Analysis of Three-Dimensional Structures

A method of analysis is presented to predict the complete load-displacement relationship for large multistory structures. The structures are composed of sets of planar bents arranged in two perpendicular directions. The structure is assumed to deform in these two principal directions and twist about a vertical axis. The actual structure is replaced by an analytical model in which the number of unknown displacements have been considerably reduced. Slope deflection equations, modified for plastic hinging, are used to relate the member displacements to the end moments. The secondary moments due to the column axial loads acting through the sway displacements are considered in formulating the equilibrium equations. The effects of axial shortening, changes in axial load, variations in stiffness and carry over factors, and shear deformations are not considered. The effect of the asymmetry of the structure is illustrated by the results of an analysis of a 10-story structure.