One-Way Concrete Shear Without Stirrups (ACI 318-19 22.5.5.1)
The one-way (beam-action) shear a footing, one-way slab, or shallow beam with NO stirrups carries.
Example
You enter
- Concrete strength f'c (psi) 4000
- Section width bw (in) 12
- Effective depth d (in) 16
- Tension steel As (in²) 1
- Lightweight factor lambda (1.0 normalweight) 1
You get
- Size-effect factor lambda_s 0.877
- Vc (psi) 76.92
- Design capacity phi Vc (phi = 0.75) 11.1 kip
Checked against published worked examples from: StructurePoint.
Details, formula, and sources
Scopeon the ACI 318-19 Table 22.5.5.1(c) detailed method that replaced the old 2 sqrt(f'c): Vc = 8 lambda_s lambda (rho_w)^(1/3) sqrt(f'c) bw d, with the size-effect factor lambda_s = sqrt(2/(1 + d/10)) capped at 1.0 (new in the 2019 edition) and rho_w = As/(bw d). A 12 in strip at d = 16 in, 4,000 psi, As = 1.0 in^2 carries just 14.8 kip (11.1 kip design), well under the 24.3 kip the old 2 sqrt(f'c) rule gave, because a deep, lightly reinforced section is penalized. lambda_s is 1.0 up to d = 10 in and drops below it for thicker members. An axial load adds Nu/(6 Ag), so 50 kip of compression on a 12 by 18 in section lifts it to 22.2 kip and enough tension takes it to zero; the stirrup-reinforced case is separate. A design aid, not the engineer of record's stamped design.
Formula or tablerho_w = As/(bw d); lambda_s = min(sqrt(2/(1 + d/10)), 1.0); vc = 8 lambda_s lambda (rho_w)^(1/3) sqrt(f'c) + Nu/(6 Ag) (sqrt(f'c) <= 100 psi; Nu + compression, Nu/(6 Ag) <= 0.05 f'c), 0 <= vc <= 5 lambda sqrt(f'c); Vc = vc bw d; phi Vc = 0.75 Vc.
Source and editionThe ACI 318-19 Table 22.5.5.1(c) one-way (beam-action) shear Vc for a member without at least minimum shear reinforcement, the 22.5.5.1.3 size-effect factor lambda_s, and phi = 0.75, by name.
Free accessACI 318 is readable free through the ACI online reading room at concrete.org; Table 22.5.5.1 and the 22.5.5.1.3 size-effect factor are in the published code.
What governsEstimate. AHJ and licensed professional govern.
API field namesfc_psi, bw_in, d_in, as_in2, lambda, lambda_s, vc_psi, phi_vc_kip
- No-stirrup case Table 22.5.5.1(c) applies only when Av < Av,min; a member with at least minimum stirrups takes the (a) or (b) expression, neither with lambda_sACI 318-19 Table 22.5.5.1
- Size-effect factor lambda_s = sqrt(2/(1 + d/10)) <= 1.0; 1.0 up to d = 10 in, smaller for deeper sectionsACI 318-19 22.5.5.1.3
- Strength cap sqrt(f'c) taken as at most 100 psiACI 318-19 22.5.3.1