Mechanics-based closed-form solutions for moment redistribution in RC beams

When it comes to the efficient design of reinforced concrete beams and frames, moment redistribution is used to: reduce the absolute maximum magnitude of the moment in the critical region, equalize the critical moments on either side of interior columns and fully utilize the capacity of the non-critical regions of a member. Although important, historically, moment redistribution has proved to be difficult to quantify due to the complexity of quantifying hinge rotations. Although numerous empirical expressions exist for plastic hinge lengths, i.e. the length over which the ultimate curvature can be integrated in order to give hinge rotations, a comparison with a global dataset yields poor results. Using a recently developed mechanics-based moment-rotation approach, it is possible to quantify the moment-rotation characteristics of reinforced concrete hinges. In the tension region, the approach applies partial interaction theory directly to simulate the mechanisms associated with slip of the reinforcement relative to the surrounding concrete as cracks widen, whereas in the compression region, partial interaction shear-friction theory is used to describe the formation and failure of concrete softening wedges. It is shown how the moment-rotation approach explicitly allows for the size dependency. Furthermore, mechanics-based solutions for moment redistribution are then derived and it is shown how these can be simplified at the ultimate limit state for use in the design office.