysis data files. For new jobs, the static analysis module recommends load cases to the user based on the load types encountered in the input file. These are usually sufficient to satisfy the piping code requirements for the Sustained and Expansion load cases. The Load Case Builder is invoked by selecting the AnalysisStatics option of the Main Menu. •

Statics

-

Static Analysis after error checking

•

Dynamics

-

Dynamic Analysis after error checking

•

SIF’s @ Intersections Factors.

-

Scratch pads

•

SIF’s @ Bends

-

Scratch pads used to calculate SIF’s

•

WRC 107

-

Calculate stresses in vessels due to piping

•

WRC 297

-

Calculate stresses in vessels due to piping

•

Flanges

-

Perform Flange stress and leakage calc.

•

B 31.G

-

Estimate pipeline remaining life

•

Expansion joint rating

-

Evaluate exp. joints using EJMA

•

AISC

-

Perform AISC code check on structural steel

•

NEMA SM23

•

API 610

-

Evaluate loads on centrifugal pumps

•

API 617

-

Evaluate loads on compressors

•

API 661

-

Evaluate loads on air cooled HE

•

HEI Standard

-

Evaluate loads on feed water heaters

•

API 560

-

Evaluate loads on fired heaters

-

to calculate

Stress

Intensification

Evaluate loads on steam turbine Nozzles

Once the load cases have been defined, the user begins the actual finite element solution through the use of the File-Analyze command on the toolbar. The solution phase commences with the generation of the element stiffness matrices and load vectors, and solves for displacements, forces and moments, reactions, and stresses. This solution phase also performs the design and selection of spring hangers, and iterative stiffness matrix modifications for non linear restraints. The user is kept apprised of the solution status throughout the calculation. A review of the static analysis results is possible immediately after a static solution, or at a later time by selecting the Output-Static option of the CAESAR II Main Menu. The static output processor presents the user with an interactive selection menu from which load cases and report options can be selected.

3.4. Output •

Static

- Static Results

•

Harmonic

- Results of Harmonic loading

•

Spectrum/ Modal - Results of natural frequency/ mode shape calculations or uniform/ force spectrum loading

•

Time History

•

Animation

- Results of time history load simulations - Animated graphic simulation of results

•

Mode Shapes

•

Harmonic

•

Time History

•

Static

3.5. Tools •

Configure/ Setup

- Configures Caesar II in a directory basis

•

Calculator

•

Make Units File

•

Convert input to new units

•

Material Data Base

- Edits or adds to Caesar II data base

•

Accounting

- Activates or customises job acc.

•

Multi-job analysis

- runs a stream of jobs without intervention

•

External Interface

- Interfaces to 3rd party software

- Creates custom units

•

Caesar II Neutral File

•

Caesar II Data Matrix

•

Batch output File

•

CADWorx/ Pipe

•

AutoCAD DXF File

•

CADPIPE

•

CATIA – CCPlant

•

Computervision

•

Intergraph

•

ISOMET

•

PRO-ISO

•

PCF

•

Auto Plant

•

LIQT

•

PIPENET

3.6. Diagnostics •

CRC Check

- Verifies, program files are not corrupted

•

Build Version

- Builds files of this version

•

Error Review

- Review description of Caesar II errors

•

DLL version Check

- Checks DLL files for this version

3.7. ESL (External Software Lock) •

Show Data

- Displays data stored on the ESL

•

Phone Update

•

Generate Fax Codes

•

Enter FAX Authorisation Codes

3.8. View •

Toolbar

•

Status Bar

3.9. Help •

Tip of the day

•

On Line Documentation •

User's Manual

•

Application Guide

•

Technical Reference Manual

•

Quick Reference Guide

•

On Line Registration

•

Information

•

About Caesar II

Throughout the CAESAR II program, context-sensitive help (including the units requested, where applicable) is available by pressing [F1] on any field.

4.

