Analysis of a Precast Box Beam

Description

Analysis of a Precast Box Beam (Super Tee) Deck For software software product(s): With product option(s):

LUSAS Bridge None

Description This example demonstrates the modelling and basic analysis of a 28m long single span  bridge with a 9.4m width width carriageway, carriageway, constructed constructed using precast open-top box sections. The section chosen in this example is the Australia/New Zealand 1200mm “Super Tee Tee”” section, with a 180mm thickness insitu deck slab. In this example first a few modelling options for such a structure will be discussed and then a grillage approach is explained step by step using the precast section generator facility. Units used are kN, m, kg, s, C throughout.

Figure 1 - Deck Cross-Section

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Analysis of a Precast Box Beam (Super Tee) Deck

Figure 2 1200mm Super Tee (T3) Section

Objectives The output requirements of the analysis are: 

Longitudinal shear forces, bending moments and stresses for the composite  beam/slab section. section.

Keywords Beam, Precast, Concrete, Super T, Super Tee, Grillage.

Modelling Idealisation of the Bridge Structure There are three main options for the modelling of this type of bridge.

Option 1 - Grillage The „traditional‟ computerised method for analysing a bridge such as this is a grillage model. In this case, because the beams are box-shaped, an additional complication is introduced. The beams do not actually connect to the slab along the beam centrelines; instead connecting along two lines at the top of the beam webs. This complicates the idealisation of the transverse slab spans, as illustrated in Figure in  Figure 3.

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Modelling

Figure 3 - Transverse Slab Spans

One possible solution is to model each web as a longitudinal grillage member as shown in Figure 4 (please note the beams shown are generic precast box sections and not super tees specifically), but this would complicate results processing because the results from adjacent members would have to be added to get results for a single actual beam.

Figure 4 –  Example Box Beam Idealisation with Each Web Represented by a Longitudinal Member (Dots Represent Longitudinal Grillage Members)

The alternative is to model the beams as a single grillage member, and create „dummy‟ longitudinal members where the main beams connect to the slab. The transverse beams can then span between the dummy longitudinal members so that they have the correct spans. The main longitudinal beams will be linked to the dummy longitudinal beams with stiff transverse members as shown in Figure 5.

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Analysis of a Precast Box Beam (Super Tee) Deck

Figure 5 –  Example Box Beam Idealisation with Each Beam Represented by a Single Longitudinal Member Connected to Two „Dummy‟ Web Members (N.B. All modelled on same plane –  main beams shown offset here for clarity)

This approach is considered preferable because each beam is represented by a single member, which is more convenient for results processing.

Option 2 –  Beam

and Shell “Pseudo-3D”

Slabs can be more accurately analysed by using thick shell elements in place of a 1 grillage . Thick beam elements (BMS3) can be attached to shell elements (QTS4) to model beam and slab decks. This approach generally simplifies modelling because it is not necessary to calculate properties for the transverse grillage members. However, in this case this approach is complicated by the fact that the beams are not attached to the slab along their centrelines. It would be necessary to model some sort of linking members between the beam and the points at the tops of the webs as shown in Figure 6.  This would complicate the modelling and on balance would probably defeat the purpose of this more sophisticated analysis type.

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 Observations on the grillage analysis of slabs. Stuart R. Gordon & Ian M. May, The Structural Engineer Volume 82 Issue 3, 2004

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Modelling

Figure 6 - Psuedo-3D Beam and Shell Idealisation

Option 3 –  Full 3D Shell Model The most rigorous of the three options presented here would be to construct the whole  bridge from shell elements. This would correctly model the global and local effects,  because distortion of the box, shear lag and warping would all be correctly accounted for. These effects are not included in a grillage analysis because beam elements are formulated assuming that plane sections remain plane. This approach would however sacrifice the ease with which beam results can be plotted using the diagrams, contours or values layers, instead requiring section slicing (Utilities: Slice Resultant Beams/Shells) to extract equivalent beam moments and shears for design.

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Analysis of a Precast Box Beam (Super Tee) Deck

Figure 7 - Full 3D Shell Model

In the following example we create a model based on the approach shown in Figure 5.

Creating a New Model 

Enter the file name as super_T

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Use the Default working folder.

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Enter the title as Super Tee Grillage Example

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Select units of kN,m,t,s,C

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Ensure the user interface is set to Structural

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Select the startup template Standard

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Select the Vertical Z axis option.

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Click the OK button.

Defining Geometry First the main beams will be drawn. Create a point at (0, 5, 0) [1]. Next sweep the point  by 2 metres in the x-direction (2, 0, 0) to define the first grillage member of the first  beam [2]. As shown in Figure 1 there are 5 beams at 2m centres, so select the line and copy it by 2m in the y direction (0, 2, 0) four times [3].

