A subsystem-based approximate method for calculating the fundamental frequency and global buckling load of coupled shear walls: Double-Beam Systems Timoshenko

Recent studies on coupled shear walls (CSW) have underscored the influence of local wall shear on their overall deformation behavior. Recognizing this mechanism has proven essential to minimize the discrepancies often observed when CSW are represented by the classical sandwich beam model. Although several generalized analytical formulations have been developed for vibration and stability assessments, their use is still constrained by their mathematical complexity and the requirement of programming skills or advanced analytical proficiency. To provide a simpler yet theoretically consistent alternative, this paper proposes approximate analytical expressions derived from a continuous Double-Beam Systems Timoshenko-type model that explicitly incorporates the local shear mechanism of the walls. The horizontal displacement induced by a generic static lateral load is decomposed into three independent subsystems: a bending-shear beam, a bending beam, and a shear beam. From these components, simplified eigenvalue relations are obtained, enabling direct evaluation of the fundamental vibration frequency and the global critical buckling load. By combining the eigenvalues of the three subsystems through Dunkerley