Work-path approach seismic modelling of hinge-controlled masonry arches

A dynamic analysis procedure for hinge-controlled masonry arches subjected to horizontal acceleration profiles is developed. Constructed from the principle of energy conservation, the establishment of equivalent systems and the path independence of conservative work, a time-incremental analysis structure is established for kinematic propagation. Equivalent systems are defined through combining kinematic equilibrium with static deformations of the single degree of freedom mechanism through parametric plotting. This generates the minimum work required to propagate the arch towards collapse. For a constant acceleration above the static limit, energy conservation requires the transformation of excess work' into kinetic energy. The path independence of work creates a spatial kinetic energy equation that is used to establish the time domain of the system. Knowing the initial position and kinetic energy thus allows the final position and kinetic energy to be determined for the time increment. A new constant acceleration and timestep then propagates the behaviour through the acceleration profile.