Monotonic moment–curvature relation of an RC beam

A monotonic moment–curvature relation to simulate the non-linear behaviour of reinforced concrete (RC) beams is introduced, and material non-linear analyses of RC beams are carried out on the basis of the introduced model. Instead of the sophisticated layered section approach, which has some limitations in application to large structures with many degrees of freedom, we use the moment–curvature relations of RC sections previously constructed through section analysis. To reduce numerical instability according to the finite-element mesh size used, a relation simulating the tension-softening branch is taken into consideration. With the purpose of removing the imprecision in calculation of ultimate resisting capacity, we include the plastic hinge length in finite-element modelling. In addition, the governing equation describing the bond-slip behaviour in beams is derived. Unlike the present bond elements using double nodes, the proposed model uses beam elements representing the structural response by two nodes at both ends simplifies the finite-element modelling and analytical process, along with effectively describing the bond-slip behaviour. Moreover, the developed algorithm is reflected in the moment–curvature relation of the RC section. Finally, correlation studies between analytical and experimental results are conducted with the objective of establishing the validity of the proposed algorithms.