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Poisson's ratio given Longitudinal strain Formula

GoPoisson's ratio for thin spherical shell given strain and internal fluid pressure Formula

GoPoisson's ratio for thin spherical shell given strain in any one direction 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{- (ε longitudinal \cdot E) + σ l}{σ θ}

𝛎 - Poisson's Ratio?ε_longitudinal - Longitudinal Strain?E - Modulus of Elasticity Of Thin Shell?σ_l - Longitudinal Stress Thick Shell?σ_θ - Hoop Stress in Thin shell?

Poisson's ratio given Longitudinal strain Example

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Here is how the Poisson's ratio given Longitudinal strain equation looks like with Values.

Here is how the Poisson's ratio given Longitudinal strain equation looks like with Units.

Here is how the Poisson's ratio given Longitudinal strain equation looks like.

-15.9776 = \frac{- (40 \cdot 10) + 0.08}{25.03}

-15.9776 = \frac{- (40 \cdot 10MPa) + 0.08MPa}{25.03MPa}

-15.9776 = \frac{- (40 \cdot 10) + 0.08}{25.03}

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Poisson's ratio given Longitudinal strain Solution

Follow our step by step solution on how to calculate Poisson's ratio given Longitudinal strain?

FIRST Step Consider the formula

𝛎 = \frac{- (ε longitudinal \cdot E) + σ l}{σ θ}

Next Step Substitute values of Variables

∴

𝛎 = \frac{- (40 \cdot 10MPa) + 0.08MPa}{25.03MPa}

Next Step Convert Units

∴

𝛎 = \frac{- (40 \cdot 1E+7Pa) + 80000Pa}{2.5E+7Pa}

Next Step Prepare to Evaluate

∴

𝛎 = \frac{- (40 \cdot 1E+7) + 80000}{2.5E+7}

Next Step Evaluate

∴

𝛎 = -15.9776268477827

LAST Step Rounding Answer

∴

𝛎 = -15.9776

Poisson's ratio given Longitudinal strain 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 can be positive or negative.

Formulas to find Poisson's Ratio

Longitudinal Strain

The Longitudinal Strain is ratio of change in length to original length.

Symbol: ε_longitudinal

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Longitudinal Strain

Modulus of Elasticity Of Thin Shell

Modulus of Elasticity Of Thin Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity Of Thin Shell

Longitudinal Stress Thick Shell

Longitudinal Stress Thick Shell is defined as the stress produced when a pipe is subjected to internal pressure.

Symbol: σ_l

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Longitudinal Stress Thick Shell

Hoop Stress in Thin shell

Hoop Stress in Thin shell is the circumferential stress in a cylinder.

Symbol: σ_θ

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Hoop Stress in Thin shell

Other Formulas to find Poisson's Ratio

Go Poisson's ratio for thin spherical shell given strain and internal fluid pressure

𝛎 = 1 - (ε \cdot \frac{4 \cdot t \cdot E}{P i \cdot D})

Go Poisson's ratio for thin spherical shell given strain in any one direction

𝛎 = 1 - (E \cdot \frac{ε}{σ θ})

Go Poisson's ratio given change in diameter of thin spherical shells

𝛎 = 1 - (∆d \cdot \frac{4 \cdot t \cdot E}{P i \cdot (D^{2})})

Go Poisson's ratio for thin cylindrical vessel given change in diameter

𝛎 = 2 \cdot (1 - \frac{∆d \cdot (2 \cdot t \cdot E)}{((P i \cdot ({D i}^{2})))})

How to Evaluate Poisson's ratio given Longitudinal strain?

Poisson's ratio given Longitudinal strain evaluator uses Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell) to evaluate the Poisson's Ratio, Poisson's ratio given Longitudinal strain is 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 Longitudinal strain using this online evaluator? To use this online evaluator for Poisson's ratio given Longitudinal strain, enter Longitudinal Strain (ε_longitudinal), Modulus of Elasticity Of Thin Shell (E), Longitudinal Stress Thick Shell (σ_l) & Hoop Stress in Thin shell (σ_θ) and hit the calculate button.

FAQs on Poisson's ratio given Longitudinal strain

What is the formula to find Poisson's ratio given Longitudinal strain?

The formula of Poisson's ratio given Longitudinal strain is expressed as Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell). Here is an example- -15.977627 = (-(40*10000000)+80000)/(25030000).

How to calculate Poisson's ratio given Longitudinal strain?

With Longitudinal Strain (ε_longitudinal), Modulus of Elasticity Of Thin Shell (E), Longitudinal Stress Thick Shell (σ_l) & Hoop Stress in Thin shell (σ_θ) we can find Poisson's ratio given Longitudinal strain using the formula - Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell).

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

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

Poisson's Ratio=1-(Strain in thin shell*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(Internal Pressure*Diameter of Sphere))
Poisson's Ratio=1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell)
Poisson's Ratio=1-(Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(Internal Pressure*(Diameter of Sphere^2)))

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Poisson's ratio given Longitudinal strain Formula

​GoPoisson's ratio for thin spherical shell given strain and internal fluid pressure Formula

​GoPoisson's ratio for thin spherical shell given strain in any one direction Formula

Poisson's ratio given Longitudinal strain Example

Poisson's ratio given Longitudinal strain Solution

Poisson's ratio given Longitudinal strain Formula Elements

Other Formulas to find Poisson's Ratio

How to Evaluate Poisson's ratio given Longitudinal strain?

FAQs on Poisson's ratio given Longitudinal strain

Variable Name

GoPoisson's ratio for thin spherical shell given strain and internal fluid pressure Formula

GoPoisson's ratio for thin spherical shell given strain in any one direction Formula