Simplified flexural response of steel fiber-reinforced concrete beams

In the present paper, an analytical model is proposed that is able to determine the flexural response of supported beams under four-point bending tests. Cases of normal strength reinforced concrete beams with longitudinal bars in the presence of reinforcing hooked steel fibers and transverse stirrups are considered. A simplified analytical model is presented that is able to calculate the load-deflection curves and the maximum and ultimate deflections occurring in the case of shear or flexure failures. In the case of shear failure, the maximum shear strength of the beams is evaluated by using a recent analytical expression proposed by the author able to account for the shear-to-moment interaction, which covers a large range of shear span-to-depth ratios. This expression is based on the evaluation of shear strength contribution due to beam and arch actions including their interaction with the fibers. In the case of flexural failure, the hypothesis of perfect bond of steel bars and concrete and limiting the range of shear-to-depth ratios to between two and four was considered to determine the ultimate moment. No tension stiffening and size effects were considered. A nonlinear finite element analysis program (ATENA) was utilized to verify the simplified model. The program was utilized by assigning the constitutive laws in compression and in tension for fibrous concrete available in the literature. Finally, on the basis of test data obtained by the author and of that available in the literature, a comparison was made to show the ability of the simplified proposed model to also predict the flexural response of beams when shear failure is attained.