Overview

Test Case

A symmetric cross-section beam of bending stiffness EI_y, and height h, totally fixed at C, simply supported at A, is subjected to a concentrated load P at point B. Verify that a load P which is slightly smaller than the theoretical load limit P_L will cause elastic deformation and that a load which is slightly larger than P_L will cause plastic deformation. Also determine the maximum deflection δ, the reaction force at the left end R_A, and the reaction moment at the right end M_c just prior to the development of a plastic hinge.

Figure 48: Limit Moment Problem Sketch

Analysis Assumptions and Modeling Notes

The load required for M_c=M_L (the limiting, or fully plastic bending moment) is calculated to be 1000 lbs. From the reference, the second plastic hinge develops at B when P_L = 2.5M_L/a = 1388.88 lb. The beam area is not necessary for this loading and is assumed to be 1.0. The beam half height (h/2) is input as a section data using the SECDATA command. K_y is arbitrarily selected to be a large value (1 x 10¹²) to minimize the elastic effect of the hinge.

Combination elements are used as breakaway hinge connections, which slide above the M_L value. An extra set of these elements are defined in parallel with an arbitrary low stiffness and a large value of real constant FSLIDE to maintain solution stability after collapse. Sliding status of the combination elements indicates that a plastic hinge has formed.

The status of the COMBIN40 is denoted by integers. If STAT = 1, the gap is closed (elastic behavior). STAT = 2 and STAT = -2 indicate positive slide and negative slide respectively (plastic behavior).

Results Comparison