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Isolated Footing Design to NSCP 2015: A Complete Worked Example

By 7 min readUpdated

The isolated (spread) footing is the first thing most of us design on our own, and the one we design most often. It is also where small shortcuts hide: forgetting the moments, using gross instead of net soil pressure, or skipping the dowel check.

This article walks through one complete design, in the order an engineer should do it. Every number comes from a real run of our Isolated Footing Designer (NSCP 2015), so you can follow it with a calculator.

The footing

Footing F-1 of a two-storey residence:

Input Value
Column400 × 400 mm, 8 Ø 16 mm bars, f'c 21 MPa
Footing2.40 × 2.40 m, 600 mm thick, 75 mm cover (cast against ground)
Concrete / steelf'c = 21 MPa, fy = 420 MPa
Soilallowable bearing qa = 250 kPa, unit weight 18 kN/m³, base 1.50 m below ground, surcharge 5 kPa
Service loadsPD = 700 kN, PL = 350 kN
Service momentsMD = 15 (x), 10 (y) kN·m; ML = 10 (x), 5 (y) kN·m
Bottom bars15 Ø 16 mm @ 150 mm each way
Footing F-1: section and plan Section A-A and plan of isolated footing F-1, roughly to scale. The footing is 2.40 m by 2.40 m and 600 mm thick, with its base 1.50 m below grade, so 0.90 m of soil (18 kN/m³) sits on it, plus a 5 kPa surcharge at grade. The 400 by 400 mm column carries 8 dowels of 16 mm. Bottom bars are 15 bars of 16 mm at 150 mm each way: the x-bars form the bottom layer and the y-bars sit on top of them. SECTION A–A grade surcharge 5 kPa 15 Ø16 @ 150 each way 8 Ø16 dowels 400 column 400 × 400 soil 18 kN/m³ 0.90 m Df = 1.50 m h = 600 2.40 m PLAN A A L = 2.40 m B = 2.40 m x y x-bars: bottom layer y-bars: on top of them
Figure 1. Footing F-1 in section and plan, roughly to scale: 2.40 × 2.40 m and 600 mm thick, base 1.50 m below grade with 0.90 m of soil on top, a 400 × 400 mm column with 8 Ø 16 mm dowels, and 15 Ø 16 mm bars @ 150 mm each way.

Step 1. Net allowable soil pressure

The 250 kPa from the geotechnical report is the pressure the soil can take in total. Part of it is already used by the footing's own weight, the soil on top of it, and the surcharge:

  • Footing: 0.60 m × 24 kN/m³ = 14.4 kPa
  • Soil above the footing: (1.50 − 0.60) m × 18 kN/m³ = 16.2 kPa
  • Surcharge: 5.0 kPa

qnet = 250 − 14.4 − 16.2 − 5.0 = 214.4 kPa

Step 2. Size the footing with service loads

Service axial load Ps = 700 + 350 = 1,050 kN.

A,req = 1,050 / 214.4 = 4.897 m². Provided: 2.40 × 2.40 = 5.760 m². Ratio 0.85, OK.

But the column also carries moments. With them, the pressure is not uniform:

  • Eccentricities: ex = 25 / 1,050 = 0.0238 m, ey = 15 / 1,050 = 0.0143 m
  • Both are well inside the kern (L/6 = 0.40 m; combined ratio 0.095), so the whole base stays in compression.
  • Section modulus S = 2.40³ / 6 = 2.304 m³

qavg = 1,050 / 5.760 = 182.3 kPa
qmax = 182.3 + 25 / 2.304 + 15 / 2.304 = 199.7 kPa ≤ 214.4 kPa, OK (ratio 0.93)
qmin = 164.9 kPa > 0, OK

The lesson: the area check alone counts only the axial load. Always check the corner pressure with the moments. If the soil were 220 kPa instead of 250, qnet would drop to 184.4 kPa. The area check would still pass (5.694 needed vs 5.760 provided), but qmax = 199.7 would be over 184.4 and the footing would fail. One line of the check catches it; skipping it does not.

