Longitudinal Stress Given Circumferential Strain In Thick Cylindrical Shell Calculator

Formula Used:

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

Hoop Stress on thick shell (σθ):

Pascal

Circumferential strain (e₁):

unitless

Modulus of Elasticity (E):

Pascal

Poisson's Ratio (ν):

unitless

Compressive Stress Thick Shell (σc):

Pascal

Longitudinal Stress Thick Shell (σl):

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1. What is Longitudinal Stress in Thick Cylindrical Shell?

Longitudinal Stress in a thick cylindrical shell is the stress produced along the length of the cylinder when it is subjected to internal pressure. It works in conjunction with hoop stress to determine the overall stress state of the cylindrical structure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \sigma_l \) — Longitudinal Stress Thick Shell (Pascal)
\( \sigma_\theta \) — Hoop Stress on thick shell (Pascal)
\( e_1 \) — Circumferential strain (unitless)
\( E \) — Modulus of Elasticity (Pascal)
\( \nu \) — Poisson's Ratio (unitless)
\( \sigma_c \) — Compressive Stress Thick Shell (Pascal)

Explanation: This formula calculates the longitudinal stress by considering the relationship between hoop stress, circumferential strain, material properties, and compressive stress in thick-walled cylindrical shells.

3. Importance of Longitudinal Stress Calculation

Details: Accurate calculation of longitudinal stress is crucial for designing pressure vessels, pipelines, and other 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 all values in appropriate units. Hoop stress, modulus of elasticity, and compressive stress should be in Pascals. Poisson's ratio should be between 0.1 and 0.5. Circumferential strain is unitless.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Poisson's Ratio?
A: For most metals and alloys, Poisson's ratio ranges between 0.1 and 0.5, with common values around 0.3 for many engineering materials.

Q2: How does longitudinal stress differ from hoop stress?
A: Hoop stress acts circumferentially around the cylinder, while longitudinal stress acts along the length of the cylinder. Both are important for pressure vessel design.

Q3: When is this formula particularly important?
A: This formula is crucial for thick-walled cylinders where stress distribution is not uniform across the wall thickness, such as in high-pressure applications.

Q4: What are common applications of this calculation?
A: This calculation is used in designing pressure vessels, hydraulic cylinders, pipelines, and any cylindrical structures subjected to internal pressure.

Q5: How does compressive stress affect the result?
A: Compressive stress adds to the calculated longitudinal stress, which is important when the cylinder is subjected to external compressive loads in addition to internal pressure.