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Shear Modulus given Young's Modulus and Bulk Modulus Formula

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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. Check FAQs

G = \frac{3 \cdot K B \cdot E y}{(9 \cdot K B) - E y}

G - Modulus of rigidity Of Bar?K_B - Bulk modulus of elasticity?E_y - Young's Modulus of elasticity?

Shear Modulus given Young's Modulus and Bulk Modulus Example

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Here is how the Shear Modulus given Young's Modulus and Bulk Modulus equation looks like with Values.

Here is how the Shear Modulus given Young's Modulus and Bulk Modulus equation looks like with Units.

Here is how the Shear Modulus given Young's Modulus and Bulk Modulus equation looks like.

17.5494 = \frac{3 \cdot 18.5 \cdot 40}{(9 \cdot 18.5) - 40}

17.5494MPa = \frac{3 \cdot 18.5MPa \cdot 40MPa}{(9 \cdot 18.5MPa) - 40MPa}

17.5494 = \frac{3 \cdot 18.5 \cdot 40}{(9 \cdot 18.5) - 40}

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Shear Modulus given Young's Modulus and Bulk Modulus Solution

Follow our step by step solution on how to calculate Shear Modulus given Young's Modulus and Bulk Modulus?

FIRST Step Consider the formula

G = \frac{3 \cdot K B \cdot E y}{(9 \cdot K B) - E y}

Next Step Substitute values of Variables

∴

G = \frac{3 \cdot 18.5MPa \cdot 40MPa}{(9 \cdot 18.5MPa) - 40MPa}

Next Step Convert Units

∴

G = \frac{3 \cdot 1.9E+7Pa \cdot 4E+7Pa}{(9 \cdot 1.9E+7Pa) - 4E+7Pa}

Next Step Prepare to Evaluate

∴

G = \frac{3 \cdot 1.9E+7 \cdot 4E+7}{(9 \cdot 1.9E+7) - 4E+7}

Next Step Evaluate

∴

G = 17549407.1146245Pa

Next Step Convert to Output's Unit

∴

G = 17.5494071146245MPa

LAST Step Rounding Answer

∴

G = 17.5494MPa

Shear Modulus given Young's Modulus and Bulk Modulus Formula Elements

Variables

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

Bulk modulus of elasticity

The Bulk modulus of elasticity is a measure of the ability of a substance to withstand changes in volume when under compression on all sides.

Symbol: K_B

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Bulk modulus of elasticity

Young's Modulus of elasticity

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

Symbol: E_y

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Young's Modulus of elasticity

Other formulas in Elastic Moduli category

Go Youngs Modulus given Shear Modulus and Bulk Modulus

E y = \frac{9 \cdot G \cdot K B}{(3 \cdot K B) + G}

Go Bulk Modulus given Shear Modulus and Young's Modulus

K B = G \cdot \frac{E y}{3 \cdot ((3 \cdot G) - E y)}

How to Evaluate Shear Modulus given Young's Modulus and Bulk Modulus?

Shear Modulus given Young's Modulus and Bulk Modulus evaluator uses Modulus of rigidity Of Bar = (3*Bulk modulus of elasticity*Young's Modulus of elasticity)/((9*Bulk modulus of elasticity)-Young's Modulus of elasticity) to evaluate the Modulus of rigidity Of Bar, The Shear Modulus given Young's Modulus and Bulk Modulus is the ratio of shear stress to the shear strain. Modulus of rigidity Of Bar is denoted by G symbol.

How to evaluate Shear Modulus given Young's Modulus and Bulk Modulus using this online evaluator? To use this online evaluator for Shear Modulus given Young's Modulus and Bulk Modulus, enter Bulk modulus of elasticity (K_B) & Young's Modulus of elasticity (E_y) and hit the calculate button.

FAQs on Shear Modulus given Young's Modulus and Bulk Modulus

What is the formula to find Shear Modulus given Young's Modulus and Bulk Modulus?

The formula of Shear Modulus given Young's Modulus and Bulk Modulus is expressed as Modulus of rigidity Of Bar = (3*Bulk modulus of elasticity*Young's Modulus of elasticity)/((9*Bulk modulus of elasticity)-Young's Modulus of elasticity). Here is an example- 1.8E-5 = (3*18500000*40000000)/((9*18500000)-40000000).

How to calculate Shear Modulus given Young's Modulus and Bulk Modulus?

With Bulk modulus of elasticity (K_B) & Young's Modulus of elasticity (E_y) we can find Shear Modulus given Young's Modulus and Bulk Modulus using the formula - Modulus of rigidity Of Bar = (3*Bulk modulus of elasticity*Young's Modulus of elasticity)/((9*Bulk modulus of elasticity)-Young's Modulus of elasticity).

Can the Shear Modulus given Young's Modulus and Bulk Modulus be negative?

No, the Shear Modulus given Young's Modulus and Bulk Modulus, measured in Pressure cannot be negative.

Which unit is used to measure Shear Modulus given Young's Modulus and Bulk Modulus?

Shear Modulus given Young's Modulus and Bulk Modulus is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Shear Modulus given Young's Modulus and Bulk Modulus can be measured.

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Shear Modulus given Young's Modulus and Bulk Modulus Formula

Shear Modulus given Young's Modulus and Bulk Modulus Example

Shear Modulus given Young's Modulus and Bulk Modulus Solution

Shear Modulus given Young's Modulus and Bulk Modulus Formula Elements

Other formulas in Elastic Moduli category

How to Evaluate Shear Modulus given Young's Modulus and Bulk Modulus?

FAQs on Shear Modulus given Young's Modulus and Bulk Modulus

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