What is the longitudinal stress developed in a thin-walled pressure vessel__________________?
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Answer: C. half of the hoop stress
Explanation
Longitudinal stress developed in a thin walled pressure vessel equals half of the hoop stress. Equilibrium equations for cylindrical shells show circumferential forces are twice longitudinal forces. Dividing internal pressure by wall geometry confirms this exact two-to-one stress ratio. Thin walled pressure vessels experience multi-axial stresses when subjected to internal fluid pressure. Hoop stress acts circumferentially around the tank wall perpendicular to the longitudinal axis. Longitudinal stress acts parallel to the cylindrical axis resisting the ends blowing apart.
Pressure vessel designers use this stress ratio to determine wall thickness requirements safely. Boilers and storage tanks must withstand hoop stresses that are twice as large as longitudinal stresses. Failure analysis of ruptured tanks typically shows longitudinal splitting caused by high hoop stress. Equal stress values ignore the geometric equilibrium equations of cylindrical pressure vessels. Twice the hoop stress inverts the actual mechanical relationship found in thin cylinders. One fourth of hoop stress represents an incorrect calculation of cylindrical stress formulas.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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