Reinforced Concrete Beam Shear and Stirrup Spacing (ACI 318-19)
Whether a rectangular concrete beam carries its shear and what stirrup spacing it needs.
Example
You enter
- Concrete strength f'c (psi) 4000
- Stirrup yield fyt (psi) 60000
- Web width bw (in) 12
- Effective depth d (in) 21.5
- Stirrup area Av, both legs (in²) 0.22
- Factored shear Vu (kip, 0 = capacity only) 40
- Lightweight factor lambda (1.0 normalweight) 1
You get
- Concrete shear Vc 32.6 kip
- Design concrete shear phi Vc (phi = 0.75) 24.5 kip
- Stirrup shear demand Vs,req 20.7 kip
- Required stirrup spacing 13.7 in
- S max (in) 10.75
Checked against published worked examples from: StructurePoint.
Details, formula, and sources
ScopeThe 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 governing maximum spacing: d/2 (d/4 when Vs is high) or the spacing where the stirrups still meet the Av,min minimum. It flags where Av,min is required (Vu above half of phi Vc) and a section too small for its shear. 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. A design aid, not a substitute for a licensed engineer's design.
Formula or tableVc = 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 = min(d/2 <= 24 in, or d/4 <= 12 in when Vs > 4 sqrt(f'c) bw d; Av fyt / (max(0.75 sqrt(f'c), 50) bw)); Av,min required when Vu > 0.75 lambda sqrt(f'c) bw d; section OK when Vs <= 8 sqrt(f'c) bw d.
Source and editionACI 318-19 (Building Code Requirements for Structural Concrete), by name: §22.5.5.1 and Table 22.5.5.1 (simplified Vc, valid with Av >= Av,min), §22.5.10.5.3 (vertical-stirrup Vs), §21.2.1 (phi = 0.75 shear), §9.7.6.2.2 (max spacing), §9.6.3.1 and §9.6.3.4 (Av,min), §22.5.1.2 (section limit).
Free accessACI 318-19 is viewable through ACI's online public-access reader; the 2 x sqrt(f'c) x bw x d and Av x fyt x d / s arithmetic is public.
What governsEstimate. AHJ and licensed professional govern.
API field namesfc, fyt, bw, d, av_in2, vu, lambda, vc_kip, phi_vc, vs_req_kip, s_req_in, s_max_in
- Simplified Vc the traditional 2 x lambda x sqrt(f'c) x bw x d concrete term for a member without axial load, not the detailed 318-19 expression with rho_w and size-effect termsACI 318-19 §22.5.5.1
- Vertical stirrups Vs = Av x fyt x d / s assumes stirrups perpendicular to the axis; Av is the total area crossing the crack (both legs)ACI 318-19 §22.5.10.5.3
- Limits checked section limit Vs <= 8 sqrt(f'c) bw d; Av,min wherever Vu > phi lambda sqrt(f'c) bw d; max spacing d/2 <= 24 in (d/4 <= 12 in when Vs > 4 sqrt(f'c) bw d) or the Av,min spacing if smallerACI 318-19 §22.5.1.2, §9.6.3.1, §9.6.3.4, §9.7.6.2.2
- Unreinforced regions where Av < Av,min, Vc is Table 22.5.5.1(c) with the size-effect factor lambda_s, not the 2 sqrt(f'c) form; not computed hereACI 318-19 Table 22.5.5.1