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

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The Longitudinal Strain is ratio of change in length to original length. Check FAQs

ε longitudinal = \frac{σ l - (𝛎 \cdot (σ θ - σ c))}{E}

ε_longitudinal - Longitudinal Strain?σ_l - Longitudinal Stress Thick Shell?𝛎 - Poisson's Ratio?σ_θ - Hoop Stress on thick shell?σ_c - Compressive Stress Thick Shell?E - Modulus of Elasticity Of Thick Shell?

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

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Here is how the Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio equation looks like with Values.

Here is how the Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio equation looks like with Units.

Here is how the Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio equation looks like.

0.094 = \frac{0.08 - (0.3 \cdot (0.002 - 0.55))}{2.6}

0.094 = \frac{0.08MPa - (0.3 \cdot (0.002MPa - 0.55MPa))}{2.6MPa}

0.094 = \frac{0.08 - (0.3 \cdot (0.002 - 0.55))}{2.6}

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

Follow our step by step solution on how to calculate Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio?

FIRST Step Consider the formula

ε longitudinal = \frac{σ l - (𝛎 \cdot (σ θ - σ c))}{E}

Next Step Substitute values of Variables

∴

ε longitudinal = \frac{0.08MPa - (0.3 \cdot (0.002MPa - 0.55MPa))}{2.6MPa}

Next Step Convert Units

∴

ε longitudinal = \frac{80000Pa - (0.3 \cdot (2000Pa - 550000Pa))}{2.6E+6Pa}

Next Step Prepare to Evaluate

∴

ε longitudinal = \frac{80000 - (0.3 \cdot (2000 - 550000))}{2.6E+6}

LAST Step Evaluate

∴

ε longitudinal = 0.094

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

Variables

Longitudinal Strain

The Longitudinal Strain is ratio of change in length to original length.

Symbol: ε_longitudinal

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Longitudinal Strain

Longitudinal Stress Thick Shell

Longitudinal Stress Thick Shell is defined as the stress produced when a pipe is subjected to internal pressure.

Symbol: σ_l

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Longitudinal Stress Thick Shell

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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Poisson's Ratio

Hoop Stress on thick shell

Hoop Stress on thick shell is the circumferential stress in a cylinder.

Symbol: σ_θ

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Hoop Stress on thick shell

Compressive Stress Thick Shell

Compressive Stress Thick Shell is the force that is responsible for the deformation of the material such that the volume of the material reduces.

Symbol: σ_c

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Compressive Stress Thick Shell

Modulus of Elasticity Of Thick Shell

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.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Modulus of Elasticity Of Thick Shell

Other formulas in Stresses in Thick Cylindrical Shell category

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

e 1 = \frac{σ θ - (𝛎 \cdot (σ l - σ c))}{E}

Go Circumferential stress given circumferential strain in thick cylindrical shell

σ θ = (e 1 \cdot E) + (𝛎 \cdot (σ l - σ c))

Go Longitudinal stress given circumferential strain in thick cylindrical shell

σ l = (\frac{σ θ - (e 1 \cdot E)}{𝛎}) + σ c

Go Compressive stress given circumferential strain in thick cylindrical shell

σ c = σ l - (\frac{σ θ - (e 1 \cdot E)}{𝛎})

How to Evaluate Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio?

Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio evaluator uses Longitudinal Strain = (Longitudinal Stress Thick Shell-(Poisson's Ratio*(Hoop Stress on thick shell-Compressive Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell to evaluate the Longitudinal Strain, The Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio formula is defined as the change in the length to the original length of an object. Longitudinal Strain is denoted by ε_longitudinal symbol.

How to evaluate Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio using this online evaluator? To use this online evaluator for Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio, enter Longitudinal Stress Thick Shell (σ_l), Poisson's Ratio (𝛎), Hoop Stress on thick shell (σ_θ), Compressive Stress Thick Shell (σ_c) & Modulus of Elasticity Of Thick Shell (E) and hit the calculate button.

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

What is the formula to find Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio?

The formula of Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio is expressed as Longitudinal Strain = (Longitudinal Stress Thick Shell-(Poisson's Ratio*(Hoop Stress on thick shell-Compressive Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell. Here is an example- 0.094 = (80000-(0.3*(2000-550000)))/2600000.

How to calculate Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio?

With Longitudinal Stress Thick Shell (σ_l), Poisson's Ratio (𝛎), Hoop Stress on thick shell (σ_θ), Compressive Stress Thick Shell (σ_c) & Modulus of Elasticity Of Thick Shell (E) we can find Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio using the formula - Longitudinal Strain = (Longitudinal Stress Thick Shell-(Poisson's Ratio*(Hoop Stress on thick shell-Compressive Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell.

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

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

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

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

Other formulas in Stresses in Thick Cylindrical Shell category

How to Evaluate Longitudinal strain given stresses in thick cylindrical shell and Poisson's ratio?

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

Variable Name