Corbel

A corbel (bracket) projecting from the face of a column, designed by ACI 318-19 16.5 with shear friction (22.9) and bearing (22.8), under the ASCE 7-22 2.3.1 load combinations (strength design). The section at the face of the column resists the factored shear Vu, the restraint force Nuc and the moment Mu = Vu av + Nuc(h − d) together; the primary tension bars Asc and the closed ties Ah follow from them. Corbels with av/d greater than 1 or Nuc greater than Vu are outside 16.5 (strut-and-tie design, Chapter 23) and are reported as not feasible.

Inputs of the corbel #

• Materials: f'c, Grade 60 or 80 bars, normalweight or lightweight concrete (λ by Table 19.2.4.1). For lightweight concrete the shear-friction μ uses λ ≤ 0.85 (Table 22.9.4.2) and the Vu/φ limits of 16.5.2.5 apply.
• Corbel: width b (usually the column width), depth h at the column face, depth at the outer edge (equal to h for a rectangular corbel), projection from the face, the column depth along the projection (for the development of the bars into the column), clear cover to the primary bars and the maximum aggregate size (clear spacing, 25.2.1). The effective depth d is taken at the face (16.5.2.1): h − cover − db/2.
• Bearing: the shear span av from the column face to the center of the bearing, and the bearing plate length (along the projection) and width (across the corbel).
• Reinforcement: the primary tension bars (size, number), how they are anchored at the front face (16.5.6.3: a welded transverse anchor bar of at least the same size, or a horizontal loop: the engineer's choice), the closed ties (size, number; two legs each) spread uniformly within 2/3 d below the primary bars (16.5.6.6), how the bars are developed into the column (standard hook with the confinement ψr and location ψo factors of Table 25.4.3.2, or straight with ψt for top bars), the bar coating, and the shear plane at the column face: monolithic (μ = 1.4λ, prefilled), against hardened concrete intentionally roughened (1.0λ), or not roughened (0.6λ).
• Loads: per load type, the unfactored vertical reaction V and any horizontal tension N at the bearing. The restraint force Nuc of 16.2.2.3 is the engineer's choice: on bearing pads, 0.2 × the sustained unfactored reaction × 1.6 (16.2.2.3(b); the sustained reaction is D plus the sustained part of L entered); a restraint force treated as a live load (16.2.2.3(a): the entered force times the live-load factor of each combination); or none (the N column only). A friction coefficient from tests caps Nuc at 1.6 μ × the sustained reaction (16.2.2.4). Vu and Nuc of the same combination act together (16.5.3.1, 16.5.3.2).

Auto-design (editor toolbar) varies the depth at the column face (1 in. steps, the outer depth kept in proportion), the primary bars (size, number) and the closed ties (size, number). Objectives: lowest cost index (concrete, reinforcement); shallowest corbel, then cost. The width, projection, bearing and loads stay the engineer's; see Auto-design.

Checks of the corbel #

Limitations #

• One bearing at a time, at mid-width; Vu and Nuc act at the bearing. Corbels with av/d > 1, Nuc > Vu or compression across the shear plane are not covered (strut-and-tie design by Chapter 23 is not offered; 22.9.4.5 is not taken).
• Nuc follows 16.2.2.3 as the engineer chooses; the 0.2Vu minimum of ACI 318-14 and earlier is not part of ACI 318-19 and is not applied (enter it as the N of a load row if wanted).
• Ah uses the primary reinforcement provided (16.5.5.2 as written); some worksheets use the required area (deviation CORBEL-AH-ASC).
• The weld of the anchor bar, the bearing plate thickness and its anchorage, the column design and the supported member are not part of the calculation; the bearing check takes no √(A2/A1) increase.
• Verified against two free vendor worksheets and hand calculations: no free corbel example to ACI 318-19 from ACI, PCA or PCI is on disk (research/DOCUMENTS_NEEDED.md).

Verification examples #

Verification status: 28 values compared in 5 examples (2 published, 3 hand calculations from the cited equations): 24 within tolerance, 4 recorded deviations. Thin: only 2 published examples. Code basis: the provisions it uses were read in the target edition.

Published (free worksheets; research/sources/design_examples). VCmaster is written to ACI 318-11, whose corbel provisions (11.8) are those of ACI 318-19 16.5; the Maple Flow worksheet is labelled ACI 318-19 but keeps the older 800 psi shear limit.

Hand calculations (closed form in backend/tests/test_verify_corbel.py):