Closed-form and numerical solution of the static and dynamic analysis of coupled shear walls by the continuous method and the modified transfer matrix method

This study investigates the static and dynamic structural analysis of symmetrical and asymmetrical coupled shear walls using the continuous and modified transfer matrix methods by idealizing the coupled shear wall as a three-field CTB-type replacement beam. The coupled shear wall is modeled as a continuous structure consisting of the parallel coupling of a Timoshenko beam in tension (with axial extensibility in the shear walls) and a shear beam (replacing the beam coupling effect between the shear walls). The variational method using the Hamilton principle is used to obtain the coupled differential equations and the boundary conditions associated with the model. Using the continuous method, closed-form analytical solutions to the differential equation for the coupled shear wall with uniform properties along the height are derived and a numerical solution using the modified transfer matrix is proposed to overcome the difficulty of coupled shear walls with nonuniform properties along height. The computational advantage of the modified transfer matrix method compared to the classical method is shown. The results of the numerical examples and the parametric analysis show that the proposed analytical and numerical model and method is accurate, reliable and involves reduced processing time for generalized static and dynamic structural analysis of coupled shear walls at a preliminary stage and can used as a verification method in the final stage of the project.