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Modelling

Figure 8 - Modelling Stages [1] to [3]

 Next the edge beams will be drawn. The edge beams are rectangular sections 255mm deep and 175mm wide. Therefore the spacing between the centreline of the outermost main beams and the centreline of the edge beams is (2m + 0.175m)/2 = 1.0875m. Copy the top line by 1.0875m in the y-direction (0, 1.0875, 0) and the bottom line by 1.0875m in the negative y-direction (0, -1.0875, 0)  [4].  Next the „dummy‟ web beams will be added. The horizontal distance between the centroid of the main beams and the tops of the webs is 445mm. Select the five main  beam lines and copy them by 0.455m in the y-direction (0, 0.455, 0) then copy them again by 0.455m in the negative y-direction (0, -0.455,0)  [5].  Next the transverse members are to be defined. The main spine beams are to be linked to the dummy web beams by relatively stiff transverse members, but the transverse slab members are not going to connect to the main spine beams as they are only connected at the web points. First the stiff link members will be created. By selecting pairs of points in order, draw lines from the starts of the main spine beams to the starts of the web members. It is important that the line directions go from the spine beam outwards  because of the location of end release that will be used later. Therefore for each pair of  points select the point on the main beam first [6].

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Analysis of a Precast Box Beam (Super Tee) Deck

Figure 9 - Modelling Stages [4] to [6]

 Next the transverse slab elements will be added. These will not be connected to the spine beams, so for clarity the spine beams will temporarily be moved downwards. Select the five main beams and move them by 1m in the negative z-direction (0, 0, -1).  Now draw the transverse slab members by holding „Ctrl‟ and selecting the 12 remaining end points in a bottom-to-top order before clicking the „create line‟ icon [7]. Check the line directions by double-clicking the Geometry drawing layer in the treeview and ticking the „show line directions‟ box. If any lines are reversed relative to the image  below, reverse them by selecting them then clicking Geometry –  Line –  Reverse.

[7]

Figure 10 - Modelling Stage 7

Later this geometry will be copied to create the rest of the bridge, but the attributes will  be assigned first to save time.

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Modelling

Mesh The model will be meshed with thick beam elements (BMS3). The benefit of BMS3 over a grillage mesh (GRIL) is that they carry axial forces as well as bending and shear. This is useful because it allows the use of non-planar geometry and offset sections. The use of BMS3 is essential if any out-of plane geometry such as columns or abutments are to be modelled. The only major benefit of GRIL elements over BMS3 is t hat Wood Armer results are available in LUSAS. Create a mesh attribute by clicking Attributes –  Mesh –  Line. Select Thick Beam, 3D and enter Number of divisions  as 1. Name the Attribute “Thick Beam BMS3 1Div ” and click OK. Double-click the new mesh attribute to re-open it. Change the name to “ Thick Beam BMS3 1Div End Release ” then click the End Releases  button. Tick the box to give the new mesh a Rotation about Y  release at the last node. Click OK twice to create the new attribute.

Figure 11 - Mesh Attribute Settings

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Analysis of a Precast Box Beam (Super Tee) Deck

Geometric Properties The main beam properties will be generated using the precast beam section property wizard. To use this feature a new model needs to be set up, so save the current model and click File –  New. Name the new file “main_beam_section ” and click OK. In LUSAS V14.6 there is a new Super Tee section entry in Precast Sections. If you are using V14.6 or later, click Utilities –  Section Property Calculator  –  Precast Section . Enter the following information and click OK. If you are using an earlier version of LUSAS, you can open and use the supplied T3_180.mdl model file instead.

Figure 12 - Precast Section Property Calculator Input

Run the section property calculator by clicking Utilities –  Section Property Calculator –  Arbitrary Section Property Calculator . Name the section “ T3 Beam with 180mm Slab ” and ensure the Add Section to Local Library  box is ticked and Press Apply (this creates a file which allows the section to be used in other Model files).

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Modelling

Figure 13 - Cross Section

 Now close this model and re-open the main grillage model. The other sections should now be defined. To define the edge beams click Utilities –  Section Property Calculator  –  Rectangular –  Solid and enter a depth of 0.255m and a breadth of 0.175m. Name the section “ Edge Beam” and click Apply. The slab is 180mm thick, and the transverse members represent a width of 2m, so rerun the rectangular section property calculator as above with a depth of 0.18m and a  breadth of 2m. Name the section “ Transverse Slab ” and click Apply again. The end slab sections only represent half the width so change the breadth to 1m and the name to “Transverse Slab Abutment ” and click Apply again. Dummy web members are also required. These are needed to „catch‟ loading and transfer it to the main beams, but they should not contribute significantly to the structural response. Enter a breadth of 0.05m and a depth of 0.05m, name the section “Dummy Web Member”  and click OK. These values are completely arbitrary and are chosen to create a member of low stiffness relative to the other sections. Note that it is inadvisable to give dummy members extremely low section properties (e.g. 1E-10)  because this could cause „diagonal decay‟ warnings. Please see the online user area (http://www.lusas.com/protected/warning/diagonal_decay.html ) for a description of this effect. Geometric attributes now need to be created for each of these sections. Click Attributes –   Geometric –  Section Library , change the element type to 3D Thick Beam (BMS3)  and select User Sections  from the top-right drop-down list. Select each of the four previously defined sections from the library, give them appropriate names and then click Apply. You should now have four attributes under the Geometric heading in the Treeview.

