Simplified Analysis of Tall Buildings for Soil–structure Interaction in Uniform and Non-uniform Buildings

Abstract

This paper presents a continuous analytical model for evaluating the static and dynamic response of tall buildings considering soil–structure interaction. The structure is represented as a parallel coupling of a bending beam and a shear beam, connected by rigid horizontal links, and supported by translational and rotational springs that account for foundation flexibility. The governing equations are derived via Hamilton's principle, explicitly including both translational and rotational inertias. For buildings with uniform properties, closed-form solutions are obtained using the Laplace transform. To extend the formulation to non-uniform buildings, a modified transfer matrix method is introduced that avoids matrix inversion, thereby reducing computational cost. Parametric studies highlight the sensitivity of natural frequencies to soil flexibility and demonstrate the influence of rotational inertia on higher vibration modes, which is often neglected in previous studies. The formulation is restricted to the linear elastic range and does not incorporate second-order (P–Δ) effects or material plasticity, thereby delineating its applicability to structures without significant geometric or material nonlinearities. Numerical comparisons with finite element results confirm the accuracy and efficiency of the proposed approach, providing a practical tool for the preliminary design and performance assessment of tall buildings on flexible foundations.