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

✖The Change in Diameter is the difference between the initial and final diameter.ⓘ Change in Diameter [∆d]			+10% -10%
✖Thickness Of Thin Spherical Shell is the distance through an object.ⓘ Thickness Of Thin Spherical Shell [t]			+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%
✖Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature.ⓘ Internal Pressure [P_i]			+10% -10%
✖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.ⓘ Diameter of Sphere [D]			+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 change in diameter of thin spherical shells [𝛎]

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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)/(P_i*(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: 173.9062 Millimeter --> 0.1739062 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)/(P_i*(D^2))) --> 1-(0.1739062*(4*0.012*10000000)/(53000*(1.5^2)))

Evaluating ... ...

𝛎 = 0.300000201257862

STEP 3: Convert Result to Output's Unit

0.300000201257862 --> No Conversion Required

FINAL ANSWER

0.300000201257862 ≈ 0.3 <-- Poisson's Ratio

(Calculation completed in 00.004 seconds)

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

Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio

LaTeX 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

LaTeX 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

LaTeX 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

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

< 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 change in diameter of thin spherical shells Formula

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)))
𝛎 = 1-(∆d*(4*t*E)/(P_i*(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 (P_i) & 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-(0.1739062*(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)/(P_i*(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 (P_i) & 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 3 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))
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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