The limiting values of Poisson's ratio are:
Try it first: pick an option, then read the explanation.
Correct answer: A. −1 and 0.5
Asked in SSC JE 2004
Detailed Explanation
The book places this elastic-constant question in the columns chapter. Poisson's ratio is bounded by the requirement that the bulk and shear moduli be positive.
\[ K = \frac{E}{3(1-2\mu)} > 0 \Rightarrow \mu < 0.5 \qquad G = \frac{E}{2(1+\mu)} > 0 \Rightarrow \mu > -1 \]
Why “−1 and 0.5” Is Correct
So theoretically −1 < μ < 0.5: the limiting values are −1 and 0.5. Common engineering materials lie between 0 and 0.5.
Why the Other Options Are Wrong
- B. −1 and −0.5: The upper limit is +0.5, not −0.5.
- C. 1 and −0.5: μ = 1 would make K negative.
- D. 0 and 0.5: 0 to 0.5 is the practical range, not the theoretical limits (auxetic materials have μ < 0).
Key Point
Theoretical range −1 < μ < 0.5; practical 0 to 0.5; μ = 0.5 means incompressible.
Key Concepts for Students
- Steel μ ≈ 0.3, concrete 0.15–0.2, rubber ≈ 0.5, cork ≈ 0.
- Auxetic materials have negative μ.
- μ = 0.5 gives zero volume change.
Practice more: this is question 38 in Columns and Struts MCQs – Part 3. Try the whole set and check every answer instantly.