maximum elastic torquea rectangular section

Question

Maximum elastic torque:

A rectangular section torsion member had dimension of 100mm by 200 mm and is built of a steel for which the shear yield point is τ_y = 100 MPa. Find out T_p for the cross-section and the ratio of T_p to T_y, where T_y is the maximum elastic torque.

Solution

Here, 2a = 100 mm and 2b = 200 mm

τ_Y = 100 MPa, = 100 N/mm²

For

b / a = 100 /50 = 2, T _Y = 3.936 τ a³

Now, T_Y   = 3.936 × 100 × (50)³  = 49200 Nm

Also,

Tp   = (20/3) τ _Y a³  = (20 /3)× 100 × (50)³  = 83333.33 Nm

Therefore, we have,

T_p / T_Y  = 83333.33/49200 = 1.6938