Question

What is the relation between Modulus of rigidity$\left(G\right),$ Youngs modulus $\left(Y\right)$ and Bulk modulus$\left(B\right)$ ?

• A. $\frac{3}{Y}=\frac{1}{3B}+\frac{1}{G}$
• B. $\frac{1}{Y}=\frac{1}{B}+\frac{1}{G}$
• C. $\frac{1}{3Y}=\frac{1}{B}+\frac{3}{G}$
• D. $\frac{1}{Y}=\frac{3}{B}+\frac{1}{G}$

Answer 1

The correct option is A $\frac{3}{Y}=\frac{1}{3B}+\frac{1}{G}$

Relations between modulii of elasticity and poissons ratio is
$Y=3B(1-2\mu )...\left(i\right)$
$Y=2G(1+\mu )..\left(ii\right)$
Form $\left(ii\right),$
$\mu =\frac{Y}{2G}-1$
Substituting in equation $\left(i\right)$
$Y=3B(1-2(\frac{Y}{2G}-1))...\left(i\right)$
$Y=3B(3-\frac{Y}{G})$
$\frac{Y}{3B}=(3-\frac{Y}{G})$
$\frac{3}{Y}=\frac{1}{3B}+\frac{1}{G}$