The image above represents shear stress.

To compute for shear stress, three essential parameters are needed and these parameters are **Twisting Moment (M), Radius (r)** and **Polar Moment of Inertia (J).**

The formula for calculating shear stress:

τ = ^{Mr}/_{J}

Where:

τ = Shear Stress

M = Twisting Moment

r = Radius

J = Polar Moment of Inertia

Let’s solve an example;

Find the shear stress when the twisting moment is 12, the radius is 8 and the polar moment of inertia is 14.

This implies that;

M = Twisting Moment = 12

r = Radius = 8

J = Polar Moment of Inertia = 14

τ = ^{Mr}/_{J}

τ = ^{(12)(8)}/_{14}

τ = ^{96}/_{14}

τ = 6.85

Therefore, the **shear stress **is **6.85 Pa.**

**Calculating the Twisting Moment when the Shear Stress, the Radius and the Polar Moment of Inertia is Given.**

M = ^{τJ} / _{r}

Where;

M = Twisting Moment

τ = Shear Stress

r = Radius

J = Polar Moment of Inertia

Let’s solve an example;

Find the twisting moment when the shear stress is 10, the radius is 6 and the polar moment of inertia is 4.

This implies that;

τ = Shear Stress = 10

r = Radius = 6

J = Polar Moment of Inertia = 4

M = ^{τJ} / _{r}

M = ^{10 x 4} / _{6}

M = ^{40} / _{6}

M = 6.67

Therefore, the **twisting moment **is **6.67.**

Continue reading How to Calculate and Solve for Shear Stress | Material Selection