Axial Force-Bending Moment Limit Domain and Flow Rule for Reinforced Concrete Elements Using Euro Code

Performance-based design approach of special moment-resistant reinforced concrete (RC) framed structures demands a thorough understanding of axial force—bending moment (P—M) yield interaction of RC elements, particularly when the structure is subjected to seismic loads. Latest design approach includes desirable features of both ultimate strength and working stress to ensure a suitable ductile deformation response. This demands a detailed understanding of nonlinear response of P—M interaction. A complete set of analytical expressions for P—M yield interaction are proposed in a closed form by defining the limit boundary with ten sub-domains based on Euro Code currently in prevalence. P—M interaction relationships are also verified for plastic flow-rule in two main sections namely: (i) tension failure resulting in yielding of steel; and (ii) compression failure resulting in crushing of concrete. The conventional limit P—M domain is described based on Euro Code as long as the plastic strain increment becomes nearly normal to the yield domain over the part of bending response in the presence of axial force. The verified flow rule shows a close agreement in all sub-domains of tension failure, while does not qualify in few of the sub-domains of crushing failure. Practical examples of RC sections are chosen to illustrate the influence of different parameters namely: (i) cross-section dimension; (ii) percentage of tension and compression reinforcements; and (iii) properties of constitutive materials on the P—M boundary. Mathematically developed P—M interaction model is capable of identifying the damage mechanism of different sub-domains in RC sections; damage identification is made on the basis of strain profile of concrete and reinforcing steel.