Poisson's Ratio Given Circumferential Stress At Center Of Solid Disc Calculator

Formula Used:

\[ Poisson's\ Ratio = \frac{8 \times Circumferential\ Stress}{Density\ Of\ Disc \times (Angular\ Velocity)^2 \times (Outer\ Radius\ Disc)^2} - 3 \]

Circumferential Stress (σc):

Pascal

Density Of Disc (ρ):

kg/m³

Angular Velocity (ω):

rad/s

Outer Radius Disc (router):

meter

Poisson's Ratio:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Poisson's Ratio?

Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson's ratio range between 0.1 and 0.5. It's a fundamental mechanical property that describes how a material deforms in directions perpendicular to the direction of loading.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Poisson's\ Ratio = \frac{8 \times Circumferential\ Stress}{Density\ Of\ Disc \times (Angular\ Velocity)^2 \times (Outer\ Radius\ Disc)^2} - 3 \]

Where:

\( Circumferential\ Stress \) — Force over area exerted circumferentially perpendicular to the axis and the radius (Pascal)
\( Density\ Of\ Disc \) — Mass per unit volume of the disc (kg/m³)
\( Angular\ Velocity \) — How fast an object rotates or revolves relative to another point (rad/s)
\( Outer\ Radius\ Disc \) — Radius of the larger of the two concentric circles that form its boundary (meter)

Explanation: This formula calculates Poisson's Ratio for a solid disc under rotational stress, considering the material properties and rotational dynamics.

3. Importance of Poisson's Ratio Calculation

Details: Accurate calculation of Poisson's Ratio is crucial for understanding material behavior under stress, designing mechanical components, predicting deformation patterns, and ensuring structural integrity in rotating disc applications.

4. Using the Calculator

Tips: Enter circumferential stress in Pascal, density in kg/m³, angular velocity in rad/s, and outer radius in meters. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of Poisson's Ratio?
A: For most materials, Poisson's Ratio ranges between 0.0 and 0.5. For metals and alloys, it typically falls between 0.25 and 0.35.

Q2: Why is Poisson's Ratio important in engineering?
A: It helps predict how materials will deform under stress, which is essential for designing structures and components that can withstand various loading conditions.

Q3: Can Poisson's Ratio be negative?
A: Yes, some materials called auxetic materials have negative Poisson's Ratio, meaning they expand laterally when stretched.

Q4: How does temperature affect Poisson's Ratio?
A: Poisson's Ratio generally remains relatively constant with temperature changes for most materials, though some variations can occur.

Q5: What are the limitations of this calculation method?
A: This formula assumes homogeneous material properties, perfect disc geometry, and may not account for all real-world conditions like temperature variations or material imperfections.