Radial Stress At Center Of Solid Disc Calculator

Radial Stress Formula:

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

Density Of Disc (ρ):

kg/m³

Angular Velocity (ω):

rad/s

Poisson's Ratio (ν):

Outer Radius Disc:

Radial Stress (σr):

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1. What is Radial Stress in Solid Disc?

Radial stress in a solid disc refers to the stress component acting along the radial direction when the disc is subjected to rotational forces. It is an important parameter in mechanical engineering for analyzing the structural integrity of rotating components.

2. How Does the Calculator Work?

The calculator uses the radial stress formula:

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

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)

Explanation: This formula calculates the radial stress at the center of a solid disc rotating about its central axis, considering material properties and rotational dynamics.

3. Importance of Radial Stress Calculation

Details: Accurate radial stress calculation is crucial for designing rotating machinery components, ensuring structural integrity, preventing failure, and optimizing material usage in mechanical systems.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of Poisson's ratio in this calculation?
A: Poisson's ratio accounts for the material's tendency to expand or contract in directions perpendicular to the applied stress, affecting the stress distribution in the rotating disc.

Q2: How does angular velocity affect radial stress?
A: Radial stress increases with the square of angular velocity, meaning higher rotational speeds significantly increase stress levels in the disc.

Q3: What are typical values for radial stress in engineering applications?
A: Values vary widely depending on material and application, but typically range from a few MPa to hundreds of MPa in high-speed rotating machinery.

Q4: Are there limitations to this formula?
A: This formula assumes homogeneous material properties, constant thickness, and applies specifically to solid discs rotating about their central axis.

Q5: How does disc radius affect radial stress?
A: Radial stress increases with the square of the outer radius, meaning larger discs experience significantly higher stresses at the same rotational speed.