Static analysis of coupled shear walls with multiple stiffening beams incorporating local shear deformation: Double-Beam Systems Timoshenko

Abstract

This paper presents closed-form solutions for the lateral displacement and interstory drift of coupled shear walls with an arbitrary number of stiffening beams of non-uniform properties and position, incorporating the local shear deformation of the walls through the Double-Beam Systems Timoshenko model. The barrier that had prevented previous solutions was strategic, not algebraic, given that the sixth-order differential equation admits an exact and orthogonal decomposition into three independent subsystems, pure bending (EBB), pure shear (SB), and bending-shear coupling (CTB), whose existence had not been recognized. From this decomposition, four results emerge that had not been previously established. First, \(n - 1\) stiffening beams act exclusively on the CTB subsystem, leaving EBB and SB strictly invariant, which reduces the algebraic system from \(4n\) equations to \(2n - 1\) without loss of accuracy. Second, local shear is absorbed into the shear component without disturbing the remaining ones, so that its incorporation does not introduce additional complexity; in contrast, the error of the classical sandwich beam model, structural and impossible to calibrate, reaches −75% for low slenderness. Third, the drift at the base is exactly invariant under any stiffening beam configuration, establishing an absolute lower bound that no stiffening strategy can surpass. Fourth, the displacement admits a physical decomposition into bending, shear, and interaction components, the latter being strictly negative and the only one upon which the stiffening beams act. The solutions cover uniform, triangular, and top-concentrated load profiles, and are extended to the fundamental period and global buckling critical load through an equivalent stiffness derived from the static solution. Validation against finite element models in SAP2000, for a slender 30-story coupled shear wall with ten non-uniform stiffening beams and for a low-slenderness wall with four stiffening beam configurations, yields errors below 5% at the base and below 1% over virtually the entire remaining height, on the conservative side, with errors below 3.6% and 5.4% for the fundamental period and the critical load, respectively. These results validate the proposed framework as a unified analytical platform for the static, dynamic, and stability analysis of coupled shear walls with multiple stiffening beams and incorporation of local shear deformation of the walls.