If Si = immediate settlement at a corner of a rectangular flexible foundation of size L × B, B = Width of the foundation, q = Uniform pressure on the foundation, Es = Modulus of elasticity of the soil beneath the foundation, ν = Poisson’s ratio of the soil, and It = Influence value, which is dependent on L/B. What is the immediate settlement of a flexible foundation ?
- ASi = q B ((1 + ν²)/Es) It
- BSi = q B ((1 − ν)/Es) It
- CSi = q ((1 + ν²)/(B Es)) It
- DSi = q B ((1 − ν²)/Es) ItCorrect
Solution
Concept
Immediate settlement formula (theory of elasticity)
Formula
Si = q B (1 − ν²) It / Es
Step-by-step solution
1. The elastic settlement of a flexible rectangular footing is Si = q B (1 − ν²) I / Es.
Explanation
The factor (1 − ν²)/Es is the plane-strain-type modulus term and It depends on L/B and on the point considered.
Why the other options are wrong
(1 + ν²) and (1 − ν) are not the correct terms, and dividing by B gives wrong dimensions.
Shortcut
Si = qB(1 − ν²)I/Es.
Common mistake
Using (1 + ν²).
Correct answer: D) S_i = q B ((1 − ν²)/E_s) I_t