Prediction of shear crack width for steel fiber reinforced concrete beams

Abstract

The shear crack width, crack behavior, and crack development of 24 reinforced concrete beams have been experimentally investigated. All the beams reinforced with longitudinal reinforcement and hooked-end steel fibers in place of transverse reinforcement. Hooked-end steel fibers 35 and 60 mm long are used at volume fractions ranging from 0.75% to 1.5% in the first case, and from 0.5% to 1% in the latter case. For extending the scope of the investigation, two types of concrete matrices (normal-strength of 25 MPa and mediumstrength of 45 MPa) have been investigated. A simple mechanics-based mathematical model is developed by determining the strains in the transverse direction of shear cracks and the average horizontal spacing between the shear cracks. The accuracy of the model has been confirmed with the experimental results and conservative predictions have been observed with mean, SD, and coefficient of variation as 0.99, 0.19, and 18.96, respectively. Based on detailed mathematical and experimental investigation, the minimum approximately Abbreviations: A v , cross-section area of stirrups, mm 2 ; A f , cross-sectional area of steel fiber, mm 2 ; A sf , average surface area of steel fiber, mm 2 ; a, shear span, mm; b, width of beam, mm; c, depth of compression zone, mm; c s , side concrete cover to shear reinforcement, mm; d, d e , effective depth, mm; d by , diameter of shear reinforcement, mm; d f , diameter of fiber, mm; E f , modulus of elasticity of steel fibers, MPa; f ' c , concrete compressive strength, MPa; k fc , coefficient for effect of concrete compressive strength,; k p , coefficient for effect of shear reinforcement ratio, used by Hassan et al (1991); k p , coefficient for the effect of compressive stress at centroid of concrete section due to prestress (σ c,ps ); k t , factor account for duration of loading (0.6 and 0.4 for short-and long-term loading); k w , coefficient for effect of shear reinforcement ratio used by Witchukreangkari et al.; k 1 , coefficient, 2.4 and 2 for plain and deformed bar, respectively, used by Hassan et al.; L c , crack length in the horizontal direction, mm; l av , average crack spacing, mm; l f , length of steel fiber, mm; l s,max , maximum shear crack spacing, mm; l sx,max , maximum vertical crack spacing, mm; l sy,max , maximum horizontal crack spacing, mm; n, total number of inclined cracks; S, normalized slip, mm; s, spacing of stirrup legs, mm; s mθÀavg , average shear crack spacing at the crack formation phase and stabilized cracking phase, mm; s r,max , maximum crack spacing, mm; s rm ,s mθ , average crack spacing, mm; s y , shear reinforcement spacing, mm; s θ , mean shear crack spacing, mm; V, total shear force, kN; V f , fiber volume fraction, %; V s , shear force resisted by the stirrups, kN; w, crack width, mm; w avg , average shear crack width, mm; w k , characteristics shear crack width, mm; w max , maximum shear crack width, mm; w ser , crack width at service, mm; x, depth of neutral axis from extreme compression fibers, mm; α, coefficient used in presen...