Question

A circular shaft of 10 cm diameter is subjected to a torque of 8 × 103 Nm. Determine the maximum shear stress and the consequent principal stresses induced in the shaft.

Answer 1

d = 10 cm = 0.1 m 

T = 8 × 10³ Nm 

ι_max = ? 

Using the relation, T_max = (σ/16) τ_max.D³ 

τ_max = 16T/π.D³ 

τ_max = (16 × 8 × 10³)/(π.(0.1)³) 

τ_max = 40.74 X 10⁶ N/m²

Principal stress = 2. τ_max 

Principal stress = 2 × 40.74 × 10⁶ 

Principal stress = 81.48 × 10⁶ N/m²