Circumferential strain given hoop stress Calculator

✖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 [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%
✖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%

✖Circumferential strain Thin Shell represents the change in length.ⓘ Circumferential strain given hoop stress [e₁]

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Formula

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Circumferential strain given hoop stress

Formula

`"e"_{"1"} = ("σ"_{"θ"}-("𝛎"*"σ"_{"l"}))/"E"`

Example

`"2.5006"=("25.03MPa"-("0.3"*"0.08MPa"))/"10MPa"`

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Circumferential strain given hoop stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Circumferential strain Thin Shell - Circumferential strain Thin Shell represents the change in length.
Hoop Stress in Thin shell - (Measured in Pascal) - Hoop Stress in Thin shell is the circumferential stress in a cylinder.
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.
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

Hoop Stress in Thin shell: 25.03 Megapascal --> 25030000 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
Longitudinal Stress Thick Shell: 0.08 Megapascal --> 80000 Pascal (Check conversion here)
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e₁ = (σ_θ-(𝛎*σ_l))/E --> (25030000-(0.3*80000))/10000000

Evaluating ... ...

e₁ = 2.5006

STEP 3: Convert Result to Output's Unit

2.5006 --> No Conversion Required

FINAL ANSWER

2.5006 <-- Circumferential strain Thin Shell

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< 15 Strain Calculators

Circumferential strain given internal fluid pressure

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

Longitudinal strain in thin cylindrical vessel given internal fluid pressure

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

Volumetric strain given internal fluid pressure

Go Volumetric Strain = (Internal Pressure in thin shell*Diameter of Shell/(2*Modulus of Elasticity Of Thin Shell*Thickness Of Thin Shell))*((5/2)-Poisson's Ratio)

Circumferential strain given hoop stress

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

Longitudinal strain given hoop and longitudinal stress

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

Volumetric strain of thin cylindrical shell given changes in diameter and length

Go Volumetric Strain = (2*Change in Diameter/Diameter of Shell)+(Change in Length/Length Of Cylindrical Shell)

Circumferential strain given volume of thin cylindrical shell

Go Circumferential strain Thin Shell = ((Change in Volume/Volume of Thin Cylindrical Shell)-Longitudinal Strain)/2

Longitudinal strain given volume of thin cylindrical shell

Go Longitudinal Strain = (Change in Volume/Volume of Thin Cylindrical Shell)-(2*Circumferential strain Thin Shell)

Circumferential strain given circumference

Go Circumferential strain Thin Shell = Change in circumference/Original Circumference

Longitudinal strain given volumetric strain for thin cylindrical shell

Go Longitudinal Strain = (Volumetric Strain-(2*Circumferential strain Thin Shell))

Circumferential strain given volumetric strain for thin cylindrical shell

Go Circumferential strain Thin Shell = (Volumetric Strain-Longitudinal Strain)/2

Volumetric strain given circumferential strain and longitudinal strain

Go Volumetric Strain = 2*Circumferential strain Thin Shell+(Longitudinal Strain)

Circumferential strain of vessel given diameter

Go Circumferential strain Thin Shell = Change in Diameter/Original Diameter

Longitudinal strain for vessel given change in length formula

Go Longitudinal Strain = Change in Length/Initial Length

Volumetric strain of thin cylindrical shell

Go Volumetric Strain = Change in Volume/Original Volume

Circumferential strain given hoop stress Formula

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

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 Circumferential strain given hoop stress?

Circumferential strain given hoop stress calculator uses Circumferential strain Thin Shell = (Hoop Stress in Thin shell-(Poisson's Ratio*Longitudinal Stress Thick Shell))/Modulus of Elasticity Of Thin Shell to calculate the Circumferential strain Thin Shell, Circumferential strain given hoop stress is the change in length. It occurs in the thin cylindrical vessel. Circumferential strain Thin Shell is denoted by e₁ symbol.

How to calculate Circumferential strain given hoop stress using this online calculator? To use this online calculator for Circumferential strain given hoop stress, enter Hoop Stress in Thin shell (σ_θ), Poisson's Ratio (𝛎), Longitudinal Stress Thick Shell (σ_l) & Modulus of Elasticity Of Thin Shell (E) and hit the calculate button. Here is how the Circumferential strain given hoop stress calculation can be explained with given input values -> 2.5006 = (25030000-(0.3*80000))/10000000.

FAQ

What is Circumferential strain given hoop stress?

Circumferential strain given hoop stress is the change in length. It occurs in the thin cylindrical vessel and is represented as e₁ = (σ_θ-(𝛎*σ_l))/E or Circumferential strain Thin Shell = (Hoop Stress in Thin shell-(Poisson's Ratio*Longitudinal Stress Thick Shell))/Modulus of Elasticity Of Thin Shell. Hoop Stress in Thin shell is the circumferential stress in a cylinder, 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 & 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 Circumferential strain given hoop stress?

Circumferential strain given hoop stress is the change in length. It occurs in the thin cylindrical vessel is calculated using Circumferential strain Thin Shell = (Hoop Stress in Thin shell-(Poisson's Ratio*Longitudinal Stress Thick Shell))/Modulus of Elasticity Of Thin Shell. To calculate Circumferential strain given hoop stress, you need Hoop Stress in Thin shell (σ_θ), Poisson's Ratio (𝛎), Longitudinal Stress Thick Shell (σ_l) & Modulus of Elasticity Of Thin Shell (E). With our tool, you need to enter the respective value for Hoop Stress in Thin shell, Poisson's Ratio, Longitudinal Stress Thick Shell & 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 Circumferential strain Thin Shell?

In this formula, Circumferential strain Thin Shell uses Hoop Stress in Thin shell, Poisson's Ratio, Longitudinal Stress Thick Shell & Modulus of Elasticity Of Thin Shell. We can use 5 other way(s) to calculate the same, which is/are as follows -

Circumferential strain Thin Shell = Change in circumference/Original Circumference
Circumferential strain Thin Shell = ((Internal Pressure in thin shell*Inner Diameter of Cylinder)/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*((1/2)-Poisson's Ratio)
Circumferential strain Thin Shell = ((Change in Volume/Volume of Thin Cylindrical Shell)-Longitudinal Strain)/2
Circumferential strain Thin Shell = (Volumetric Strain-Longitudinal Strain)/2
Circumferential strain Thin Shell = Change in Diameter/Original Diameter

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