Limit state analysis of historical structures using graphic statics related to the Principle of Virtual Work

Because of the incomplete knowledge we have of the mechanical characteristics and of the history of loading of historical structures, these are often advantageously analyzed by means of graphic statics, e.g. using thrust lines as possible load paths within masonry arches to demonstrate their stability. In this context, theory of plasticity provides a powerful theoretical framework for the limit state analysis of structures, in particular for those in masonry on condition of several key assumptions: infinite strength in compression but zero in traction; no sliding failure. Starting with the analysis of a simple trussed framework and to basic bended structures, this paper emphasizes that limit analyses implying graphic statics can lead to similar conclusions about the collapse load factor that the ones obtained using the Principle of Virtual Works. Then it states a way to adapt this methodology to ancient masonry structures and presents results obtained for a simple arch analysis.