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

✖The Volumetric Strain is the ratio of change in volume to original volume.ⓘ Volumetric Strain [ε_v]			+10% -10%
✖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.ⓘ Modulus of Elasticity Of Thin Shell [E]			+10% -10%
✖Thickness of Thin Shell is the distance through an object.ⓘ Thickness of Thin Shell [t]			+10% -10%
✖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.ⓘ Internal Pressure in thin shell [P_i]			+10% -10%
✖Diameter of Shell is the maximum width of cylinder in transverse direction.ⓘ Diameter of Shell [D]			+10% -10%

✖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.ⓘ Poisson's ratio given volumetric strain of thin cylindrical shell [𝛎]

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Formula

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Poisson's ratio given volumetric strain of thin cylindrical shell

Formula

`"𝛎" = (5/2)-("ε"_{"v"}*2*"E"*"t")/("P"_{"i"}*"D")`

Example

`"2.425974"=(5/2)-("30"*2*"10MPa"*"3.8mm")/("14MPa"*"2200mm")`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
𝛎 = (5/2)-(ε_v*2*E*t)/(P_i*D)
This formula uses 6 Variables

Variables Used

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.
Volumetric Strain - The Volumetric Strain is the ratio of change in volume to original volume.
Modulus of Elasticity Of Thin Shell - (Measured in Pascal) - 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.
Thickness of Thin Shell - (Measured in Meter) - Thickness of Thin Shell is the distance through an object.
Internal Pressure in thin shell - (Measured in Pascal) - 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.
Diameter of Shell - (Measured in Meter) - Diameter of Shell is the maximum width of cylinder in transverse direction.

STEP 1: Convert Input(s) to Base Unit

Volumetric Strain: 30 --> No Conversion Required
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Thickness of Thin Shell: 3.8 Millimeter --> 0.0038 Meter (Check conversion here)
Internal Pressure in thin shell: 14 Megapascal --> 14000000 Pascal (Check conversion here)
Diameter of Shell: 2200 Millimeter --> 2.2 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛎 = (5/2)-(ε_v*2*E*t)/(P_i*D) --> (5/2)-(30*2*10000000*0.0038)/(14000000*2.2)

Evaluating ... ...

𝛎 = 2.42597402597403

STEP 3: Convert Result to Output's Unit

2.42597402597403 --> No Conversion Required

FINAL ANSWER

2.42597402597403 ≈ 2.425974 <-- Poisson's Ratio

(Calculation completed in 00.005 seconds)

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< 7 Poisson's Ratio Calculators

Poisson's ratio given change in length of cylindrical shell

Go 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 given circumferential strain

Go 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))

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

Go 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 given longitudinal strain and internal fluid pressure in vessel

Go Poisson's Ratio = (1/2)-((Longitudinal Strain*2*Thickness of Thin Shell*Modulus of Elasticity Of Thin Shell)/((Internal Pressure in thin shell*Inner Diameter of Cylinder)))

Poisson's ratio given volumetric strain of thin cylindrical shell

Go 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)

Poisson's ratio given circumferential strain and hoop stress

Go Poisson's Ratio = (Hoop Stress in Thin shell-(Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Longitudinal Stress Thick Shell

Poisson's ratio given Longitudinal strain

Go Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell)

Poisson's ratio given volumetric strain of thin cylindrical shell 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)
𝛎 = (5/2)-(ε_v*2*E*t)/(P_i*D)

What is the relation between lateral strain and longitudinal strain?

Lateral strain is defined as the ratio of decrease in the length of the bar in the perpendicular direction of applied load to that of the original length (gauge length). Poisson's ratio is the ratio of lateral strain to that of the longitudinal strain is termed Poisson's ratio and it is represented by ϻ or 1/m.

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

Poisson's ratio given volumetric strain of thin cylindrical shell calculator 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 calculate 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 calculate Poisson's ratio given volumetric strain of thin cylindrical shell using this online calculator? To use this online calculator 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. Here is how the Poisson's ratio given volumetric strain of thin cylindrical shell calculation can be explained with given input values -> 2.425974 = (5/2)-(30*2*10000000*0.0038)/(14000000*2.2).

FAQ

What is Poisson's ratio given volumetric strain of thin cylindrical shell?

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 and is represented as 𝛎 = (5/2)-(ε_v*2*E*t)/(P_i*D) or 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). The Volumetric Strain is the ratio of change in volume to original volume, 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, Thickness of Thin Shell is the distance through an object, 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 & Diameter of Shell is the maximum width of cylinder in transverse direction.

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

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 is calculated using 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 calculate Poisson's ratio given volumetric strain of thin cylindrical shell, you need 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). With our tool, you need to enter the respective value for Volumetric Strain, Modulus of Elasticity Of Thin Shell, Thickness of Thin Shell, Internal Pressure in thin shell & Diameter of Shell and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Poisson's Ratio?

In this formula, Poisson's Ratio uses Volumetric Strain, Modulus of Elasticity Of Thin Shell, Thickness of Thin Shell, Internal Pressure in thin shell & Diameter of Shell. We can use 6 other way(s) to calculate the same, which is/are as follows -

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))
Poisson's Ratio = (Hoop Stress in Thin shell-(Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Longitudinal Stress Thick Shell
Poisson's Ratio = (1/2)-((Longitudinal Strain*2*Thickness of Thin Shell*Modulus of Elasticity Of Thin Shell)/((Internal Pressure in thin shell*Inner Diameter of Cylinder)))
Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell)

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