A fully graphical approach for limit state analysis of existing structures:Application to plane elastic-plastic bended structures and to plane masonry arches.

When classical elastic analysis fails to model correctly the structural behaviour of historical masonry structures because of the brittle, rigid, anisotropic and inhomogeneous characteristics of their building material, equilibrium-based limit state analysis constitutes an efficient alternative for their structural assessment. Since the lack of knowledge about the history of loading makes the actual state of stresses likely impossible to determine for these statically indeterminate structures, Plastic Theory provides a powerful theoretical framework and defines a rather simple way to assess the structural safety level. The lower-bound theorem of plasticity can be applied using graphic statics because it ensures that equilibrium and yield conditions may be respected when applying specific constraints to the nodes of the reciprocal diagrams. This paper focuses on graphic statics for statically indeterminate structures by (1) defining graphically safety domains; (2) identifying specific collapse modes; (3) measuring related collapse load factors of bended structures and masonry arche