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Poisson's ratio given initial radial width 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 r - ((\frac{du}{dr}) \cdot E)}{σ c}

𝛎 - Poisson's Ratio?σ_r - Radial Stress?du - Increase in Radial Width?dr - Initial Radial Width?E - Modulus Of Elasticity Of Disc?σ_c - Circumferential Stress?

Poisson's ratio given initial radial width of disc Example

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

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

Here is how the Poisson's ratio given initial radial width of disc equation looks like.

1.1367 = \frac{100 - ((\frac{3.4}{3}) \cdot 8)}{80}

1.1367 = \frac{100N/m² - ((\frac{3.4mm}{3mm}) \cdot 8N/m²)}{80N/m²}

1.1367 = \frac{100 - ((\frac{3.4}{3}) \cdot 8)}{80}

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Strength of Materials » fx Poisson's ratio given initial radial width of disc

Poisson's ratio given initial radial width of disc Solution

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

FIRST Step Consider the formula

𝛎 = \frac{σ r - ((\frac{du}{dr}) \cdot E)}{σ c}

Next Step Substitute values of Variables

∴

𝛎 = \frac{100N/m² - ((\frac{3.4mm}{3mm}) \cdot 8N/m²)}{80N/m²}

Next Step Convert Units

∴

𝛎 = \frac{100Pa - ((\frac{0.0034m}{0.003m}) \cdot 8Pa)}{80Pa}

Next Step Prepare to Evaluate

∴

𝛎 = \frac{100 - ((\frac{0.0034}{0.003}) \cdot 8)}{80}

Next Step Evaluate

∴

𝛎 = 1.13666666666667

LAST Step Rounding Answer

∴

𝛎 = 1.1367

Poisson's ratio given initial radial width 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

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

Increase in Radial Width

Increase in Radial Width is the increase in radial width due to strain.

Symbol: du

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Increase in Radial Width

Open Variable

Initial Radial Width

Initial Radial Width is the radial width without any strain.

Symbol: dr

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Initial Radial Width

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

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

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 radius of disc

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

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 initial radial width of disc?

Poisson's ratio given initial radial width of disc evaluator uses Poisson's Ratio = (Radial Stress-((Increase in Radial Width/Initial Radial Width)*Modulus Of Elasticity Of Disc))/(Circumferential Stress) to evaluate the Poisson's Ratio, Poisson's ratio given initial radial width of disc formula is defined as a measure of the relationship between radial and circumferential stresses in a rotating disc, indicating how material deforms in response to applied forces. Poisson's Ratio is denoted by 𝛎 symbol.

How to evaluate Poisson's ratio given initial radial width of disc using this online evaluator? To use this online evaluator for Poisson's ratio given initial radial width of disc, enter Radial Stress (σ_r), Increase in Radial Width (du), Initial Radial Width (dr), Modulus Of Elasticity Of Disc (E) & Circumferential Stress (σ_c) and hit the calculate button.

FAQs on Poisson's ratio given initial radial width of disc

What is the formula to find Poisson's ratio given initial radial width of disc?

The formula of Poisson's ratio given initial radial width of disc is expressed as Poisson's Ratio = (Radial Stress-((Increase in Radial Width/Initial Radial Width)*Modulus Of Elasticity Of Disc))/(Circumferential Stress). Here is an example- 1.136667 = (100-((0.0034/0.003)*8))/(80).

How to calculate Poisson's ratio given initial radial width of disc?

With Radial Stress (σ_r), Increase in Radial Width (du), Initial Radial Width (dr), Modulus Of Elasticity Of Disc (E) & Circumferential Stress (σ_c) we can find Poisson's ratio given initial radial width of disc using the formula - Poisson's Ratio = (Radial Stress-((Increase in Radial Width/Initial Radial Width)*Modulus Of Elasticity Of Disc))/(Circumferential 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=(Circumferential Stress-((Increase in Radius/Radius of Disc)*Modulus of Elasticity of Disc))/Radial Stress

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