{live-template:Test Problem}

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The internal forces and capacities of a beam are calculated with respect to the cross-section center of gravity. This test problem studies the modeling of a rectangular and continuous beam which is solid along the left segment and hollow along the right. This void is located along the bottom of the element.

Default insertion-point settings locate each segment such that the center of gravity aligns with the element chord. As shown in the image at the top of Figures 1-4, this results in misalignment between each segment because the center of gravity is higher for the hollow section. This may be corrected through either of the following methods:

# Draw element chords to account for the difference in center-of-gravity location, as shown in the middle image of each figure.
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# Use a bottom-center [insertion point|kb:Insertion point] to draw the two segments along the same line as shown in the bottom image of each figure.

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!geometry.png|align=center,border=0!

{center-text}Figure 1 - Modeling approaches{center-text}

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!extruded shape.png|align=center,border=0!

{center-text}Figure 2 - Corresponding depth profile{center-text}

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To demonstrate how each of these conditions affects response, a straight [tendon|kb:Tendon] is modeled below each beam. Tendon deflection and internal moment (relative to cross-section centroid) is presented. Results are correctly reported only for the second and third case, where the solid and hollow sections properly align.

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!deformed shape.png|align=center,border=0!

{center-text}Figure 3 - Displacement{center-text}

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!moment diagrams.png|align=center,border=0!

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


h1. Attachments

* [SAP2000 V14.2.0 model |Align solid and hollow sections^SAP2000 V14.2.0 model A.zip] (zipped SDB file)

{related-incident:no=25048|comment=Aligning solid and hollow sections.}