Radial Stress In Solid Disc Given Outer Radius Calculator

Radial Stress Formula:

\[ \sigma_r = \frac{\rho \times \omega^2 \times (3 + \nu) \times (r_{outer}^2 - r^2)}{8} \]

Density Of Disc (ρ):

kg/m³

Angular Velocity (ω):

rad/s

Poisson's Ratio (ν):

Outer Radius Disc (r_outer):

Radius of Element (r):

Radial Stress (σ_r):

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1. What is Radial Stress in Solid Disc?

Radial stress in a solid disc refers to the stress component acting perpendicular to the radius of the disc. It is induced by centrifugal forces when the disc rotates at high angular velocities and is an important consideration in mechanical design and analysis.

2. How Does the Calculator Work?

The calculator uses the radial stress formula:

\[ \sigma_r = \frac{\rho \times \omega^2 \times (3 + \nu) \times (r_{outer}^2 - r^2)}{8} \]

Where:

\( \sigma_r \) — Radial Stress (Pa)
\( \rho \) — Density of Disc (kg/m³)
\( \omega \) — Angular Velocity (rad/s)
\( \nu \) — Poisson's Ratio
\( r_{outer} \) — Outer Radius of Disc (m)
\( r \) — Radius of Element (m)

Explanation: The formula calculates the radial stress distribution in a rotating solid disc, accounting for material properties and geometric parameters.

3. Importance of Radial Stress Calculation

Details: Accurate radial stress calculation is crucial for designing rotating machinery components, ensuring structural integrity, and preventing failure due to centrifugal forces.

4. Using the Calculator

Tips: Enter density in kg/m³, angular velocity in rad/s, Poisson's ratio (typically 0.1-0.5), outer radius in meters, and element radius in meters. All values must be valid positive numbers.

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.

Q2: How does angular velocity affect radial stress?
A: Radial stress increases with the square of angular velocity, making high-speed rotation particularly critical for stress analysis.

Q3: Where is radial stress maximum in a solid disc?
A: In a solid rotating disc, radial stress is typically maximum at the center (r = 0) of the disc.

Q4: What units should be used for input values?
A: Use SI units: kg/m³ for density, rad/s for angular velocity, meters for radii, and dimensionless for Poisson's ratio.

Q5: Are there limitations to this formula?
A: This formula assumes homogeneous, isotropic material properties and constant thickness. It may not be accurate for complex geometries or anisotropic materials.