Hoop Stress Calculator
Calculate stresses in cylindrical and spherical pressure vessels
Pressure Vessel Configuration
Geometry
Required for volume change calculations
Internal Pressure
Material Properties
Stress Analysis Results
Example Calculation
Pressure Vessel Design
Application: Cylindrical pressure vessel (tank)
Diameter: 3000 mm
Wall thickness: 16.67 mm
Internal pressure: 1.5 MPa
Material: Steel (no joint efficiency)
Stress Calculations
1. Hoop stress: σ_h = (p × d) / (2 × t)
2. σ_h = (1.5 MPa × 3000 mm) / (2 × 16.67 mm) = 135 MPa
3. Longitudinal stress: σ_l = σ_h / 2 = 67.5 MPa
4. Thickness ratio: t/r = 16.67/1500 = 0.011 (thin wall ✓)
5. Result: Hoop stress dominates with 135 MPa maximum stress
Stress Types
Wall Classification
Thin Wall
t/r ≤ 0.1 (10%)
Simple formulas apply
Thick Wall
t/r > 0.1 (10%)
Requires Lamé equations
Material Properties
Design Tips
Hoop stress is usually the critical stress
For cylinders: σ_h = 2 × σ_l
Consider factor of safety (typically 2-4)
Joint efficiency reduces effective strength
Account for pressure test conditions
Understanding Hoop Stress and Pressure Vessel Design
What is Hoop Stress?
Hoop stress, also known as circumferential stress, is the stress that acts around the circumference of a pressure vessel. When internal pressure is applied, the vessel tends to expand, creating tensile stress in the circumferential direction. This is typically the largest stress in thin-walled pressure vessels and often governs the design.
Stress Components
Pressure vessels experience three principal stresses: hoop stress (circumferential), longitudinal stress (axial for cylinders), and radial stress (through thickness). For thin-walled vessels, radial stress is negligible compared to the other two components.
Applications
- •Boilers: Steam pressure vessels in power generation
- •Gas Cylinders: Storage of compressed gases
- •Pipelines: Oil, gas, and water transmission
- •Storage Tanks: Chemical and petroleum storage
Stress Formulas
Cylindrical Vessel
σ_h = (p × d) / (2 × t)
σ_l = (p × d) / (4 × t)
σ_h = hoop stress, σ_l = longitudinal stress
Spherical Vessel
σ_h = σ_l = (p × d) / (4 × t)
Biaxial stress state (equal in all directions)
p: Internal pressure
d: Internal diameter
t: Wall thickness
η: Joint efficiency (0.6-1.0)
Design Note: Always check that calculated stresses are below the allowable stress of the material, considering appropriate factors of safety and service conditions.