If G = 40 GPa and ν =0.3, what is the value of E?
- A104 GPaCorrect
- B100 GPa
- C80 GPa
- D96 GPa
Solution
Concept
Elastic constants relationship between E and G
Formula
E = 2 × G × (1 + ν)
Step-by-step solution
1. The relationship between elastic constants for an isotropic elastic solid is E = 2 × G × (1 + ν). 2. Given shear modulus G = 40 GPa and Poisson's ratio ν = 0.3. 3. E = 2 × 40 × (1 + 0.3) = 80 × 1.3. 4. E = 104 GPa. Answer: A
Explanation
The fundamental relationship connecting Young's modulus of elasticity (E), shear modulus (G), and Poisson's ratio (ν) for an isotropic elastic material is E = 2·G·(1 + ν). Given G = 40 GPa and ν = 0.3: E = 2 × 40 × (1 + 0.3) = 80 × 1.3 = 104 GPa.
Why the other options are wrong
B) 100 GPa results from omitting Poisson's ratio (2 × 40 × 1.25). C) 80 GPa is 2·G without multiplying by (1 + ν). D) 96 GPa results from using (1 - ν) instead of (1 + ν).
Shortcut
E = 2G(1 + ν) = 2 × 40 × 1.3 = 104 GPa.
Common mistake
Using the bulk modulus relation E = 3K(1 - 2ν) incorrectly with shear modulus.
Correct answer: A) 104 GPa