Poisson's ratio for thin spherical shell given strain in any one direction Calculator

✖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%
✖Strain in thin shell is simply the measure of how much an object is stretched or deformed.ⓘ Strain in thin shell [ε]			+10% -10%
✖Hoop Stress in Thin shell is the circumferential stress in a cylinder.ⓘ Hoop Stress in Thin shell [σ_θ]			+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 for thin spherical shell given strain in any one direction [𝛎]

⎘ Copy

👎

Formula

✖

Poisson's ratio for thin spherical shell given strain in any one direction

Formula

`"𝛎" = 1-("E"*"ε"/"σ"_{"θ"})`

Example

`"-0.198562"=1-("10MPa"*"3"/"25.03MPa")`

Calculator

LaTeX

Reset

👍

Download Strength of Materials Formula PDF

Poisson's ratio for thin spherical shell given strain in any one direction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson's Ratio = 1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell)
𝛎 = 1-(E*ε/σ_θ)
This formula uses 4 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.
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.
Strain in thin shell - Strain in thin shell is simply the measure of how much an object is stretched or deformed.
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

Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Strain in thin shell: 3 --> No Conversion Required
Hoop Stress in Thin shell: 25.03 Megapascal --> 25030000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛎 = 1-(E*ε/σ_θ) --> 1-(10000000*3/25030000)

Evaluating ... ...

𝛎 = -0.198561725928885

STEP 3: Convert Result to Output's Unit

-0.198561725928885 --> No Conversion Required

FINAL ANSWER

-0.198561725928885 ≈ -0.198562 <-- Poisson's Ratio

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Change in Dimension of Thin Spherical Shell due to Internal Pressure » Poisson's ratio for thin spherical shell given strain in any one direction

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!

< 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 for thin spherical shell given strain in any one direction Formula

Poisson's Ratio = 1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell)
𝛎 = 1-(E*ε/σ_θ)

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 for thin spherical shell given strain in any one direction?

Poisson's ratio for thin spherical shell given strain in any one direction calculator uses Poisson's Ratio = 1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell) to calculate the Poisson's Ratio, The Poisson's ratio for thin spherical shell given strain in any one direction 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 for thin spherical shell given strain in any one direction using this online calculator? To use this online calculator for Poisson's ratio for thin spherical shell given strain in any one direction, enter Modulus of Elasticity Of Thin Shell (E), Strain in thin shell (ε) & Hoop Stress in Thin shell (σ_θ) and hit the calculate button. Here is how the Poisson's ratio for thin spherical shell given strain in any one direction calculation can be explained with given input values -> -0.198562 = 1-(10000000*3/25030000).

FAQ

What is Poisson's ratio for thin spherical shell given strain in any one direction?

The Poisson's ratio for thin spherical shell given strain in any one direction 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-(E*ε/σ_θ) or Poisson's Ratio = 1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell). 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, Strain in thin shell is simply the measure of how much an object is stretched or deformed & Hoop Stress in Thin shell is the circumferential stress in a cylinder.

How to calculate Poisson's ratio for thin spherical shell given strain in any one direction?

The Poisson's ratio for thin spherical shell given strain in any one direction 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-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell). To calculate Poisson's ratio for thin spherical shell given strain in any one direction, you need Modulus of Elasticity Of Thin Shell (E), Strain in thin shell (ε) & Hoop Stress in Thin shell (σ_θ). With our tool, you need to enter the respective value for Modulus of Elasticity Of Thin Shell, Strain in thin 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 Modulus of Elasticity Of Thin Shell, Strain in thin shell & Hoop Stress in Thin shell. We can use 2 other way(s) to calculate the same, which is/are as follows -

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-(Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(Internal Pressure*(Diameter of Sphere^2)))

Home

FREE PDFs

🔍 Search