Service soil pressure under F-1 with the moments Pressure under the footing for service loads Ps = 1,050 kN with moments Mx = 25 and My = 15 kN·m, drawn along the diagonal from the least to the most loaded corner, from zero. The pressure varies linearly from qmin = 164.9 kPa to qmax = 199.7 kPa, with qavg = 182.3 kPa at the centre. Eccentricities ex = 0.0238 m and ey = 0.0143 m are well inside the kern (L/6 = 0.40 m). The green line is the net allowable pressure qnet = 214.4 kPa for qa = 250 kPa: PASS, ratio 0.93. The red line is qnet = 184.4 kPa if qa were 220 kPa: the corner pressure exceeds it (FAIL) although the area check alone would still pass, 5.694 m² needed against 5.760 m² provided. PLAN qmin corner qmax corner kern x y ex = 0.0238 m ey = 0.0143 m kern L/6 = 0.40 m Ps = 1,050 kN Mx = 25, My = 15 kN·m footing, corner to corner qmin 164.9 qavg 182.3 qmax 199.7 qnet 184.4 (qa 220) qnet 214.4 (qa 250) pressure in kPa, drawn from zero PASS qa = 250 kPa: qmax 199.7 ≤ qnet 214.4 kPa, ratio 0.93 FAIL qa = 220 kPa: qmax 199.7 > qnet 184.4 kPa The area check alone would still pass: 5.694 m² needed, 5.760 m² provided.
Figure 2. Service soil pressure along the diagonal of F-1, drawn from zero: 164.9 kPa at the least loaded corner, 182.3 kPa at the centre and 199.7 kPa at the most loaded corner. It is within qnet = 214.4 kPa, but would exceed qnet = 184.4 kPa if qa were 220 kPa.

Step 3. Factored loads

NSCP 2015 load combination 1.2D + 1.6L:

Pu = 1.2 × 700 + 1.6 × 350 = 1,400 kN
Mu,x = 1.2 × 15 + 1.6 × 10 = 34.0 kN·m; Mu,y = 1.2 × 10 + 1.6 × 5 = 20.0 kN·m
qu,avg = 1,400 / 5.760 = 243.1 kPa

The soil and footing weight are left out of the strength checks: they push down and up equally and cause no shear or bending in the footing.

Step 4. Effective depth

d (x) = 600 − 75 − 16/2 = 517 mm; d (y) = 517 − 16 = 501 mm (the second layer sits on top)
Average d for punching = 509 mm

Step 5. One-way (beam) shear

The critical section is at a distance d from the column face. φ = 0.75, and

φVc = 0.75 × 0.17 λ √f'c × b × d

Direction Vu φVc Ratio
x295.4 kN725.0 kN0.41 OK
y299.3 kN702.5 kN0.43 OK

Step 6. Two-way (punching) shear

The critical perimeter is at d/2 from the column faces: each side = 400 + 509 = 909 mm, so

bo = 4 × 909 = 3,636 mm

For a square interior column, the governing stress is

φvc = 0.75 × 0.33 λ √f'c = 0.75 × 0.33 × √21 = 1.134 MPa

Punching stress (including the effect of the moments): vu = 0.684 MPa. Ratio 0.60, OK.

For footings, punching usually governs the thickness. If you are tempted to go thinner, check this first. In this example, at h = 450 mm punching fails (1.23 MPa against 1.134).

Critical sections for shear in footing F-1 Plan of the 2.40 by 2.40 m footing with the 400 by 400 mm column, to scale. One-way shear sections lie at d from the column face: 517 mm for the x direction and 501 mm for the y direction; the strip beyond each section loads it. Vu = 295.4 kN against φVc = 725.0 kN in x (ratio 0.41) and Vu = 299.3 kN against φVc = 702.5 kN in y (ratio 0.43), both PASS. The punching perimeter lies at d/2 from the column faces (average d = 509 mm): 909 by 909 mm, bo = 3,636 mm; vu = 0.684 MPa against φvc = 1.134 MPa, ratio 0.60, PASS. At h = 450 mm punching would fail: 1.23 MPa against 1.134. PLAN OF F-1: CRITICAL SECTIONS FOR SHEAR column 400 × 400 909 bo = 4 × 909 = 3,636 mm d = 517 d = 501 loads Vu (x) loads Vu (y) L = 2.40 m B = 2.40 m One-way shear, x at d = 517 from the face Vu 295.4 ≤ φVc 725.0 kN PASS ratio 0.41 One-way shear, y at d = 501 from the face Vu 299.3 ≤ φVc 702.5 kN PASS ratio 0.43 Punching at d/2 bo = 3,636 mm, d = 509 vu 0.684 ≤ φvc 1.134 MPa PASS ratio 0.60 Same footing at h = 450 mm: FAIL vu 1.23 > 1.134 MPa
Figure 3. Critical sections for shear in F-1, to scale: one-way shear at d from the column face, 517 mm in x and 501 mm in y, and the punching perimeter at d/2 from the column faces, 909 × 909 mm.

Step 7. Flexure

The cantilever from the column face to the edge is (2.40 − 0.40) / 2 = 1.00 m.

