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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 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{σ c - ((\frac{R i}{r disc}) \cdot E)}{σ r}

𝛎 - Poisson's Ratio?σ_c - Circumferential Stress?R_i - Increase in radius?r_disc - Disc Radius?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{R i}{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 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

Open Variable

Circumferential Stress

Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.

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 is the increase in inner radius of outer cylinder of compound cylinder.

Symbol: R_i

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Increase in radius

Open Variable

Disc Radius

Disc Radius is a radial line from the focus to any point of a curve.

Symbol: r_disc

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Disc Radius

Open Variable

Modulus Of Elasticity Of Disc

Modulus Of Elasticity Of Disc is a quantity that measures disc's resistance to being deformed elastically when a stress is applied to it.

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 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

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 - (e r \cdot E)}{σ c}

Go Poisson's ratio given initial radial width of disc

𝛎 = \frac{σ r - ((\frac{du}{dr}) \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/Disc Radius)*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 (R_i), Disc Radius (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/Disc Radius)*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 (R_i), Disc Radius (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/Disc Radius)*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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