Poisson's ratio given circumferential strain and hoop stress Calculator

✖Hoop Stress in Thin shell is the circumferential stress in a cylinder.ⓘ Hoop Stress in Thin shell [σ_θ]			+10% -10%
✖Circumferential strain Thin Shell represents the change in length.ⓘ Circumferential Strain Thin Shell [e₁]			+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%

✖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 circumferential strain and hoop stress [𝛎]

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Poisson's ratio given circumferential strain and hoop stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson's Ratio = (Hoop Stress in Thin shell-(Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Longitudinal Stress Thick Shell
𝛎 = (σ_θ-(e₁*E))/σ_l
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.
Hoop Stress in Thin shell - (Measured in Pascal) - Hoop Stress in Thin shell is the circumferential stress in a cylinder.
Circumferential Strain Thin Shell - Circumferential strain Thin Shell represents the change in 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.

STEP 1: Convert Input(s) to Base Unit

Hoop Stress in Thin shell: 25.03 Megapascal --> 25030000 Pascal (Check conversion here)
Circumferential Strain Thin Shell: 2.5 --> 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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛎 = (σ_θ-(e₁*E))/σ_l --> (25030000-(2.5*10000000))/80000

Evaluating ... ...

𝛎 = 0.375

STEP 3: Convert Result to Output's Unit

0.375 --> No Conversion Required

FINAL ANSWER

0.375 <-- Poisson's Ratio

(Calculation completed in 00.004 seconds)

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< Poisson's Ratio Calculators

Poisson's ratio given change in length of cylindrical shell

LaTeX 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

LaTeX 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

LaTeX 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 circumferential strain and hoop stress

LaTeX 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 Calculators

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

LaTeX 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 change in diameter of thin spherical shells

LaTeX Go 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)))

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

LaTeX Go 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 for thin spherical shell given strain in any one direction

LaTeX Go Poisson's Ratio = 1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell)

Poisson's ratio given circumferential strain and hoop stress Formula

LaTeX Go

Poisson's Ratio = (Hoop Stress in Thin shell-(Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Longitudinal Stress Thick Shell
𝛎 = (σ_θ-(e₁*E))/σ_l

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 circumferential strain and hoop stress?

Poisson's ratio given circumferential strain and hoop stress calculator uses Poisson's Ratio = (Hoop Stress in Thin shell-(Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Longitudinal Stress Thick Shell to calculate the Poisson's Ratio, Poisson's ratio given circumferential strain and hoop stress 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 circumferential strain and hoop stress using this online calculator? To use this online calculator for Poisson's ratio given circumferential strain and hoop stress, enter Hoop Stress in Thin shell (σ_θ), Circumferential Strain Thin Shell (e₁), Modulus of Elasticity Of Thin Shell (E) & Longitudinal Stress Thick Shell (σ_l) and hit the calculate button. Here is how the Poisson's ratio given circumferential strain and hoop stress calculation can be explained with given input values -> 0.375 = (25030000-(2.5*10000000))/80000.

FAQ

What is Poisson's ratio given circumferential strain and hoop stress?

Poisson's ratio given circumferential strain and hoop stress 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 = (σ_θ-(e₁*E))/σ_l or Poisson's Ratio = (Hoop Stress in Thin shell-(Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Longitudinal Stress Thick Shell. Hoop Stress in Thin shell is the circumferential stress in a cylinder, Circumferential strain Thin Shell represents the change in 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.

How to calculate Poisson's ratio given circumferential strain and hoop stress?

Poisson's ratio given circumferential strain and hoop stress 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 = (Hoop Stress in Thin shell-(Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Longitudinal Stress Thick Shell. To calculate Poisson's ratio given circumferential strain and hoop stress, you need Hoop Stress in Thin shell (σ_θ), Circumferential Strain Thin Shell (e₁), Modulus of Elasticity Of Thin Shell (E) & Longitudinal Stress Thick Shell (σ_l). With our tool, you need to enter the respective value for Hoop Stress in Thin shell, Circumferential Strain Thin Shell, Modulus of Elasticity Of Thin Shell & Longitudinal Stress Thick 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 Hoop Stress in Thin shell, Circumferential Strain Thin Shell, Modulus of Elasticity Of Thin Shell & Longitudinal Stress Thick Shell. We can use 3 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))

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