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

Graphic statics provides an elegant and efficient method for equilibrium analysis of various types of structures. This is particularly the case for pin-jointed frameworks, for which the use of reciprocal form and force diagrams gives direct and simultaneous insights on the static behaviour of every structural member. On the other hand, plastic theory offers a superb theoretical framework for the limit state analysis of structures presenting a certain degree of static indeterminacy as well as for equilibriumdesign purposes. Based on graphic statics and plastic theory, this paper proposes a graphical methodology for the analysis of 2D statically indeterminate networks, including pin-jointed frameworks and strut-and-tie models within a continuum of material. This approach can be used for determining the collapse load factor and the corresponding collapse mechanism of existing structures, as well as for evaluating the load-bearing capacity of structures during the design process. In order to validate the methodology, the geometrically obtained collapse load factor is compared with the ones determined using classical static and kinematic approaches. The graphical methodology is then used to solve more complex cases with several degrees of static indeterminacy. Finally, the advantages for structural optimization, as well as the perspectives towards an extension to 3D networks are outlined