Identification of the Tensile Force in Tie-rods of Historical Constructions

  • Hoa T. M. Luong
  • Luís F. Ramos
  • Rafael Aguilar
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


This paper addresses the problem of the bending curvature due to self-weight of tie-rods when using dynamical approach to identify the tensile force in tie-rods of historical constructions. Although several dynamic testing methods have been proposed in the literature, the effect of bending curvature due to self-weight of the rods on their frequency values has not been studied. In this work, the bending curvature due to self-weight of tie-rods with small cross-section-to-length ratios is proven to have significant effect on their frequency values of the first vibration mode at low tensile stresses. As a result, the accuracy of the identified tensile force in tie-rods will be affected if the effect is not accurately considered. Four tie-rod specimens of different characteristics were tested in laboratory by dynamic tests. A numerical model was developed for axially loaded tie-rod using a FE program, assuming Euler beam with uniform cross-section and rotational springs at both supports. By calibrating the experimental and numerical results, the most suitable dynamical analysis for tie-rod models to take into account the effect of bending curvature due to their self-weights is concluded. In particular, the analysis should be performed in two steps: (i) first, the static geometric non-linear analysis to obtain the deflected shape of the tie-rod due to its self-weight and an applied tensile force; (ii) then, the modal analysis is run on the deflected tie-rod to achieve the frequencies and mode shapes via free vibration at that applied tensile force. When the effect of bending curvature due to self-weight of tie-rods is neglected, the frequency of the first mode should be excluded. Based on these conclusions, two techniques to identify in-situ the tensile stress in tie-rods are discussed. They are frequency-based identification techniques that minimize the measurement errors. In addition, a methodology to estimate a range of tensile stress using a formula or two selfconstructed standard charts is proposed.


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Copyright information

© Springer Science + Business Media, LLC 2011

Authors and Affiliations

  • Hoa T. M. Luong
    • 1
  • Luís F. Ramos
    • 1
  • Rafael Aguilar
    • 1
  1. 1.Department of Civil EngineeringISISE, University of MinhoGuimarãesPortugal

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