Hoop stress in thin cylindrical vessel given Longitudinal strain Calculator

✖The Longitudinal Strain is ratio of change in length to original length.ⓘ Longitudinal Strain [ε_longitudinal]			+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%
✖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%
✖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%

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

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Formula

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Hoop stress in thin cylindrical vessel given Longitudinal strain

Formula

`"σ"_{"θ"} = (-("ε"_{"longitudinal"}*"E")+"σ"_{"l"})/("𝛎")`

Example

`"-1333.066667MPa"=(-("40"*"10MPa")+"0.08MPa")/("0.3")`

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Hoop stress in thin cylindrical vessel given Longitudinal strain Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hoop Stress in Thin shell = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Poisson's Ratio)
σ_θ = (-(ε_longitudinal*E)+σ_l)/(𝛎)
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.
Longitudinal Strain - The Longitudinal Strain is ratio of change in length to original 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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Longitudinal Strain: 40 --> No Conversion Required
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Longitudinal Stress Thick Shell: 0.08 Megapascal --> 80000 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_θ = (-(ε_longitudinal*E)+σ_l)/(𝛎) --> (-(40*10000000)+80000)/(0.3)

Evaluating ... ...

σ_θ = -1333066666.66667

STEP 3: Convert Result to Output's Unit

-1333066666.66667 Pascal -->-1333.06666666667 Megapascal (Check conversion here)

FINAL ANSWER

-1333.06666666667 ≈ -1333.066667 Megapascal <-- Hoop Stress in Thin shell

(Calculation completed in 00.004 seconds)

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< 23 Effect of Internal Pressure on Dimension of Thin Cylindrical Shell Calculators

Diameter of cylindrical shell given change in length of cylindrical shell

Go Diameter of Shell = (Change in Length*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell*Length Of Cylindrical Shell))*((1/2)-Poisson's Ratio))

Length of cylindrical shell given change in length of cylindrical shell

Go Length Of Cylindrical Shell = (Change in Length*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell*Diameter of Shell))*((1/2)-Poisson's Ratio))

Internal fluid pressure given change in length of cylindrical shell

Go Internal Pressure in thin shell = (Change in Length*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Diameter of Shell*Length Of Cylindrical Shell))*((1/2)-Poisson's Ratio))

Internal diameter of thin cylindrical vessel given circumferential strain

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

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))

Internal fluid pressure in thin cylindrical vessel given change in diameter

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

Internal fluid pressure in thin cylindrical vessel given longitudinal strain

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

Internal diameter of thin cylindrical vessel given longitudinal strain

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

Original diameter of vessel given change in diameter

Go Original Diameter = (Change in Diameter*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell))*(1-(Poisson's Ratio/2)))^(1/2)

Length of cylindrical shell given change in volume of cylindrical shell

Go Length Of Cylindrical Shell = ((Change in Volume/(pi/4))-(Change in Length*(Diameter of Shell^2)))/(2*Diameter of Shell*Change in Diameter)

Diameter of thin cylindrical shell given volumetric strain

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

Internal fluid pressure in shell given volumetric strain

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

Longitudinal stress given circumferential strain

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

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

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

Longitudinal stress in thin cylindrical vessel given Longitudinal strain

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

Diameter of thin cylindrical strain given volumetric strain

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

Length of thin cylindrical strain given volumetric strain

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

Volume of thin cylindrical shell given circumferential and longitudinal strain

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

Original circumference of thin cylindrical vessel given circumferential strain

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

Original diameter of thin cylindrical vessel given circumferential strain

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

Original length of vessel given longitudinal strain

Go Initial Length = Change in Length/Longitudinal Strain

Original volume of cylindrical shell given volumetric strain

Go Original Volume = Change in Volume/Volumetric Strain

Hoop stress in thin cylindrical vessel given Longitudinal strain Formula

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

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 in thin cylindrical vessel given Longitudinal strain?

Hoop stress in thin cylindrical vessel given Longitudinal strain calculator uses Hoop Stress in Thin shell = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Poisson's Ratio) to calculate the Hoop Stress in Thin shell, Hoop stress in thin cylindrical vessel given Longitudinal 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 in thin cylindrical vessel given Longitudinal strain using this online calculator? To use this online calculator for Hoop stress in thin cylindrical vessel given Longitudinal strain, enter Longitudinal Strain (ε_longitudinal), Modulus of Elasticity Of Thin Shell (E), Longitudinal Stress Thick Shell (σ_l) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Hoop stress in thin cylindrical vessel given Longitudinal strain calculation can be explained with given input values -> -0.001333 = (-(40*10000000)+80000)/(0.3).

FAQ

What is Hoop stress in thin cylindrical vessel given Longitudinal strain?

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

How to calculate Hoop stress in thin cylindrical vessel given Longitudinal strain?

Hoop stress in thin cylindrical vessel given Longitudinal strain is the stress around the circumference of the pipe due to a pressure gradient is calculated using Hoop Stress in Thin shell = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Poisson's Ratio). To calculate Hoop stress in thin cylindrical vessel given Longitudinal strain, you need Longitudinal Strain (ε_longitudinal), Modulus of Elasticity Of Thin Shell (E), Longitudinal Stress Thick Shell (σ_l) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Longitudinal Strain, Modulus of Elasticity Of Thin Shell, Longitudinal Stress Thick Shell & Poisson's Ratio 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 Longitudinal Strain, Modulus of Elasticity Of Thin Shell, Longitudinal Stress Thick Shell & Poisson's Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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