Input

4.1. Piping

3.2.7. Static analysis cannot be performed until the error-checking portion of the piping pre processor has been successfully completed. Required analysis data files are created only after this. If the input is changed, error checking has to be done before reading the output. 3.2.8. This is initiated from the quit options upon exit of piping input. 3.2.9. If there are no errors a centre of gravity report is given. If there are errors, Return to piping input Return to Caesar II Main Menu Restart Error Processing from the Beginning 3.2.10.Analysis – Static 3.2.11.Static load case editor screen list all available loads that are defined in the input, available stress type and the current load cases offered for analysis. 3.2.12.Up to 20 load cases can be defined in the load list area. Load cases may be built from the loads defined in the input. 3.2.13.The only wind load information required in the input is the shape factor. When wind is used in the model a screen is made available to define the extra wind load data. Once defined this is stored and may be changed on subsequent entries into the static analysis processor. 3.2.14.In the static analysis performed by Caesar II the element stiffnesses are combined to form a global system stiffness matrix . Each basic load cases define a set of loads for the ends of all the elements. These elemental load sets are combined into system load vectors. Using the relationship of force equals stiffness times displacement (F=KX) the unknown system deflections and rotations can be calculated. The knowns may however change during the analysis as hanger sizing; non-linear supports and friction all affect both the stiffness matrix and load vectors. 3.2.15.Definition of a load case - A load case is a group of piping system loads that are analysed together, i.e., that are assumed to be occurring at the same time. An example of a load case is an operating analysis composed of the thermal, dead weight and pressure loads together. Another is an as installed analysis of dead weights alone. A load case may also be composed of the combinations of the results of other load cases.

3.2.16.The piping system loads which compose the basic load sets relate to various input items found on the piping input screen. The details are listed below; W

Dead weight

Pipe density, insulation density (with insulation thickness), fluid density or rigid weight

WNC

Weight

Pipe density, insulation density (with insulation thickness), rigid weight

T1

Thermal Set 1

Temperature # 1

T2

Thermal Set 2

Temperature # 2

T3

Thermal Set 3

Temperature # 3

P1

Pressure Set 1

Pressure #1

P2

Pressure Set 2

Pressure #2

D1

Displacement Set 1

Displacements (1st Vector)

D2

Displacement Set 2

Displacements (2nd Vector)

D3

Displacement Set 3

Displacements (3rd Vector)

F1

Force Set 1

Forces/ Moments (1st Vector), cold spring (Material #18 or 19) and spring initial loads

F2

Force Set 2

Forces/ Moments (2nd Vector),

F3

Force Set 3

Forces/ Moments (3rd Vector),

WIND

Wind

Wind Loads

U1

Uniform Loads

Uniform Loads (1st Vector)

U2

Uniform Loads

Uniform Loads (2nd Vector)

U3

Uniform Loads

Uniform Loads (3rd Vector)

3.2.17.The following family of load cases provides a valid example of algebraic combinations. 1

W1+T1+P1+D1+F1 (OPE)

The case

operating

load

2

W1+P1+F1 (SUS)

The installed load case (for sustained stress calculations)

3

U1 (OCC)

A uniform load case modelling a sesimic load.

4

DS! – DS2 (EXP)

Difference between displacements of LC#1 (Operating) and LC#2

(Installed) 5

3.2.18.

ST2 + ST3 (OCC)

Recommended Load Cases 1. W+D1+T1+P1+F1 (OPE)

Operating

2. W+P1++F1 (SUS)

Sustained Load Case

3. DS1 – DS2 (EXP) 3.2.19 taken.

The stresses from LC#2 (Sustained) plus the stresses from LC#3 (occassional) used to compare the occassional stresses with their allowables.

Expansion Load Case

If spring hangers are to be designed then two additional load case are to

1. W+F1

Weight for hanger loads (Restrained wt)

2. W+D1+T1+P1+F1

Op. for hanger travel (free thermal)

3. W+D1+T1+P1+F1 (OPE)

Operating

4. W+P1++F1 (SUS)

Sustained Load Case

5. DS1 – DS2 (EXP)

Chapter 7 Chapter 8 Chapter 9 Chapter 10 Applications Guide

Expansion Load Case

Support/ End Connections Anchor Accurate input of piping boundary conditions (restraints) is probably the most important part of system modelling in Caesar II. Anchors with displacements Flexible Anchors Flexible Anchors with Initial Displacements Flexible Nozzle (WRC 297) Flexible Nozzle with Initial Displacements(WRC 297) Flexible Nozzle with Full Vessel Model (WRC 297) Double Acting Restraints (Translational) Double Acting Restraints (Rotational) Plastic Hinge 1-D Restraint Guides Limit Stops Windows Rotational Directional Restraints with Gaps 1-D Restraint with Initial Displacement 1-D Restraint and Guide with Gap and Initial Displacemnt Restraint Settlement Skewed Double Acting Restraint Skewed 1 –D Restraint Skewed Guide Restraint Between Two Pipes (CNODE) Restraint Between Vessel and Pipe Models Restraints on a Bend at (45) Degrees Restraints on a Bend at 30 and 60 Degrees Vertical Dummy Leg on Bends Near (or Far) Point Coding Model On Curvature Coding Model Offset Element Coding Vertical Leg Attachment to Angle Horizontal Dummy Leg on Bends Node Position Definition for points on the Bend Curvature Input Plot of Horizontal Dummy Leg going to 45 Deg. Point on Bend Output Plot of horizontal Dummy Leg Going to 45 Deg. Point on Bend

