Question

Based on the limiting factor to prevent bursting in thin cylinder, the design is primarily made based on which stress

• A. Maximum volumetric stress
• B. Maximum longitudinal stress
• C. Maximum shear stress
• D. Maximum hoop stress

Hint:

Since hoop stress is twice as large as longitudinal stress (\( \sigma_h = 2\sigma_l \)), thin-walled pipes and boiling sausages always split open along their lengthwise seams when overpressurized, never around their circumferences!

Answer 1

The Correct Option is D

Both stresses in a thin cylinder come from the same internal pressure, but they don't grow at the same rate. Hoop stress works out to \( pd/2t \) while longitudinal stress is only \( pd/4t \), exactly half of it. So no matter how much the pressure is raised, the hoop stress always stays twice the longitudinal stress and reaches the material's safe limit first. This is why the wall thickness of a pressure vessel is always chosen using the hoop stress rather than the longitudinal one; checking only the longitudinal stress would let the cylinder split open along its length long before that stress got close to its limit. So the governing design stress is the maximum hoop stress, option (D).