The gross bearing capacity of a strip footing 1.5 m wide, located at a depth of 1.2 m in clay, is 420 kN/m². If the unit weight of the soil is 20 kN/m³, estimate the net bearing capacity in kN/m².
Try it first: pick an option, then read the explanation.
Asked in SSC JE 04/12/2023 (Morning)
Detailed Explanation
Gross bearing capacity is the total pressure at the base of the footing at failure. Part of that pressure was already there before construction — the weight of soil that was dug out, γDf. The net bearing capacity is only the extra pressure the soil can take.
\[ q_{nu} = q_u - \gamma D_f \]
\[ q_{nu} = 420 - 20 \times 1.2 = 420 - 24 = 396\ \text{kN/m}^2 \]
The footing width (1.5 m) is not needed here.
Why “396” Is Correct
Subtracting the overburden pressure of 24 kN/m² from the gross value of 420 kN/m² gives a net bearing capacity of 396 kN/m².
| Term | Meaning |
|---|---|
| Gross ultimate bearing capacity, qu | Total pressure at the base of the footing that causes shear failure |
| Net ultimate bearing capacity, qnu | qu − γDf (pressure in excess of the overburden removed) |
| Net safe bearing capacity, qns | qnu ÷ factor of safety (usually 2.5 to 3) — safe against shear only |
| Safe bearing pressure (settlement) | Net pressure at which settlement just reaches the permissible value |
| Allowable bearing pressure, qa | Lower of the two: safe against shear failure AND settlement within limits |
Why the Other Options Are Wrong
- A. 366: 366 subtracts 54 kN/m², which does not match γDf = 24.
- C. 390: 390 subtracts 30 (that would be 20 × 1.5, using the width instead of the depth).
- D. 400: 400 is just a rounded value with no calculation behind it.
Key Point
Net = gross − γD_f. Use the depth, not the width.
Key Concepts for Students
- Net safe bearing capacity = net ultimate ÷ FOS.
- Gross safe = net safe + γD_f.
- For φ = 0 clay, q_nu = c·N_c (about 5.7c by Terzaghi).
Practice more: this is question 8 in Shallow and Deep Foundation MCQs – Part 1. Try the whole set and check every answer instantly.