Alternative mathematical modeling for plastic hinge of reinforced concrete beam

The presentation of the plastic zone for flexural members is basic as it administrates the load carrying and deformation capacities of the member. Therefore, plastic hinge study has been of great attention to structural researchers for decades. The behavior of plastic hinge is very tricky due to the high nonlinearity of materials, and relative movement between the component materials and strain localization. As a result, most researchers investigated the problem experimentally or by using programs which depend on the materials nonlinearity such as ANSYS, ABAQUS or ADINA programs. This paper tries to investigate the problem analytically by proposing a simple approximate equation to compute the plastic hinge rotation. A lot of parameters such as the tension and compression steel ratios, concrete strength, steel yield, section geometry and the load position were considered in the suggested equation. The analytical results of simply supported beams under middle concentrated load with different parameters were presented and compared with the conjectures of the various formulations, software programs (ANSYS and NONLACS2) and experimental results. The simplified suggested equation gave satisfying results. Moreover this paper presented a structural mathematical model based on the suggested equation to predict the deformations behavior of the beams.The plastic rotation and deflections can be predicted by the mathematical model after yielding till the failure moment, not only at the failure moment as in the common formulations. The mathematical model was verified and gave values of deflections matching experimental results.