Closed‐Form Solutions for the Static Analysis of One‐bay Stiffened Coupled Shear Walls Using the Three‐Field CTB Beam

ABSTRACT An efficient strategy to control lateral displacements and interstory drifts in coupled shear walls is the introduction of stiffening beams. However, existing analytical solutions have been restricted to particular and simplified cases without generalization, and typically neglect the deformation mechanisms associated with local shear and axial extensibility of the walls—two deformation mechanisms that significantly enhance the accuracy of classical continuous models. To overcome these limitations, this study employs a generalized continuous model of the Three‐Field CTB Beam type, which incorporates these two deformation mechanisms, to propose, for the first time, a closed‐form solution for the static analysis of stiffened coupled shear walls subjected to arbitrary lateral load distributions (uniform, triangular and concentrated). It is shown that the lateral displacement of the three‐field CTB beam can be obtained as a linear combination of three independent subsystems: the bending beam, the shear beam, and the beam resulting from the parallel coupling of bending and shear beams—classical continuous beams established in the literature. This decomposition allows the static problem to be solved in a simple yet mathematically exact manner with respect to the original problem. It is demonstrated that horizontal deflection and interstory drift can be decomposed into three distinct components relevant to structural engineering: bending, shear, and interaction. The effect of the stiffening beam is confined to the interaction component and does not affect the components associated with bending and shear. The local shear deformation mechanism of the walls is introduced in the shear and interaction components through the dimensionless parameter η . Numerical applications reveal that the classical continuous model is valid only for slender walls, which can be modeled as bending beams. Its application to nonslender walls results in a significant underestimation (maximum error of −60.43%), thereby compromising structural safety. In contrast, the introduction of the dimensionless parameter η extends the applicability of the model to nonslender walls, which are better represented as Timoshenko beams, reducing the maximum error to 3.67%.