Reinforced Concrete Beam Shear and Stirrup Spacing (ACI 318-19)
Whether a rectangular concrete beam carries its shear and what stirrup spacing it needs: the simplified concrete contribution Vc = 2 x lambda x sqrt(f'c) x bw x d, the design phi Vc at phi = 0.75, the stirrup demand Vs = Vu/phi - Vc when the demand exceeds phi Vc, the required spacing s = Av x fyt x d / Vs, and the d/2 code maximum. A 12 x 21.5 in beam on 4,000 psi concrete carries 24.5 kip on concrete alone; a 40 kip demand needs #3 stirrups at 10 in (the d/2 cap governs over the computed 13.7 in). Uses the simplified Vc for a member without axial load; the section upper limit and minimum-reinforcement triggers are separate checks. A design aid, not a substitute for a licensed engineer's design.
Formula and source
Vc = 2 x lambda x sqrt(f'c) x bw x d; phi Vc = 0.75 x Vc; Vs,req = Vu/0.75 - Vc when Vu > phi Vc; s = Av x fyt x d / Vs; s_max = d/2.
ACI 318-19 (Building Code Requirements for Structural Concrete), by name: §22.5.5.1 (simplified Vc), §22.5.10.5.3 (vertical-stirrup Vs), §21.2.1 (phi = 0.75 shear), §9.7.6.2.2 (d/2 max spacing).
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