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Poisson's ratio for thick spherical shell given compressive radial strain Formula

GoPoisson's Ratio for Thick Spherical Shell given Tensile Radial Strain Formula

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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. Check FAQs

𝛎 = \frac{1}{\frac{2 \cdot σ θ}{(E \cdot ε compressive) - P v}}

𝛎 - Poisson's Ratio?σ_θ - Hoop Stress on thick shell?E - Modulus of Elasticity Of Thick Shell?ε_compressive - Compressive Strain?P_v - Radial Pressure?

Poisson's ratio for thick spherical shell given compressive radial strain Example

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Here is how the Poisson's ratio for thick spherical shell given compressive radial strain equation looks like with Values.

Here is how the Poisson's ratio for thick spherical shell given compressive radial strain equation looks like with Units.

Here is how the Poisson's ratio for thick spherical shell given compressive radial strain equation looks like.

61.5 = \frac{1}{\frac{2 \cdot 0.002}{(2.6 \cdot 0.1) - 0.014}}

61.5 = \frac{1}{\frac{2 \cdot 0.002MPa}{(2.6MPa \cdot 0.1) - 0.014MPa/m²}}

61.5 = \frac{1}{\frac{2 \cdot 0.002}{(2.6 \cdot 0.1) - 0.014}}

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Poisson's ratio for thick spherical shell given compressive radial strain Solution

Follow our step by step solution on how to calculate Poisson's ratio for thick spherical shell given compressive radial strain?

FIRST Step Consider the formula

𝛎 = \frac{1}{\frac{2 \cdot σ θ}{(E \cdot ε compressive) - P v}}

Next Step Substitute values of Variables

∴

𝛎 = \frac{1}{\frac{2 \cdot 0.002MPa}{(2.6MPa \cdot 0.1) - 0.014MPa/m²}}

Next Step Convert Units

∴

𝛎 = \frac{1}{\frac{2 \cdot 2000Pa}{(2.6E+6Pa \cdot 0.1) - 14000Pa/m²}}

Next Step Prepare to Evaluate

∴

𝛎 = \frac{1}{\frac{2 \cdot 2000}{(2.6E+6 \cdot 0.1) - 14000}}

LAST Step Evaluate

∴

𝛎 = 61.5

Poisson's ratio for thick spherical shell given compressive radial strain Formula Elements

Variables

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 should be greater than 0.

Formulas to find Hoop Stress on 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 should be greater than 0.

Formulas to find Modulus of Elasticity Of Thick Shell

Compressive Strain

The Compressive Strain is the ratio of change in length to the original length of the body when subjected to a compressive load.

Symbol: ε_compressive

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Compressive Strain

Radial Pressure

Radial Pressure is pressure towards or away from the central axis of a component.

Symbol: P_v

Measurement: Radial PressureUnit: MPa/m²

Note: Value can be positive or negative.

Formulas to find Radial Pressure

Other Formulas to find Poisson's Ratio

Go Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain

𝛎 = (\frac{1}{2 \cdot σ θ}) \cdot ((- E \cdot ε tensile) - P v)

Other formulas in Thick Spherical Shells category

Go Compressive radial strain for thick spherical shells

ε compressive = \frac{P v + (2 \cdot \frac{σ θ}{M})}{F' c}

Go Radial pressure on thick spherical shell given compressive radial strain

P v = (F' c \cdot ε compressive) - (2 \cdot \frac{σ θ}{M})

Go Hoop stress on thick spherical shell given compressive radial strain

σ θ = ((E \cdot ε compressive) - P v) \cdot \frac{M}{2}

Go Mass of thick spherical shell given compressive radial strain

M = \frac{2 \cdot σ θ}{(E \cdot ε compressive) - P v}

How to Evaluate Poisson's ratio for thick spherical shell given compressive radial strain?

Poisson's ratio for thick spherical shell given compressive radial strain evaluator uses Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)) to evaluate the Poisson's Ratio, Poisson's ratio for thick spherical shell given compressive radial strain formula is defined as a measure of the relationship between radial strain and circumferential stress in thick spherical shells. It helps in understanding the material's deformation behavior under compressive loads, which is crucial in engineering applications. Poisson's Ratio is denoted by 𝛎 symbol.

How to evaluate Poisson's ratio for thick spherical shell given compressive radial strain using this online evaluator? To use this online evaluator for Poisson's ratio for thick spherical shell given compressive radial strain, enter Hoop Stress on thick shell (σ_θ), Modulus of Elasticity Of Thick Shell (E), Compressive Strain (ε_compressive) & Radial Pressure (P_v) and hit the calculate button.

FAQs on Poisson's ratio for thick spherical shell given compressive radial strain

What is the formula to find Poisson's ratio for thick spherical shell given compressive radial strain?

The formula of Poisson's ratio for thick spherical shell given compressive radial strain is expressed as Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)). Here is an example- 61.5 = 1/((2*2000)/((2600000*0.1)-14000)).

How to calculate Poisson's ratio for thick spherical shell given compressive radial strain?

With Hoop Stress on thick shell (σ_θ), Modulus of Elasticity Of Thick Shell (E), Compressive Strain (ε_compressive) & Radial Pressure (P_v) we can find Poisson's ratio for thick spherical shell given compressive radial strain using the formula - Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)).

What are the other ways to Calculate Poisson's Ratio?

Here are the different ways to Calculate Poisson's Ratio-

Poisson's Ratio=(1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)

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Poisson's ratio for thick spherical shell given compressive radial strain Formula

​GoPoisson's Ratio for Thick Spherical Shell given Tensile Radial Strain Formula

Poisson's ratio for thick spherical shell given compressive radial strain Example

Poisson's ratio for thick spherical shell given compressive radial strain Solution

Poisson's ratio for thick spherical shell given compressive radial strain Formula Elements

Other Formulas to find Poisson's Ratio

Other formulas in Thick Spherical Shells category

How to Evaluate Poisson's ratio for thick spherical shell given compressive radial strain?

FAQs on Poisson's ratio for thick spherical shell given compressive radial strain

Variable Name

GoPoisson's Ratio for Thick Spherical Shell given Tensile Radial Strain Formula