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h1. Model Overview

TheThis purposetutorial ofdemonstrates thisthe modelevaluation is to evaluate internal forces dueof [shrinkage|kb:Shrinkage] forces internal to shrinkage of a deck for 1-span and a 2-span, continuous bridge structuresstructure. The bridges have the following properties:

* spanSpan length = 10m

* deckDeck-section sectiontype: tee-beamTee deckBeam section with a 0.5m -deep, and 3m -wide deck and two 0.5m -wide, and 1.5 -deep beams


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

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

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

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The Geometrycross-sectional geometry of the bridge deck sectionis ofshown thein bridgeFigure model2:

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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 Modelingmodeling Stepssteps

* Define shrinkage characteristics for the default, 4000psi [concrete|kb:Concrete] material "4000psi". First, createCreate a copy of thethis default concrete material and namelabel theit material "'4000psi no shrinkage"'. ThisConcrete materialgirders will beuse usedthis for the concrete girders, for which thenew material, and shrinkage will not be considered. SecondNext, add shrinkage properties to the "4000psi" concrete material as follows:
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** UseThrough the "Define > Materials" menu command.
** Check ", check Show Advanced Properties" and clickselect "Modify/Show Material..." button. Click " > Modify/Show Material Properties..."
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** ClickSelect "Time Dependent Properties", which will open formthe "Time Dependent Properties for Concrete" menu. Check "Shrinkage" under the "Under Time Dependence Considered For" heading", 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,. whileThe the 1-span bridge will have a beginning station at 30m and an end station at 4040m.

* Define the bridge deck section as "Tee Beam", with dimensions aslisted listedabove in the Model Overview section above. AlthoughAssign both4000psi theconcrete deckmaterial andto the girders will be made of concretedeck, useand differentthe concrete'4000psi propertyno forshrinkage' thematerial deckto and for the girders. This will enable toshrinkage easily considerconsideration shrinkage for the deck (material "4000psi"), but and not for the girders (material "4000psi no shrinkage").

* 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 of.

* Directly within the column.

* Define staged construction  bridge object definition (Bridge Object Data > Staged Construction Groups > Modify/Show), define [staged construction|kb:Staged construction] groups for the deck and the girders forof 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 a staged -construction [load case named "STAGED"|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 the time progresses. MakeBe sure to check "Time Dependent Material Properties" on the "Nonlinear Parameters" formmenu.

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


h1. Results

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

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

For the 1-span bridge, there are no internal forces being generated{center-text}Figure 3 - Shrinkage deflection{center-text}

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For the 1-span bridge, since the bridgestructure is statically determinate, no internal forces are generated. However, the 2-span bridge is statically indeterminate, and the redundant reactions do cause internal moments (with. At the interior pier, tension is generated in the top fibers at the interior pier), as shown in Figure the4:
screenshot
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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 V12.0.2model model|^SAP2000 V12.0.2 model.zip] (Zippedzipped SDB file)