Fictitious crack propagation in fiber-reinforced concrete beams

A nonlinear cracked hinge model is developed, aimed at the analysis of the bending fracture of fiber-reinforced concrete beams. The model is based on the fracture mechanics concepts of the fictitious crack model with a bilinear stress-crack opening relationship. Closed-form solutions are presented for the moment-rotation relationship of the hinge as a crack propagates, and the case of a nonzero normal force is covered. Special shapes of the stress-crack opening relationship are treated separately. These shapes are the so-called drop-linear and the drop-horizontal for which simplified expressions are obtained. The applicability of the hinge model is demonstrated through analysis of the bending fracture process in the case of a three-point bending beam and an infinitely long beam on a Winkler foundation, the latter analysis comprising the effect of a constant tensile normal force.