About this calculator
This tool sizes a square isolated spread footing under a single column load, then checks it against the standard reinforced-concrete foundation limit states: bearing on soil, one-way (beam) shear, two-way (punching) shear, and flexure. It is intended for structural engineers and designers doing preliminary sizing of shallow foundations per ACI 318 / NSCP 2015.
Method & formulas
Plan area is sized from unfactored service loads against the allowable soil bearing pressure, then the section is checked at factored loads:
A_req = (P_D + P_L) / q_a → B = √A_req (square footing)
P_u = 1.2·P_D + 1.6·P_L q_u = P_u / A_provided
Effective depth uses d = h − cover − 1.5·db (average of a two-layer bottom mat). One-way shear is checked at a section d from the column face, and two-way (punching) shear at a critical perimeter bo located d/2 from the column faces, per ACI 318 §22.5 / §22.6:
Vc,one-way = 0.17·λ·√f'c·b·d φ = 0.75
Vc,two-way = min[0.17(1+2/β), 0.083(αsd/bo+2), 0.33]·λ·√f'c·bo·d
where β = 1 and αs = 40 for a square interior column. Flexural steel is designed for the cantilever moment at the column face using the standard singly-reinforced rectangular-section method:
Mu = qu·b·Lc²/2 Rn = Mu/(φbd²) ρ = (0.85f'c/fy)[1 − √(1 − 2Rn/0.85f'c)]
subject to As,min = max(1.4/fy, √f'c/4fy)·b·d, the same minimum used for flexural beams.
Worked example
Using the tool's own defaults — PD=800 kN, PL=500 kN, qa=200 kPa, 400 mm column, h=500 mm, cover=75 mm, db=20 mm, f'c=21 MPa, fy=420 MPa: Areq = (800+500)/200 = 6.5 m² → B ≈ 2.55 m square. Effective depth d = 500 − 75 − 30 = 395 mm. Pu = 1.2(800)+1.6(500) = 1760 kN, so qu = 1760/6.5 ≈ 270.8 kPa. The cantilever from the column face is Lc = (2549−400)/2 ≈ 1075 mm, giving Mu ≈ 156 kN·m per metre width. Solving Rn/ρ gives ρ ≈ 0.0027, which is below ρmin ≈ 0.0033 — so the minimum-steel case governs, requiring roughly 1320 mm²/m, i.e. Ø20 bars at about 230 mm o.c. each way.
Assumptions & limitations
- Assumes a concentric axial column load only — no overturning moment, eccentricity, or uplift is checked.
- Footing self-weight and backfill are not added to the bearing check; inflate PD or reduce qa to account for them.
- Column dowel development length and embedment into the footing are not checked.
- For a true rectangular footing, verify both shear perimeters and both-direction moments independently — the tool's sizing logic is derived for a square plan.
- Verify results against the governing code and a licensed engineer's judgment before construction.
FAQ
- Does the tool account for footing self-weight?
- No — it sizes area from service D+L against qa directly. Add an allowance (typically 5–10% of the bearing pressure) to PD, or reduce qa, to cover footing and backfill weight.
- Which shear check usually governs?
- For a stocky square column on a compact footing, two-way (punching) shear at d/2 from the column face usually governs. Slender footings or widely spaced piers can shift governance to one-way shear — always check both.
- Can I use this for a rectangular footing?
- The rectangular toggle changes the plan aspect, but B·L sizing still derives from the square-equivalent area. For true rectangular footings, size the long/short sides deliberately and re-check both shear perimeters and both-direction flexure by hand.