Page Comparison

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[SAP2000|sap2000:home] provides various ways to model the [composite behavior|kb:Composite behavior] of a beam-slab assembly. Attached are four SAP2000 models which demonstrate these different approaches. The geometric and material properties of the model used for comparison are as follows:

* Slab width = 2.0 m
* Slab thickness = 0.2 m
* Total girder height = 1.2 m
* Top and bottom flange width = 1.0 m
* Top and bottom flange thickness = 0.1 m
* Web thickness = 0.1 m
* Applied load at midspan = 100 kN
* Modulus of elasticity, E = 33000000 kN/m ^2^
* Span length L = 20 m
* Boundary condition: fixed at both ends

The midspan deflections are calculated as follows:

* Naked girder, Δ = 0.0018m

* Composite girder, Δ = 0.00083m


h1. Model overview

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{center-text}Figure 1 - Model overview{center-text}


h1. Approaches to modeling composite behavior

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{center-text}Figure 2 - Modeling composite behavior {center-text}


h1. 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:

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|| Beam Designation || Behavior || Midspan Deflection \\
\[mm\] || Comments ||
| 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 elements 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 non-composite behavior. \\ |
| Beam 6 \\ | noncomposite \\ | 1.7938 | Links are used to model non-composite 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. \\ |

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As implied by the list above, the [composite action|kb:Composite behavior] of a beam-slab assembly may be modeled using either area offsets, body constraints, [frame|kb:Frame] [insertion points|kb:Insertion point], or [links|kb:Link].


h1. Simply-supported beam model

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

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|| Beam Designation || Behavior || Midspan Deflection \\
\[mm\] || Comments ||
| 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 elements 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 non-composite behavior. \\ |
| Beam 6 \\ | noncomposite \\ | 7.1752 \\ | Links are used to model non-composite 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. \\ |


h1. Attachments

* [Modeling composite behavior in SAP2000.zip |^Modeling_composite_behavior_in_SAP2000.zip] (zipped SDB file)
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The file above contains the following files:
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** SAP2000 V12.0.0 file demonstrating composite-behavior modeling for eight fixed beams.
** SAP2000 V12.0.0 file demonstrating composite-behavior modeling for eight simply-supported beams.
** Sketches which illustrate the modeling of composite, non-composite, and partially-composite behavior in SAP2000.


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*NoteNOTE:*

The attached file, Modeling composite behavior in SAP2000.zip attachment file, can be emailed to directly answer support questions.
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