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Poisson's ratio given volumetric strain of thin cylindrical shell Formula

GoPoisson's ratio for thin cylindrical vessel given change in diameter Formula

GoPoisson's ratio given change in length of cylindrical shell 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{5}{2}) - \frac{ε v \cdot 2 \cdot E \cdot t}{P i \cdot D}

𝛎 - Poisson's Ratio?ε_v - Volumetric Strain?E - Modulus of Elasticity Of Thin Shell?t - Thickness of Thin Shell?P_i - Internal Pressure in thin shell?D - Diameter of Shell?

Poisson's ratio given volumetric strain of thin cylindrical shell Example

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Here is how the Poisson's ratio given volumetric strain of thin cylindrical shell equation looks like with Values.

Here is how the Poisson's ratio given volumetric strain of thin cylindrical shell equation looks like with Units.

Here is how the Poisson's ratio given volumetric strain of thin cylindrical shell equation looks like.

2.426 = (\frac{5}{2}) - \frac{30 \cdot 2 \cdot 10 \cdot 3.8}{14 \cdot 2200}

2.426 = (\frac{5}{2}) - \frac{30 \cdot 2 \cdot 10MPa \cdot 3.8mm}{14MPa \cdot 2200mm}

2.426 = (\frac{5}{2}) - \frac{30 \cdot 2 \cdot 10 \cdot 3.8}{14 \cdot 2200}

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Poisson's ratio given volumetric strain of thin cylindrical shell Solution

Follow our step by step solution on how to calculate Poisson's ratio given volumetric strain of thin cylindrical shell?

FIRST Step Consider the formula

𝛎 = (\frac{5}{2}) - \frac{ε v \cdot 2 \cdot E \cdot t}{P i \cdot D}

Next Step Substitute values of Variables

∴

𝛎 = (\frac{5}{2}) - \frac{30 \cdot 2 \cdot 10MPa \cdot 3.8mm}{14MPa \cdot 2200mm}

Next Step Convert Units

∴

𝛎 = (\frac{5}{2}) - \frac{30 \cdot 2 \cdot 1E+7Pa \cdot 0.0038m}{1.4E+7Pa \cdot 2.2m}

Next Step Prepare to Evaluate

∴

𝛎 = (\frac{5}{2}) - \frac{30 \cdot 2 \cdot 1E+7 \cdot 0.0038}{1.4E+7 \cdot 2.2}

Next Step Evaluate

∴

𝛎 = 2.42597402597403

LAST Step Rounding Answer

∴

𝛎 = 2.426

Poisson's ratio given volumetric strain of thin cylindrical shell 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

Volumetric Strain

The Volumetric Strain is the ratio of change in volume to original volume.

Symbol: ε_v

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Volumetric 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

Thickness of Thin Shell

Thickness of Thin Shell is the distance through an object.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Thin Shell

Internal Pressure in thin shell

Internal Pressure in thin shell is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature.

Symbol: P_i

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Internal Pressure in thin shell

Diameter of Shell

Diameter of Shell is the maximum width of cylinder in transverse direction.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shell

Other Formulas to find Poisson's Ratio

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})))})

Go Poisson's ratio given change in length of cylindrical shell

𝛎 = (\frac{1}{2}) - (\frac{ΔL \cdot (2 \cdot t \cdot E)}{(P i \cdot D \cdot L cylinder)})

Go Poisson's ratio given circumferential strain

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

Go Poisson's ratio given circumferential strain and hoop stress

𝛎 = \frac{σ θ - (e 1 \cdot E)}{σ l}

How to Evaluate Poisson's ratio given volumetric strain of thin cylindrical shell?

Poisson's ratio given volumetric strain of thin cylindrical shell evaluator uses Poisson's Ratio = (5/2)-(Volumetric Strain*2*Modulus of Elasticity Of Thin Shell*Thickness of Thin Shell)/(Internal Pressure in thin shell*Diameter of Shell) to evaluate the Poisson's Ratio, The Poisson's ratio given volumetric strain of thin cylindrical shell formula is defined as the deformation in the material in a direction perpendicular to the direction of the applied force. Poisson's Ratio is denoted by 𝛎 symbol.

How to evaluate Poisson's ratio given volumetric strain of thin cylindrical shell using this online evaluator? To use this online evaluator for Poisson's ratio given volumetric strain of thin cylindrical shell, enter Volumetric Strain (ε_v), Modulus of Elasticity Of Thin Shell (E), Thickness of Thin Shell (t), Internal Pressure in thin shell (P_i) & Diameter of Shell (D) and hit the calculate button.

FAQs on Poisson's ratio given volumetric strain of thin cylindrical shell

What is the formula to find Poisson's ratio given volumetric strain of thin cylindrical shell?

The formula of Poisson's ratio given volumetric strain of thin cylindrical shell is expressed as Poisson's Ratio = (5/2)-(Volumetric Strain*2*Modulus of Elasticity Of Thin Shell*Thickness of Thin Shell)/(Internal Pressure in thin shell*Diameter of Shell). Here is an example- 2.425974 = (5/2)-(30*2*10000000*0.0038)/(14000000*2.2).

How to calculate Poisson's ratio given volumetric strain of thin cylindrical shell?

With Volumetric Strain (ε_v), Modulus of Elasticity Of Thin Shell (E), Thickness of Thin Shell (t), Internal Pressure in thin shell (P_i) & Diameter of Shell (D) we can find Poisson's ratio given volumetric strain of thin cylindrical shell using the formula - Poisson's Ratio = (5/2)-(Volumetric Strain*2*Modulus of Elasticity Of Thin Shell*Thickness of Thin Shell)/(Internal Pressure in thin shell*Diameter of Shell).

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

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

Poisson's Ratio=2*(1-(Change in Diameter*(2*Thickness of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell*(Inner Diameter of Cylinder^2)))))
Poisson's Ratio=(1/2)-((Change in Length*(2*Thickness of Thin Shell*Modulus of Elasticity Of Thin Shell))/((Internal Pressure in thin shell*Diameter of Shell*Length Of Cylindrical Shell)))
Poisson's Ratio=(1/2)-((Circumferential strain Thin Shell*(2*Thickness of Thin Shell*Modulus of Elasticity Of Thin Shell))/(Internal Pressure in thin shell*Inner Diameter of Cylinder))

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: Unit

Poisson's ratio given volumetric strain of thin cylindrical shell Formula

​GoPoisson's ratio for thin cylindrical vessel given change in diameter Formula

​GoPoisson's ratio given change in length of cylindrical shell Formula

Poisson's ratio given volumetric strain of thin cylindrical shell Example

Poisson's ratio given volumetric strain of thin cylindrical shell Solution

Poisson's ratio given volumetric strain of thin cylindrical shell Formula Elements

Other Formulas to find Poisson's Ratio

How to Evaluate Poisson's ratio given volumetric strain of thin cylindrical shell?

FAQs on Poisson's ratio given volumetric strain of thin cylindrical shell

Variable Name

GoPoisson's ratio for thin cylindrical vessel given change in diameter Formula

GoPoisson's ratio given change in length of cylindrical shell Formula