This test problem demonstrates the difference between body constraints and equal constraints, as applied to a simply supported beam model. The primary difference between these constraint types is that DOF are coupled when a body constraint is applied. This causes the constrained joints to translate and rotate as a rigid body.

Modeling

A simply supported beam is modeled once with body constraints joining the beam to its supports, then again with equal constraints. Geometric configuration is shown in Figure 1:

Figure 1 - Structural configuration

Analysis

Once each system is subjected to a uniform distributed load, analysis generates the results shown in Figures 2-4:

Figure 2 - Deflected configuration

Figure 3 - Shear response

Figure 4 - Moment response

Commentary

Conclusions may be drawn as follows:

• From the deflected shape of the first beam, it is evident that the support and the coincident-beam joints rotate as a rigid body, allowing the beam to effectively span between the actual supports.

• As seen in the deflected shape of the second beam, beam end-joints do not deflect downward. This is because the equal constraint, applied to the UZ direction, constrains joint displacement with that of the support, which is zero. This produces a stiffer system in that the beam effectively spans between its end joints, and not the support joints.

Attachments

• SAP2000 V11.0.8 model (zipped SDB file)

Metadata

• Name: Body vs. equal constraint
• Description: Comparison between body-constraint and equal-constraint application to a simply supported beam.
• Program: SAP2000
• Program Version: 11.0.8
• Model ID: na