Limit state analysis of hemispherical domes with finite friction

While it is recognised that often masonry vaulted structures fails by way of sliding, because this condition involves violation of the normality rule for plastic analysis, most of the existing procedures assume that sliding is prevented by sufficiently high friction at the interface between blocks or voussoirs and that failure is achieved by relative rotation of blocks. The inclusion of the sliding mechanism poses the problem of the uniqueness of the solution found applying standard limit-state analysis procedures. The paper first provides a simple proof of the uniqueness based on the condition of symmetry and equilibrium for domes with general load conditions. The proof of the unique solution allows a straightforward treatment of this class of problems as one of standard limit-state analysis. On these bases a computer procedure, using a lower bound approach, has been developed to de-fine the condition of stability of such structures. Particularly for domes this procedure leads to determine admissible membrane surfaces within the thickness.