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 = (-(εlongitudinal*E)+σl)/(σθ)
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 = (-(εlongitudinal*E)+σl)/(σθ) --> (-(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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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 Longitudinal strain Formula

​LaTeX ​Go
Poisson's Ratio = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Hoop Stress in Thin shell)
𝛎 = (-(εlongitudinal*E)+σl)/(σθ)

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 longitudinal), Modulus of Elasticity Of Thin Shell (E), Longitudinal Stress Thick Shell l) & Hoop Stress in Thin shell 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 = (-(εlongitudinal*E)+σl)/(σθ) 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 longitudinal), Modulus of Elasticity Of Thin Shell (E), Longitudinal Stress Thick Shell l) & Hoop Stress in Thin shell 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 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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