Limit state analysis of 2D externally statically indeterminate networks using graphic statics

Graphic statics represents a powerful tool in the field of structural design analysis and design, because the reciprocity between form and force diagrams allows for a constant and simultaneous control of both the geometry and the load-bearing behavior of a structure in terms of internal and external forces. When combined to plastic theory, graphic statics can be used for the limit state analysis of strut-and-tie networks used to model the load paths acting inside continuous structures. The method helps finding the set of statically admissible force distributions that respect equilibrium and yield conditions, and gives insight on the maximum external load that can be applied on the structure. The present paper describes a methodology for the limit state analysis of externally statically indeterminate networks using graphic statics. Two case studies then highlight how this methodology can be used to determine the load bearing capacity of a structure.