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Analysis of a Precast Box Beam (Super Tee) Deck

Some of the torsion constants need to be decreased for use in a grillage analysis. This is to avoid double-counting the torsional stiffnesses by including them in the longitudinal and transverse directions. Open the „Transverse Slab ‟ geometric attribute by doubleclicking it, and change the torsion constant Jxx to half the calculated value (hint –  arithmetic expressions can be entered in the dialog boxes, so simply adding „/2‟ after the current torsion constant will divide it by two). It will be necessary to change the Definition from „From Library‟ to „Enter Properties‟ to do this.  Note down the new value of the torsion constant (1.83377E-3). Now do the same for the „Transverse Slab Abutment ‟ attribute. The longitudinal slab is included in the section properties of the main beams. In grillage analysis it is common practice to assume 50% of the torsion capacity of the slab is taken  by the transverse beams and 50% by the longitudinal beams. The torsion constant of the spine beams will be reduced by 50% of the torsion constant of the slab. Open the „T3 Beam with 180mm Slab ‟ geometric attribute and reduce its torsion constant by the same amount as the transverse slab. This can be done by typing „ -1.83377E-3 ‟ after the current torsion constant value (see Figure 14). Click OK. It is apparent that this is a tiny change to the T3 torsion constant proportionally, but in other bridges it could be more significant.

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Modelling

Figure 14 –  Editing the Main Beam Torsion Constant

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Analysis of a Precast Box Beam (Super Tee) Deck

Material Properties It is common for precast beams to be cast in a stronger grade of concrete than the insitu slab. Multiple material attributes cannot be assigned to a single BMS3 cross-section so if this difference in materials needed to be taken into account it would need to be by transforming the cross-section to account for the difference in stiffness. This is beyond the scope of this example so we will assume that both are made in the same grade of concrete. Create a material attribute by clicking „ Attributes –  Material –  Material Library –  Concrete‟ and selecting „Ungraded‟ concrete.

Supports Create two support attributes, one named “ Pin” with supports in the X, Y and Z directions, and one named “ Roller” with supports in just the Y and Z directions.

Loading Assigning a full live load arrangement is not the aim of this example so a single lane load will be applied as a test load in order to demonstrate extraction of results. Create a single loading attribute by clicking „ Bridge –  Bridge Loading –  New Zealand –  Lane Load‟. Enter a length of 28m, leave the other entries as default and click „ OK ‟. Please note that applying gravity loading to this model may involve complications  because the deck is constructed in stages –  the self weight of the beams and slab would act on the beams alone because the slab would not be cast at that stage. The composite section would only start to carry load after casting of the slab, so superimposed dead load and live load would be valid on the model. The dead load forces and moments could easily be calculated by hand (because there would be no interaction between the  beams) and the resulting stresses added to the results from the other loadcases for design of the beams. Alternatively a nonlinear analysis with shell elements and Activation/Deactivation could be used to model the construction sequence and the wet concrete load.

Search Area In this analysis we need to control which members have load applied to them. All load that is applied to the main beams should be transmitted through the dummy web members to ensure that any eccentric forces cause the correct torsional response. In LUSAS a „Search Area‟ attribute is used to control which features have load applied. To create one, click „ Attributes –   Search Area ‟, name it “Members for Loading ” and click „OK‟.

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Modelling

Assigning Attributes Select all of the lines using „Ctrl+A‟ and drag and drop the „Concrete Ungraded ‟ material attribute and „Thick Beam BMS3 1Div ‟ mesh attribute onto them. Now select only the inclined linking members (highlighted below) and drag the „ Thick Beam BMS3 1Div End Release ‟ mesh attribute onto them. You should see a  number of „THY‟ labels appear, signifying the end releases.

Figure 15 - Mesh View Showing Location of Beam End Releases

 Now assign the geometric attributes one at a time by dragging and dropping the various geometric attributes onto the relevant lines as shown in  Figure 16. Note that because the current geometry will be copied to create the rest of the deck, the standard „Transverse Slab‟ properties should be assigned, rather than the „Transverse Slab Abutment‟  properties. The T3 beam properties are also assigned to the transverse link members as recommended by Hambly (section 6.5). Check the geometric assignments by doubleclicking the Geometry drawing layer and selecting „Colour by Geometry‟ .

