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Analytical and numerical solution of generalized static analysis of tall buildings: double-beam systems Timoshenko

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Abstract

This article introduces a method for statically analyzing tall buildings using a combination of the continuum method and the transfer matrix method. The approach offers both analytical and numerical solutions, enabling the assessment of critical parameters such as lateral, rotational displacements, and drifts in tall buildings. The continuous model used consists of the parallel coupling of two Timoshenko beams. This model captures the interaction between flexural and shear stiffness, presenting a comprehensive understanding of tall building behavior. Moreover, it incorporates three distinct kinematic fields that encompass both translational and rotational movements. The flexibility of the model enables an expansive analysis across various structural configurations, including frames, shear walls, coupled shear walls, and tall buildings with complex structural systems. The equilibrium equations and essential boundary conditions are obtained by a variational approach based on Hamilton’s principle. For tall buildings with uniform properties along their height, a closed-form solution is proposed, while a numerical solution is presented for structures with varying geometric and structural properties along their height by analytically deriving their transfer matrix. Numerical demonstrations showcase the precision and reliability of the proposed analytical and numerical techniques. Furthermore, the method offers the advantage of reduced processing time, making it particularly suitable for preliminary analysis of tall buildings and serving as a valuable tool for verifying structural integrity and performance in later stages of the project.

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Acknowledgements

The research described in this document was possible thanks to the support of Jesus Christ. The author wants to dedicate this research to his brilliant daughter Zoé Juliette Pinto (my beautiful girl). The author acknowledges the support from the Multiphysics Modeling and Simulation Group at Institute Tecgraf PUC-Rio.

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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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  1. Mao Cristian Pinto-Cruz
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MCPC contributed to writing—review and editing, writing—original draft, visualization, validation, supervision, resources, project administration, methodology, investigation, funding acquisition, formal analysis, data curation and conceptualization and provided software.

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Correspondence to Mao Cristian Pinto-Cruz.

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Pinto-Cruz, M.C. Analytical and numerical solution of generalized static analysis of tall buildings: double-beam systems Timoshenko. J Braz. Soc. Mech. Sci. Eng. 46, 368 (2024). https://doi.org/10.1007/s40430-024-04809-x

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