Ball Joints and Struts Large Rotation Rods (Basic Model) Large Rotation Rods (Chain Supports) Large Rotation Rods (Spring Hangers) Large Rotation Rods (Constant Effort Hangers) Large Rotation Rods (Struts) Bilinear Supports Static Snubbers Bends Single and Double Flanged Bends or Stiffened Bends 180 Degree Return (FTF 90 Degree Bends) Mitered Bends Closely Spaced Mitered Bend Wideley Spaced Mitered Bend Elbows – Different Wall Thickness Hangers Hanger Location Entry Single Can Design Constant Effort Support Design Input Constant Effort Supports (No Design) Entering Existing Springs ( No Design) Multiple Can Design Old Spring Redesign Pipe and Hanger Supported from Vessel Hanger Design with Thermal Support Movement Hanger Between Two Pipes Hanger Design with Anchors in the Vicinity Hanger Design with User Specified Operating Load Spring Can Models with “Bottom out” and “Lift Off” Capability Spring Hanger Models with Rods, “Bottom out” and “Lift Off” Capability Simple “Bottom Out” Spring Model Spring Cans with Friction Expansion Joints Simple Bellows with Pressure Thrust Tied Bellows (Simple vs. Complex Model) Tied Bellows Expansion Joint (Simple Model) Tied Bellows Expansion Joint (Complex Model) Universal Expansion Joint (Simple Models) Universal Joint (Comprehensive Tie Rood Model))

Universal Joint with Lateral Control Stops(Comprehensive Tie Rood Model) Hinged Joint Slotted Hinge Joint (Simple) Slotted Hinge Joint (Comprehensive) Slip Joint Gimbal Joint Dual Gimbal Joint Pressure Balanced Tee’s and Elbows Connecting Equipment Vertical Vessels Horizontal Vessels Rotating Equipment Models with Spring Hanger Design Miscellaneous Models Jacketed Pipe Cold Spring Plastic Pipe

5.

Dynamic Input and Analysis

The dynamic analysis capabilities found in CAESAR II include the following: 1.

Natural frequency calculations Natural frequency information can indicate the tendency of a piping system to respond to dynamic loads. A system’s modal natural frequencies typically should not be too close to equipment operating frequencies and, as a general rule, higher natural frequencies usually cause less trouble than low natural frequencies.

2.

Harmonic analysis This is analysis of dynamic loads that are cyclic in nature. Applications of harmonic analyses include fluid pulsation in reciprocating pump lines or vibration due to rotating equipment. Harmonic responses represent the maximum dynamic amplitude the piping system undergoes and have the same form as a static analysis - node deflections and rotations, local forces and moments, restraint loads, and stresses. For example, if the results show an X displacement at node 45 of 5.8 cm. Then the dynamic motion due to the cyclic excitation would be from +5.8 cm. to -5.8 cm. at this point in the system. The stresses shown are one half of, or one amplitude of, the full cyclic stress range.

3.

Response spectrum analysis The response spectrum method allows an impulse type transient event to be characterized by a response vs. frequency spectra. Each mode of vibration of the piping system is related to one response on the spectrum. These modal responses are summed together to produce the total system response. The stresses for these analyses, summed with the sustained stresses, should be compared to the occasional stress allowable defined by the piping code. Ground motion associated with a seismic event is supplied as displacement, velocity, or acceleration response spectra. The assumption is that all the supports move with the defined ground motion and the piping system “catches up” to the supports; it is this inertial effect, which loads the system. The shock spectra, which define the ground motion, may vary between the three global directions and may even change for different groups of supports (independent as opposed to uniform support motion). Another response spectrum application is based on single point loading rather than a uniform inertial loading. CAESAR II makes effective use of this technique to analyze a wide variety of impulse type transient loads. Relief valve loads, water hammer loads, slug flow loads, and rapid valve closure type loads all cause single impulse dynamic loads at various points in the piping system. The response to these dynamic forces can be confidently and conservatively predicted using the force spectrum method.

4.

Time history analysis This is one of the most accurate methods, in that it uses numeric integration of the dynamic equation of motion to simulate the system response throughout the load duration. CAESAR II time history analysis method can solve any type of dynamic loading, but due to its exact solution, requires more resources (memory, calculation speed and time) than other methods. Therefore, it may not pay to use this method when, for example the spectrum method offers sufficient accuracy.

6.

Buried Pipes Modelling

The “Modeler” performs the following functions: •

Allows for the direct input of soil properties.

