Structural analysis of historical masonry arches

The purpose of this paper is to define an analytical and numerical procedure for determining the pressure curve in the case of circular arches under general loading and arbitrary bonding conditions. The exact formulation of a curved beam finite element for static analysis is presented, and also aims at taking into account axial extension and transverse shear effects, too. The basic equations are combined in the coupled fundamental system in terms of radial displacement v, tangential displacement u and rotation ϕ . The stiffness matrix of the curved beam element is determined. The element formulation is based on shape functions that satisfy the homogeneous form of the fundamental system of differential equations. Relations between kinematics variables and curvature χ are established by using the constitutive equations and the relations between generalized stress and strain components. The de-coupling of the above displacement fields makes it possible to express the exact system solution in terms of six independent constants leading to a simple two-node element with three degrees of freedom per node. The solution obtained is applicable to the analysis of both thin and thick curved beams.