Circumferential Stress At Center Of Solid Disc Calculator

Formula Used:

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

Density Of Disc (ρ):

kg/m³

Angular Velocity (ω):

rad/s

Poisson's Ratio (ν):

Outer Radius Disc (r_outer):

Circumferential Stress (σ_c):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Circumferential Stress At Center Of Solid Disc?

Circumferential Stress at the center of a solid disc is the stress acting along the circumference of the disc when it is subjected to rotational forces. It is a critical parameter in mechanical engineering for designing rotating components like flywheels, turbines, and gears.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \sigma_c \) — Circumferential Stress (Pa)
\( \rho \) — Density of the disc material (kg/m³)
\( \omega \) — Angular velocity (rad/s)
\( \nu \) — Poisson's ratio (dimensionless)
\( r_{outer} \) — Outer radius of the disc (m)

Explanation: This formula calculates the circumferential stress at the center of a solid rotating disc, accounting for material properties and rotational dynamics.

3. Importance of Circumferential Stress Calculation

Details: Accurate calculation of circumferential stress is essential for ensuring the structural integrity and safety of rotating machinery. It helps in preventing failures due to excessive stress and optimizing material usage.

4. Using the Calculator

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

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 circumferential stress?
A: Circumferential stress increases with the square of angular velocity, making it highly sensitive to rotational speed.

Q3: What units should be used for input values?
A: Density in kg/m³, angular velocity in rad/s, Poisson's ratio (dimensionless), and outer radius in meters.

Q4: Why is circumferential stress important in disc design?
A: It helps determine if the disc can withstand rotational forces without failure, ensuring safety and reliability.

Q5: Can this formula be used for hollow discs?
A: No, this formula is specifically for solid discs. Hollow discs require a different stress calculation approach.