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Determination of active members and zero-stress states for symmetric prestressed cable–strut structures

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Abstract

A prestressed cable–strut structure is generally flexible and exhibits strong coupling between its stress state and configuration. The zero-stress state offers the basis for design and analysis of cable–strut structures and has significant influence on the prestress state and the load state. Here, a computational method is proposed for seeking zero-stress states of symmetric cable–strut structures. By evaluating distributed static indeterminacy and symmetry representations using group theory, the active member with proper importance index and high-order symmetry is chosen from different types of members. Moreover, natural lengths and the involved elongations of the members are established from the initial prestresses and geometric properties. Then, based on the Newton method and the Moore–Penrose inverse theory, internal forces of the members are actively reduced. The structural configuration and tangent stiffness matrix are iteratively updated during the whole process from the prestress state to the zero-stress state. The feasibility and accuracy of the proposed approach are verified by some numerical examples, whereas the results are compared with analytical solutions and FEM simulation. The results show that one zero-stress configuration is associated with a specific prestress state, and the process between zero-stress state and prestress state is reversible. This work has theoretical significance for the design of novel cable–strut structures and provides a reference for the construction process of prestressed cable–strut structures in practical applications.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China (Grant Nos. 51978150 and 51850410513), the Southeast University ”Zhongying Young Scholars” Project, and the Fundamental Research Funds for the Central Universities. Yao Chen would like to acknowledge financial support from the Alexander von Humboldt-Foundation for his visiting research at Max-Planck-Institut für Eisenforschung GmbH, Germany. The authors are grateful to the anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. School of Civil Engineering, Sanjiang University, Nanjing, 210012, China

    Linzi Fan

  2. School of Civil Engineering, Southeast University, Nanjing, 211189, China

    Yue Sun, Weiyin Fan & Jian Feng

  3. Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, and National Prestress Engineering Research Center, Southeast University, Nanjing, 211189, China

    Yao Chen

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  1. Linzi Fan
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Correspondence to Yao Chen.

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Fan, L., Sun, Y., Fan, W. et al. Determination of active members and zero-stress states for symmetric prestressed cable–strut structures. Acta Mech 231, 3607–3620 (2020). https://doi.org/10.1007/s00707-020-02741-4

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  • DOI: https://doi.org/10.1007/s00707-020-02741-4

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