Longitudinal stress given circumferential strain Solution

STEP 0: Pre-Calculation Summary
Formula Used
Longitudinal Stress Thick Shell = (Hoop Stress in Thin shell-(Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Poisson's Ratio
σl = (σθ-(e1*E))/𝛎
This formula uses 5 Variables
Variables Used
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.
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.
STEP 1: Convert Input(s) to Base Unit
Hoop Stress in Thin shell: 25.03 Megapascal --> 25030000 Pascal (Check conversion here)
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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σl = (σθ-(e1*E))/𝛎 --> (25030000-(2.5*10000000))/0.3
Evaluating ... ...
σl = 100000
STEP 3: Convert Result to Output's Unit
100000 Pascal -->0.1 Megapascal (Check conversion here)
FINAL ANSWER
0.1 Megapascal <-- Longitudinal Stress Thick Shell
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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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

Longitudinal stress given circumferential strain Formula

Longitudinal Stress Thick Shell = (Hoop Stress in Thin shell-(Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Poisson's Ratio
σl = (σθ-(e1*E))/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 Longitudinal stress given circumferential strain?

Longitudinal stress given circumferential strain calculator uses Longitudinal Stress Thick Shell = (Hoop Stress in Thin shell-(Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Poisson's Ratio to calculate the Longitudinal Stress Thick Shell, Longitudinal stress given circumferential strain is the stress produced when a pipe is subjected to internal pressure. Longitudinal Stress Thick Shell is denoted by σl symbol.

How to calculate Longitudinal stress given circumferential strain using this online calculator? To use this online calculator for Longitudinal stress given circumferential strain, enter Hoop Stress in Thin shell θ), Circumferential strain Thin Shell (e1), Modulus of Elasticity Of Thin Shell (E) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Longitudinal stress given circumferential strain calculation can be explained with given input values -> 1E-7 = (25030000-(2.5*10000000))/0.3.

FAQ

What is Longitudinal stress given circumferential strain?
Longitudinal stress given circumferential strain is the stress produced when a pipe is subjected to internal pressure and is represented as σl = (σθ-(e1*E))/𝛎 or Longitudinal Stress Thick Shell = (Hoop Stress in Thin shell-(Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Poisson's Ratio. Hoop Stress in Thin shell is the circumferential stress in a cylinder, 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.
How to calculate Longitudinal stress given circumferential strain?
Longitudinal stress given circumferential strain is the stress produced when a pipe is subjected to internal pressure is calculated using Longitudinal Stress Thick Shell = (Hoop Stress in Thin shell-(Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Poisson's Ratio. To calculate Longitudinal stress given circumferential strain, you need Hoop Stress in Thin shell θ), Circumferential strain Thin Shell (e1), Modulus of Elasticity Of Thin Shell (E) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Hoop Stress in Thin shell, Circumferential strain Thin Shell, Modulus of Elasticity Of Thin 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 Longitudinal Stress Thick Shell?
In this formula, Longitudinal Stress Thick Shell uses Hoop Stress in Thin shell, Circumferential strain Thin Shell, Modulus of Elasticity Of Thin Shell & Poisson's Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Longitudinal Stress Thick Shell = ((Longitudinal Strain*Modulus of Elasticity Of Thin Shell))+(Poisson's Ratio*Hoop Stress in Thin shell)
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