Page Comparison

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There are various ways of modeling composite behavior of beam-and-slab assembly in SAP2000. For your reference and study, we have attached four SAP2000 models that show different ways for modeling composite action for girder-and-slab assembly. The model description used for the comparison is as follows:

* The Slab width = 2 m
* Slab thickness = .2 m
* Girder total height = 1.2 m
* Top and bottom flanges width = 1 m
* Top and bottom flange thickness = .1 m
* Web thickness = .1 m

* The applied load at mid span is 100 kN
* Modules of elasticity E= 33000000 kN/m2
* Span length = 20 m, fixed at both ends

The deflection at mid-span is calculated for the naked girder and composite girder as 0.0018m and 0.00083m respectively.

h1. Model Overview

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h1. Various Approaches to Modeling Composite Behavior

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h1. Fixed Beams Model

The model contains contains 8 beams that are fixed at their both ends and the composite behavior is modeled using the 8 approaches outlined in the figure above.

|| Beam Designation || Behavior || Midspan Deflection \\
\[mm\] || Comments ||
| Theoretical Beam | composite \\ | 0.8181 | Theoretical deflection based on the {math}\frac{PL^3}{192EI}{math} formula. Please note that the SAP2000 calculated deflections are slightly higher because the program considers shear deformations. |
| Beam 1 \\
(top 
In this model, thebeam) \\
\\ | nocomposite \\ | 1.7938 | The center line of deck slab coincides with  the neutral axis of the  section. Hence, the contribution of deck slab  to the flexural stiffness  of the section will be negligible and the  deflection at mid-span for  this model should be close to the deflection  for naked girder (i.e. no  composite action). In| this|
case,| theBeam deflection2 at\\ midspan| is 0.00179m.

h1. Model 2
composite \\ | 0.8313 | In this model, the shell elements representing the slab are drawn at the  CG of the girder and then offset above the girder to model the  composite action. The shells are offset such that the soffit of the slab  is at the top of the girder top flange. |
The| deflectionBeam at3 midspan\\ in| thiscomposite case\\ is| 0.0008313m.

h1. Model 3

8313 | In this model the girder and slab are drawn at their respective  centerlines and then the corresponding joints of the girder and the slab  are connected together through body constraints. This is another way to  model the composite action. The|
deflection| atBeam midspan,4 in\\ this| casecomposite is\\ also| 0.00083138313 as expected.


h1. Model 4

| In this model the concept of frame insertion points is used to model the  composite action. The deflection at midspan, in this case is 0.0008313 which is same as for Model2 and Model3. |
| Beam 5 \\ | noncompostite \\ | 1.7938 | Equal constrain is used to model noncomposite behavior. \\ |
| Beam 6 \\ | noncomposite \\ | 1.7938 | Link is used to model noncomposite behavior. \\ |
| Beam 7 \\ | partially composite \\ | 1.0302 | Link is used to model partially composite behavior \\ |
| Beam 8 \\
(bottom beam) \\ | composite \\ | 0.8313 | Link is used to model composite behavior. \\ |

In view of the foregoing, you can use either area offsets or, body constraints, or frame insertion points or links to model composite action of the beam-and-slab assembly.


h1. Attachments

* [Modeling Simply Supported Beams Model

The model contains contains 8 beams that are simply supported at their both ends and the composite behavior is modeled using the 8 approaches outlined in SAP2000.zip|^Modeling_composite_behavior_in_SAP2000.zip] \- revised models for fixed beam and simply supported beam with additional modeling approaches using springs and detailed sketches illustrating modeling composite, noncomposite and partially composite behavior in SAP2000 (Zipped archive with two SDB model files and a PDF file)
* [Composite section models V12.0.2.zip|^Composite_section_models_V12.0.2.zip] \- Models 1 to 4 SAP2000 V12.0.0 files (Zipped SDB files)the figure above.

|| Beam Designation || Behavior || Midspan Deflection \\
\[mm\] || Comments ||
| Theoretical Beam | composite \\ | 3.2725 | Theoretical deflection based on the {math}\frac{PL^3}{48EI}{math} formula. Please note that the SAP2000 calculated deflections are slightly higher because the program considers shear deformations. |
| Beam 1 \\
(top beam) \\
\\ | nocomposite \\ | 7.1752 | The center line of deck slab coincides with  the neutral axis of the  section. Hence, the contribution of deck slab  to the flexural stiffness  of the section will be negligible and the  deflection at mid-span for  this model should be close to the deflection  for naked girder (i.e. no  composite action). | |
| Beam 2 \\ | composite \\ | 3.2624\\ | In this model, the shell elements representing the slab are drawn at the  CG of the girder and then offset above the girder to model the  composite action. The shells are offset such that the soffit of the slab  is at the top of the girder top flange. |
| Beam 3 \\ | composite \\ | 3.2624\\ | In this model the girder and slab are drawn at their respective  centerlines and then the corresponding joints of the girder and the slab  are connected together through body constraints. This is another way to  model the composite action. |
| Beam 4 \\ | composite \\ | 3.2624\\ | In this model the concept of frame insertion points is used to model the  composite action. |
| Beam 5 \\ | noncompostite \\ | 7.1752\\ | Equal constrain is used to model noncomposite behavior. \\ |
| Beam 6 \\ | noncomposite \\ | 7.1752\\ | Link is used to model noncomposite behavior. \\ |
| Beam 7 \\ | partially composite \\ | 3.5036\\ | Link is used to model partially composite behavior \\ |
| Beam 8 \\
(bottom beam) \\ | composite \\ | 3.2624\\ | Link is used to model composite behavior. \\ |

h1. Attachments

* [Modeling composite behavior in SAP2000.zip|^Modeling_composite_behavior_in_SAP2000.zip] - The zipped file contains the following files:
** SAP2000 V12.0.0 file for with 8 fixed beams for which the composite behavior is modeled using different approaches.
** SAP2000 V12.0.0 file for with 8 simply supported beams for which the composite behavior is modeled using different approaches.
** Sketches illustrating modeling composite, noncomposite and partially composite behavior in SAP2000 (PDF file).

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