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The pinned-support configuration restrains each beam against longitudinal displacement. For Case 2, this longitudinal restraint is not at the centroid of the cross-section (10), but at the top-center insertion point (8). This prevents the top fibers from shortening, and introduces a longitudinal tension force which acts on an arm about the neutral axis. Eccentricity creates a negative moment which reduces the positive moment induced by applied loading. This also reduces midspan displacement. Figure 1 displays beam geometry and deflection, and Figure 2 presents moment- and axial-force diagrams.

Figure 1 - Beam geometry and deflection

Figure 2 - Moment- and axial-force diagrams

The insertion of a roller support at one of the previous pin locations would free the beam from longitudinal response. This is shown in Figure 3:

Figure 3 - Longitudinal release from roller support

See Also

• Effect of insertion point on beam reactions test problem

• Verification Problem 1-011, available in Context Help through the Help > Documentation > Analysis Verification > Frames menu