{live-template:Test Problem}

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


h1. 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:

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!Figure 1.png|align=center,border=1!

{center-text}Figure 1 - Structural configuration{center-text}


h1. Analysis

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

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!Figure 2.png|align=center,border=1!

{center-text}Figure 2 - Deflected configuration{center-text}

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!Figure 3.png|align=center,border=1!

{center-text}Figure 3 - Shear response{center-text}

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!Figure 4.png|align=center,border=1!

{center-text}Figure 4 - Moment response{center-text}


h1. 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.


h1. Attachments

* [SAP2000 V11.0.8 model |Body vs. equal constraint^SAP2000 V11.0.8 model.zip] (zipped SDB