Circumferential Stress Given Initial Radial Width Of Disc Calculator

Formula Used:

\[ \sigma_c = \frac{\sigma_r - \left(\frac{\Delta u}{u_0} \times E\right)}{\nu} \]

Radial Stress (σr):

Pascal

Increase in Radial Width (Δu):

Meter

Initial Radial Width (u₀):

Meter

Modulus Of Elasticity (E):

Pascal

Poisson's Ratio (ν):

Circumferential Stress (σc):

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1. What is Circumferential Stress?

Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius in a disc or cylindrical structure. It represents the stress component acting tangentially to the circumference.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_c = \frac{\sigma_r - \left(\frac{\Delta u}{u_0} \times E\right)}{\nu} \]

Where:

\( \sigma_c \) — Circumferential Stress (Pascal)
\( \sigma_r \) — Radial Stress (Pascal)
\( \Delta u \) — Increase in Radial Width (Meter)
\( u_0 \) — Initial Radial Width (Meter)
\( E \) — Modulus Of Elasticity (Pascal)
\( \nu \) — Poisson's Ratio

Explanation: This formula calculates the circumferential stress in a disc by considering the radial stress, strain-induced width changes, material elasticity, and Poisson's ratio effect.

3. Importance of Circumferential Stress Calculation

Details: Accurate circumferential stress calculation is crucial for structural integrity analysis, failure prediction, and safe design of rotating discs, pressure vessels, and cylindrical components in mechanical engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (Pascal for stresses, Meter for dimensions). Ensure Poisson's Ratio is between 0.1 and 0.5 as per standard material properties. All input values must be positive.

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 steel and 0.33 for aluminum.

Q2: How does circumferential stress differ from radial stress?
A: Circumferential stress acts tangentially around the circumference, while radial stress acts along the radius direction. Both are important for complete stress analysis.

Q3: When is this formula most applicable?
A: This formula is particularly useful for thin rotating discs, pressure vessels, and cylindrical structures where elastic deformation assumptions hold true.

Q4: What are the limitations of this calculation?
A: The formula assumes linear elastic material behavior, small deformations, and homogeneous material properties. It may not be accurate for large deformations or plastic regions.

Q5: How does temperature affect the calculation?
A: Temperature changes can affect material properties (E and ν). For precise calculations at different temperatures, temperature-compensated material properties should be used.