A footing 3 m × 1.5 m in plan transmits a pressure of 160 kN/m² on a cohesive soil having E = 8 × 10⁴ kN/m² and μ = 0.48. What is the immediate settlement at the centre, assuming the footing to be flexible? (Take Iw = 1.52)
- A2.11 mm
- B3.21 mm
- C3.51 mmCorrect
- D4.62 mm
Solution
Concept
Immediate settlement is found from elastic theory using the footing width, the pressure, the soil modulus, Poisson's ratio and an influence factor.
Formula
Si = q × B × (1 − μ2) × Iw / E
Step-by-step solution
1. Data: q = 160 kN/m², B = 1.5 m (smaller side), E = 8 × 104 kN/m², μ = 0.48, Iw = 1.52. 2. 1 − μ2 = 1 − 0.2304 = 0.7696. 3. q × B = 160 × 1.5 = 240 kN/m. 4. Si = 240 × 0.7696 × 1.52 / (8 × 104). 5. Si = 280.75 / 80000 = 0.00351 m = 3.51 mm. Answer is (C).
Explanation
For a flexible footing on clay, the immediate settlement comes from elastic theory. Use the smaller side (B = 1.5 m) as the width, and use the given influence factor for the centre. This gives about 3.51 mm.
Why the other options are wrong
A: 2.11 mm does not come from the correct formula with these values. B: 3.21 mm usually comes from an error in the (1 − μ2) term. D: 4.62 mm comes from using a wrong width or wrong factor.
Shortcut
qB/E = 0.003 m. Then 0.003 × 0.77 × 1.52 ≈ 3.51 mm.
Common mistake
Using the longer side (3 m) as B, or forgetting to square μ.
Correct answer: C) 3.51 mm