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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 beam) \\
\\ | 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). | |
| Beam 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. |
| Beam 3 \\ | composite \\ | 0.8313 | 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. |
| Beam 4 \\ | composite \\ | 0.8313 | In this model the concept of frame insertion points is used to model the composite action. |
| 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, body constraints, frame insertion points or links to model composite action of the beam-and-slab assembly.
h1. 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 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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This article is for SAP2000, but the same concepts apply also to CSiBridge. |
On this page:
SAP2000 provides various ways to model the composite behavior of a beam-slab assembly. Attached are four SAP2000 models which demonstrate various approaches. The geometric and material properties of the model used for comparison are listed as follows:
Total girder height = 1.2m
Top and bottom flange width = 1.0m
Top and bottom flange thickness = 0.1m
Applied load at midspan = 100kN
Modulus of elasticity, E = 33000000 kN/m2
Boundary condition: fixed at both ends
Midspan deflections are calculated as follows:
Naked girder, Δ = 0.0018m
Composite girder, Δ = 0.00083m
Model overview
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Figure 1 - Model overview
Approaches to modeling composite behavior
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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] | 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 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.
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:
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 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.
Metadata
Name: Composite section
Description: Several approaches to the modeling of composite sections.
Program: SAP2000
Program Version: 12.0.0
Model ID: na
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NOTE: The attached file, Modeling composite behavior in SAP2000.zip, may be emailed directly to users to answer support questions. |