Modulus Of Elasticity Given Radial Strain On Disc Calculator

Formula Used:

\[ E = \frac{\sigma_r - (\mu \cdot \sigma_c)}{e_r} \]

Radial Stress (σr):

Pascal

Poisson's Ratio (μ):

Circumferential Stress (σc):

Pascal

Radial Strain (er):

Modulus Of Elasticity Of Disc (E):

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1. What is the Modulus of Elasticity Formula?

The Modulus of Elasticity formula calculates a material's resistance to deformation when subjected to stress. For a disc under radial strain, it relates radial stress, circumferential stress, Poisson's ratio, and radial strain.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{\sigma_r - (\mu \cdot \sigma_c)}{e_r} \]

Where:

\( E \) — Modulus of Elasticity of Disc (Pascal)
\( \sigma_r \) — Radial Stress (Pascal)
\( \mu \) — Poisson's Ratio
\( \sigma_c \) — Circumferential Stress (Pascal)
\( e_r \) — Radial Strain

Explanation: The formula calculates the modulus of elasticity by accounting for the combined effects of radial and circumferential stresses, adjusted by Poisson's ratio, and divided by the radial strain.

3. Importance of Modulus of Elasticity Calculation

Details: Accurate calculation of modulus of elasticity is crucial for material characterization, structural design, and predicting material behavior under various loading conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units. Radial and circumferential stresses should be in Pascal, Poisson's ratio as a dimensionless value between 0.1-0.5, and radial strain as a dimensionless value.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for modulus of elasticity?
A: Modulus of elasticity values vary widely by material, from about 1 GPa for rubbers to over 200 GPa for steels.

Q2: Why is Poisson's ratio important in this calculation?
A: Poisson's ratio accounts for the lateral contraction/expansion that occurs when a material is stretched/compressed, affecting the stress distribution.

Q3: What units should be used for input values?
A: Stresses should be in Pascal, Poisson's ratio is dimensionless, and radial strain is dimensionless.

Q4: Can this formula be used for all materials?
A: This formula is specifically for calculating modulus of elasticity in discs under radial strain conditions.

Q5: What if the radial strain is zero?
A: The formula becomes undefined when radial strain is zero, as division by zero is mathematically undefined.