Concrete Corbel / Bracket Design (ACI 318-19 16.5)
The primary tension steel of a concrete corbel or bracket by ACI 318-19 16.5.
Example
You enter
- Factored shear Vu (lb) 40000
- Shear span av (in, av/d <= 1) 4
- Effective depth d (in) 12
- Total height h (in) 14
- Width b (in) 14
- Concrete f'c (psi) 4000
- Steel fy (psi) 60000
- Shear-friction mu 1.4
You get
- Mandatory tension Nuc 8,000 lb
- Asc (in²) 0.601
- Shear cap phiVn 100800
Checked against published worked examples from: ACI 318-19 Section 16.5 (brackets and corbels).
Details, formula, and sources
ScopeThe mandatory 0.2 Vu horizontal tension, the greatest of the flexure-plus-tension path, the shear-friction-plus-tension path, and the 0.04 (f'c/fy) b d minimum (which governs flips with the shear span), and the min-of-three shear cap. The corbel checks a bare shear-friction check misses.
Formula or tableNuc = max(input, 0.2 Vu); Avf = Vu/(phi mu fy); Mu = Vu av + Nuc(h - d); Af = Mu/(phi fy 0.85 d); An = Nuc/(phi fy); Asc = max(Af + An, (2/3)Avf + An, 0.04 (f'c/fy) b d); phiVn = phi min(0.2 f'c, 480 + 0.08 f'c, 1600) b d (phi = 0.75).
Source and editionThe ACI 318-19 Section 16.5 brackets-and-corbels design provisions, by name.
Free accessACI 318 is readable free through the ACI online reading room at concrete.org; the Section 16.5 corbel provisions are in the published code.
What governsEstimate. AHJ and licensed professional govern.
API field namesfactored_shear_lb, shear_span_av_in, eff_depth_d_in, height_h_in, width_b_in, fc_psi, fy_psi, friction_mu, nuc_lb, asc_in2, phi_vn_lb
- Mandatory tension Nuc >= 0.2 Vu regardless of the applied horizontal loadACI 318-19 16.5.3.5
- Greatest-of-three steel Asc = max(Af + An, (2/3)Avf + An, 0.04 (f'c/fy) b d); the governing path flips with the shear span; the minimum governs a lightly loaded corbelACI 318-19 16.5.5
- Shear cap Vn <= min(0.2 f'c, 480 + 0.08 f'c, 1600) b d, not the usual sqrt(f'c) shearACI 318-19 16.5.2.4