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# Page History

## Key

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• Boundary condition: fixed at both ends

Midspan deflections are calculated as follows:

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• Composite girder, Δ = 0.00083m

# Model overview

Figure 1 - Model overview

# Approaches to modeling composite behavior

Figure 2 - Modeling composite behavior

# Fixed-beam model

The eight approaches to modeling composite behavior, described above, are applied using eight different beam models which are fixed at either end. Results are summarized as follows:

Beam Designation

Behavior

Midspan Deflection
[mm]

Theoretical Beam

composite

0.8181

Theoretical deflection is based on the PL^3/192EI formulation. Please note that SAP2000 calculations produce slightly greater values because shear deformation is considered in deflection.

Beam 1
(top beam)

nocomposite

1.7938

The deck-slab center line coincides with the section neutral axis. Therefore, the deck-slab contribution to section flexural stiffness will be negligible. Further, because there is no composite action, midspan deflection should be close to that of a naked girder.

 Beam 2 composite 0.8313 In this model, slab shell objects are drawn at the girder center of gravity (COG), and then offset vertically, above the girder, to model composite action. The shells are offset such that the slab soffit is located above the girder top flange. Beam 3 composite 0.8313 In this model, the girder and the slab are drawn at their respective center-lines. The corresponding girder and slab joints are then connected through body constraints. Beam 4 composite 0.8313 In this model, composite action is modeled using frame insertion points. Beam 5 noncompostite 1.7938 Equal constraints are used to model noncomposite behavior. Beam 6 noncomposite 1.7938 Links are used to model noncomposite behavior. Beam 7 partially composite 1.0302 Links are used to model partially composite behavior. Beam 8 (bottom beam) composite 0.8313 Links are used to model composite behavior.

As implied by the list above, the composite action of a beam-slab assembly may be modeled using either area offsets, body constraints, frame insertion points, or links.

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The eight approaches to composite-behavior modeling, described above, are applied using eight different simply supported beam models. Results are summarized as follows:

Beam Designation

Behavior

Midspan Deflection
[mm]

Theoretical Beam

composite

3.2725

Theoretical deflection is based on the PL^3/48EI formulation. Please note that SAP2000 calculations produce slightly greater values because shear deformation is considered in deflection.

Beam 1
(top beam)

nocomposite

7.1752

The deck-slab center line coincides with the section neutral axis. Therefore, the deck-slab contribution to section flexural stiffness will be negligible. Further, because there is no composite action, midspan deflection should be close to that of a naked girder.

 Beam 2 composite 3.2624 In this model, slab shell objects are drawn at the girder center of gravity (COG), and then offset vertically, above the girder, to model composite action. The shells are offset such that the slab soffit is located above the girder top flange. Beam 3 composite 3.2624 In this model, the girder and the slab are drawn at their respective center-lines. The corresponding girder and slab joints are then connected through body constraints. Beam 4 composite 3.2624 In this model, composite action is modeled using frame insertion points. Beam 5 noncompostite 7.1752 Equal constraints are used to model noncomposite behavior. Beam 6 noncomposite 7.1752 Links are used to model noncomposite behavior. Beam 7 partially composite 3.5036 Links are used to model partially composite behavior. Beam 8 (bottom beam) composite 3.2624 Links are used to model composite behavior.

# Attachments

• Modeling composite behavior in SAP2000.zip (zipped SDB file), which contains:

• SAP2000 V12.0.0 file which demonstrates the modeling of composite behavior for eight fixed beams.
• SAP2000 V12.0.0 file which demonstrates the modeling of composite behavior for eight simply supported beams.
• Sketches which illustrate the modeling of composite, noncomposite, and partially composite behavior.

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