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Poisson's ratio given radius of disc Formula

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GoPoisson's ratio given circumferential strain on disc Formula

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GoPoisson's ratio given radial strain on disc Formula

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Poisson's ratio is a material property that describes the relationship between the lateral strain and the longitudinal strain. Check FAQs

𝛎 = \frac{σ c - ((\frac{ΔR}{r disc}) \cdot E)}{σ r}

𝛎 - Poisson's Ratio?σ_c - Circumferential Stress?ΔR - Increase in Radius?r_disc - Radius of Disc?E - Modulus of Elasticity of Disc?σ_r - Radial Stress?

Poisson's ratio given radius of disc Example

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Here is how the Poisson's ratio given radius of disc equation looks like with Values.

Here is how the Poisson's ratio given radius of disc equation looks like with Units.

Here is how the Poisson's ratio given radius of disc equation looks like.

0.7995 = \frac{80 - ((\frac{6.5}{1000}) \cdot 8)}{100}

0.7995 = \frac{80N/m² - ((\frac{6.5mm}{1000mm}) \cdot 8N/m²)}{100N/m²}

0.7995 = \frac{80 - ((\frac{6.5}{1000}) \cdot 8)}{100}

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Strength of Materials » fx Poisson's ratio given radius of disc

Poisson's ratio given radius of disc Solution

Follow our step by step solution on how to calculate Poisson's ratio given radius of disc?

FIRST Step Consider the formula

𝛎 = \frac{σ c - ((\frac{ΔR}{r disc}) \cdot E)}{σ r}

Next Step Substitute values of Variables

∴

𝛎 = \frac{80N/m² - ((\frac{6.5mm}{1000mm}) \cdot 8N/m²)}{100N/m²}

Next Step Convert Units

∴

𝛎 = \frac{80Pa - ((\frac{0.0065m}{1m}) \cdot 8Pa)}{100Pa}

Next Step Prepare to Evaluate

∴

𝛎 = \frac{80 - ((\frac{0.0065}{1}) \cdot 8)}{100}

Next Step Evaluate

∴

𝛎 = 0.79948

LAST Step Rounding Answer

∴

𝛎 = 0.7995

Poisson's ratio given radius of disc Formula Elements

Variables

Poisson's Ratio

Poisson's ratio is a material property that describes the relationship between the lateral strain and the longitudinal strain.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 10.

Formulas to find Poisson's Ratio

Open Variable

Circumferential Stress

Circumferential stress is the stress that acts along the circumference of a cylindrical or spherical object, the stress that develops when the object is subjected to internal or external pressure.

Symbol: σ_c

Measurement: StressUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Circumferential Stress

Open Variable

Increase in Radius

Increase in radius refers to the change or growth in the radius of a circular object (such as a disc, cylinder, or sphere) due to external or internal factors.

Symbol: ΔR

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Increase in Radius

Open Variable

Radius of Disc

Radius of disc is the distance from the center of the disc to any point on its edge (circumference).

Symbol: r_disc

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Disc

Open Variable

Modulus of Elasticity of Disc

Modulus of elasticity of disc refers to a material property that measures its ability to resist deformation under stress, specifically in response to stretching or compressing forces.

Symbol: E

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Disc

Open Variable

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

Open Variable

Other Formulas to find Poisson's Ratio

Go Poisson's ratio given circumferential strain on disc

𝛎 = \frac{σ c - (e 1 \cdot E)}{σ r}

Go Poisson's ratio given radial strain on disc

𝛎 = \frac{σ r - (ε r \cdot E)}{σ c}

Go Poisson's ratio given initial radial width of disc

𝛎 = \frac{σ r - ((\frac{Δr}{d r}) \cdot E)}{σ c}

Other formulas in Relation of Parameters category

Go Hoop stress in thin cylinder

σ θ = ρ \cdot ω \cdot r disc

Go Density of cylinder material given hoop stress (for thin cylinder)

ρ = \frac{σ θ}{ω \cdot r disc}

Go Mean radius of cylinder given hoop stress in thin cylinder

r disc = \frac{σ θ}{ρ \cdot ω}

Go Angular speed of rotation for thin cylinder given hoop stress in thin cylinder

ω = \frac{σ θ}{ρ \cdot r disc}

See More

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How to Evaluate Poisson's ratio given radius of disc?

Poisson's ratio given radius of disc evaluator uses Poisson's Ratio = (Circumferential Stress-((Increase in Radius/Radius of Disc)*Modulus of Elasticity of Disc))/Radial Stress to evaluate the Poisson's Ratio, Poisson's ratio given radius of disc formula is defined as a measure of the relationship between lateral strain and axial stress in a rotating disc, providing insights into material behavior under rotational forces and stress conditions. Poisson's Ratio is denoted by 𝛎 symbol.

How to evaluate Poisson's ratio given radius of disc using this online evaluator? To use this online evaluator for Poisson's ratio given radius of disc, enter Circumferential Stress (σ_c), Increase in Radius (ΔR), Radius of Disc (r_disc), Modulus of Elasticity of Disc (E) & Radial Stress (σ_r) and hit the calculate button.

FAQs on Poisson's ratio given radius of disc

What is the formula to find Poisson's ratio given radius of disc?

The formula of Poisson's ratio given radius of disc is expressed as Poisson's Ratio = (Circumferential Stress-((Increase in Radius/Radius of Disc)*Modulus of Elasticity of Disc))/Radial Stress. Here is an example- 0.79948 = (80-((0.0065/1)*8))/100.

How to calculate Poisson's ratio given radius of disc?

With Circumferential Stress (σ_c), Increase in Radius (ΔR), Radius of Disc (r_disc), Modulus of Elasticity of Disc (E) & Radial Stress (σ_r) we can find Poisson's ratio given radius of disc using the formula - Poisson's Ratio = (Circumferential Stress-((Increase in Radius/Radius of Disc)*Modulus of Elasticity of Disc))/Radial Stress.

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

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

Poisson's Ratio=(Circumferential Stress-(Circumferential Strain*Modulus of Elasticity of Disc))/(Radial Stress)
Poisson's Ratio=(Radial Stress-(Radial Strain*Modulus of Elasticity of Disc))/(Circumferential Stress)
Poisson's Ratio=(Radial Stress-((Increase in Radial Width/Initial Radial Width)*Modulus of Elasticity of Disc))/(Circumferential Stress)

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