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Poisson's Ratio given max circumferential stress in solid disc 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 a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain. Check FAQs

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

𝛎 - Poisson's Ratio?σ_c - Circumferential Stress?ρ - Density Of Disc?ω - Angular Velocity?r_outer - Outer Radius Disc?

Poisson's Ratio given max circumferential stress in solid disc Example

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Here is how the Poisson's Ratio given max circumferential stress in solid disc equation looks like with Values.

Here is how the Poisson's Ratio given max circumferential stress in solid disc equation looks like with Units.

Here is how the Poisson's Ratio given max circumferential stress in solid disc equation looks like.

0.9368 = (\frac{8 \cdot 100}{2 \cdot ({11.2}^{2}) \cdot (900^{2})}) - 3

0.9368 = (\frac{8 \cdot 100N/m²}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({900mm}^{2})}) - 3

0.9368 = (\frac{8 \cdot 100}{2 \cdot ({11.2}^{2}) \cdot (900^{2})}) - 3

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Poisson's Ratio given max circumferential stress in solid disc Solution

Follow our step by step solution on how to calculate Poisson's Ratio given max circumferential stress in solid disc?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

𝛎 = 0.936759889140842

LAST Step Rounding Answer

∴

𝛎 = 0.9368

Poisson's Ratio given max circumferential stress in solid disc Formula Elements

Variables

Poisson's Ratio

Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 10.

Formulas to find Poisson's Ratio

Circumferential Stress

Circumferential stress, also known as hoop stress, is a type of normal stress that acts tangentially to the circumference of a cylindrical or spherical object.

Symbol: σ_c

Measurement: StressUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Circumferential Stress

Density Of Disc

Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Of Disc

Angular Velocity

Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to 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 distance from the center of the disc to its outer edge or boundary.

Symbol: r_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Radius Disc

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 in solid disc and outer radius

𝛎 = (\frac{8 \cdot σ r}{ρ \cdot (ω^{2}) \cdot (({r outer}^{2}) - (R^{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 max circumferential stress in solid disc?

Poisson's Ratio given max circumferential stress in solid disc evaluator uses Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3 to evaluate the Poisson's Ratio, The Poisson's Ratio given max circumferential stress in solid disc 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 max circumferential stress in solid disc using this online evaluator? To use this online evaluator for Poisson's Ratio given max circumferential stress in solid disc, enter Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Outer Radius Disc (r_outer) and hit the calculate button.

FAQs on Poisson's Ratio given max circumferential stress in solid disc

What is the formula to find Poisson's Ratio given max circumferential stress in solid disc?

The formula of Poisson's Ratio given max circumferential stress in solid disc is expressed as Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3. Here is an example- 0.93676 = ((8*100)/(2*(11.2^2)*(0.9^2)))-3.

How to calculate Poisson's Ratio given max circumferential stress in solid disc?

With Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Outer Radius Disc (r_outer) we can find Poisson's Ratio given max circumferential stress in solid disc using the formula - Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^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 max circumferential stress in solid disc 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 max circumferential stress in solid disc Example

Poisson's Ratio given max circumferential stress in solid disc Solution

Poisson's Ratio given max circumferential stress in solid disc Formula Elements

Other Formulas to find Poisson's Ratio

Other formulas in Stresses in Disc category

How to Evaluate Poisson's Ratio given max circumferential stress in solid disc?

FAQs on Poisson's Ratio given max circumferential stress in solid disc

Variable Name

GoPoisson's ratio given Radial stress in solid disc Formula

GoPoisson's ratio given Circumferential stress in solid disc Formula