Table of Contents
What Is Hoop Stress?
Hoop stress (circumferential stress) is the stress in the wall of a cylindrical pressure vessel acting in the circumferential direction. It results from the internal pressure trying to expand the cylinder. Hoop stress is always twice the axial (longitudinal) stress in thin-walled cylinders, making it the critical stress for design purposes.
This is why cylindrical pressure vessels, pipes, and boilers tend to fail along their length (splitting open along a longitudinal seam) rather than at their ends. Understanding hoop stress is essential for designing safe pipes, tanks, pressure vessels, blood vessels, and any cylindrical container holding pressurized fluid.
Hoop Stress Formula
Where P is internal pressure, r is inner radius, and t is wall thickness. Valid for thin-walled vessels (r/t >= 10).
Material Yield Strengths
| Material | Yield Strength (MPa) |
|---|---|
| Mild Steel | 250 |
| Stainless Steel 304 | 205 |
| Aluminum 6061-T6 | 276 |
| Titanium Ti-6Al-4V | 880 |
Frequently Asked Questions
Why is hoop stress twice the axial stress?
Consider force balance: the pressure acting on a longitudinal cross-section (force = P × 2rL) is resisted by stress in two wall areas (2 × t × L × sigma_hoop). For a transverse cross-section, the pressure force (P × pi × r²) is resisted by stress in the wall ring (2 × pi × r × t × sigma_axial). The geometry gives sigma_hoop = 2 × sigma_axial.
What is the safety factor for pressure vessels?
ASME pressure vessel codes typically require safety factors of 3.5 on ultimate tensile strength or 2/3 of yield strength, whichever is lower. Additional factors are applied for weld efficiency, corrosion allowance, and temperature derating. Nuclear and aerospace applications use even higher safety factors.