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

✖Change in Length is after the application of force, change in the dimensions of the object.ⓘ Change in Length [ΔL]			+10% -10%
✖Thickness of Thin Shell is the distance through an object.ⓘ Thickness of Thin Shell [t]			+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%
✖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%
✖Length Of Cylindrical Shell is the measurement or extent of cylinder from end to end.ⓘ Length Of Cylindrical Shell [L_cylinder]			+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 change in length of cylindrical shell [𝛎]

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Poisson's ratio given change in length of cylindrical shell

Formula

`"𝛎" = (1/2)-(("ΔL"*(2*"t"*"E"))/(("P"_{"i"}*"D"*"L"_{"cylinder"})))`

Example

`"0.499095"=(1/2)-(("1100mm"*(2*"3.8mm"*"10MPa"))/(("14MPa"*"2200mm"*"3000mm")))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
𝛎 = (1/2)-((ΔL*(2*t*E))/((P_i*D*L_cylinder)))
This formula uses 7 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.
Change in Length - (Measured in Meter) - Change in Length is after the application of force, change in the dimensions of the object.
Thickness of Thin Shell - (Measured in Meter) - Thickness of Thin Shell is the distance through an object.
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.
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.
Length Of Cylindrical Shell - (Measured in Meter) - Length Of Cylindrical Shell is the measurement or extent of cylinder from end to end.

STEP 1: Convert Input(s) to Base Unit

Change in Length: 1100 Millimeter --> 1.1 Meter (Check conversion here)
Thickness of Thin Shell: 3.8 Millimeter --> 0.0038 Meter (Check conversion here)
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (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)
Length Of Cylindrical Shell: 3000 Millimeter --> 3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛎 = (1/2)-((ΔL*(2*t*E))/((P_i*D*L_cylinder))) --> (1/2)-((1.1*(2*0.0038*10000000))/((14000000*2.2*3)))

Evaluating ... ...

𝛎 = 0.499095238095238

STEP 3: Convert Result to Output's Unit

0.499095238095238 --> No Conversion Required

FINAL ANSWER

0.499095238095238 ≈ 0.499095 <-- Poisson's Ratio

(Calculation completed in 00.022 seconds)

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Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Effect of Internal Pressure on Dimension of Thin Cylindrical Shell » Poisson's Ratio » Poisson's ratio given change in length of cylindrical shell

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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 change in length of cylindrical shell Formula

What is volumetric stress?

When the deforming force or applied force acts from all dimensions resulting in the change of volume of the object then such stress is called volumetric stress or Bulk stress. In short, when the volume of the body changes due to the deforming force it is termed Volume stress.

How to Calculate Poisson's ratio given change in length of cylindrical shell?

Poisson's ratio given change in length of cylindrical shell calculator uses 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))) to calculate the Poisson's Ratio, The Poisson's ratio given change in length of 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 change in length of cylindrical shell using this online calculator? To use this online calculator for Poisson's ratio given change in length of cylindrical shell, enter Change in Length (ΔL), Thickness of Thin Shell (t), Modulus of Elasticity Of Thin Shell (E), Internal Pressure in thin shell (P_i), Diameter of Shell (D) & Length Of Cylindrical Shell (L_cylinder) and hit the calculate button. Here is how the Poisson's ratio given change in length of cylindrical shell calculation can be explained with given input values -> 0.499095 = (1/2)-((1.1*(2*0.0038*10000000))/((14000000*2.2*3))).

FAQ

What is Poisson's ratio given change in length of cylindrical shell?

The Poisson's ratio given change in length of 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 = (1/2)-((ΔL*(2*t*E))/((P_i*D*L_cylinder))) or 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))). Change in Length is after the application of force, change in the dimensions of the object, Thickness of Thin Shell is the distance through an object, 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, 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 & Length Of Cylindrical Shell is the measurement or extent of cylinder from end to end.

How to calculate Poisson's ratio given change in length of cylindrical shell?

The Poisson's ratio given change in length of 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 = (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))). To calculate Poisson's ratio given change in length of cylindrical shell, you need Change in Length (ΔL), Thickness of Thin Shell (t), Modulus of Elasticity Of Thin Shell (E), Internal Pressure in thin shell (P_i), Diameter of Shell (D) & Length Of Cylindrical Shell (L_cylinder). With our tool, you need to enter the respective value for Change in Length, Thickness of Thin Shell, Modulus of Elasticity Of Thin Shell, Internal Pressure in thin shell, Diameter of Shell & Length Of Cylindrical 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 Change in Length, Thickness of Thin Shell, Modulus of Elasticity Of Thin Shell, Internal Pressure in thin shell, Diameter of Shell & Length Of Cylindrical 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)-((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 = (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 = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell)

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