Longitudinal Stress In Cylinder Given Circumferential Strain In Cylinder Calculator

Longitudinal Stress Formula:

\[ \sigma_l = \frac{\sigma_c - (e_1 \times E)}{\nu} \]

Circumferential Stress Due To Fluid Pressure (σc):

Pascal

Circumferential Strain (e₁):

(dimensionless)

Young's Modulus Cylinder (E):

Pascal

Poisson's Ratio (ν):

(dimensionless)

Longitudinal Stress (σl):

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1. What is Longitudinal Stress In Cylinder?

Longitudinal stress is the stress that develops along the length of a cylindrical object when it is subjected to internal pressure. It represents the force per unit area acting parallel to the cylinder's axis.

2. How Does the Calculator Work?

The calculator uses the longitudinal stress formula:

\[ \sigma_l = \frac{\sigma_c - (e_1 \times E)}{\nu} \]

Where:

\( \sigma_l \) — Longitudinal stress (Pascal)
\( \sigma_c \) — Circumferential stress due to fluid pressure (Pascal)
\( e_1 \) — Circumferential strain (dimensionless)
\( E \) — Young's Modulus of the cylinder material (Pascal)
\( \nu \) — Poisson's Ratio (dimensionless)

Explanation: This formula calculates the longitudinal stress in a cylindrical object by accounting for the relationship between circumferential stress, circumferential strain, material properties, and Poisson's effect.

3. Importance of Longitudinal Stress Calculation

Details: Calculating longitudinal stress is crucial for designing pressure vessels, pipelines, and cylindrical structures to ensure they can withstand internal pressures without failure. It helps engineers determine appropriate wall thickness and material selection.

4. Using the Calculator

Tips: Enter circumferential stress in Pascal, circumferential strain (dimensionless), Young's Modulus in Pascal, and Poisson's Ratio (between 0.1-0.5). All values must be valid and Poisson's Ratio must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between longitudinal and circumferential stress?
A: Longitudinal stress acts parallel to the cylinder's axis, while circumferential stress (hoop stress) acts tangentially around the cylinder's circumference.

Q2: When does longitudinal stress become significant?
A: Longitudinal stress becomes significant in closed-end pressure vessels where internal pressure creates stress along the length of the cylinder.

Q3: What are typical values for Poisson's Ratio?
A: For most metals and alloys, Poisson's Ratio ranges between 0.25 and 0.35. Rubber-like materials can have values close to 0.5.

Q4: How does temperature affect longitudinal stress calculations?
A: Temperature changes can affect material properties (Young's Modulus) and cause thermal expansion, which should be considered in precise engineering calculations.

Q5: Can this formula be used for composite materials?
A: This formula is primarily for isotropic materials. For composite materials with anisotropic properties, more complex formulas accounting for material directionality are needed.