Analysis of a Precast Box Beam (Super Tee) Deck - Ningapi.ning.com/.../BoxBeamandSlabAnalysisSuperTSections.pdf · beam/slab section. Keywords ... Analysis of a Precast Box Beam (Super

Description

1

Analysis of a

Precast Box Beam

(Super Tee) Deck

For software product(s): LUSAS Bridge

With product option(s): None

Description

This example demonstrates the modelling and basic analysis of a 28m long single span

bridge with a 9.4m width carriageway, constructed using precast open-top box sections.

The section chosen in this example is the Australia/New Zealand 1200mm “Super 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

Analysis of a Precast Box Beam (Super Tee) Deck

2

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.

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 3.

Modelling

3

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.


4

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

grillage1. 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.

1 Observations on the grillage analysis of slabs. Stuart R. Gordon & Ian M. May, The

Structural Engineer Volume 82 Issue 3, 2004

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)

Modelling

5

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.


6

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

Use the Default working folder.

Enter the title as Super Tee Grillage Example

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

Ensure the user interface is set to Structural

Select the startup template Standard

Select the Vertical Z axis option.

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].

Modelling

7

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].


8

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.

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.

[7]

Modelling

9

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 that 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


10

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).

Modelling

11

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 re-

run 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.

http://www.lusas.com/protected/warning/diagonal_decay.html


12

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 double-

clicking 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.

Modelling

13

Figure 14 – Editing the Main Beam Torsion Constant


14

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‟.

Modelling

15

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 double-

clicking the Geometry drawing layer and selecting „Colour by Geometry‟.


16

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

Modelling

17

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


18

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

There are discussions in both Hambly and O‟Brien & Keogh2 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

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

Running the Analysis

19

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


20

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

Viewing the Results

21

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).


22

Figure 25 - Contours of Axial Stress Sx

This completes the example.

Documents

Analysis of a Precast Box Beam (Super Tee) Deck - Ningapi.ning.com/.../BoxBeamandSlabAnalysisSuperTSections.pdf · beam/slab section. Keywords ... Analysis of a Precast Box Beam (Super