A thick cylinder of inner dia 'D', wall thickness t2 and length 'L' is sealed at its both ends with caps. The thickness of the cap is t1. Allowable tensile yield stress = \sigma_y and allowable shear stress = \tau_y. A gas is pumped into this cylinder at pressure 'p'. The cap will yield in shear at circumference of diameter 'D' when the gas pressure applied is more than
- A. 4 t_1 \tau_y / D
- B. 8 t_1 \tau_y / D
- C. 4 t_1 \sigma_y / D
- D. 2 t_1 \tau_y / D
Answer: A. 4 t_1 \tau_y / D
Explanation: Force due to pressure F = P * (\pi D² / 4). Resisting shear area A_s = \pi D t_1. Shear stress \tau = F / A_s = (P \pi D² / 4) / (\pi D t_1) = PD / 4t_1. For yielding, P = 4 t_1 \tau_y / D.