Thin Cylindrical Pressure Vessels The hoop stress developed in a thin-walled cylindrical shell under internal pressure is best described as which type of stress?

Introduction:Thin-walled pressure vessels develop two main membrane stresses: circumferential (hoop) and longitudinal. Understanding their nature guides safe design of boilers, pipes, and tanks.

Given Data / Assumptions:

• Thin cylinder: wall thickness t much smaller than diameter.
• Uniform internal pressure p.
• Neglect radial stress through thickness compared to membrane stresses.

Concept / Approach:The hoop stress acts tangentially around the circumference and is tensile. In contrast, longitudinal stress acts along the axis, and radial stress across thickness is small for thin shells.

Step-by-Step Solution:Hoop stress magnitude: sigma_h = p * d / (2 * t)Longitudinal stress magnitude: sigma_l = p * d / (4 * t)Direction: sigma_h is circumferential tension; sigma_l is axial tension; radial stress is compressive on the inner surface but negligible for thin shells.

Verification / Alternative check:Free-body of half-cylinder shows hoop force balancing pressure on the cut; algebra yields sigma_h as above, confirming tensile circumferential action.

Why Other Options Are Wrong:longitudinal stress: different direction; not the hoop stress.compressive stress: hoop is tensile for internal pressure.radial stress: small in thin shells and not the defined hoop stress.

Common Pitfalls:Confusing magnitudes and directions; remember sigma_h = 2 * sigma_l for thin cylinders.

Final Answer:circumferential tensile stress