Circumferential Stress (Hoop Stress) In Cylinderical Shell Calculator

Formula Used:

\[ \text{Circumferential Stress} = \frac{\text{Internal Pressure} \times \text{Mean Diameter}}{2 \times \text{Thickness}} \] \[ \sigma_c = \frac{P_{\text{Internal}} \times D}{2 \times t_c} \]

Circumferential Stress (σ_c):

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1. What is Circumferential Stress (Hoop Stress)?

Circumferential Stress, also known as Hoop Stress, is the stress exerted circumferentially in the wall of a cylindrical pressure vessel. It is perpendicular to both the axis and the radius of the vessel, and is a critical factor in pressure vessel design.

2. How Does the Calculator Work?

The calculator uses the formula for circumferential stress in a thin-walled cylindrical pressure vessel:

\[ \sigma_c = \frac{P_{\text{Internal}} \times D}{2 \times t_c} \]

Where:

\( \sigma_c \) — Circumferential Stress (Pa)
\( P_{\text{Internal}} \) — Internal Pressure (Pa)
\( D \) — Mean Diameter of the shell (m)
\( t_c \) — Thickness of the cylindrical shell (m)

Explanation: This formula calculates the stress in the circumferential direction of a cylindrical pressure vessel subjected to internal pressure.

3. Importance of Circumferential Stress Calculation

Details: Accurate calculation of circumferential stress is crucial for designing safe pressure vessels, determining appropriate wall thickness, and ensuring structural integrity under internal pressure loads.

4. Using the Calculator

Tips: Enter internal pressure in Pascals (Pa), mean diameter in meters (m), and thickness in meters (m). All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between circumferential stress and longitudinal stress?
A: Circumferential stress acts around the circumference of the cylinder, while longitudinal stress acts along the length of the cylinder. Circumferential stress is typically twice the longitudinal stress in thin-walled cylinders.

Q2: When is this formula applicable?
A: This formula is valid for thin-walled pressure vessels where the wall thickness is less than about 1/10 of the radius.

Q3: What are typical units for these calculations?
A: While Pascals are used here, engineering practice often uses MPa or psi for stress, and corresponding units for pressure and dimensions.

Q4: How does temperature affect circumferential stress?
A: Temperature changes can cause thermal expansion/contraction, which may induce additional stresses that need to be considered in the overall stress analysis.

Q5: What safety factors should be applied to the calculated stress?
A: Engineering codes and standards specify appropriate safety factors based on material properties, operating conditions, and application requirements.