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Poisson's ratio given Radial stress in solid disc and outer radius Formula

GoPoisson's ratio given Radial stress in solid disc Formula

GoPoisson's ratio given Circumferential stress in solid disc Formula

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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. Check FAQs

𝛎 = (\frac{8 \cdot σ r}{ρ \cdot (ω^{2}) \cdot (({r outer}^{2}) - (r^{2}))}) - 3

𝛎 - Poisson's Ratio?σ_r - Radial Stress?ρ - Density Of Disc?ω - Angular Velocity?r_outer - Outer Radius Disc?r - Radius of Element?

Poisson's ratio given Radial stress in solid disc and outer radius Example

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Here is how the Poisson's ratio given Radial stress in solid disc and outer radius equation looks like with Values.

Here is how the Poisson's ratio given Radial stress in solid disc and outer radius equation looks like with Units.

Here is how the Poisson's ratio given Radial stress in solid disc and outer radius equation looks like.

0.9369 = (\frac{8 \cdot 100}{2 \cdot ({11.2}^{2}) \cdot ((900^{2}) - (5^{2}))}) - 3

0.9369 = (\frac{8 \cdot 100N/m²}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot (({900mm}^{2}) - ({5mm}^{2}))}) - 3

0.9369 = (\frac{8 \cdot 100}{2 \cdot ({11.2}^{2}) \cdot ((900^{2}) - (5^{2}))}) - 3

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Poisson's ratio given Radial stress in solid disc and outer radius Solution

Follow our step by step solution on how to calculate Poisson's ratio given Radial stress in solid disc and outer radius?

FIRST Step Consider the formula

𝛎 = (\frac{8 \cdot σ r}{ρ \cdot (ω^{2}) \cdot (({r outer}^{2}) - (r^{2}))}) - 3

Next Step Substitute values of Variables

∴

𝛎 = (\frac{8 \cdot 100N/m²}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot (({900mm}^{2}) - ({5mm}^{2}))}) - 3

Next Step Convert Units

∴

𝛎 = (\frac{8 \cdot 100Pa}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot (({0.9m}^{2}) - ({0.005m}^{2}))}) - 3

Next Step Prepare to Evaluate

∴

𝛎 = (\frac{8 \cdot 100}{2 \cdot ({11.2}^{2}) \cdot (({0.9}^{2}) - ({0.005}^{2}))}) - 3

Next Step Evaluate

∴

𝛎 = 0.93688139782596

LAST Step Rounding Answer

∴

𝛎 = 0.9369

Poisson's ratio given Radial stress in solid disc and outer radius Formula Elements

Variables

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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 10.

Formulas to find Poisson's Ratio

Radial Stress

Radial Stress induced by a bending moment in a member of constant cross section.

Symbol: σ_r

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Radial Stress

Density Of Disc

Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Of Disc

Angular Velocity

The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

Outer Radius Disc

Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.

Symbol: r_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Radius Disc

Radius of Element

The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Element

Other Formulas to find Poisson's Ratio

Go Poisson's ratio given Radial stress in solid disc

𝛎 = (\frac{((\frac{C}{2}) - σ r) \cdot 8}{ρ \cdot (ω^{2}) \cdot ({r disc}^{2})}) - 3

Go Poisson's ratio given Circumferential stress in solid disc

𝛎 = \frac{(\frac{((\frac{C 1}{2}) - σ c) \cdot 8}{ρ \cdot (ω^{2}) \cdot ({r disc}^{2})}) - 1}{3}

Go Poisson's ratio given constant at boundary condition for circular disc

𝛎 = (\frac{8 \cdot C 1}{ρ \cdot (ω^{2}) \cdot ({r outer}^{2})}) - 3

Go Poisson's ratio given Radial stress at center of solid disc

𝛎 = (\frac{8 \cdot σ r}{ρ \cdot (ω^{2}) \cdot ({r outer}^{2})}) - 3

Other formulas in Stresses in Disc category

Go Radial stress in solid disc

σ r = (\frac{C 1}{2}) - (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot (3 + 𝛎)}{8})

Go Constant at boundary condition given Radial stress in solid disc

C 1 = 2 \cdot (σ r + (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot (3 + 𝛎)}{8}))

Go Circumferential stress in solid disc

σ c = (\frac{C 1}{2}) - (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot ((3 \cdot 𝛎) + 1)}{8})

Go Constant at boundary condition given Circumferential stress in solid disc

C 1 = 2 \cdot (σ c + (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot ((3 \cdot 𝛎) + 1)}{8}))

How to Evaluate Poisson's ratio given Radial stress in solid disc and outer radius?

Poisson's ratio given Radial stress in solid disc and outer radius evaluator uses Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3 to evaluate the Poisson's Ratio, The Poisson's ratio given Radial stress in solid disc and outer radius formula is defined as a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression. Poisson's Ratio is denoted by 𝛎 symbol.

How to evaluate Poisson's ratio given Radial stress in solid disc and outer radius using this online evaluator? To use this online evaluator for Poisson's ratio given Radial stress in solid disc and outer radius, enter Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Outer Radius Disc (r_outer) & Radius of Element (r) and hit the calculate button.

FAQs on Poisson's ratio given Radial stress in solid disc and outer radius

What is the formula to find Poisson's ratio given Radial stress in solid disc and outer radius?

The formula of Poisson's ratio given Radial stress in solid disc and outer radius is expressed as Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3. Here is an example- 0.936881 = ((8*100)/(2*(11.2^2)*((0.9^2)-(0.005^2))))-3.

How to calculate Poisson's ratio given Radial stress in solid disc and outer radius?

With Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Outer Radius Disc (r_outer) & Radius of Element (r) we can find Poisson's ratio given Radial stress in solid disc and outer radius using the formula - Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3.

What are the other ways to Calculate Poisson's Ratio?

Here are the different ways to Calculate Poisson's Ratio-

Poisson's Ratio=((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3
Poisson's Ratio=(((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-1)/3
Poisson's Ratio=((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3

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Poisson's ratio given Radial stress in solid disc and outer radius Formula

​GoPoisson's ratio given Radial stress in solid disc Formula

​GoPoisson's ratio given Circumferential stress in solid disc Formula

Poisson's ratio given Radial stress in solid disc and outer radius Example

Poisson's ratio given Radial stress in solid disc and outer radius Solution

Poisson's ratio given Radial stress in solid disc and outer radius Formula Elements

Other Formulas to find Poisson's Ratio

Other formulas in Stresses in Disc category

How to Evaluate Poisson's ratio given Radial stress in solid disc and outer radius?

FAQs on Poisson's ratio given Radial stress in solid disc and outer radius

Variable Name

GoPoisson's ratio given Radial stress in solid disc Formula

GoPoisson's ratio given Circumferential stress in solid disc Formula