Axial force-bending moment failure interaction and deformation of reinforced concrete beams using Eurocode

The limit state design procedure of reinforced concrete elements has undergone major revision by most of the international codes in recent times in accordance to the performance based engineering approach. A thorough understanding of axial force-bending moment (P-M) yield interaction of RC elements is necessary to perform a satisfactory design catering to displacement demands particularly when the structure is subjected to seismic loads. This study presents detailed mathematical modeling of P-M yield interaction of RC rectangular beams based on Eurocode currently in prevalence by defining the boundaries of the sub-domains. A complete set of analytical expressions for P-M yield interaction and moment-curvature relationship are proposed and also illustrated through relevant examples. Results obtained for failure interaction curve of RC rectangular sections under P-M yield interaction show that by adopting Euro Code strain limits, boundary curve is divided into two main parts namely i) tension failure with weak reinforcement resulting in yielding of steel; and ii) compression failure with strong reinforcement resulting in crushing of concrete. The curves are given in analytical form for every feasible coupling of bending moment and axial force. A simple procedure proposed for bending moment-curvature relationship of rectangular beams in presence of constant axial force furnishes closed form expressions for elastic-plastic zones. Studies conducted on RC rectangular beams show moment-curvature response is basically bi-linear: after the first linear response, a further linear plastic branch is present, with a little slope. The whole response is very close to elastic-plastic response characterized by a sort of small hardening effect. With the help of presented mathematical model and proposed expressions for P-M yield interaction and moment-curvature relationships, structural design of new structures and assessment of existing RC structures can be performed with better understanding and improved accuracy.