Circumferential stress given circumferential strain in thick cylindrical shell Calculator

✖Circumferential strain represents the change in length.ⓘ Circumferential strain [e₁]			+10% -10%
✖Modulus of Elasticity Of Thick 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 Thick 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%
✖Compressive Stress Thick Shell is the force that is responsible for the deformation of the material such that the volume of the material reduces.ⓘ Compressive Stress Thick Shell [σ_c]			+10% -10%

✖Hoop Stress on thick shell is the circumferential stress in a cylinder.ⓘ Circumferential stress given circumferential strain in thick cylindrical shell [σ_θ]

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Formula

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Circumferential stress given circumferential strain in thick cylindrical shell

Formula

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

Example

`"6.359MPa"=("2.5"*"2.6MPa")+("0.3"*("0.08MPa"-"0.55MPa"))`

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Circumferential stress given circumferential strain in thick cylindrical shell Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hoop Stress on thick shell = (Circumferential strain*Modulus of Elasticity Of Thick Shell)+(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell))
σ_θ = (e₁*E)+(𝛎*(σ_l-σ_c))
This formula uses 6 Variables

Variables Used

Hoop Stress on thick shell - (Measured in Pascal) - Hoop Stress on thick shell is the circumferential stress in a cylinder.
Circumferential strain - Circumferential strain represents the change in length.
Modulus of Elasticity Of Thick Shell - (Measured in Pascal) - Modulus of Elasticity Of Thick 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.
Compressive Stress Thick Shell - (Measured in Pascal) - Compressive Stress Thick Shell is the force that is responsible for the deformation of the material such that the volume of the material reduces.

STEP 1: Convert Input(s) to Base Unit

Circumferential strain: 2.5 --> No Conversion Required
Modulus of Elasticity Of Thick Shell: 2.6 Megapascal --> 2600000 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
Longitudinal Stress Thick Shell: 0.08 Megapascal --> 80000 Pascal (Check conversion here)
Compressive Stress Thick Shell: 0.55 Megapascal --> 550000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_θ = (e₁*E)+(𝛎*(σ_l-σ_c)) --> (2.5*2600000)+(0.3*(80000-550000))

Evaluating ... ...

σ_θ = 6359000

STEP 3: Convert Result to Output's Unit

6359000 Pascal -->6.359 Megapascal (Check conversion here)

FINAL ANSWER

6.359 Megapascal <-- Hoop Stress on thick shell

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< 25 Stresses in Thick Cylindrical Shell Calculators

Poisson's ratio given longitudinal strain in thick cylindrical shell

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

Radius of thick cylindrical shell given stress on cylindrical shell and Poisson's ratio

Go Radius Of Cylindrical Shell = Change in radius/((Hoop Stress on thick shell-(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell)

Change in radius of thick cylindrical shell given stresses and poison's ratio

Go Change in radius = Radius Of Cylindrical Shell*((Hoop Stress on thick shell-(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell)

Modulus of elasticity given change in radius of thick cylindrical shell

Go Modulus of Elasticity Of Thick Shell = Radius Of Cylindrical Shell*((Hoop Stress on thick shell-(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell)))/Change in radius)

Longitudinal stress given change in radius of thick cylindrical shell

Go Longitudinal Stress Thick Shell = ((Hoop Stress on thick shell-(Change in radius*Modulus of Elasticity Of Thick Shell/Radius Of Cylindrical Shell))/(Poisson's Ratio))+Compressive Stress Thick Shell

Compressive stress given change in radius of thick cylindrical shell

Go Compressive Stress Thick Shell = Longitudinal Stress Thick Shell-((Hoop Stress on thick shell-(Change in radius*Modulus of Elasticity Of Thick Shell/Radius Of Cylindrical Shell))/(Poisson's Ratio))

Poisson's ratio given change in radius of thick cylindrical shell

Go Poisson's Ratio = ((Hoop Stress on thick shell-(Change in radius*Modulus of Elasticity Of Thick Shell/Radius Of Cylindrical Shell))/(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell))

Circumferential stress given change in radius of thick cylindrical shell

Go Hoop Stress on thick shell = (Change in radius*Modulus of Elasticity Of Thick Shell/Radius Of Cylindrical Shell)+(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell))

Longitudinal stress given circumferential strain in thick cylindrical shell

Go Longitudinal Stress Thick Shell = ((Hoop Stress on thick shell-(Circumferential strain*Modulus of Elasticity Of Thick Shell))/(Poisson's Ratio))+Compressive Stress Thick Shell

Compressive stress given circumferential strain in thick cylindrical shell

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

Circumferential strain given stresses on cylindrical shell and Poisson's ratio

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

Circumferential stress given circumferential strain in thick cylindrical shell

Go Hoop Stress on thick shell = (Circumferential strain*Modulus of Elasticity Of Thick Shell)+(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell))

Modulus of elasticity given circumferential strain in thick cylindrical shell

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

Poisson's ratio given circumferential strain in thick cylindrical shell

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

Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio

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

Circumferential stress given longitudinal strain in thick cylindrical shell

Go Hoop Stress on thick shell = ((Longitudinal Stress Thick Shell-(Longitudinal Strain*Modulus of Elasticity Of Thick Shell))/Poisson's Ratio)+Compressive Stress Thick Shell

