Effects of the stress field on the dynamic properties of masonry bell towers

A new numerical procedure for the modal analysis of masonry structures in the presence of thermal variations has been implemented in the finite element code NOSA-ITACA, which models masonry as a nonlinear elastic material with zero tensile strength and infinite compressive strength. The numerical procedure proposed in this paper consists of two steps. In the first step, the equilibrium problem of the structure subjected to the assigned loads (both mechanical and thermal) is solved, and its numerical solution (consisting of displacements, stress and strain fields) calculated. In the second step the tangent stiffness matrix Kd is calculated by using the derivative of the stress with respect to the strain, obtained in the previous step, and the generalized eigenvalue problem involving matrix Kd and mass matrix M is solved. The procedure allows for taking into account the effects of the stress field due to thermal variations within the structure on its natural frequencies and mode shapes. The new procedure is applied to the medieval "Clock Tower" in Lucca.