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Analysis of a Precast Box Beam (Super Tee) Deck

Figure 16 - Geometric Properties Check

Select all of the lines again and copy them by 2m in the X-direction 14 times (enter number of copies = 14). Delete the protruding longitudinal lines at the far end of the  bridge to be left with the 28m long complete grillage. Now assign the „Transverse Slab Abutment‟ geometric attributes to the transverse abutment lines as shown in  Figure 17.

Figure 17 - Full Grillage Geometric Assignments

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Modelling

Assign the Pin supports to the left-hand ends of the main beams, and the Roller supports to the right-hand ends. Assign the Search Area to the Dummy Web, Transverse Slab and Transverse Slab Abutment members by right-clicking the three geometric attributes and clicking „Select Assignments‟ before dragging and dropping the Search Area attribute onto the model. Check the assignment by right-clicking the Search area attribute and clicking „Select Assignments‟. The selection should look like Figure 18.

Figure 18 - Search Area Assignments

Select the point at coordinates (14, 11, -1) (see arrow below) and drag and drop the lane load attribute onto the model. In the Patch Loading Assignment dialog, specify the Search Area „Members for Loading‟ and leave the other fields as default (Project over area, Exclude all load, Loadcase 1, Load factor 1). Click OK. Double- click the „Patch Divisions‟ title in the load attributes section of the treeview and change the distance  between loads to 0.5m.

Figure 19 - Patch Load Application

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Analysis of a Precast Box Beam (Super Tee) Deck

Finally, the main beams will be moved back up to make the whole model planar. Select the longitudinal T3 beams by viewing the model along the X- axis (click the „X: N/A‟ at the bottom of the modeller interface to do this) then box-selecting the lower longitudinal lines. Put them into a group by clicking the icon (name it „Longitudinal T3 Beams‟ or similar), then move them vertically by 1m (0, 0, 1).

Figure 20 - Selecting the Longitudinal T3 Beams 2

There are discussions in both Hambly and O‟Brien & Keogh  about the relative merits of planar and downstand grillages. Due to the additional complications introduced to the analysis by the in- plane „push/pull‟ effects in a downstand grillage, it is considered simpler and safer to use a planar grillage in this case. The model should now look like Figure 21 and is now ready to be solved.

Figure 21 - Completed Model

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Bridge Deck Analysis, O‟Brien and Keogh, E&F Spon, 1999.

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Running the Analysis

Running the Analysis Save the model and click the

icon to generate and load a results file.

Viewing the Results Plotting Deformed Shapes Ensure the Mesh, Geometry and Attributes layers are turned off in the treeview. With no features selected click the right-hand mouse button in a blank part of the Graphics area and click „Deformed Mesh‟ to add the deformed mesh layer to the treeview. In the deformed mesh dialog box set a deformation factor of 1000 and select the Window summary  option and click the OK  button to display the deformed mesh for the single vehicle loadcase.

Figure 22 - Deformed Mesh Plot

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Analysis of a Precast Box Beam (Super Tee) Deck

Displaying Forces and Bending Moments The maximum and minimum bending moments, shear forces and stresses in the main  beams are required. In the Groups treeview , right-click the „Longitudinal T3 Beam ‟ group and select „Set as Only Visible ‟. This will remove all of the transverse , edge and dummy members from the view for clarity and to avoid averaging of results in different directions at the connections. With no features selected, right-click the model background and create a „ Contours‟ drawing layer. Select entity „ Force/Moment –  Thick Beam‟ and component „ My‟. Click OK. Right-click the background again and create a „Values‟ drawing layer. Select the same entity and component as the contours layer, and open the „ Values Display ‟ tab. Tick the boxes to show the maximum and minimum values, and enter a value of 0% to only show the single highest and lowest results. Change the number of significant figures to 4 and the font size to 20pt by clicking „Choose Font‟. Then click the „Pen‟ button and select a red pen. Click OK.

Figure 23 - Contour Plot of Bending Moment My on Main Beams

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Viewing the Results

Shear forces will now be displayed using the Diagrams Layer. Turn off the Contours and Values layers from the treeview, then right-click the model background and add a Diagrams layer. Select entity „ Force/Moment –  Thick Beam‟ and component „Fz‟. Click OK.

Figure 24 –  Diagram of Shear Force Fz on Main Beams

Turn off the Diagram layer and turn back on the Contour Layer. Change the Contour layer entity to „ Stress –  Thick 3D Beam‟. Select component „Sx (Fx, My, Mz) ‟. Select the “Contour Range” tab and input maximum as 1200 and Minimum as -800 and click OK. Turn on section fleshing to view the stresses on the full cross-sections (Figure 25).

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Analysis of a Precast Box Beam (Super Tee) Deck

Figure 25 - Contours of Axial Stress Sx

This completes the example.

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