Closed-form Solutions for Lateral Displacement of Single-bay Coupled Shear Walls Using a Subsystem-based Three-field CTB Beam

Abstract

Local shear deformation and axial extensibility of walls have recently been recognized as critical, yet previously overlooked, sources of error in predicting the lateral displacement of coupled shear walls. Existing analytical models often face limited practical application due to solution complexity and insufficient physical clarity. Using a generalized continuous model, this paper proposes a simple, exact, closed-form analytical formulation based on an independent subsystem approach, enabling fast and accurate estimation of lateral displacements. The generalized continuous model couples, in parallel, an extensible Timoshenko beam and a shear beam, thereby capturing both shear deformation and axial extensibility. The total lateral displacement is expressed as a linear combination of three independent subsystems: bending, shear, and bending–shear coupling. Closed-form solutions are derived for each subsystem under uniform, triangular, and top-concentrated loading. The displacement components—bending, shear, and interaction—are physically interpreted, with the interaction term arising exclusively from the coupling subsystem. Numerical examples illustrate the physical meaning of each component, while a parametric analysis establishes applicability limits, showing a maximum safe-side error of +7.30%, compared to the −56.04% unsafe-side error of the classical solution. The proposed formulation ensures structural safety, maintains analytical simplicity, and is well-suited for practical engineering design.