{live-template:Test Problem}

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h1. Model Overview

The purpose of this model is to evaluate internal forces due to shrinkage of a deck for 1-span and 2-span continuous bridge structures. The bridges have the following properties:

* span length = 10m
* deck section: tee-beam deck section with 0.5m deep and 3m wide deck and two 0.5m wide and 1.5 deep beams

View of the bridge model:


Geometry of the deck section of the bridge model:


h1. Key Modeling Steps

* Define shrinkage characteristics for the default concrete material "4000psi". First, create a copy of the default concrete material and name the material "4000psi no shrinkage". This material will be used for the concrete girders, for which the shrinkage will not be considered. Second, add shrinkage properties to the "4000psi" concrete material:
** Use "Define > Materials" menu command.
** Check "Show Advanced Properties" and click "Modify/Show Material..." button. Click "Modify/Show Material Properties..."
** Click "Time Dependent Properties", which will open form "Time Dependent Properties for Concrete". Check "Shrinkage" under the "Time Dependence Considered For" heading"

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

* Define bridge deck section "Tee Beam" with dimensions as listed in the Model Overview section above. Although both the deck and the girders will be made of concrete, use different concrete property for the deck and for the girders. This will enable to easily consider shrinkage for the deck (material "4000psi"), but not for the girders (material "4000psi no shrinkage").

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

* Define staged construction groups for the deck and the girders for the 1-span and 2-span bridge objects directly within the bridge object definition. This can be done on the "Bridge Object Data" form, by selecting "Staged Construction Groups" and clicking "Modify/Show..." button.

* Define staged construction load case named "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 the time progresses. Make sure to check "Time Dependent Material Properties" on the "Nonlinear Parameters" form.

* Run the analysis and use "Display > Show Bridge Forces/Stresses" menu command to review the results for the staged construction load case.

h1. Results

The deformed shape for both the 1-span and the 2-span bridge objects indicates that the deck shrinkage causes shortening of the deck fibers and causes the entire bridge to bow downwards, which is expected:


For the 1-span bridge, there are no internal forces being generated, since the bridge is statically determinate. However, the 2-span bridge is statically indeterminate and the redundant reactions cause internal moments (with tension in the top fibers at the interior pier) as shown in the screenshot below:


h1. Attachments

* [SAP2000 V12.0.2 model|^SAP2000 V12.0.2 model.zip] (Zipped SDB file)