Closed-form solutions for flexural response of fiber-reinforced concrete beams

A constitutive law for fiber-reinforced concrete materials consisting of an elastic perfectly plastic model for compression and an elastic-constant postpeak response for tension is presented. The material parameters are described by using Young's modulus and first cracking strain in addition to four nondimensional parameters to define postpeak tensile strength, compressive strength, and ultimate strain levels in tension and compression. The closed-form solutions for moment-curvature response are derived and normalized with respect to their values at the cracking moment. Further simplification of the moment-curvature response to a bilinear model, and the use of the moment-area method results in another set of closed-form solutions to calculate midspan deflection of a beam under three- and four-point bending tests. Model simulations are correlated with a variety of test results available in literature. The simulation of a three- and four-point bending test reveals that the direct use of uniaxial tensile response underpredicts the flexural response.