Explicit solutions for depressed masonry arches loaded until collapse—Part II: a solution method for statically indeterminate systems

In this second part of the paper we use the results obtained in the first part in order to build the solution to two statically indeterminate cases of a depressed masonry arch. As in the first part, the arch is modeled as a one-dimensional curved nonlinear elastic beam made of a material that is by hypothesis incapable of withstanding significant tensile stresses. We find the explicit expressions for the displacements and rotations of the cross-sections of the arch subject to a uniformly distributed load. Such explicit analyt- ical expressions may constitute an effective bench- mark for validating numerical solution methods. The evolution of the solution with increasing load is described thoroughly, and an extension of the pro- posed method to general constraint conditions illus- trated. Finally, some considerations are advanced regarding the mechanical behavior of depressed masonry arches near collapse.