A reinforced concrete foundation, of dimensions 18 m × 36 m, exerts a uniform pressure of 180 kN/m² on a soil mass, with E-value 45 MN/m². What is the value of immediate settlement under the foundation ?
- A1 m
- B1·54 m
- C18 mm
- D54 mmCorrect
Solution
Concept
Elastic settlement of a foundation
Formula
Si = q B (1 − ν²) I / E
Step-by-step solution
1. q B / E = 180 × 18 / 45 000 = 0.072 m = 72 mm. 2. With ν = 0.5, (1 − ν²) = 0.75, and an influence factor of about 1: Si = 72 × 0.75 = 54 mm.
Explanation
The immediate settlement is proportional to the contact pressure and the width, and inversely proportional to the modulus. The result is of the order of tens of millimetres.
Why the other options are wrong
1 m and 1.54 m are far too large for such a stiff soil (E = 45 MN/m²). 18 mm would need a much smaller influence factor.
Shortcut
Si ≈ q B (1−ν²) I/E.
Common mistake
Forgetting to convert MN/m² to kN/m².
Correct answer: D) 54 mm