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h1. Model Overview

This tutorial demonstrates the evaluation of [shrinkage|kb:Shrinkage] forces internal to a 1-span and a 2-span, continuous bridge structure. The bridges have the following properties:

* Span length = 10m

* Deck-section type: Tee Beam section with a 0.5m-deep, 3m-wide deck and two 0.5m-wide, 1.5-deep beams

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A 3D view of the 1-span and 2-span bridge models is shown in Figure 1:

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!Shrinkage_bridge_example_-_bridge_view.png|align=center,border=0,width=800px!

{center-text}Figure 1 - Bridge model{center-text}

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The cross-sectional geometry of the bridge deck is shown in Figure 2:

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!Shrinkage_bridge_example_-_deck_section.png|align=center,border=0!

{center-text}Figure 2 - Bridge deck section{center-text}


h1. Key modeling steps

* Define shrinkage characteristics for the default, 4000psi [concrete|kb:Concrete] material. Create a copy of this material and label it '4000psi no shrinkage'. Concrete girders will use this new material, and shrinkage will not be considered. Next, add shrinkage properties to the 4000psi concrete material as follows:
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** Through the Define > Materials menu, check Show Advanced Properties and select Modify/Show Material > Modify/Show Material Properties.
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** Select Time Dependent Properties, which will open the Time Dependent Properties for Concrete menu. Under Time Dependence Considered For, check Shrinkage.

* Define the two bridges using a single, straight layout line. The 2-span bridge will have a beginning station at 0m and an end station 20m. The 1-span bridge will have a beginning station at 30m and an end station at 40m.

* Define the bridge deck section as Tee Beam, with dimensions listed above in the Model Overview section. Assign 4000psi concrete material to the deck, and the '4000psi no shrinkage' material to the girders. This will enable shrinkage consideration for the deck and not for the girders.

* Define a pinned-bearing condition for the start abutment, and roller-bearing condition for the end abutment. For the 2-span bridge, defined a fixed foundation spring at the bottom of the column, and pinned bearings at the top.

* Directly within the bridge object definition (Bridge Object Data > Staged Construction Groups > Modify/Show), define [staged construction|kb:Staged construction] groups for the deck and girders of the 1-span and 2-span bridge objects.

* Define a staged-construction [load case|kb:Load case] labeled STAGED. Add the entire structure in the first stage and define several empty stages with nonzero durations in order to evaluate response due to shrinkage as time progresses. Be sure to check Time Dependent Material Properties on the Nonlinear Parameters menu.

* Run the analysis, then use the Display > Show Bridge Forces/Stresses menu command to review the staged-construction load-case results.


h1. Results

For both the 1-span and the 2-span bridge objects, the deformed shape indicates that deck shrinkage causes shortening of deck fibers, and it causes the entire bridge to bow downwards, as expected. This behavior is shown in Figure 3:

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!Shrinkage_bridge_example_-_deflections_due_to_shrinkage.png|align=center,border=0,width=800px!

{center-text}Figure 3 - Shrinkage deflection{center-text}

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For the 1-span bridge, since the structure is statically determinate, no internal forces are generated. However, the 2-span bridge is statically indeterminate, and redundant reactions do cause internal moments. At the interior pier, tension is generated in the top fibers, as shown in Figure 4:

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!Shrinkage_bridge_example_-_moment_due_to_shrinkage_for_2-span_bridge.png|align=center,border=0!

{center-text}Figure 4 - Shrinkage moment{center-text}


h1. Attachments

* [SAP2000 model |Bridge shrinkage example^SAP2000 V12.0.2 model.zip] (zipped SDB file)