A vibration-based method for the evaluation of axial load in tie-rods: two main case studies

The knowledge of the tensile load in reinforcement tie-rods is of crucial importance to assure structural integrity and safety in ancient buildings. This work addresses the problem of identify-ing this tensile load in tie-rods of ancient masonry arches and vaults. The proposed procedure is a non-destructive and non-invasive method. It consists in matching the first six natural frequen-cies of the tie-rod, acquired by a classical accelerometer, with numerically obtained frequencies. This matching procedure is accomplished by an optimization algorithm in which the length of the rod, the presence of concentrated masses along it, and an elastic foundation at the edges are the optimization variables. In this way the main unknown, i.e. the axial load, is determined by a mathematical algorithm that automatically minimizes the difference between experimental and numerical results, on the basis of the choice of multiple parameters combinations. Here two main case studies in which the method is successfully applied are shown; the first case study regards the determination of the axial load in the tie-rods of an ancient Dome, the se-cond case study reports the experiments in an historical palace. In both cases, a deep investiga-tion about the stress state in the tie-rods is carried out via a non-linear finite element analysis: in this way structural considerations about the safety of the buildings are drawn.