Hoop Stress At Radius X For Inner Cylinder Calculator

Hoop Stress Formula:

\[ \sigma_{\theta} = \frac{b_2}{r_{\text{cylindrical shell}}^2} + a_2 \]

Hoop Stress on thick shell:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Hoop Stress on Thick Shell?

Hoop Stress on thick shell is the circumferential stress in a cylinder. It represents the stress acting tangentially to the circumference of the cylinder and is a critical parameter in pressure vessel design and analysis.

2. How Does the Calculator Work?

The calculator uses the Hoop Stress formula:

\[ \sigma_{\theta} = \frac{b_2}{r_{\text{cylindrical shell}}^2} + a_2 \]

Where:

\( \sigma_{\theta} \) — Hoop Stress on thick shell (Pa)
\( b_2 \) — Constant 'b' for inner cylinder
\( r_{\text{cylindrical shell}} \) — Radius Of Cylindrical Shell (m)
\( a_2 \) — Constant 'a' for inner cylinder

Explanation: This formula calculates the circumferential stress at a given radius in a thick-walled cylinder using Lame's constants.

3. Importance of Hoop Stress Calculation

Details: Accurate hoop stress calculation is crucial for pressure vessel design, pipeline engineering, and structural integrity assessment. It helps determine the maximum pressure a cylinder can withstand before failure.

4. Using the Calculator

Tips: Enter the constant values b₂ and a₂, and the radius of the cylindrical shell. All values must be valid (radius > 0).

5. Frequently Asked Questions (FAQ)

Q1: What are Lame's constants?
A: Lame's constants (a and b) are parameters used in the theory of elasticity to describe the stress distribution in thick-walled cylinders under internal and external pressure.

Q2: How is this different from thin-walled cylinder stress?
A: Thin-walled cylinder formulas assume uniform stress distribution, while thick-walled formulas account for radial variation of stress through the wall thickness.

Q3: What units should be used for input values?
A: Radius should be in meters (m), and the result will be in Pascals (Pa). Ensure consistent units for accurate results.

Q4: When is this formula applicable?
A: This formula is valid for thick-walled cylinders with internal and/or external pressure, assuming linear elastic, isotropic material behavior.

Q5: How does radius affect hoop stress?
A: Hoop stress varies inversely with the square of the radius, meaning stress decreases rapidly as radius increases.