Bearing on concrete
The bearing strength of concrete under a plate or a bearing member by ACI 318-19 22.8: the loaded area A1, the area A2 of the 1:2 frustum inside the support, the √(A2/A1) ≤ 2 increase of Table 22.8.3.2, φ = 0.65, with the ASCE 7-22 combinations of the bearing loads.
Inputs of the bearing #
- Support: f'c of the supporting concrete (grout stronger than it is ignored), its plan length and width and its depth below the bearing surface. Area A2: from the geometry (the frustum with sides of 1 vertical to 2 horizontal, the same spread on every side: the least edge distance or twice the depth), entered by you for a sloped or stepped support (Fig. R22.8.3.2), or no increase (Table 22.8.3.2(c)).
- Loaded area: the plate (or the bearing member's section) B × N and its offset from the support centre. A1 is not greater than the plate (22.8.3.2).
- Bearing force: loads per type (the ASCE 7-22 2.3.1 combinations) or a factored force; enter the component normal to the bearing surface.
- Conditions: a post-tensioned anchorage zone (22.8 does not apply: 25.9), tension in the plane of bearing (R22.8.3.2: an advisory), a force not normal to the surface (a note).
Auto-design varies the plate length and width (1/2 in. steps) for the smallest loaded area; the support, its depth, f'c, the plate position and the loads stay yours.
Checks performed #
| Check | Basis |
|---|---|
| Applicability | 22.8.1.2 (not post-tensioned anchorage zones); the plate on the support |
| A2 | 22.8.3.2: the frustum wholly inside the support, spread = min(edge distances, 2 × depth) |
| Bearing strength | Bn = 0.85 f'c A1 √(A2/A1) ≤ 2(0.85 f'c A1), or 0.85 f'c A1 (Table 22.8.3.2); φBn ≥ Bu (Eq. 22.8.3.1), φ = 0.65 (Table 21.2.1) |
| Tension in the plane of bearing | Advisory (R22.8.3.2) |
The drawings show the plan with A1 and the frustum base A2 (dashed), and the section with the frustum sides.
Limitations #
- A rectangular loaded area on a rectangular support; the frustum is taken similar and concentric with A1 (the usual reading of "the largest frustum"); wedge-shaped supports and other plan shapes: enter A2.
- The support (punching shear 22.6, the pedestal, wall or footing), dowels, anchor rods, the grout and the plate are not designed; confinement reinforcement is not credited.
Verification examples #
Verification status: 11 values compared in 7 examples (3 published, 4 hand calculations from the cited equations): 11 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| AISC DE J.6 | 22 × 22 in. plate on a 24 × 24 in. pedestal, f'c 3 ksi (AISC 360 J8 is the same expression) | Pu 690 kips, A2 576 in², φPp 875 kips | same |
| StructurePoint spread footing 5.1, 5.2 | 18 in. column on the footing (factor 2) and at the column base (f'c 5 ksi, no increase), ACI 318-14 | 1,070 kips, 895 kips | same |
Hand calculations: an eccentric plate (the 2 in. edge distance governs), a thin slab (twice the depth governs), the factor 2 cap, and A2 entered.