Equilibrium of masonry arches

Abstract

The state of a masonry arch, as of any hyperstatic structure, must conform to the equations of static equilibrium, but is determined by displacements imposed by the environment. These ‘boundary conditions' are in general unknown, but very small movements (as for example of the abutments of an arch bridge) can alter markedly the internal stresses in the structure. An elastic analysis purports to determine an actual state, but in fact requires a knowledge of the boundary conditions which is not possessed by the engineer, and any elastic solution must therefore be viewed with reservation. Further, predicted elastic deformations are small, and do not correspond to observed displacements of a masonry arch. The ‘traditional' nineteenth-century examination of equilibrium by means of ‘lines of thrust' is free of these defects (the analysis can be made today by use of computers and can involve properly constructed finite elements); such equilibrium solutions are, by virtue of the plastic theorems, safe.