Example

This example considers a simply-supported beam with pin supports at either end. A point load, oriented in the gravity direction, is applied to the beam midspan. The two cases considered for beam design include the following:

• Case 1: Default insertion point at the midspan centroid (point 10)

• Case 2: Top-center insertion point at the midspan (point 8)

Upon completion of analysis, it is observed that the midspan deflection for Case 1 is larger than that for Case 2. While beam stiffness is the same for each instance, this discrepancy may be attributed to the difference in boundary condition which results from variable insertion point location.

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), preventing the top fibers from shortening. This also 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 point loading, therefore also reducing midspan displacement. Figure 1 displays beam geometry and deflection, and Figure 2 presents 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:

The attached verification problem (1-011), also available through the Help > Documentation > Analysis Verification > Frames menu, provides additional information on insertion points.