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Poisson's Ratio using Modulus of Rigidity Formula

GoPoisson's ratio given tensile strain due to compressive stress in diagonal BD 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{E}{2 \cdot G}) - 1

𝛎 - Poisson's Ratio?E - Young's Modulus Bar?G - Modulus of rigidity Of Bar?

Poisson's Ratio using Modulus of Rigidity Example

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Here is how the Poisson's Ratio using Modulus of Rigidity equation looks like with Values.

Here is how the Poisson's Ratio using Modulus of Rigidity equation looks like with Units.

Here is how the Poisson's Ratio using Modulus of Rigidity equation looks like.

-0.9992 = (\frac{0.023}{2 \cdot 15}) - 1

-0.9992 = (\frac{0.023MPa}{2 \cdot 15MPa}) - 1

-0.9992 = (\frac{0.023}{2 \cdot 15}) - 1

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Poisson's Ratio using Modulus of Rigidity Solution

Follow our step by step solution on how to calculate Poisson's Ratio using Modulus of Rigidity?

FIRST Step Consider the formula

𝛎 = (\frac{E}{2 \cdot G}) - 1

Next Step Substitute values of Variables

∴

𝛎 = (\frac{0.023MPa}{2 \cdot 15MPa}) - 1

Next Step Convert Units

∴

𝛎 = (\frac{23000Pa}{2 \cdot 1.5E+7Pa}) - 1

Next Step Prepare to Evaluate

∴

𝛎 = (\frac{23000}{2 \cdot 1.5E+7}) - 1

Next Step Evaluate

∴

𝛎 = -0.999233333333333

LAST Step Rounding Answer

∴

𝛎 = -0.9992

Poisson's Ratio using Modulus of Rigidity 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 should be between -1 to 0.5.

Formulas to find Poisson's Ratio

Young's Modulus Bar

Young's Modulus Bar is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Young's Modulus Bar

Modulus of rigidity Of Bar

Modulus of rigidity of Bar is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

Symbol: G

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of rigidity Of Bar

Other Formulas to find Poisson's Ratio

Go Poisson's ratio given tensile strain due to compressive stress in diagonal BD

𝛎 = \frac{ε diagonal \cdot E bar}{σ tp}

Other formulas in Direct Strains of Diagonal category

Go Tensile Strain in Diagonal of Square Block due to Tensile Stress

ε tensile = \frac{σ t}{E bar}

Go Tensile strain in diagonal BD of square block ABCD due to compressive stress

ε tensile = \frac{𝛎 \cdot σ t}{E bar}

Go Total Tensile Strain in Diagonal of Square Block

ε diagonal = (\frac{σ t}{E bar}) \cdot (1 + 𝛎)

Go Total Compressive Strain in Diagonal AC of Square Block ABCD

ε diagonal = (\frac{σ t}{E bar}) \cdot (1 + 𝛎)

How to Evaluate Poisson's Ratio using Modulus of Rigidity?

Poisson's Ratio using Modulus of Rigidity evaluator uses Poisson's Ratio = (Young's Modulus Bar/(2*Modulus of rigidity Of Bar))-1 to evaluate the Poisson's Ratio, Poisson's Ratio using Modulus of Rigidity formula is defined as a measure of the relationship between lateral strain and axial strain in a material when subjected to stress. It provides insight into the material's deformation characteristics, crucial for understanding its mechanical behavior under load. Poisson's Ratio is denoted by 𝛎 symbol.

How to evaluate Poisson's Ratio using Modulus of Rigidity using this online evaluator? To use this online evaluator for Poisson's Ratio using Modulus of Rigidity, enter Young's Modulus Bar (E) & Modulus of rigidity Of Bar (G) and hit the calculate button.

FAQs on Poisson's Ratio using Modulus of Rigidity

What is the formula to find Poisson's Ratio using Modulus of Rigidity?

The formula of Poisson's Ratio using Modulus of Rigidity is expressed as Poisson's Ratio = (Young's Modulus Bar/(2*Modulus of rigidity Of Bar))-1. Here is an example- -0.999233 = (39000000/(2*15000000))-1.

How to calculate Poisson's Ratio using Modulus of Rigidity?

With Young's Modulus Bar (E) & Modulus of rigidity Of Bar (G) we can find Poisson's Ratio using Modulus of Rigidity using the formula - Poisson's Ratio = (Young's Modulus Bar/(2*Modulus of rigidity Of Bar))-1.

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

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

Poisson's Ratio=(Tensile Strain In Diagonal*Modulus of Elasticity Of Bar)/Permissible Tensile Stress

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