Buckling of flexural-shear plates

In this paper, tall buildings with shear-wall structures and with narrow rectangular plane configuration are modeled as flexural-shear plates for buckling analysis. The differential equations that govern the buckling behavior of flexural-shear plates, with and without considering shear deformation of shear-wall structures, are established. The general solutions of uniform flexural-shear plates with various end conditions are derived and used to obtain the eigenvalue equation for multistep flexural-shear plates. The new exact approach that combines the transfer matrix method and the derived closed-form solutions is presented for the buckling analysis of multistep flexural-shear plates. The exact solutions for buckling of nonuniform flexural-shear plates are derived for two types of distributions of variable stiffness. It is proved that a flexural-shear plate with two edges free in the longitudinal direction can be simplified as a flexural bar and that a multistep uniform flexural-shear plate may be treated as a nonuniform plate with a continuously varying cross section for buckling analysis. A numerical example demonstrates that the present methods are easy to implement and efficient for analyzing the entire and partial buckling of multistep flexural-shear plates, with or without considering shear deformation of shear-wall structures, subjected to axial loads acting on the top of each step plate.