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