Lateral-Load Analysis of Asymmetric Multistory Structures

The object of the present paper is to provide a more complete three-dimensional continuous method for structures comprising simple or coupled, prismatic or nonprismatic, shear walls and frames arranged asymmetrically in the floor plane. The unknowns of the problem are three continuous functions of horizontal displacements; two for the translations parallel to the structure axes, and one for the angle of twist. These functions are derived from a system of three third-degree nonhomogeneous differential equations with constant coefficients. The homogeneous part of the solution relates to an eigenvalue problem of a third-degree matrix, involving nine arbitrary constants obtainable from the boundary conditions. The particular solution depends on the type of loading; a uniform lateral load yields a second-order polynomial and a trapezoidal load yields a third-order one. With the three functions known the three displacement functions for each of the stiffening elements and elastic media can be calculated and the internal forces established. The present method is applicable to structures with nonuniform geometric properties by dividing them into uniform zones, solving for each zone separately, and determining the relevant constants from interzone boundary conditions.