Overview

Test Case

A very stiff beam of length L, subjected to a lateral load F, is initially at position AB on a horizontal table. Point A is pinned to the table and restrained from rotation by a relatively weak torsion spring. Determine the final position of the beam in terms of δ_x, δ_y, and Θ. Show that the bending stress in the beam σ_bend is negligible.

Figure 56: Rigid Beam Problem Sketch

Analysis Assumptions and Modeling Notes

The problem is solved using two approaches:

In the thick beam approach, the "rigid" beam properties are arbitrarily selected as area = 100 in², I = 1000 in⁴, thickness = 10 in.

In the constraint equation approach, a constraint equation is used to enforce the assumption of a rigid beam. The constraint equation is of the form: δ_y = (L)(Θ). The beam properties are arbitrarily based on a 0.25 square inch cross-section.

The weak spring is modeled with either MATRIX27 or COMBI250.

Results Comparison