Design-Oriented Solutions for the Shear Capacity of Reinforced Concrete Beams with and without Fibers

The inclusion of fibers substantially improves the shear resistance of reinforced concrete beams. Fibers can, therefore, be used as a partial or full substitute for traditional transverse reinforcement. Before replacement of traditional reinforcement with fibers can be undertaken, reliable expressions that incorporate the effect of fibers are required. In a previous study, a mechanics approach based on quantifying the presliding shear capacity of fiber-reinforced concrete beams was developed, broadly validated, and compared with existing design approaches. Although accurate, the numerical solution is too complicated for routine design, and hence, in this paper, simplified solutions are developed. This is achieved by (1) approximating the neutral axis depth at the initiation of shear failure, (2) developing a closed-form solution for the angle of the critical diagonal shear crack, removing the need to iterate, and (3) incorporating a simple approach to estimate the stress in the fibers crossing cracks, removing the need to integrate fiber stresses over a range of crack widths. To validate the simplified solutions, they are used to predict the capacity of tests on 626 reinforced concrete beams without stirrups, 176 reinforced concrete beams with stirrups, and 23 fiber-reinforced concrete beams. Importantly, these simplified solutions largely retain the accuracy of the numerical approach and show an improved fit compared with currently available solutions.