## Shear Modulus

Consider an unknown test material experiences a shear strain of 0.5 when placed under a shear stress of 20 GPa. What is its shear modulus? Assume the Young’s modulus is 200 GPa.

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__**Hint**

**Hint**

The shear modulus (modulus of rigidity) is a shearing force’s coefficient of elasticity. It is the ratio of shear stress to the displacement per unit length (shear strain).

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__**Hint 2**

**Hint 2**

$$$G=\frac{\tau }{\gamma }$$$

where
$$\tau$$
is shear stress and
$$\gamma$$
is shear strain.

The shear modulus (modulus of rigidity) is a shearing force’s coefficient of elasticity. It is the ratio of shear stress to the displacement per unit length (shear strain).

$$$G=\frac{\tau }{\gamma }$$$

where
$$\tau$$
is shear stress and
$$\gamma$$
is shear strain.

$$$G=\frac{20GPa}{0.5}=40\:GPa$$$

40 GPa