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 = (σθ-(e1*E))/σl
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 = (σθ-(e1*E))/σl --> (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 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Payal Priya
Birsa Institute of Technology (BIT), Sindri
Payal Priya has verified this Calculator and 1900+ more calculators!

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 circumferential strain and hoop stress Formula

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

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 θ), Circumferential strain Thin Shell (e1), Modulus of Elasticity Of Thin Shell (E) & Longitudinal Stress Thick Shell 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 = (σθ-(e1*E))/σl 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 θ), Circumferential strain Thin Shell (e1), Modulus of Elasticity Of Thin Shell (E) & Longitudinal Stress Thick Shell 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 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 = (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)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!