Mu (x) = 304.5 kN·m, Mu (y) = 299.2 kN·m (with the moment-induced pressure)
As,req (x) = 1,581.6 mm²
As,min = 0.0018 × b × h = 0.0018 × 2,400 × 600 = 2,592 mm² (governs)
Provided: 15 Ø 16 = 3,015.9 mm², OK

Capacity φMn = 572.5 kN·m (x) and 554.3 kN·m (y). The strain in the steel εt = 0.040, far above 0.005, so the section is tension-controlled and φ = 0.90 is correct.

Bar spacing: clear spacing 134 mm, maximum allowed 450 mm. OK.

Notice that the minimum steel governs, not the moment. That is normal for footings of this size; it is why a thicker footing does not automatically need more bars.

Step 8. Development of the bottom bars

The bars must develop their strength between the column face (where the moment is largest) and the end of the bar:

ld (Ø 16, NSCP 425.4.2) = 698.3 mm
Available = 1,000 − 75 (cover) = 925 mm. Ratio 0.75, OK, straight bars are enough.

If the footing were smaller, the bars might need hooks at the ends.

Flexure, effective depth and bar development in footing F-1 Half-section of the footing along x, roughly to scale, from the column centre line to the edge. h = 600 mm, cover 75 mm, d (x) = 517 mm for the bottom layer and d (y) = 501 mm for the layer on top. The critical section for flexure is the column face, with a cantilever of (2.40 - 0.40)/2 = 1.00 m and Mu (x) = 304.5 kN·m. The bars need ld = 698.3 mm and have 1,000 - 75 = 925 mm available: PASS, ratio 0.75, straight bars. The dowels need h of about 571 mm; 600 mm is provided. Bars: As,req = 1,581.6 mm², As,min = 2,592 mm² (governs), provided 15 bars of 16 mm = 3,015.9 mm². φMn = 572.5 and 554.3 kN·m; εt = 0.040, tension-controlled. HALF-SECTION ALONG x, FROM THE COLUMN CENTRE LINE TO THE EDGE CL column face: critical section Mu (x) = 304.5 kN·m dowels 8 Ø16 need h ≥ about 571 mm; 600 provided cantilever (2.40 − 0.40) / 2 = 1.00 m ld = 698.3 mm (Ø16, NSCP 425.4.2) PASS 0.75 available 1,000 − 75 = 925 mm 75 h = 600 d (y) = 501 d (x) = 517 cover 75 mm factored soil pressure, average qu,avg = 243.1 kPa BOTTOM STEEL, x DIRECTION (mm²) As,req from Mu 1,581.6 As,min = 0.0018 b h 2,592 (governs) Provided 15 Ø16 3,015.9 φMn = 572.5 (x) and 554.3 (y) kN·m; εt = 0.040 > 0.005, so φ = 0.90
Figure 4. Half-section of F-1 from the column centre line to the edge, roughly to scale: the effective depths, the column face as the critical section, the 925 mm available for the 698.3 mm development length, and the bottom steel, where the minimum steel governs.

Step 9. Load transfer from column to footing

Bearing on the column base: φBn = 0.65 × 0.85 × 21 × 400 × 400 = 1,856.4 kN ≥ Pu = 1,400 kN, OK (ratio 0.75). No compression has to be carried by the dowels.

Dowels: NSCP 416.3 requires at least 0.005 × column area = 0.005 × 160,000 = 800 mm². Provided 8 Ø 16 = 1,608.5 mm², OK.

The dowels must also develop into the footing in compression. The footing must be deep enough for that: here the sheet needs h ≥ about 571 mm, and 600 mm is provided. At 550 mm this line would turn to "CHECK" (use hooks or a smaller bar).

Result

All 26 checks pass: FOOTING ADEQUATE.

Check Ratio
Soil pressure with moments0.93
One-way shear (x / y)0.41 / 0.43
Punching0.60
Development of bottom bars0.75
Bearing at the column0.75
Dowels0.50
The end of the design check summary in our Isolated Footing Designer for F-1: the last 11 of the 26 checks, all PASS, and the overall result FOOTING ADEQUATE.
Figure 5. The end of the design check summary in our Isolated Footing Designer for F-1: the last 11 of the 26 checks, all PASS, and the overall result FOOTING ADEQUATE.

Five mistakes I see most

  1. Using qa instead of qnet for sizing.
  2. Checking the area with the axial load only and forgetting the moments.
  3. Using one d for both directions; the top layer has a smaller d.
  4. Forgetting As,min (0.0018bh) when the moment is small.
  5. Skipping the dowel and development checks, which often decide the minimum thickness.

General information only. Use the soil data from your own geotechnical investigation and follow the engineer of record.