Poisson's ratio given change in diameter of thin spherical shells Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
𝛎 = 1-(∆d*(4*t*E)/(Pi*(D^2)))
This formula uses 6 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.
Change in Diameter - (Measured in Meter) - The Change in Diameter is the difference between the initial and final diameter.
Thickness Of Thin Spherical Shell - (Measured in Meter) - Thickness Of Thin Spherical Shell is the distance through an object.
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.
Internal Pressure - (Measured in Pascal) - Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature.
Diameter of Sphere - (Measured in Meter) - Diameter of Sphere, is a chord that runs through the center point of the circle. It is the longest possible chord of any circle. The center of a circle is the midpoint of its diameter.
STEP 1: Convert Input(s) to Base Unit
Change in Diameter: 50.5 Millimeter --> 0.0505 Meter (Check conversion here)
Thickness Of Thin Spherical Shell: 12 Millimeter --> 0.012 Meter (Check conversion here)
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Internal Pressure: 0.053 Megapascal --> 53000 Pascal (Check conversion here)
Diameter of Sphere: 1500 Millimeter --> 1.5 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝛎 = 1-(∆d*(4*t*E)/(Pi*(D^2))) --> 1-(0.0505*(4*0.012*10000000)/(53000*(1.5^2)))
Evaluating ... ...
𝛎 = 0.796729559748428
STEP 3: Convert Result to Output's Unit
0.796729559748428 --> No Conversion Required
FINAL ANSWER
0.796729559748428 0.79673 <-- Poisson's Ratio
(Calculation completed in 00.004 seconds)

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17 Change in Dimension of Thin Spherical Shell due to Internal Pressure Calculators

Diameter of spherical shell given change in diameter of thin spherical shells
Go Diameter of Sphere = sqrt((Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Internal Pressure))
Thickness of spherical shell given change in diameter of thin spherical shells
Go Thickness Of Thin Spherical Shell = ((Internal Pressure*(Diameter of Sphere^2))/(4*Change in Diameter*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)
Modulus of elasticity given change in diameter of thin spherical shells
Go Modulus of Elasticity Of Thin Shell = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Change in Diameter))*(1-Poisson's Ratio)
Change in diameter of thin spherical shell
Go Change in Diameter = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)
Modulus of elasticity for thin spherical shell given strain and internal fluid pressure
Go Modulus of Elasticity Of Thin Shell = ((Internal Pressure*Diameter of Sphere)/(4*Thickness Of Thin Spherical Shell*Strain in thin shell))*(1-Poisson's Ratio)
Internal fluid pressure in thin spherical shell given strain in any one direction
Go Internal Pressure = (Strain in thin shell*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere)
Internal fluid pressure given change in diameter of thin spherical shells
Go Internal Pressure = (Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere^2)
Thickness of thin spherical shell given strain in any one direction
Go Thickness Of Thin Spherical Shell = ((Internal Pressure*Diameter of Sphere)/(4*Strain in thin shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)
Diameter of thin spherical shell given strain in any one direction
Go Diameter of Sphere = (Strain in thin shell*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Internal Pressure)
Poisson's ratio given change in diameter of thin spherical shells
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)))
Strain in thin spherical shell given internal fluid pressure
Go Strain in thin shell = ((Internal Pressure*Diameter of Sphere)/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)
Poisson's ratio for thin spherical shell given strain and internal fluid pressure
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))
Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio
Go Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell
Modulus of elasticity of thin spherical shell given strain in any one direction
Go Modulus of Elasticity Of Thin Shell = (Hoop Stress in Thin shell/Strain in thin shell)*(1-Poisson's Ratio)
Hoop stress induced in thin spherical shell given strain in any one direction
Go Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell
Strain in any one direction of thin spherical shell
Go Strain in thin shell = (Hoop Stress in Thin shell/Modulus of Elasticity Of Thin Shell)*(1-Poisson's Ratio)
Poisson's ratio for thin spherical shell given strain in any one direction
Go Poisson's Ratio = 1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell)

Poisson's ratio given change in diameter of thin spherical shells Formula

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)))
𝛎 = 1-(∆d*(4*t*E)/(Pi*(D^2)))

How do you reduce stress hoop?

We can suggest that the most efficient method is to apply double cold expansion with high interferences along with axial compression with strain equal to 0.5%. This technique helps to reduce the absolute value of hoop residual stresses by 58%, and decrease radial stresses by 75%.

How to Calculate Poisson's ratio given change in diameter of thin spherical shells?

Poisson's ratio given change in diameter of thin spherical shells calculator uses 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))) to calculate the Poisson's Ratio, The Poisson's ratio given change in diameter of thin spherical shells formula is defined as the ratio of the change in the width per unit width of a material, to the change in its length per unit length, as a result of strain. Poisson's Ratio is denoted by 𝛎 symbol.

How to calculate Poisson's ratio given change in diameter of thin spherical shells using this online calculator? To use this online calculator for Poisson's ratio given change in diameter of thin spherical shells, enter Change in Diameter (∆d), Thickness Of Thin Spherical Shell (t), Modulus of Elasticity Of Thin Shell (E), Internal Pressure (Pi) & Diameter of Sphere (D) and hit the calculate button. Here is how the Poisson's ratio given change in diameter of thin spherical shells calculation can be explained with given input values -> 0.79673 = 1-(0.0505*(4*0.012*10000000)/(53000*(1.5^2))).

FAQ

What is Poisson's ratio given change in diameter of thin spherical shells?
The Poisson's ratio given change in diameter of thin spherical shells formula is defined as the ratio of the change in the width per unit width of a material, to the change in its length per unit length, as a result of strain and is represented as 𝛎 = 1-(∆d*(4*t*E)/(Pi*(D^2))) or 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))). The Change in Diameter is the difference between the initial and final diameter, Thickness Of Thin Spherical Shell is the distance through an object, 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, Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature & Diameter of Sphere, is a chord that runs through the center point of the circle. It is the longest possible chord of any circle. The center of a circle is the midpoint of its diameter.
How to calculate Poisson's ratio given change in diameter of thin spherical shells?
The Poisson's ratio given change in diameter of thin spherical shells formula is defined as the ratio of the change in the width per unit width of a material, to the change in its length per unit length, as a result of strain is calculated using 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))). To calculate Poisson's ratio given change in diameter of thin spherical shells, you need Change in Diameter (∆d), Thickness Of Thin Spherical Shell (t), Modulus of Elasticity Of Thin Shell (E), Internal Pressure (Pi) & Diameter of Sphere (D). With our tool, you need to enter the respective value for Change in Diameter, Thickness Of Thin Spherical Shell, Modulus of Elasticity Of Thin Shell, Internal Pressure & Diameter of Sphere 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 Change in Diameter, Thickness Of Thin Spherical Shell, Modulus of Elasticity Of Thin Shell, Internal Pressure & Diameter of Sphere. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Poisson's Ratio = 1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell)
  • 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))
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