Thrust line analysis revisited and applied to optimization of masonry arches

An original revisitation of the thrust line analysis is presented, within a theoretical framework which unifies the classical equilibrium formulations of masonry arches and enlightens the relationships among them. Diverse optimization problems generalizing the classical Heyman-Couplet problem are investigated in this framework. It is proven that a catenary arch with finite thickness subjected to its self-weight admits a shear-free stress state, but not a bending-moment-free stress state. However, the latter can be recovered with a suitable small perturbation of the catenary mid-curve. On considering also horizontal forces proportional to the self-weight, the mid-curve of an arch of minimum weight is obtained, as well as the stereotomy and the thickness distribution of a circular arch of minimum weight. Besides their own merit, these results confirm the present formulation to provide a powerful theoretical setting for the thrust line analysis of masonry arches.