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A Numerical and Closed-Form Analytical Solution of the Global Buckling Critical Load of Tall Buildings Including Soil Flexibility: Timoshenko Beam

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Abstract

Purpose

The global buckling critical load ratio is a paramount parameter dictating the overall performance of tall buildings, yet its exploration has been notably lacking in the existing literature. This study addresses this gap by delivering a comprehensive theoretical investigation, along with presenting both analytical and numerical methods for computing the global buckling critical load ratio.

Methodology

These methods are designed to accommodate uniform and non-uniform tall buildings, taking into account diverse vertical load profiles, including considerations for soil flexibility. In this endeavor, a continuous Timoshenko-type model is employed, characterized by flexural and shear stiffness parameters defined by a dimensionless factor. To enhance the versatility of the analysis, an analytical solution method has been devised for uniform tall buildings. In contrast, a numerical solution method has been formulated to address the intricacies posed by tall structures exhibiting variable properties along their height, including soil flexibility.

Results and Conclusions

Notably, our investigation uncovers that the rotational flexibility of the underlying soil significantly influences the eigenvalues. Furthermore, the parametric analyses carried out in this study underscore the exceptional convergence achieved by the proposed solution methods and highlight the superiority of the continuous model, enabling the execution of parametric studies with minimal computational expenses.

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Acknowledgements

The research described in this document was possible thanks to the support of Jesus Christ. The author dedicates this research to his mother, Lucía Cruz Trujillo, for being an example of overcoming challenges, perseverance, and the pillar of his life (I love you infinitely). The author acknowledges the support from the Multiphysics Modeling and Simulation Group at Instituto Tecgraf PUCRio.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Mao Cristian Pinto-Cruz

  2. Department of Civil Engineering, National University of Engineering, Lima, Peru

    Mao Cristian Pinto-Cruz

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Contributions

Mao Cristian Pinto-Cruz: Conceptualization, Methodology, Validation, Writing—original draft, Writing—review & editing, Software, Data curation, Validation.

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Correspondence to Mao Cristian Pinto-Cruz.

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Pinto-Cruz, M.C. A Numerical and Closed-Form Analytical Solution of the Global Buckling Critical Load of Tall Buildings Including Soil Flexibility: Timoshenko Beam. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01316-0

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  • DOI: https://doi.org/10.1007/s42417-024-01316-0

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