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A thin-walled long cylindrical tank of inside radius r is subjected simultaneously to internal gas pressure p and axial compressive force F at its ends. In order to produce ‘pure shear’ state of stress in the wall of the cylinder,F should be equal to
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- πpr2
- 2πpr2
- 3πpr2
- 4πpr2
Correct Option: C
Consider a thin long cylindrical tank
2σ × t × l = p.2r.l
| ∴ σ0 = | (tensile) | t |
Due to pressure at longitudinal section
πr2 × p = 2πrt × σz
| σz = | 2t |
Due to compressive force, F
| Longitudinal force = | 2πrt |
∴ Total longitudinal stress
| = | - | (compressive) | ||
| 2t | 2πrt |
| τ = | 2 |
| ⇒ | = - |  | - |  | t | 2t | 2πrt |
| ⇒ | = | |||
| 2πrt | 2t |
⇒ F = 3πpr2
