Strain in any one direction of thin spherical shell Calculator

✖Hoop Stress in Thin shell is the circumferential stress in a cylinder.ⓘ Hoop Stress in Thin shell [σ_θ]			+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%
✖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 [𝛎]			+10% -10%

✖Strain in thin shell is simply the measure of how much an object is stretched or deformed.ⓘ Strain in any one direction of thin spherical shell [ε]

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Formula

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Strain in any one direction of thin spherical shell

Formula

`"ε" = ("σ"_{"θ"}/"E")*(1-"𝛎")`

Example

`"1.7521"=("25.03MPa"/"10MPa")*(1-"0.3")`

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Strain in any one direction of thin spherical shell Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain in thin shell = (Hoop Stress in Thin shell/Modulus of Elasticity Of Thin Shell)*(1-Poisson's Ratio)
ε = (σ_θ/E)*(1-𝛎)
This formula uses 4 Variables

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Hoop Stress in Thin shell: 25.03 Megapascal --> 25030000 Pascal (Check conversion here)
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε = (σ_θ/E)*(1-𝛎) --> (25030000/10000000)*(1-0.3)

Evaluating ... ...

ε = 1.7521

STEP 3: Convert Result to Output's Unit

1.7521 --> No Conversion Required

FINAL ANSWER

1.7521 <-- Strain in thin shell

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Change in Dimension of Thin Spherical Shell due to Internal Pressure » Strain in any one direction of thin spherical shell

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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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)

Strain in any one direction of thin spherical shell Formula

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

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 Strain in any one direction of thin spherical shell?

Strain in any one direction of thin spherical shell calculator uses Strain in thin shell = (Hoop Stress in Thin shell/Modulus of Elasticity Of Thin Shell)*(1-Poisson's Ratio) to calculate the Strain in thin shell, The Strain in any one direction of thin spherical shell formula is defined as simply the measure of how much an object is stretched or deformed. Strain in thin shell is denoted by ε symbol.

How to calculate Strain in any one direction of thin spherical shell using this online calculator? To use this online calculator for Strain in any one direction of thin spherical shell, enter Hoop Stress in Thin shell (σ_θ), Modulus of Elasticity Of Thin Shell (E) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Strain in any one direction of thin spherical shell calculation can be explained with given input values -> 1.7521 = (25030000/10000000)*(1-0.3).

FAQ

What is Strain in any one direction of thin spherical shell?

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

How to calculate Strain in any one direction of thin spherical shell?

The Strain in any one direction of thin spherical shell formula is defined as simply the measure of how much an object is stretched or deformed is calculated using Strain in thin shell = (Hoop Stress in Thin shell/Modulus of Elasticity Of Thin Shell)*(1-Poisson's Ratio). To calculate Strain in any one direction of thin spherical shell, you need Hoop Stress in Thin shell (σ_θ), Modulus of Elasticity Of Thin Shell (E) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Hoop Stress in Thin shell, Modulus of Elasticity Of Thin Shell & Poisson's Ratio 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 Strain in thin shell?

In this formula, Strain in thin shell uses Hoop Stress in Thin shell, Modulus of Elasticity Of Thin Shell & Poisson's Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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