Cyclic moment–curvature relation of an RC beam

Abstract

A hysteretic moment–curvature relation to simulate the behaviour of a reinforced concrete (RC) beam under cyclic loading is introduced in this paper, and the non-linear behaviour of RC beams subjected to flexural cyclic loading is analysed by means of the introduced model. Unlike previous moment–curvature models and the layered section approach, the proposed model takes into consideration the bond-slip effect by using the monotonic moment–curvature relation introduced in the companion paper. This model was constructed on the basis of the bond-slip relation and corresponding equilibrium equation at each nodal point. In addition, unlike linearised hysteretic curves, the use of curved unloading and reloading branches inferred from the stress–strain relation of steel considering the Bauschinger effect is employed. This gives more exact structural responses, following a correct assessment of the energy-absorbing capacity of a structure at the large deformation stage. The advantages of the proposed model, compared to the layered section approach, may be on the reduction in calculation time and memory space in application to large-frame structures with many degrees of freedom. The modifications of the moment–curvature relation to reflect fixed-end rotation, axial force and pinching effect are also introduced. Finally, correlation studies between analytical results and experimental studies are conducted to establish the validity of the proposed model.