Hoop stress given circumferential strain Calculator

✖Circumferential strain Thin Shell represents the change in length.ⓘ Circumferential Strain Thin Shell [e₁]			+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%
✖Longitudinal Stress Thick Shell is defined as the stress produced when a pipe is subjected to internal pressure.ⓘ Longitudinal Stress Thick Shell [σ_l]			+10% -10%

✖Hoop Stress in Thin shell is the circumferential stress in a cylinder.ⓘ Hoop stress given circumferential strain [σ_θ]

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Hoop stress given circumferential strain Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hoop Stress in Thin shell = (Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell)+(Poisson's Ratio*Longitudinal Stress Thick Shell)
σ_θ = (e₁*E)+(𝛎*σ_l)
This formula uses 5 Variables

Variables Used

Hoop Stress in Thin shell - (Measured in Pascal) - Hoop Stress in Thin shell is the circumferential stress in a cylinder.
Circumferential Strain Thin Shell - Circumferential strain Thin Shell represents the change in length.
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.
Longitudinal Stress Thick Shell - (Measured in Pascal) - Longitudinal Stress Thick Shell is defined as the stress produced when a pipe is subjected to internal pressure.

STEP 1: Convert Input(s) to Base Unit

Circumferential Strain Thin Shell: 2.5 --> No Conversion Required
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
Longitudinal Stress Thick Shell: 0.08 Megapascal --> 80000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_θ = (e₁*E)+(𝛎*σ_l) --> (2.5*10000000)+(0.3*80000)

Evaluating ... ...

σ_θ = 25024000

STEP 3: Convert Result to Output's Unit

25024000 Pascal -->25.024 Megapascal (Check conversion here)

FINAL ANSWER

25.024 Megapascal <-- Hoop Stress in Thin shell

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Effect of Internal Pressure on Dimension of Thin Cylindrical Shell » Mechanical » Stress and Strain » Hoop stress given circumferential strain

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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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< Stress and Strain Calculators

Internal diameter of thin cylindrical vessel given circumferential strain

LaTeX Go Inner Diameter of Cylinder = (Circumferential Strain Thin Shell*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell))*((1/2)-Poisson's Ratio))

Internal fluid pressure given circumferential strain

LaTeX Go Internal Pressure in thin shell = (Circumferential Strain Thin Shell*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Inner Diameter of Cylinder))*((1/2)-Poisson's Ratio))

Longitudinal stress given circumferential strain

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

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 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 given circumferential strain Formula

LaTeX Go

Hoop Stress in Thin shell = (Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell)+(Poisson's Ratio*Longitudinal Stress Thick Shell)
σ_θ = (e₁*E)+(𝛎*σ_l)

What is meant by hoop stress?

The hoop stress, or tangential stress, is the stress around the circumference of the pipe due to a pressure gradient. The maximum hoop stress always occurs at the inner radius or the outer radius depending on the direction of the pressure gradient.

How to Calculate Hoop stress given circumferential strain?

Hoop stress given circumferential strain calculator uses Hoop Stress in Thin shell = (Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell)+(Poisson's Ratio*Longitudinal Stress Thick Shell) to calculate the Hoop Stress in Thin shell, Hoop stress given circumferential strain is the stress around the circumference of the pipe due to a pressure gradient. Hoop Stress in Thin shell is denoted by σ_θ symbol.

How to calculate Hoop stress given circumferential strain using this online calculator? To use this online calculator for Hoop stress given circumferential strain, enter Circumferential Strain Thin Shell (e₁), Modulus of Elasticity Of Thin Shell (E), Poisson's Ratio (𝛎) & Longitudinal Stress Thick Shell (σ_l) and hit the calculate button. Here is how the Hoop stress given circumferential strain calculation can be explained with given input values -> 2.5E-5 = (2.5*10000000)+(0.3*80000).

FAQ

What is Hoop stress given circumferential strain?

Hoop stress given circumferential strain is the stress around the circumference of the pipe due to a pressure gradient and is represented as σ_θ = (e₁*E)+(𝛎*σ_l) or Hoop Stress in Thin shell = (Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell)+(Poisson's Ratio*Longitudinal Stress Thick Shell). Circumferential strain Thin Shell represents the change in length, 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 & Longitudinal Stress Thick Shell is defined as the stress produced when a pipe is subjected to internal pressure.

How to calculate Hoop stress given circumferential strain?

Hoop stress given circumferential strain is the stress around the circumference of the pipe due to a pressure gradient is calculated using Hoop Stress in Thin shell = (Circumferential Strain Thin Shell*Modulus of Elasticity Of Thin Shell)+(Poisson's Ratio*Longitudinal Stress Thick Shell). To calculate Hoop stress given circumferential strain, you need Circumferential Strain Thin Shell (e₁), Modulus of Elasticity Of Thin Shell (E), Poisson's Ratio (𝛎) & Longitudinal Stress Thick Shell (σ_l). With our tool, you need to enter the respective value for Circumferential Strain Thin Shell, Modulus of Elasticity Of Thin Shell, Poisson's Ratio & Longitudinal Stress Thick 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 Circumferential Strain Thin Shell, Modulus of Elasticity Of Thin Shell, Poisson's Ratio & Longitudinal Stress Thick Shell. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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