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Radial strain given stresses on thick cylinder and poisson's ratio Formula

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Strain is simply the measure of how much an object is stretched or deformed. Check FAQs

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

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

Radial strain given stresses on thick cylinder and poisson's ratio Example

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Here is how the Radial strain given stresses on thick cylinder and poisson's ratio equation looks like with Values.

Here is how the Radial strain given stresses on thick cylinder and poisson's ratio equation looks like with Units.

Here is how the Radial strain given stresses on thick cylinder and poisson's ratio equation looks like.

-0.221 = \frac{- 0.55 - (0.3 \cdot (0.002 + 0.08))}{2.6}

-0.221 = \frac{- 0.55MPa - (0.3 \cdot (0.002MPa + 0.08MPa))}{2.6MPa}

-0.221 = \frac{- 0.55 - (0.3 \cdot (0.002 + 0.08))}{2.6}

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Radial strain given stresses on thick cylinder and poisson's ratio Solution

Follow our step by step solution on how to calculate Radial strain given stresses on thick cylinder and poisson's ratio?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

LAST Step Evaluate

∴

ε = -0.221

Radial strain given stresses on thick cylinder and poisson's ratio Formula Elements

Variables

Strain

Strain is simply the measure of how much an object is stretched or deformed.

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Strain

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

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

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

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 Radial strain given stresses on thick cylinder and poisson's ratio?

Radial strain given stresses on thick cylinder and poisson's ratio evaluator uses Strain = (-Compressive Stress Thick Shell-(Poisson's Ratio*(Hoop Stress on thick shell+Longitudinal Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell to evaluate the Strain, The Radial strain given stresses on thick cylinder and poisson's ratio formula is defined as the measure of how much radius of the cylindrical shell is stretched or deformed. Strain is denoted by ε symbol.

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

FAQs on Radial strain given stresses on thick cylinder and poisson's ratio

What is the formula to find Radial strain given stresses on thick cylinder and poisson's ratio?

The formula of Radial strain given stresses on thick cylinder and poisson's ratio is expressed as Strain = (-Compressive Stress Thick Shell-(Poisson's Ratio*(Hoop Stress on thick shell+Longitudinal Stress Thick Shell)))/Modulus of Elasticity Of Thick Shell. Here is an example- -0.221 = (-550000-(0.3*(2000+80000)))/2600000.

How to calculate Radial strain given stresses on thick cylinder and poisson's ratio?

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

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Radial strain given stresses on thick cylinder and poisson's ratio Formula

Radial strain given stresses on thick cylinder and poisson's ratio Example

Radial strain given stresses on thick cylinder and poisson's ratio Solution

Radial strain given stresses on thick cylinder and poisson's ratio Formula Elements

Other formulas in Stresses in Thick Cylindrical Shell category

How to Evaluate Radial strain given stresses on thick cylinder and poisson's ratio?

FAQs on Radial strain given stresses on thick cylinder and poisson's ratio

Variable Name