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)
σθ = (e1*E)+(𝛎*σl)
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
σθ = (e1*E)+(𝛎*σl) --> (2.5*10000000)+(0.3*80000)
Evaluating ... ...
σθ = 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 00.004 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 given circumferential strain Formula

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

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 σθ 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 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 σθ = (e1*E)+(𝛎*σl) 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 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 1 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)
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