Longitudinal Stress Given Change In Radius Of Thick Cylindrical Shell Calculator

Formula Used:

\[ Longitudinal\ Stress = \frac{Hoop\ Stress - \left(\frac{Change\ in\ radius \times Modulus\ of\ Elasticity}{Radius\ of\ Cylindrical\ Shell}\right)}{Poisson's\ Ratio} + Compressive\ Stress \]

Hoop Stress on thick shell (σθ):

Pascal

Change in radius (Δr):

Meter

Modulus of Elasticity (E):

Pascal

Radius of Cylindrical Shell (r):

Meter

Poisson's Ratio (ν):

(unitless)

Compressive Stress (σc):

Pascal

Longitudinal Stress Thick Shell (σl):

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1. What is Longitudinal Stress in Thick Cylindrical Shells?

Longitudinal stress in thick cylindrical shells is the stress component acting parallel to the longitudinal axis of the cylinder. It's an important parameter in pressure vessel design and structural analysis of cylindrical components subjected to internal or external pressure.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \sigma_l = \frac{\sigma_\theta - \left(\frac{\Delta r \times E}{r}\right)}{\nu} + \sigma_c \]

Where:

\( \sigma_l \) — Longitudinal Stress (Pascal)
\( \sigma_\theta \) — Hoop Stress (Pascal)
\( \Delta r \) — Change in radius (Meter)
\( E \) — Modulus of Elasticity (Pascal)
\( r \) — Radius of Cylindrical Shell (Meter)
\( \nu \) — Poisson's Ratio (unitless)
\( \sigma_c \) — Compressive Stress (Pascal)

Explanation: This formula calculates the longitudinal stress in thick-walled cylindrical shells by considering the hoop stress, change in radius due to deformation, material properties, and additional compressive stress.

3. Importance of Longitudinal Stress Calculation

Details: Accurate calculation of longitudinal stress is crucial for designing pressure vessels, pipelines, and cylindrical structures to ensure they can withstand internal pressures without failure. It helps in determining the required wall thickness and material specifications.

4. Using the Calculator

Tips: Enter all values in appropriate units (Pascal for stresses, Meter for dimensions). Ensure all inputs are positive values. Poisson's ratio should be between 0.1 and 0.5 for most engineering materials.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hoop stress and longitudinal stress?
A: Hoop stress acts circumferentially around the cylinder, while longitudinal stress acts parallel to the cylinder's axis. Both are important in pressure vessel design.

Q2: When is this formula applicable?
A: This formula is specifically designed for thick-walled cylindrical shells where wall thickness is significant compared to the radius.

Q3: What are typical values for Poisson's ratio?
A: For most metals and alloys, Poisson's ratio ranges between 0.25-0.35. For rubber-like materials, it approaches 0.5.

Q4: How does change in radius affect longitudinal stress?
A: The change in radius due to deformation directly influences the stress distribution in the cylindrical shell, affecting both hoop and longitudinal stresses.

Q5: What safety factors should be considered?
A: Engineering designs typically include safety factors of 1.5-4.0 depending on the application, material properties, and operating conditions.