Circumferential Stress Given Circumferential Strain On Disc Calculator

Formula Used:

\[ \sigma_c = (e_1 \times E) + (\mu \times \sigma_r) \]

Circumferential Strain (e₁):

unitless

Modulus Of Elasticity Of Disc (E):

Pascal

Poisson's Ratio (μ):

unitless

Radial Stress (σᵣ):

Pascal

Circumferential Stress (σc):

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1. What is the Circumferential Stress Formula?

The circumferential stress formula calculates the stress acting circumferentially on a disc or cylindrical object when subjected to strain and other forces. It combines the effects of circumferential strain, material elasticity, Poisson's ratio, and radial stress.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_c = (e_1 \times E) + (\mu \times \sigma_r) \]

Where:

\( \sigma_c \) — Circumferential Stress (Pascal)
\( e_1 \) — Circumferential strain (unitless)
\( E \) — Modulus Of Elasticity Of Disc (Pascal)
\( \mu \) — Poisson's Ratio (unitless)
\( \sigma_r \) — Radial Stress (Pascal)

Explanation: The formula accounts for both the direct effect of circumferential strain through Hooke's law and the contribution from radial stress through Poisson's effect.

3. Importance of Circumferential Stress Calculation

Details: Accurate circumferential stress calculation is crucial for designing and analyzing mechanical components like discs, cylinders, and pressure vessels to ensure structural integrity and prevent failure under load.

4. Using the Calculator

Tips: Enter circumferential strain (unitless), modulus of elasticity (Pascal), Poisson's ratio (between 0-0.5), and radial stress (Pascal). All values must be valid and non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What is circumferential stress?
A: Circumferential stress is the force per unit area acting tangentially to the circumference of a cylindrical or disc-shaped object.

Q2: What is Poisson's ratio?
A: Poisson's ratio is the ratio of transverse strain to axial strain when a material is stretched. For most metals, it ranges between 0.1 and 0.5.

Q3: When is this formula applicable?
A: This formula is applicable for isotropic materials under elastic deformation conditions in disc or cylindrical geometries.

Q4: What are typical values for modulus of elasticity?
A: Modulus of elasticity varies by material: steel ~200 GPa, aluminum ~70 GPa, rubber ~0.01-0.1 GPa.

Q5: How does radial stress affect circumferential stress?
A: Through Poisson's effect, radial stress contributes to circumferential stress - tensile radial stress increases circumferential stress, compressive radial stress decreases it.