Analytical study of stiffened multibay planar coupled shear walls

Placing stiffening coupling beams at some levels of a coupled shear wall (CSW) structure is a proper way to enhance the coupling effects and reduce the interstory drifts of the structure. The resulting structural systems are called stiffened CSWs. To date, rigorous closed-form solutions for stiffened multibay planar CSWs subjected to lateral loading have not yet been derived. To solve this problem, a new approach based on the displacement method was proposed to establish the governing equations and boundary conditions, in which the rotation of the cross sections of walls was decomposed into two components: one associated with the axial deformations of wall piers and the other associated with the flexural and shear deformations of coupling beams. The closed-form solutions for the lateral displacement and rotation components were derived for standard load cases, which were verified to have high accuracy. The analytical solutions indicate that the distributions of the lateral displacements and rotation components along the structural height only depend on four dimensionless parameters, which are related to the composition ratio of the moment of inertia of the wall piers about their common centroid, the ratios of the span stiffness of the ordinary coupling beams to that of the wall piers and that of the stiffening beams, and the relative stiffness level, respectively. Parametric studies were further conducted to investigate the influence of these governing parameters on the degree of coupling, interstory drift ratios, and rotation components. It was found that the optimal stiffening levels for achieving the maximum degree of coupling commonly range from 0.06 to 0.50, and those for achieving the minimum of the maximum interstory drift ratio commonly range from 0.59 to 0.80. These findings provide useful implications for the optimization design of stiffened multibay CSWs.