Isolated Footing Design (NSCP 2015 / ACI 318): Bearing, One-Way & Punching Shear, Flexure — Worked Example

By Engr. Ruel H. Cepeda, Structural Engineer

An isolated footing is the simplest way to carry a column load down to soil. Getting it right means clearing five checks in sequence — bearing area, factored soil pressure, punching shear, one-way shear, and flexure — plus development length and dowels. This article works through all of it on one square footing, every arithmetic step shown, per NSCP 2015 (whose concrete provisions are drawn from ACI 318-14), flagging the ACI 318-19 changes where they alter a result.

Design Data

Column 400 mm × 400 mm; service loads P_d = 400 kN, P_l = 300 kN; allowable soil bearing q_a = 150 kPa; f′_c = 21 MPa; f_y = 415 MPa. Assume footing depth D_f = 1.5 m and average unit weight γ_avg = 20 kN/m³ for soil plus concrete above bearing level — take both from the project's own geotechnical report, not this assumption.

Required Footing Area from Allowable Bearing

q_a from a geotechnical report is a gross value; subtract the overburden the footing and backfill reintroduce above bearing level:

q_a,net = q_a − γ_avgD_f = 150 − (20 × 1.5) = 150 − 30 = 120 kPa

Required area, using unfactored service loads (bearing is always a service-level check):

A_req = (P_d+P_l)/q_a,net = 700/120 = 5.833 m²

For a square footing, B = √5.833 = 2.415 m; round up to B = 2.5 m, giving A = 2.5 × 2.5 = 6.25 m². Check: q = 700/6.25 = 112.0 kPa < 120 kPa OK, a 93% bearing utilization; cross-check with the sister site's footing sizer on RHCES.

Factored Soil Pressure for Structural Design

Shear and flexure use the factored net pressure from the column load alone — footing and backfill self-weight bear directly on the soil beneath and do not stress the footing, so they are excluded:

P_u = 1.2P_d + 1.6P_l = 1.2(400) + 1.6(300) = 480 + 480 = 960 kN

q_u = P_u/A = 960/6.25 = 153.6 kPa (0.1536 MPa) — the demand for every check below.

Two-Way (Punching) Shear and Effective Depth

Punching shear usually governs footing thickness, so it is checked first. The critical perimeter b_o runs at d/2 from each column face; for a square column of side c, b_o = 4(c+d). Per NSCP 2015 / ACI 318, concrete shear stress capacity v_c is the least of three (φ = 0.75, λ = 1.0, β = column long/short side ratio, α_s = 40, interior column; ACI 318-19 adds a size-effect factor λ_s to these, which its foundations chapter permits footings to neglect):

v_c1 = 1.51 MPa governs. Try h = 400 mm, 75 mm cover, 16 mm bars: d = 400−75−8 = 317 mm, b_o = 4(400+317) = 2868 mm. (This d is to the centre of the lower bar layer; the upper layer sits at 301 mm and many designers use the 309 mm average. The margins below are wide enough that every check still passes at d = 301 mm, so adopt whichever convention your office standard uses.)

V_u = q_u[B²−(c+d)²] = 0.1536 × (6,250,000−514,089) = 881,036 N ≈ 881 kN

φV_c = φ(0.33λ√f′_c)b_od = 0.75 × 1.512 × 2868 × 317 ≈ 1031 kN

881 kN < 1031 kN, OK at 85% — close to the economical minimum. The sister site's punching shear calculator on RHCES automates this same check.

One-Way (Beam) Shear Check

Critical section: a line across width B at distance d from the column face. Overhang: l₁ = (B−c)/2 − d = 1050−317 = 733 mm.

V_u = q_uBl₁ = 0.1536 × 2500 × 733 = 281,472 N ≈ 282 kN

φV_c = φ(0.17λ√f′_c)Bd = 0.75 × 0.17 × 4.583 × 2500 × 317 ≈ 463 kN

282 kN < 463 kN, OK at 61% — comfortable reserve, confirming punching shear governs here.

ACI 318-19 note: the 0.17λ√f′_c expression above is the NSCP 2015 (ACI 318-14) one-way shear strength. ACI 318-19 replaced it, for members without shear reinforcement, with V_c = 0.66λ_sλ(ρ_w)^1/3√f′_cb_wd, where footings may take λ_s = 1.0. With the ρ_w ≈ 0.0025 provided below, that gives φV_c ≈ 0.75 × 0.66 × 0.136 × 4.583 × 2500 × 317 ≈ 245 kN < 282 kN — so a footing designed strictly to ACI 318-19 would need to be thicker (about 450 mm here). Check which edition your project has adopted before relying on the 400 mm result.

Flexural Design at the Column Face

Cantilever length l = (B−c)/2 = 1050 mm = 1.05 m, loaded by the uniform factored soil pressure:

M_u = q_uBl²/2 = 153.6 × 2.5 × 1.1025/2 = 211.68 kN·m total, or m_u = 84.67 kN·m/m for a 1 m design strip.

R_n = M_u/(φbd²), φ = 0.90: R_n = 84.67 × 10&sup6;/(0.9 × 1000 × 317²) = 84.67 × 10&sup6;/90,440,100 = 0.936 MPa.

