Which of the following equation is used for the estimation of radius of relative stiffness?
- A[E·h³ / (12·k·(1–μ²))]1/2
- B[E·h² / (12·k·(1–μ²))]1/4
- C[E·h² / (12·k·(1–μ))]1/4
- D[E·h³ / (12·k·(1–μ²))]1/4Correct
Solution
Concept
Radius of Relative Stiffness
Formula
l = [E·h³ / (12·k·(1–μ²))]1/4
Step-by-step solution
1. Identify the given values for Modulus of Elasticity (E), slab thickness (h), modulus of subgrade reaction (k), and Poisson's ratio (μ). 2. Calculate the numerator: Multiply E by the cube of slab thickness (E \* h³). 3. Calculate the denominator: Multiply 12 by k and (1 - μ²). 4. Divide the numerator by the denominator. 5. Take the fourth root (raise to the power of 1/4) of the result to find the radius of relative stiffness (l).
Explanation
Option D gives the correct formula derived by Westergaard to measure the relative stiffness of a concrete slab compared to the foundation underneath it. In this formula, E is the elastic modulus of concrete, h is the slab thickness, k is the subgrade reaction modulus, and μ is Poisson's ratio. The entire expression is raised to the power of 1/4 (fourth root) to calculate the radius of relative stiffness.
Common mistake
A common mistake is confusing the overall power with 1/2 instead of 1/4 (selecting Option A) or confusing the power of thickness h as h² instead of h³ (selecting Option B or C).
Correct answer: D) [E*h³ / (12*k*(1–μ²))]^(1/4)