A numerical and closed-form analytical solution for the global buckling critical load of tall buildings considering soil flexibility: A coupled shear-flexural model

Abstract

The critical global buckling load is a fundamental parameter governing the performance of tall buildings, however, the existing literature lacks an efficient solution that comprehensively captures the behavior of tall structures with uniform or variable properties. In response to this gap, this study introduces a novel and generalized solution, employing the coupled shear-flexural model. This solution is designed for determining the critical global buckling load in tall buildings subjected to vertical loads with diverse profiles, while also incorporating soil flexibility. The analytical solution, designed for the uniform continuous model, offers a breakthrough by providing graphical representations facilitating the direct determination of eigenvalues based on a single dimensionless parameter. Addressing the unique challenge posed by tall buildings with variable properties, a numerical transfer matrix method based on a Laplacian approach is proposed. This method enables the direct calculation of the transfer matrix for each level, displaying exceptional convergence in just three iterations. The study sheds light on a crucial finding that emphasizes the adverse impact of rotational flexibility on soil, leading to a decrease in eigenvalues as soil flexibility increases. Importantly, the proposed solution methods not only show excellent accuracy but also serve as invaluable tools for performing parametric analyses. Furthermore, they present cost-effective alternatives to exact methods, providing a solid foundation for studying the overall stability of tall buildings. This research contributes significantly to the existing literature by introducing efficient methodologies that improve our understanding and analysis of the behavior of tall buildings under vertical loads.