A thin-walled cylindrical vessel subjected to internal fluid pressure develops which principal membrane stress in the circumferential direction?

Introduction / Context:
Thin pressure vessels are classic subjects in mechanics of materials. Under internal pressure, the cylinder wall carries membrane stresses in two perpendicular directions: circumferential (hoop) and longitudinal.

Given Data / Assumptions:

• Thin cylinder: wall thickness t is much smaller than diameter.
• Uniform internal pressure p.
• Neglect radial stress across thickness (thin-wall assumption).

Concept / Approach:
For a thin cylinder, hoop stress sigma_h = p * d / (2 * t) acts around the circumference, and longitudinal stress sigma_l = p * d / (4 * t) along the axis. Both are tensile under internal pressure, with hoop stress being twice the longitudinal stress.

Step-by-Step Solution:

Verification / Alternative check:
Check equilibrium of half cylinder in circumferential direction; stresses must balance the pressure resultant on the projected area.

Why Other Options Are Wrong:
Compression is incorrect for internal pressure; shear options do not represent the principal membrane state; “no stress” contradicts pressure vessel theory.

Common Pitfalls:
Confusing thin-wall with thick-wall formulas; mixing units; using radius instead of diameter without adjusting constants.

Final Answer:
Hoop tension (circumferential tension)