Shear Strength of UHPFRC Beams: Mesoscale Fiber-Matrix Discrete Model

Abstract

A theoretical method, termed the mesoscale fiber-matrix discrete model (MFDM), has been developed that can be used for estimating the shear contribution of steel fibers and calculating shear strength of ultrahigh-performance fiber-reinforced concrete (UHPFRC) beams. In the proposed model, an effective fiber distributed region (EDR) along the critical diagonal shear crack, where fibers are efficient at providing shear resistance, is defined. The total quantity of fibers within EDR is calculated by the EDR volume proportion of the beam based on a uniform distribution of steel fibers. Two concepts to determine the width of EDR are proposed: (1) probability theory and (2) the basis of the pullout load slip relationship. The bond strength between a single fiber and the matrix is determined by the probability method based on a uniform distribution of fibers. Combining the number of efficient fibers and the bond strength of a single fiber, the shear contribution of fibers is derived. The shear contribution of concrete is obtained using Rankine’s failure criteria and strain and stress distribution of compression zone while the shear contribution of stirrups is determined by the truss model. To evaluate the accuracy and reliability of the proposed model, an experimental program on ten simply supported UHPFRC beams was executed. Through comparison with test results, the proposed model shows good agreement with testing results.