A direct treatment of distributed loads in the collapse analysis and design of rigid frames

The rigid–plastic analysis and minimum weight design of planar bending frames is developed as the lower-bound form of a linear programming formulation. The analysis is extended to consider geometric variation of nodes intermediate along member lengths subjected to distributed loading by the technique of sequential linear programming. Linearized geometric sensitivities for use with the sequential process are developed analytically. The geometric variation algorithm is shown to be effective for the determination of collapse loads and minimum weight designs. Load and weight functions produced by the direct determination method do not generally vary greatly from those derived by an approximating point load approach, but more significant variation is found in plastic moment distributions associated with minimum weight designs.