•

Automatically breaks down straight and curved lengths of pipe. CAESAR II uses a three Zone concept to break down straight and curved sections. Zone 1 - Those ends of pipe identified as “transverse bearing lengths” (or bearing span lengths or lateral bearing length or Lb) are broken down into Zone 1 lengths. Zone 1 represents the smallest element lengths selected to properly distribute the lateral forces to the soil. Zone 2 - Between Zone 1 and Zone 3 is Zone 2. The lengths in Zone 2 vary linearly from the Zone 1 end to the Zone 3 end. They are also known as intermediate lengths. Zone 3 - At distances far away from Zone 1 are Zone 3 lengths. These are long lengths of pipe selected to transmit axial loads (or axial displacement lengths). Node numbers for the extra lengths of pipe are automatically selected by CAESAR

II. •

Allows for the direct input of user’s soil stiffnesses on 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.

The Buried Pipe Modeler is started by selecting an existing job, and then choosing menu option Input-Underground from the CAESAR II Main Menu. The Modeler is designed to read in a standard CAESAR II input data file that describes the basic layout of the piping system. From this basic input CAESAR II creates a second input data file that contains the buried pipe model. This second input file typically contains a much larger number of elements and restraints than the first job. •

The first job that serves as the “pattern” is termed the original job.

•

The second file that contains the element mesh refinement and the buried pipe restraints is termed the buried job.

CAESAR II defaults the buried job by appending a “B” to the name of the original job. The original job must already exist and serves as the pattern for the buried pipe model building. The spreadsheet initiated permits the following: •

It allows the user to define which part of the piping system is buried.

•

It allows the user to define mesh spacing at specific element ends.

•

It allows the input of user defined soil stiffnesses

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 modeled. 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” and can be calculated by the equation: Lb = 0.75 (π )[ 4 EI / K tr ]

Where:

0.25

E

=

Pipe modulus of elasticity

I

=

Pipe moment of inertia

Ktr

=

Transverse soil stiffness (on a per length basis)

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 intermediate lengths in a piping system are called the Zone 2 lengths. 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*D0 long at the Zone 3 end.

•

The axial displacement lengths in a piping system are called the Zone 3 lengths, Zone 3 element lengths (to properly transmit axial loads) are computed by 100*D0, where D0 is the outside diameter of the piping.

A critical part of the modeling 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

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 tell CAESAR II where the other zone 1 areas are in the piping system. There are 13 columns in the Buried Element Description Spreadsheet. 1.

The first two columns contain the element node numbers for each piping element included in the original system.

2.

The second three columns are discussed in detail below:

•

Soil Model No.—This column is used to define which of the elements in the model are buried. A nonzero entry in this column implies that the associated element is buried. A 1 in this column implies that the user wishes to enter user-defined stiffnesses (on a per length of pipe basis) at this point in the model. These stiffnesses must follow in the columns 6 through 13. Any number greater than 1 in the SOIL MODEL NO. column points to a CAESAR II soil restraint model generated (using the equations outlined later under Soil Models from user entered soil data).

•

From/ To End Mesh Type—“A” in either of these columns implies that a lateral loading mesh should be placed at the corresponding element end. For example: FROM NODE

TO NODE

SOIL MODEL

5

10

2

FROM MESH

TO MESH

•

The element 5 to 10 is buried. CAESAR II will generate the soil stiffnesses from user-defined soil data #2, and the node 5 end will have a fine mesh so that lateral bearing will be properly modeled. CAESAR II places lateral bearing meshes on each side of a bend by default.

•

Since CAESAR II automatically places lateral bearing meshes adjacent to all buried elbows, the user must only be concerned with the identification of buried tees and points of soil entry or exit.

The commands available in this module are;

• File-Open—Opens a new piping file as the original job. • File-Change Buried Pipe Job Name—Renames the buried job (in the event that the user does not wish to use the CAESAR II default of “B” appended to the original job name). • File Print—Prints the element description data spreadsheet. • Buried Pipe - Soil Models—Allows the user to specify soil data for CAESAR II to use in generating one or more soil restraint systems. • Buried Pipe - Convert Input—Converts the original job into the buried job by meshing the existing elements and adding soil restraints. The conversion process creates all of the necessary elements to satisfy the Zone 1, Zone 2, and Zone 3 requirements, and places restraints on the elements in these zones accordingly. All elbows are broken down into at least two curved sections, and very long radius elbows are broken down into segments whose lengths are not longer than the elements in the immediately adjacent Zone 1 pipe section. Node numbers are generated by adding “1” to the element’s FROM node number. CAESAR II checks before using a node number to make sure that it will be unique in the model. All densities on buried pipe elements are zeroed, to simulate the continuous support of the pipe weight. A conversion log is also generated, which details the process in full.