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Poisson's ratio given Radial stress in solid disc Formula

GoPoisson's ratio given Circumferential stress in solid disc Formula

GoPoisson's ratio given constant at boundary condition for circular 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{((\frac{C}{2}) - σ r) \cdot 8}{ρ \cdot (ω^{2}) \cdot ({r disc}^{2})}) - 3

𝛎 - Poisson's Ratio?C - Constant at Boundary?σ_r - Radial Stress?ρ - Density Of Disc?ω - Angular Velocity?r_disc - Disc Radius?

Poisson's ratio given Radial stress in solid disc Example

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

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

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

0.1888 = (\frac{((\frac{400}{2}) - 100) \cdot 8}{2 \cdot ({11.2}^{2}) \cdot (1000^{2})}) - 3

0.1888 = (\frac{((\frac{400}{2}) - 100N/m²) \cdot 8}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1000mm}^{2})}) - 3

0.1888 = (\frac{((\frac{400}{2}) - 100) \cdot 8}{2 \cdot ({11.2}^{2}) \cdot (1000^{2})}) - 3

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Poisson's ratio given Radial stress in solid disc Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝛎 = (\frac{((\frac{400}{2}) - 100N/m²) \cdot 8}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1000mm}^{2})}) - 3

Next Step Convert Units

∴

𝛎 = (\frac{((\frac{400}{2}) - 100Pa) \cdot 8}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1m}^{2})}) - 3

Next Step Prepare to Evaluate

∴

𝛎 = (\frac{((\frac{400}{2}) - 100) \cdot 8}{2 \cdot ({11.2}^{2}) \cdot (1^{2})}) - 3

Next Step Evaluate

∴

𝛎 = 0.188775510204082

LAST Step Rounding Answer

∴

𝛎 = 0.1888

Poisson's ratio given Radial 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

Constant at Boundary

Constant at boundary condition refers to a type of boundary condition in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant at Boundary

Radial Stress

Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.

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 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

Disc Radius

Disc radius is the distance from the center of the disc to any point on its circumference.

Symbol: r_disc

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Disc Radius

Other Formulas to find Poisson's Ratio

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

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?

Poisson's ratio given Radial stress in solid disc evaluator uses Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3 to evaluate the Poisson's Ratio, The Poisson's ratio given Radial 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 Radial stress in solid disc using this online evaluator? To use this online evaluator for Poisson's ratio given Radial stress in solid disc, enter Constant at Boundary (C), Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω) & Disc Radius (r_disc) and hit the calculate button.

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

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

The formula of Poisson's ratio given Radial stress in solid disc is expressed as Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3. Here is an example- 0.188776 = ((((400/2)-100)*8)/(2*(11.2^2)*(1^2)))-3.

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

With Constant at Boundary (C), Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω) & Disc Radius (r_disc) we can find Poisson's ratio given Radial stress in solid disc using the formula - Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^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 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
Poisson's Ratio=((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3

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Poisson's ratio given Radial stress in solid disc Formula

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

​GoPoisson's ratio given constant at boundary condition for circular disc Formula

Poisson's ratio given Radial stress in solid disc Example

Poisson's ratio given Radial stress in solid disc Solution

Poisson's ratio given Radial 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 Radial stress in solid disc?

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

Variable Name

GoPoisson's ratio given Circumferential stress in solid disc Formula

GoPoisson's ratio given constant at boundary condition for circular disc Formula