{Test Problem

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

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Model overview

Internal shrinkage forces are evaluated for one-span and continuous two-span bridge structures. These bridges have the following properties:

• span

  Span length = 10m

• deck

  Deck-section type:

  tee

  T-beam

  deck

  section with a 0.5m-deep

  and

  , 3m-wide deck and two 0.5m-wide

  and

  , 1.

  5

  5m-deep beams

View A 3D view of the bridge model:

Image Removed

Geometry of the deck section of the bridge model:

Image Removed

...

one and two-span bridge models is shown in Figure 1:

Image Added

Figure 1 - Bridge model

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

Image Added

Figure 2 - Bridge deck section

Key modeling steps

• Define shrinkage characteristics for the default, 4000psi concrete material

  "4000psi". First, create

  . Create a copy of

  the default concrete

  this material and

  name the material "

  label it '4000psi no shrinkage

  ". This material will be used for the concrete girders, for which the

  '. Concrete girders will use this new material, and shrinkage will not be considered.

  Second

  Next, add shrinkage properties to the

  "

  4000psi

  "

  concrete material as follows:
  
  

  • Use "

    Define > Materials" menu command.Check "Show Advanced Properties" and click

    Components Tab > Properties > Materials > select 4000psi material > click the Modify button" to ope the "Material Property Data" form

  • Check the "Switch to Advanced Property Display" checkbox

  • Click the "Modify/Show Material Properties..." button

    . Click "Modify/Show Material Properties..."Click

    to open "Material Property Data" form

  • Click the "Time Dependent Properties

    ", which will open form

    ..." button to open "Time Dependent Properties for Concrete"

    . Check "Shrinkage" under the "

    form

  • Under "Time Dependence Considered For" heading

    "

    , check Shrinkage.

• Define the two bridges using a single, straight layout line. The

  2

  two-span bridge will have a beginning station at 0m and an end station 20m

  , while the 1

  . The one-span bridge will have a beginning station at 30m and an end station

  40

  at 40m.

• Define the bridge deck section

  "

  as Tee Beam

  "

  , with dimensions

  as

  listed above in the Model Overview section

  above. Although both

  . Assign 4000psi concrete material to the deck

  and the girders will be made of concrete, use different concrete property for the deck and for the

  , and the '4000psi no shrinkage' material to the girders. This will enable

  to easily consider

  shrinkage consideration 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

  two-span bridge, defined a fixed foundation spring at the bottom of the column, and pinned bearings at the top

  of the column

  .

• Define

  Directly within the bridge object definition (Bridge Tab > Bridge Object > Groups), define staged construction bridge groups for the deck and

  the

  girders

  for

  of the

  1

  one-span and

  2

  two-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"

  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

  Be sure to check

  "

  Time Dependent Material Properties

  "

  on the

  "

  Nonlinear Parameters

  " form

  menu.

• Run the analysis

  and

  , then use the "Home Tab > Display > Show Bridge Superstructure Forces/Stresses" menu command to review the

  results for the

  staged-construction load-case results.

Results

The deformed shape for For both the 1one-span and the 2two-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 is expected:Image Removedas expected. This behavior is shown in Figure 3:

Image Added

Figure 3 - Shrinkage deflection

For the 1one-span bridge, there are no internal forces being generated, since the bridge structure is statically determinate, no internal forces are generated. However, the 2two-span bridge is statically indeterminate, and the redundant reactions do cause internal moments (with tension . At the interior pier, tension is generated in the top fibers at the interior pier) , as shown in the screenshot below:Image RemovedFigure 4:

Image Added

Figure 4 - Shrinkage moment

Attachments

• File | filename = Shrinkage

  shrinkage bridge model

  SAP2000 V12.0.2 model.zip | title = SAP2000 V12.0.2 file (Zipped SDB file)

...

• (CSiBridge V18.1.1).zip (zipped BDB file)

Metadata

• Name: Bridge shrinkage example

• Description: Evaluate shrinkage for a one-span and a continuous two-span bridge system.

• Program: CSiBridge

• Program Version: 18.1.1

• Model ID: 1402