The relationship among modulus of elasticity E, modulus of rigidity G and bulk modulus K is
- A3/E = 9/G − 1/K
- B3/E = 9/G + 1/K
- C9/E = 3/G − 1/K
- D9/E = 3/G + 1/KCorrect
Solution
Concept
E, G and K relationship
Formula
9/E = 3/G + 1/K (E = 2G(1+ν) = 3K(1−2ν))
Step-by-step solution
1. E = 2G(1 + ν) ⇒ ν = E/2G − 1. 2. E = 3K(1 − 2ν) = 3K(1 − E/G + 2) = 3K(3 − E/G). 3. Simplifying: 9/E = 3/G + 1/K.
Explanation
Eliminating Poisson's ratio between E = 2G(1+ν) and E = 3K(1−2ν) gives 9/E = 3/G + 1/K.
Why the other options are wrong
Options with a minus sign or with 3/E are not obtained from these two relations.
Shortcut
9/E = 3/G + 1/K.
Common mistake
Writing 3/E on the left.
Correct answer: D) 9/E = 3/G + 1/K