Static, dynamic, and stability analysis of coupled shear walls: Correction factors due to local shear deformation of the walls

A newly introduced deformation mechanism due to the local shear of walls has recently been incorporated into the classical sandwich beam formulation. However, the proposed solutions present complexities, have limited applicability, and do not provide a clear understanding of the actual structural behavior. Therefore, using an innovative generalized sandwich-type continuous beam, resulting from the serial coupling of the classical sandwich beam and the shear beam, this paper proposes simple, practical, and safe closed-form "back-of-theenvelope" analytical solutions for calculating the lateral displacement, fundamental frequency, and global critical buckling load of symmetric and/or asymmetric coupled shear walls with single and multiple bays. A subsystembased approach is employed, demonstrating that lateral displacement can be decomposed as the sum of three independent subsystems: a bending beam, a shear beam, and a bending-shear beam. Since analytical solutions for these subsystems are well established in the literature, the lateral displacement can be obtained directly. A careful arrangement of terms allows expressing the lateral displacement as the sum of three components: bending, shear, and interaction, where interaction is always beneficial as it reduces the structure's lateral displacement. Analytical solutions are proposed for three classical lateral loading scenarios. It is observed that the introduction of this new mechanism only affects the shear-induced displacement, and a static correction factor is proposed to incorporate this deformation mechanism into the lateral displacement equation available in the literature. Furthermore, this approach is extended to dynamic and stability analyses, and a dynamic and stability correction factor is proposed for the approximate solutions obtained using Dunkerley's formula to calculate the fundamental frequency and global critical buckling load, respectively. The validity ranges of the correction factors are determined through a rigorous parametric analysis, yielding errors of + 3.30%, +/- 3.17%, and +/- 4.16%, compared to the literature errors of - 56.04%, + 35.21%, and +144.71% for lateral displacement, fundamental vibration period, and global buckling load calculations, respectively. These small, engineering-tolerable errors ensure the safe application of the proposed approach in structural engineering practice.