Vector analysis and the stationary potential energy for assessing equilibrium of curved masonry structures

Curved structures have enabled masons, engineers, and architects to carry heavy loads cover large spans with the use of low-tensile strength materials for centuries, while creating marvels world’s architectural heritage. Despite long history these practices, finding optimal structural forms assessing stability safety curved remains as topical ever. This is due an increasing interest preserve heritage reduce material in construction, replacing steel concrete low-carbon natural materials. The analogy between inverted hanging chains shape masonry arches a concept deeply rooted our analysis practices. paper revisits equilibrium chain, following transition from Newtonian Lagrangian Mechanics. Understanding ideas reveals that are two incompatible systems. discusses limitations describing two-dimensional objects finite thickness (e.g., arches) by using one-dimensional infinitesimal chains, funicular lines) on geometry structure loading conditions can be assumed practice. These manifest themselves applying force carefully considers stereotomy exercised, which becomes particularly critical when studying vertical sections or considering seismic loads. shows taking logical progression towards Mechanics, one may obtain rigorous solutions limit state principle stationary action. approach liberates analyst need consider each individual block geometrically load path thrust forces.