The dynamical identification of the tensile force in ancient tie-rods

The paper addresses the problem of identifying the tensile axial force of metallic tie-rods in masonry arches and vaults. The identification procedure uses the first three modal frequencies of the tie-rod, measured by means of a dynamic test. The reference structural system consists of a beam with uniform section, subjected to an axial tensile force and spring-hinged at both ends. Besides the axial tensile force, the unknown variables are the bending stiffness of the section and the stiffness of the rotational springs. Since the characteristic equation of this structural system does not allow analytical solutions, the paper proposes an approximate numerical solution, based on a minimization procedure of a suitable error function. The robustness of the method is tested by identifying a number of ideal tie-rods, modelled by means of a FEM code. Moreover, since the homogeneity of the tie-rod's mechanical stiffness throughout its axis and the equality of the constraint conditions of its extremes are hypothesised, it is verified how such hypotheses may influence the tensile force estimation. Finally, the method is tested on real tie-rods.