Beam Shear Capacity Calculator

Shear in a reinforced concrete beam is resisted by two mechanisms that ACI 318 treats additively: the concrete contribution Vc and the stirrup contribution Vs. The real failure mode is diagonal tension, where principal tensile stress inclined at roughly 45 degrees to the beam axis opens a crack running from the support region up toward the load. Because such a crack can propagate with almost no warning deflection, shear failure is brittle, which is why the strength reduction factor for shear is 0.75 rather than the 0.90 permitted for tension-controlled flexure. The simplified concrete term Vc = 2 sqrt(fc) bw d is empirical, with fc in psi and bw and d in inches, returning pounds. For 4,000 psi concrete that corresponds to about 126 psi of nominal shear stress across the web. Stirrups act as the tension ties of an internal truss: Vs = Av fy d / s, where Av counts both legs of the stirrup, 0.22 sq in for a two-leg No. 3, fy is typically 60,000 psi, and s is the spacing. ACI caps Vs at 8 sqrt(fc) bw d because beyond that the concrete compression diagonals crush before the steel can yield, and the only remedy is a larger cross section. Maximum stirrup spacing is d/2 or 24 inches, halved once Vs exceeds 4 sqrt(fc) bw d. The critical section is normally taken at distance d from the support face. This simplified form omits axial load effects, the lightweight concrete lambda factor, and the size effect that reduces shear strength in deep members.

Shear design of concrete grew out of the truss analogy proposed by the Swiss engineer Wilhelm Ritter in 1899 and developed experimentally by Emil Morsch in Germany from about 1902. Ritter and Morsch pictured a cracked beam as a truss with concrete compression diagonals at 45 degrees and stirrups serving as vertical tension members, an image that still underlies the Vs term used today. Their model conservatively assigned all shear to the steel, and decades of subsequent testing showed that the uncracked compression zone, aggregate interlock across the crack faces, and dowel action of the longitudinal bars together carry a substantial share. The American Concrete Institute issued early recommendations for reinforced concrete construction in 1910 and its numbered ACI 318 building code in 1941. The 2 sqrt(fc) expression familiar to generations of engineers came from the joint ACI-ASCE Committee 326 report on shear and diagonal tension, published in 1962, which fitted a lower bound through several hundred beam test results. Strength design with a phi factor of 0.85 for shear carried through the 1960s and 1970s editions, and the factor was lowered to 0.75 in ACI 318-02 when the code adopted unified design provisions. ACI 318-19 introduced a revised Vc expression that explicitly accounts for member size effect and longitudinal reinforcement ratio, while retaining the older 2 sqrt(fc) form as a permitted simplified alternative.