Answer to Question #156661 in Math for ali

Question

The block of material shown below has a shear modulus of 50 GPa. Determine the shear

stress and the shear strain induced by the 2 kN shearing force.

Answer 1

A block of material $a \ mm\times b\ mm\times c\ mm$ has a shear modulus of 50 GPa. Determine the shear stress and the shear strain induced by the 2kN shearing force.

The shear stress is

$$\tau=\dfrac{P}{A}=\dfrac{2\times10^3\ N}{(b\times10^{-3}m)(c\times10^{-3}m)}$$

The shear strain is

$$\gamma=\dfrac{\tau}{G}=\dfrac{2\times10^3\ N}{(b\times10^{-3}m)(c\times10^{-3}m)(50\times 10^9Pa)}$$

If a block of material $150 \ mm\times 50\ mm\times 75\ mm$ is given

$$\tau=\dfrac{P}{A}=\dfrac{2\times10^3\ N}{(50\times10^{-3}m)(75\times10^{-3}m)}$$

$$=5.333\times10^5 Pa=0.533\ MPa$$

$$\gamma=\dfrac{\tau}{G}=\dfrac{2\times10^3\ N}{(50\times10^{-3}m)(75\times10^{-3}m)(50\times 10^9Pa)}$$

$$=1.067\times10^{-5}$$