Modern Formulation for Preelastic Theories on Masonry Arches

Abstract

The masonry arch as a system of rigid voussoirs subject to unilateral constraints has been investigated applying the principle of virtual work in order to define a general criterion providing the necessary and sufficient conditions for the equilibrium of the system. Since the assumptions of the formulation coincide with those of the preelastic theories, the main historical approaches have been revisited, showing that their criteria are encompassed in the present formulation. A parametric analysis has been carried out with reference to geometry and friction for a semicircular arch of constant thickness and subject to its own weight. The ranges of values for the thrust at the crown required for the equilibrium to exist have been thus determined and a geometric safety factor has been defined. A comparison of these results for the arch of minimum thickness with those obtained from the historical theories and more recent formulations has also been made.