Poisson's ratio for thick spherical shell given compressive radial strain Solution

STEP 0: Pre-Calculation Summary
Formula Used
Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure))
𝛎 = 1/((2*σθ)/((E*εcompressive)-Pv))
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 on thick shell - (Measured in Pascal) - Hoop Stress on thick shell is the circumferential stress in a cylinder.
Modulus of Elasticity Of Thick Shell - (Measured in Pascal) - Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
Compressive Strain - The Compressive Strain is the ratio of change in length to the original length of the body when subjected to a compressive load.
Radial Pressure - (Measured in Pascal per Square Meter) - Radial Pressure is pressure towards or away from the central axis of a component.
STEP 1: Convert Input(s) to Base Unit
Hoop Stress on thick shell: 0.002 Megapascal --> 2000 Pascal (Check conversion ​here)
Modulus of Elasticity Of Thick Shell: 2.6 Megapascal --> 2600000 Pascal (Check conversion ​here)
Compressive Strain: 0.1 --> No Conversion Required
Radial Pressure: 0.014 Megapascal per Square Meter --> 14000 Pascal per Square Meter (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝛎 = 1/((2*σθ)/((E*εcompressive)-Pv)) --> 1/((2*2000)/((2600000*0.1)-14000))
Evaluating ... ...
𝛎 = 61.5
STEP 3: Convert Result to Output's Unit
61.5 --> No Conversion Required
FINAL ANSWER
61.5 <-- Poisson's Ratio
(Calculation completed in 00.004 seconds)

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Thick Spherical Shells Calculators

Mass of thick spherical shell given compressive radial strain
​ LaTeX ​ Go Mass Of Shell = (2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)
Hoop stress on thick spherical shell given compressive radial strain
​ LaTeX ​ Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)*Mass Of Shell/2
Radial pressure on thick spherical shell given compressive radial strain
​ LaTeX ​ Go Radial Pressure = (Adjusted design value*Compressive Strain)-(2*Hoop Stress on thick shell/Mass Of Shell)
Compressive radial strain for thick spherical shells
​ LaTeX ​ Go Compressive Strain = (Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Adjusted design value

Poisson's ratio for thick spherical shell given compressive radial strain Formula

​LaTeX ​Go
Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure))
𝛎 = 1/((2*σθ)/((E*εcompressive)-Pv))

What is meant by hoop stress?

The hoop stress is the force over the area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall.

How to Calculate Poisson's ratio for thick spherical shell given compressive radial strain?

Poisson's ratio for thick spherical shell given compressive radial strain calculator uses Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)) to calculate the Poisson's Ratio, Poisson's ratio for thick spherical shell given compressive radial strain formula is defined as the negative of the ratio of transverse strain to lateral or axial strain. Poisson's Ratio is denoted by 𝛎 symbol.

How to calculate Poisson's ratio for thick spherical shell given compressive radial strain using this online calculator? To use this online calculator for Poisson's ratio for thick spherical shell given compressive radial strain, enter Hoop Stress on thick shell θ), Modulus of Elasticity Of Thick Shell (E), Compressive Strain compressive) & Radial Pressure (Pv) and hit the calculate button. Here is how the Poisson's ratio for thick spherical shell given compressive radial strain calculation can be explained with given input values -> 61.5 = 1/((2*2000)/((2600000*0.1)-14000)).

FAQ

What is Poisson's ratio for thick spherical shell given compressive radial strain?
Poisson's ratio for thick spherical shell given compressive radial strain formula is defined as the negative of the ratio of transverse strain to lateral or axial strain and is represented as 𝛎 = 1/((2*σθ)/((E*εcompressive)-Pv)) or Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)). Hoop Stress on thick shell is the circumferential stress in a cylinder, Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it, The Compressive Strain is the ratio of change in length to the original length of the body when subjected to a compressive load & Radial Pressure is pressure towards or away from the central axis of a component.
How to calculate Poisson's ratio for thick spherical shell given compressive radial strain?
Poisson's ratio for thick spherical shell given compressive radial strain formula is defined as the negative of the ratio of transverse strain to lateral or axial strain is calculated using Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)). To calculate Poisson's ratio for thick spherical shell given compressive radial strain, you need Hoop Stress on thick shell θ), Modulus of Elasticity Of Thick Shell (E), Compressive Strain compressive) & Radial Pressure (Pv). With our tool, you need to enter the respective value for Hoop Stress on thick shell, Modulus of Elasticity Of Thick Shell, Compressive Strain & Radial Pressure 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 on thick shell, Modulus of Elasticity Of Thick Shell, Compressive Strain & Radial Pressure. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Poisson's Ratio = (1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)
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