Geometric considerations of plasticity in structural concrete analysis and design

The methods of plasticity have proved to be very useful to designers of engineering structures. The use of graphical methods also has a history of providing considerable benefit to the designer and still plays a role both in providing estimates of numerical answers in analysis and in aiding an intuitive grasp of structural actions, stress distributions and mechanisms. This paper considers different yield criteria for concrete elements-both plain and reinforced-under combined stress states. Graphical representation of these yield criteria in two dimensions allows geometric constructions which provide information on structural actions. The common cases of membrane action in reinforced concrete flexural slabs and shear in plane stress are considered. Geometric considerations of the associated concrete elements are shown to provide useful mental models of these systems, allowing potentially valuable visualisations at the conceptual phase in a designer's thinking.