Thrust in a symmetric masonry arch with frictional joints on spreading supports

The effect of a supports settlement in a symmetric masonry arch is studied by modeling the arch as a system of rigid plastic blocks with frictional sliding. It is shown that in a collapse state due to a horizontal settlement the thrust attains its minimum statically admissible value, so extending to the case of frictional sliding a well-known result of standard limit analysis, which considers collapse states only due to the opening of joints. The case of both vertical and horizontal settlements is also analyzed. It is demonstrated that the collapse thrust in case of horizontal settlement is a lower bound for the collapse thrust in case of generic settlement. Extensive numerical analyses illustrate the above results.