In thin-walled pressure vessels (mechanical design), the “hoop stress” refers specifically to which type of stress acting around the shell of a cylindrical tank?

Introduction / Context:In mechanical and process equipment design, thin cylindrical shells (such as storage tanks, boilers, and heat-exchanger shells) develop distinct stress components when subjected to internal pressure. Two principal membrane stresses are important for safe design: the hoop (circumferential) stress and the longitudinal (axial) stress. Correctly identifying the hoop stress helps engineers size the wall thickness and select materials to prevent failure.

Given Data / Assumptions:

• Thin-walled cylinder assumption (wall thickness much smaller than diameter).
• Uniform internal pressure acting on the inner surface.
• Elastic behavior; neglecting local discontinuities and nozzle effects for the concept.

Concept / Approach:Hoop stress acts tangentially around the circumference of the cylinder as the shell “tries to split open” along a longitudinal line. Under thin-wall theory, hoop stress is larger than longitudinal stress by a factor of two for a closed-end cylinder at the same pressure and radius, hence it is often the governing stress state for thickness calculation.

Step-by-Step Solution:

Verification / Alternative check:From thin-wall formulas: hoop stress σ_h = p * r / t; longitudinal stress σ_l = p * r / (2 * t). The larger value and direction confirm its circumferential tensile nature.

Why Other Options Are Wrong:

• Radial: small through-thickness stress; not the hoop stress.
• Compressive: internal pressure creates tension in the wall, not compression.
• Longitudinal: a real component, but different from hoop stress.

Common Pitfalls:Confusing hoop with longitudinal stress; applying thick-wall formulas when the thin-wall criterion is not satisfied; ignoring joint efficiency and corrosion allowance in real designs.

Final Answer:circumferential tensile