If the ratio G/E (G = modulus of rigidity, E = Young's modulus of elasticity) is 0.4, then what is the value of the Poisson ratio?
- A0.25Correct
- B0.2
- C0.66
- D0.33
Solution
Concept
Calculation of Poisson ratio from elastic constants
Formula
E = 2G(1 + v)
Step-by-step solution
1. The relationship between Young's modulus E, Modulus of rigidity G, and Poisson's ratio μ is E = 2G(1 + μ). 2. Rearranging the equation gives 1 + μ = E / (2G) = 1 / (2 × (G / E)). 3. Substituting G / E = 0.4 yields 1 + μ = 1 / (2 × 0.4) = 1 / 0.8 = 1.25, so μ = 1.25 - 1 = 0.25. Answer: A
Explanation
The relationship between Young's modulus E, shear modulus G, and Poisson's ratio v is given by the formula E equals 2G times one plus v. Rearranging this equation gives the ratio G/E equal to 1 divided by 2 times one plus v. Substituting 0.4 for G/E yields 1 plus v equals 1.25, which gives a Poisson's ratio of 0.25.
Why the other options are wrong
B) 0.2 corresponds to a G/E ratio of ~0.417 using E = 2G(1+v). C) 0.66 exceeds the theoretical maximum Poisson's ratio limit of 0.5 for elastic isotropic materials. D) 0.33 corresponds to a G/E ratio of ~0.375 using E = 2G(1+v).
Shortcut
Use E = 2G(1 + μ): if E/G = 2.5, then 1 + μ = 1.25, giving Poisson's ratio μ = 0.25.
Common mistake
Misapplying or incorrectly rearranging the elastic relation formula connecting Young's modulus, shear modulus, and Poisson's ratio.
Correct answer: A) 0.25