Stress and Displacement Estimates for Arches

This paper presents analytical estimates of the behavior exhibited by curved, archlike structures under radially directed and gravitational line loads. The behavior is shown to range from elementary beam bending at one end to a state of pure compression at the other, and its behavior can be tracked by an arch rise parameter that is a function of the arch’s semivertex angle, radius and thickness. The principal results are useful estimates of the dependence of the major displacements and stress resultants on the arch rise parameter. The results also offer some insight into the assumptions underlying Robert Maillart’s arch designs.