Longitudinal strain given hoop and longitudinal stress Calculator

✖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 shell [σ_θ]			+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%

✖The Longitudinal Strain is ratio of change in length to original length.ⓘ Longitudinal strain given hoop and longitudinal stress [ε_longitudinal]

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Formula

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Longitudinal strain given hoop and longitudinal stress

Formula

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

Example

`"-0.7429"=("0.08MPa"-("0.3"*"25.03MPa"))/"10MPa"`

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Longitudinal strain given hoop and longitudinal stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Longitudinal Strain - The Longitudinal Strain is ratio of change in length to original length.
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.
Hoop Stress in Thin shell - (Measured in Pascal) - Hoop Stress in Thin shell is the circumferential stress in a cylinder.
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

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

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

Evaluating ... ...

ε_longitudinal = -0.7429

STEP 3: Convert Result to Output's Unit

-0.7429 --> No Conversion Required

FINAL ANSWER

-0.7429 <-- Longitudinal Strain

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Effect of Internal Pressure on Dimension of Thin Cylindrical Shell » Strain » Longitudinal strain given hoop and longitudinal stress

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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

Longitudinal strain given hoop and longitudinal stress Formula

Longitudinal Strain = (Longitudinal Stress Thick Shell-(Poisson's Ratio*Hoop Stress in Thin shell))/Modulus of Elasticity Of Thin Shell
ε_longitudinal = (σ_l-(𝛎*σ_θ))/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 Longitudinal strain given hoop and longitudinal stress?

Longitudinal strain given hoop and longitudinal stress calculator uses Longitudinal Strain = (Longitudinal Stress Thick Shell-(Poisson's Ratio*Hoop Stress in Thin shell))/Modulus of Elasticity Of Thin Shell to calculate the Longitudinal Strain, Longitudinal strain given hoop and longitudinal stress is the change in the length to the original length of an object. It is caused due to longitudinal stress and is denoted by the Greek letter epsilon 𝜺. Longitudinal Strain is denoted by ε_longitudinal symbol.

How to calculate Longitudinal strain given hoop and longitudinal stress using this online calculator? To use this online calculator for Longitudinal strain given hoop and longitudinal stress, enter Longitudinal Stress Thick Shell (σ_l), Poisson's Ratio (𝛎), Hoop Stress in Thin shell (σ_θ) & Modulus of Elasticity Of Thin Shell (E) and hit the calculate button. Here is how the Longitudinal strain given hoop and longitudinal stress calculation can be explained with given input values -> -0.7429 = (80000-(0.3*25030000))/10000000.

FAQ

What is Longitudinal strain given hoop and longitudinal stress?

Longitudinal strain given hoop and longitudinal stress is the change in the length to the original length of an object. It is caused due to longitudinal stress and is denoted by the Greek letter epsilon 𝜺 and is represented as ε_longitudinal = (σ_l-(𝛎*σ_θ))/E or Longitudinal Strain = (Longitudinal Stress Thick Shell-(Poisson's Ratio*Hoop Stress in Thin shell))/Modulus of Elasticity Of Thin Shell. 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, Hoop Stress in Thin shell is the circumferential stress in a cylinder & 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 Longitudinal strain given hoop and longitudinal stress?

Longitudinal strain given hoop and longitudinal stress is the change in the length to the original length of an object. It is caused due to longitudinal stress and is denoted by the Greek letter epsilon 𝜺 is calculated using Longitudinal Strain = (Longitudinal Stress Thick Shell-(Poisson's Ratio*Hoop Stress in Thin shell))/Modulus of Elasticity Of Thin Shell. To calculate Longitudinal strain given hoop and longitudinal stress, you need Longitudinal Stress Thick Shell (σ_l), Poisson's Ratio (𝛎), Hoop Stress in Thin shell (σ_θ) & Modulus of Elasticity Of Thin Shell (E). With our tool, you need to enter the respective value for Longitudinal Stress Thick Shell, Poisson's Ratio, Hoop Stress in Thin 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 Longitudinal Strain?

In this formula, Longitudinal Strain uses Longitudinal Stress Thick Shell, Poisson's Ratio, Hoop Stress in Thin shell & Modulus of Elasticity Of Thin Shell. We can use 4 other way(s) to calculate the same, which is/are as follows -

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

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