Modulus Of Elasticity Given Tensile Radial Strain And Poisson's Ratio Calculator

Formula Used:

\[ F'c = \frac{P_v + (2 \times \sigma_{\theta} \times \nu)}{\varepsilon_{tensile}} \]

Radial Pressure (Pv):

Pascal per Square Meter

Hoop Stress on thick shell (σθ):

Pascal

Poisson's Ratio (ν):

(unitless)

Tensile Strain (εtensile):

(unitless)

Adjusted design value (F'c):

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1. What is the Modulus of Elasticity Formula?

The formula calculates the adjusted design value for compression by considering radial pressure, hoop stress, Poisson's ratio, and tensile strain. It provides a corrected design value using specific material and stress factors.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F'c = \frac{P_v + (2 \times \sigma_{\theta} \times \nu)}{\varepsilon_{tensile}} \]

Where:

\( F'c \) — Adjusted design value (Pascal)
\( P_v \) — Radial Pressure (Pascal per Square Meter)
\( \sigma_{\theta} \) — Hoop Stress on thick shell (Pascal)
\( \nu \) — Poisson's Ratio (unitless)
\( \varepsilon_{tensile} \) — Tensile Strain (unitless)

Explanation: The formula accounts for the combined effects of radial pressure, hoop stress, and material properties through Poisson's ratio to determine the adjusted design value under tensile strain conditions.

3. Importance of Adjusted Design Value Calculation

Details: Accurate calculation of the adjusted design value is crucial for structural engineering applications, material selection, and ensuring the safety and reliability of components under various stress conditions.

4. Using the Calculator

Tips: Enter radial pressure in Pascal per Square Meter, hoop stress in Pascal, Poisson's ratio (between 0.1 and 0.5), and tensile strain. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is Poisson's Ratio?
A: Poisson's Ratio is defined as the ratio of lateral strain to axial strain. For many metals and alloys, values range between 0.1 and 0.5.

Q2: What is the significance of hoop stress?
A: Hoop stress is the circumferential stress in a cylindrical object when pressure is applied uniformly from the inside or outside.

Q3: When should this calculation be used?
A: This calculation is particularly useful in pressure vessel design, piping systems, and any cylindrical structure subjected to internal or external pressure.

Q4: Are there limitations to this formula?
A: The formula assumes linear elastic material behavior and may be less accurate for materials with non-linear stress-strain relationships or under extreme conditions.

Q5: What units should be used for input values?
A: Radial pressure should be in Pascal per Square Meter, hoop stress in Pascal, while Poisson's ratio and tensile strain are dimensionless quantities.