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

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Circumferential strain represents the change in length. Check FAQs

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

e₁ - Circumferential Strain?σ_θ - Hoop Stress on thick shell?𝛎 - Poisson's Ratio?σ_l - Longitudinal Stress Thick Shell?σ_c - Compressive Stress Thick Shell?E - Modulus of Elasticity Of Thick Shell?

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

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

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

Here is how the Circumferential strain given stresses on cylindrical shell and Poisson's ratio equation looks like.

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

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

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

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Strength of Materials » fx Circumferential strain given stresses on cylindrical shell and Poisson's ratio

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

e 1 = \frac{0.002MPa - (0.3 \cdot (0.08MPa - 0.55MPa))}{2.6MPa}

Next Step Convert Units

∴

e 1 = \frac{2000Pa - (0.3 \cdot (80000Pa - 550000Pa))}{2.6E+6Pa}

Next Step Prepare to Evaluate

∴

e 1 = \frac{2000 - (0.3 \cdot (80000 - 550000))}{2.6E+6}

LAST Step Evaluate

∴

e 1 = 0.055

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

Variables

Circumferential Strain

Circumferential strain represents the change in length.

Symbol: e₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Circumferential Strain

Open Variable

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

Open Variable

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

Open Variable

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

Open Variable

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

Open Variable

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

Open Variable

Other formulas in Stresses in Thick Cylindrical Shell category

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})

Go Poisson's ratio given circumferential strain in thick cylindrical shell

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

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How to Evaluate Circumferential strain given stresses on cylindrical shell and Poisson's ratio?

Circumferential strain given stresses on cylindrical shell and Poisson's ratio evaluator uses Circumferential Strain = (Hoop Stress on thick shell-(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell to evaluate the Circumferential Strain, The Circumferential strain given stresses on cylindrical shell and Poisson's ratio formula represents the change in length. Circumferential Strain is denoted by e₁ symbol.

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

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

What is the formula to find Circumferential strain given stresses on cylindrical shell and Poisson's ratio?

The formula of Circumferential strain given stresses on cylindrical shell and Poisson's ratio is expressed as Circumferential Strain = (Hoop Stress on thick shell-(Poisson's Ratio*(Longitudinal Stress Thick Shell-Compressive Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell. Here is an example- 0.055 = (2000-(0.3*(80000-550000)))/2600000.

How to calculate Circumferential strain given stresses on cylindrical shell and Poisson's ratio?

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

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