Poisson's ratio given Longitudinal strain Calculator

✖The Longitudinal Strain is ratio of change in length to original length.ⓘ Longitudinal Strain [ε_longitudinal]			+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%
✖Longitudinal Stress Thick Shell is defined as the stress produced when a pipe is subjected to internal pressure.ⓘ Longitudinal Stress Thick Shell [σ_l]			+10% -10%
✖Hoop Stress in Thin shell is the circumferential stress in a cylinder.ⓘ Hoop Stress in Thin shell [σ_θ]			+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 Longitudinal strain [𝛎]

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Formula

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Poisson's ratio given Longitudinal strain

Formula

`"𝛎" = (-("ε"_{"longitudinal"}*"E")+"σ"_{"l"})/("σ"_{"θ"})`

Example

`"-15.977627"=(-("40"*"10MPa")+"0.08MPa")/("25.03MPa")`

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Poisson's ratio given Longitudinal strain Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell)
𝛎 = (-(ε_longitudinal*E)+σ_l)/(σ_θ)
This formula uses 5 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.
Longitudinal Strain - The Longitudinal Strain is ratio of change in length to original length.
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.
Longitudinal Stress Thick Shell - (Measured in Pascal) - Longitudinal Stress Thick Shell is defined as the stress produced when a pipe is subjected to internal pressure.
Hoop Stress in Thin shell - (Measured in Pascal) - Hoop Stress in Thin shell is the circumferential stress in a cylinder.

STEP 1: Convert Input(s) to Base Unit

Longitudinal Strain: 40 --> No Conversion Required
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Longitudinal Stress Thick Shell: 0.08 Megapascal --> 80000 Pascal (Check conversion here)
Hoop Stress in Thin shell: 25.03 Megapascal --> 25030000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛎 = (-(ε_longitudinal*E)+σ_l)/(σ_θ) --> (-(40*10000000)+80000)/(25030000)

Evaluating ... ...

𝛎 = -15.9776268477827

STEP 3: Convert Result to Output's Unit

-15.9776268477827 --> No Conversion Required

FINAL ANSWER

-15.9776268477827 ≈ -15.977627 <-- Poisson's Ratio

(Calculation completed in 00.004 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 Longitudinal strain Formula

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

What is meant by hoop stress?

The hoop stress, or tangential stress, is the stress around the circumference of the pipe due to a pressure gradient. The maximum hoop stress always occurs at the inner radius or the outer radius depending on the direction of the pressure gradient.

How to Calculate Poisson's ratio given Longitudinal strain?

Poisson's ratio given Longitudinal strain calculator uses Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell) to calculate 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 calculate Poisson's ratio given Longitudinal strain using this online calculator? To use this online calculator 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. Here is how the Poisson's ratio given Longitudinal strain calculation can be explained with given input values -> -15.977627 = (-(40*10000000)+80000)/(25030000).

FAQ

What is Poisson's ratio given Longitudinal strain?

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 and is represented as 𝛎 = (-(ε_longitudinal*E)+σ_l)/(σ_θ) or Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell). The Longitudinal Strain is ratio of change in length to original length, 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, Longitudinal Stress Thick Shell is defined as the stress produced when a pipe is subjected to internal pressure & Hoop Stress in Thin shell is the circumferential stress in a cylinder.

How to calculate Poisson's ratio given Longitudinal strain?

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 is calculated using Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell). To calculate Poisson's ratio given Longitudinal strain, you need Longitudinal Strain (ε_longitudinal), Modulus of Elasticity Of Thin Shell (E), Longitudinal Stress Thick Shell (σ_l) & Hoop Stress in Thin shell (σ_θ). With our tool, you need to enter the respective value for Longitudinal Strain, Modulus of Elasticity Of Thin Shell, Longitudinal Stress Thick Shell & Hoop Stress in Thin 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 Longitudinal Strain, Modulus of Elasticity Of Thin Shell, Longitudinal Stress Thick Shell & Hoop Stress in Thin 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 = (5/2)-(Volumetric Strain*2*Modulus of Elasticity Of Thin Shell*Thickness of Thin Shell)/(Internal Pressure in thin shell*Diameter of Shell)

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