Modulus of elasticity given longitudinal strain in thick cylindrical shell

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

Longitudinal stress given longitudinal strain in thick cylindrical shell

Go Longitudinal Stress Thick Shell = (Longitudinal Strain*Modulus of Elasticity Of Thick Shell)+(Poisson's Ratio*(Hoop Stress on thick shell-Compressive Stress Thick Shell))

Compressive stress given longitudinal strain in thick cylindrical shell

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

Circumferential stress given radial strain in thick cylindrical shell

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

Modulus of elasticity given radial strain in thick cylindrical shell

Go Modulus of Elasticity Of Thick Shell = (-Compressive Stress Thick Shell-(Poisson's Ratio*(Hoop Stress on thick shell+Longitudinal Stress Thick Shell)))/Strain

Radial strain given stresses on thick cylinder and poisson's ratio

Go Strain = (-Compressive Stress Thick Shell-(Poisson's Ratio*(Hoop Stress on thick shell+Longitudinal Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell

Longitudinal stress given radial strain in thick cylindrical shell

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

Compressive stress given radial strain in thick cylindrical shell

Go Compressive Stress Thick Shell = -(Strain*Modulus of Elasticity Of Thick Shell)-(Poisson's Ratio*(Hoop Stress on thick shell+Longitudinal Stress Thick Shell))

Poisson's ratio given radial strain in thick cylindrical shell

Go Poisson's Ratio = (-Compressive Stress Thick Shell-(Strain*Modulus of Elasticity Of Thick Shell))/(Hoop Stress on thick shell+Longitudinal Stress Thick Shell)

Circumferential stress given circumferential strain in thick cylindrical shell Formula

What is the strain in physics?

Strain is simply the measure of how much an object is stretched or deformed. A strain occurs when force is applied to an object. Strain deals mostly with the change in length of the object.

How to Calculate Circumferential stress given circumferential strain in thick cylindrical shell?

Circumferential stress given circumferential strain in thick cylindrical shell calculator uses Hoop Stress on thick shell = (Circumferential strain*Modulus of Elasticity Of Thick Shell)+(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell)) to calculate the Hoop Stress on thick shell, Circumferential stress given circumferential strain in thick cylindrical shell formula is defined as a normal stress in the tangential (azimuth) direction. axial stress, a normal stress parallel to the axis of cylindrical symmetry. Hoop Stress on thick shell is denoted by σ_θ symbol.

How to calculate Circumferential stress given circumferential strain in thick cylindrical shell using this online calculator? To use this online calculator for Circumferential stress given circumferential strain in thick cylindrical shell, enter Circumferential strain (e₁), Modulus of Elasticity Of Thick Shell (E), Poisson's Ratio (𝛎), Longitudinal Stress Thick Shell (σ_l) & Compressive Stress Thick Shell (σ_c) and hit the calculate button. Here is how the Circumferential stress given circumferential strain in thick cylindrical shell calculation can be explained with given input values -> 6.4E-6 = (2.5*2600000)+(0.3*(80000-550000)).

FAQ

What is Circumferential stress given circumferential strain in thick cylindrical shell?

Circumferential stress given circumferential strain in thick cylindrical shell formula is defined as a normal stress in the tangential (azimuth) direction. axial stress, a normal stress parallel to the axis of cylindrical symmetry and is represented as σ_θ = (e₁*E)+(𝛎*(σ_l-σ_c)) or Hoop Stress on thick shell = (Circumferential strain*Modulus of Elasticity Of Thick Shell)+(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell)). Circumferential strain represents the change in length, Modulus of Elasticity Of Thick 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 & Compressive Stress Thick Shell is the force that is responsible for the deformation of the material such that the volume of the material reduces.

How to calculate Circumferential stress given circumferential strain in thick cylindrical shell?

Circumferential stress given circumferential strain in thick cylindrical shell formula is defined as a normal stress in the tangential (azimuth) direction. axial stress, a normal stress parallel to the axis of cylindrical symmetry is calculated using Hoop Stress on thick shell = (Circumferential strain*Modulus of Elasticity Of Thick Shell)+(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell)). To calculate Circumferential stress given circumferential strain in thick cylindrical shell, you need Circumferential strain (e₁), Modulus of Elasticity Of Thick Shell (E), Poisson's Ratio (𝛎), Longitudinal Stress Thick Shell (σ_l) & Compressive Stress Thick Shell (σ_c). With our tool, you need to enter the respective value for Circumferential strain, Modulus of Elasticity Of Thick Shell, Poisson's Ratio, Longitudinal Stress Thick Shell & Compressive 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 on thick shell?

In this formula, Hoop Stress on thick shell uses Circumferential strain, Modulus of Elasticity Of Thick Shell, Poisson's Ratio, Longitudinal Stress Thick Shell & Compressive Stress Thick Shell. We can use 3 other way(s) to calculate the same, which is/are as follows -

Hoop Stress on thick shell = ((Longitudinal Stress Thick Shell-(Longitudinal Strain*Modulus of Elasticity Of Thick Shell))/Poisson's Ratio)+Compressive Stress Thick Shell
Hoop Stress on thick shell = ((-Compressive Stress Thick Shell-(Strain*Modulus of Elasticity Of Thick Shell))/Poisson's Ratio)-Longitudinal Stress Thick Shell
Hoop Stress on thick shell = (Change in radius*Modulus of Elasticity Of Thick Shell/Radius Of Cylindrical Shell)+(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell))

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