ρ = (0.85f′_c/f_y)[1 − √(1 − 2R_n/0.85f′_c)] = 0.04301 × [1 − √0.8951] = 0.04301 × 0.0539 = 0.00232

Flexure requires A_s = ρbd = 0.00232 × 1000 × 317 = 735 mm²/m. Now compare with the minimum: footings take the slab minimum on the gross section bh, and for f_y < 420 MPa that ratio is 0.0020 (0.0018 × 420/f_y applies only at f_y ≥ 420 MPa), so A_s,min = 0.0020 × 1000 × 400 = 800 mm²/m — the minimum governs, as it often does when punching shear sets the thickness. Using 16 mm bars (201 mm² each): s = 1000 × 201/800 = 251 mm → adopt 16 mm bars at 250 mm o.c., each way (identical steel both directions, square column on square footing). A_s,prov = 804 mm²/m > 800, OK; flexural demand alone uses 91% of it. Maximum spacing under the slab provisions the footing chapter points to is at most 450 mm; 250 mm is well within it.

Development Length of the Flexural Bars

For 16 mm bottom bars with adequate spacing/cover, uncoated (ψ_t = ψ_e = λ = 1.0), the simplified ACI 318-19 / NSCP 2015 tension development length for bars 20 mm and smaller:

l_d = (f_yψ_tψ_e/2.1λ√f′_c)d_b = (415/9.624) × 16 = 690 mm

Available embedment, footing edge less the 75 mm end cover, is 1050−75 = 975 mm. Since 690 mm < 975 mm, development is satisfied at 71% utilization — no hooks needed.

Dowel Bars for Column-to-Footing Load Transfer

Minimum dowel area is 0.5% of column gross area (and in practice at least four bars, one per column corner): A_g = 400 × 400 = 160,000 mm²; A_s,min = 0.005 × 160,000 = 800 mm². Eight 12 mm bars (113 mm² each) give 904 mm² > 800, OK. Hooks are not credited in compression, so straight embedment l_dc is the greater of:

l_dc = greater of (0.24f_yd_b/λ√f′_c) and (0.043f_yd_b) = greater of (260.8, 214.1) = 261 mm (and not less than 200 mm)

The dowels rest on top of the two-way bottom mat, so the straight embedment available ≈ h − cover − two mat bar diameters = 400−75−2(16) = 293 mm > 261 mm OK, 89% utilization. The dowels also get a short 90° bend on the bottom mat for placement only (not credited toward l_dc), and should match the column's actual longitudinal bars, not just the 0.5% minimum, whenever the column design calls for more.

Design Summary

Final design: 2.5 m × 2.5 m × 400 mm footing, 16 mm bars at 250 mm o.c. each way (d = 317 mm), 75 mm bottom cover, eight 12 mm dowels.

Assumptions & Limitations

• Concentric, purely axial column load — a footing with significant moment needs a non-uniform (trapezoidal) pressure check instead.
• D_f = 1.5 m and γ_avg = 20 kN/m³ were assumed for illustration; use the project's own geotechnical report values.
• No groundwater, seismic/wind uplift, or adjacent-footing interaction was considered — each can reduce net allowable bearing pressure.
• α_s = 40 assumes an interior column footing; use 30 (edge) or 20 (corner) in v_c3.
• Direct concrete bearing strength at the column-footing interface was not checked and should be verified separately.
• NSCP 2015 is based on ACI 318-14. ACI 318-19 keeps the same bearing, punching, flexure and development provisions used here (its size-effect factor may be neglected for footings), but its revised one-way shear equation for members without shear reinforcement would require a thicker footing in this example — confirm against the code edition adopted by the building official of record.

Frequently Asked Questions

Why does punching (two-way) shear usually govern footing thickness?

Punching shear acts on a perimeter wrapping all four column faces, so resisting concrete scales roughly with depth times perimeter — a two-dimensional effect. One-way shear resists load at a single straight section — effectively one-dimensional. For typical square, moderately loaded footings the punching check reaches its limit at a shallower depth, so it usually governs, though long footings or lightly loaded columns can reverse that — which is why both checks are always run.

Do I need different reinforcement in the two directions of a square footing?

Not for a concentrically loaded square footing under a square column — pressure and cantilever length are identical both ways, so required steel matches. A rectangular footing, or a square footing under a rectangular column, needs the flexural check repeated per direction, with a portion of short-direction steel banded near the column per NSCP 2015 / ACI 318-19.

What are my options if punching shear fails, besides adding depth?

Increasing h is the most direct fix since V_c scales with depth (and b_o = 4(c+d) grows with it too). Enlarging the plan dimensions does not help punching: b_o depends only on the column size and d, and the demand V_u = P_u[1 − (c+d)²/B²] actually creeps up toward P_u as B grows — a bigger plan helps bearing and one-way shear instead. A larger column or a pedestal enlarges b_o directly. Shear reinforcement is permitted but rarely used in ordinary footings since it complicates placement. A higher f′_c raises V_c too, though only with √f′_c, so the gain is smaller than adding depth.

Bearing, shear, and flexure are only the structural half of a foundation design — settlement and the geotechnical capacity calculation deserve equal attention before finalizing any footing schedule. Browse RHC Engineering's free web tools for related structural calculators.