Vibration-based identification of tensile forces in tie rods

Tie rods have been widely adopted in ancient and monumental buildings for static purposes, in order to counter-act horizontal loads in arches and vaults. The correct evaluation of the current axial load is essential for diagnosis and restoration of those building especially considering the low tensile strength offered by ancient metallurgy. Static and dynamic methods are generally adopted for axial load evaluation. In this paper, a vibration-based method is proposed to estimate the axial forces in the tie rods from the experimentally identified natural frequencies. A Rayleigh-Ritz method is used to predict the analytical natural frequencies of the system as a function of axial load. In this application, it is proposed to use a set of linearly independent and refined admissible functions to obtain the discretized equations of motion of a continuous system. Use of the proposed admissible functions will reduce the computational demand and improve accuracy of the results even with a low number of functions. Sensitivity and uncertainty analysis is carried out to highlight the influence of the governing parameters on the axial load estimation, in particular the rotational stiffness associated to the boundary conditions. Performance of the proposed method is validated numerically using data from a refined finite element model and experimentally using measured vibration (acceleration) data in the laboratory.