About the number of hinges at failure of semicircular and pointed masonry arches

The collapse of masonry arches under static loads mainly occurs because some voussoir interfaces open and form hinges and eventually transform the structure into a mechanism. There is an interest in the maximum number of concurrent hinges at a given arch geometry and stereotomy, which latter refers to the cutting pattern of the voussoirs. This paper applies the governing equations of a geometrically exact rod to thrust line analysis while it adopts the Heymanian assumptions. With the new model, the number of concurrent hinges can be investigated in an organized and predictive manner generalizing the numerical and analytical results of the literature. Specifically, this paper proves that the number of hinges for a symmetric, circular pointed arch loaded by self-weight cannot exceed seven in the cases of vertical stereotomy and constant thickness in the vertical or normal directions. The maximum number of hinges is also seven for an arch with constant thickness and radial stereotomy.