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

✖Strain in thin shell is simply the measure of how much an object is stretched or deformed.ⓘ Strain in thin shell [ε]			+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%
✖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%

✖Hoop Stress in Thin shell is the circumferential stress in a cylinder.ⓘ Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio [σ_θ]

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

σ_θ = (ε/(1-𝛎))*E --> (3/(1-0.3))*10000000

Evaluating ... ...

σ_θ = 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 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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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)

< Hoop stress Calculators

Hoop stress given circumferential strain

LaTeX Go Hoop Stress in Thin shell = (Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell)+(Poisson's Ratio*Longitudinal Stress Thick Shell)

Hoop stress in thin cylindrical vessel given Longitudinal strain

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

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

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

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

LaTeX Go

Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell
σ_θ = (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 in thin spherical shell given strain in any one direction and Poisson's ratio?

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

How to calculate Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio using this online calculator? To use this online calculator for Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio, 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 in thin spherical shell given strain in any one direction and Poisson's ratio calculation can be explained with given input values -> 4.3E-5 = (3/(1-0.3))*10000000.

FAQ

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

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

Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio 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 in thin spherical shell given strain in any one direction and Poisson's ratio, 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 3 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
Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell
Hoop Stress in Thin shell = (Internal Pressure in thin shell*Inner Diameter of Cylinderical Vessel)/(2*Thickness Of Thin Shell*Efficiency of Longitudinal Joint)

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