Hoop stress induced in thin spherical shell given strain in any one direction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell
σθ = (ε/(1-𝛎))*E
This formula uses 4 Variables
Variables Used
Hoop Stress in Thin shell - (Measured in Pascal) - Hoop Stress in Thin shell is the circumferential stress in a cylinder.
Strain in thin shell - Strain in thin shell is simply the measure of how much an object is stretched or deformed.
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.
STEP 1: Convert Input(s) to Base Unit
Strain in thin shell: 3 --> No Conversion Required
Poisson's Ratio: 0.3 --> No Conversion Required
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σθ = (ε/(1-𝛎))*E --> (3/(1-0.3))*10000000
Evaluating ... ...
σθ = 42857142.8571429
STEP 3: Convert Result to Output's Unit
42857142.8571429 Pascal -->42.8571428571429 Megapascal (Check conversion here)
FINAL ANSWER
42.8571428571429 42.85714 Megapascal <-- Hoop Stress in Thin shell
(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)

Hoop stress induced in thin spherical shell given strain in any one direction Formula

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

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 Hoop stress induced in thin spherical shell given strain in any one direction?

Hoop stress induced in thin spherical shell given strain in any one direction calculator uses Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell to calculate the Hoop Stress in Thin shell, The Hoop stress induced in thin spherical shell given strain in any one direction formula is defined as the force over area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall. Hoop Stress in Thin shell is denoted by σθ symbol.

How to calculate Hoop stress induced in thin spherical shell given strain in any one direction using this online calculator? To use this online calculator for Hoop stress induced in thin spherical shell given strain in any one direction, enter Strain in thin shell (ε), Poisson's Ratio (𝛎) & Modulus of Elasticity Of Thin Shell (E) and hit the calculate button. Here is how the Hoop stress induced in thin spherical shell given strain in any one direction calculation can be explained with given input values -> 4.3E-5 = (3/(1-0.3))*10000000.

FAQ

What is Hoop stress induced in thin spherical shell given strain in any one direction?
The Hoop stress induced in thin spherical shell given strain in any one direction formula is defined as the force over area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall and is represented as σθ = (ε/(1-𝛎))*E or Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell. Strain in thin shell is simply the measure of how much an object is stretched or deformed, 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 is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
How to calculate Hoop stress induced in thin spherical shell given strain in any one direction?
The Hoop stress induced in thin spherical shell given strain in any one direction formula is defined as the force over area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall is calculated using Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell. To calculate Hoop stress induced in thin spherical shell given strain in any one direction, you need Strain in thin shell (ε), Poisson's Ratio (𝛎) & Modulus of Elasticity Of Thin Shell (E). With our tool, you need to enter the respective value for Strain in thin shell, Poisson's Ratio & Modulus of Elasticity Of 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 Hoop Stress in Thin shell?
In this formula, Hoop Stress in Thin shell uses Strain in thin shell, Poisson's Ratio & Modulus of Elasticity Of Thin Shell. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell
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