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Modulus of rigidity of shaft given total strain energy in hollow shaft Formula

GoModulus of rigidity given shear strain energy Formula

GoModulus of rigidity of shaft given shear strain energy in ring of radius 'r' Formula

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Modulus of rigidity of Shaft 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{(𝜏^{2}) \cdot (({d outer}^{2}) + ({d inner}^{2})) \cdot V}{4 \cdot U \cdot ({d outer}^{2})}

G - Modulus of rigidity of Shaft?𝜏 - Shear stress on surface of shaft?d_outer - Outer Diameter of Shaft?d_inner - Inner Diameter of Shaft?V - Volume of Shaft?U - Strain Energy in body?

Modulus of rigidity of shaft given total strain energy in hollow shaft Example

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Here is how the Modulus of rigidity of shaft given total strain energy in hollow shaft equation looks like with Values.

Here is how the Modulus of rigidity of shaft given total strain energy in hollow shaft equation looks like with Units.

Here is how the Modulus of rigidity of shaft given total strain energy in hollow shaft equation looks like.

1.1E-8 = \frac{({4E-6}^{2}) \cdot ((4000^{2}) + (1000^{2})) \cdot 125.6}{4 \cdot 50 \cdot (4000^{2})}

1.1E-8MPa = \frac{({4E-6MPa}^{2}) \cdot (({4000mm}^{2}) + ({1000mm}^{2})) \cdot 125.6m³}{4 \cdot 50KJ \cdot ({4000mm}^{2})}

1.1E-8 = \frac{({4E-6}^{2}) \cdot ((4000^{2}) + (1000^{2})) \cdot 125.6}{4 \cdot 50 \cdot (4000^{2})}

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Modulus of rigidity of shaft given total strain energy in hollow shaft Solution

Follow our step by step solution on how to calculate Modulus of rigidity of shaft given total strain energy in hollow shaft?

FIRST Step Consider the formula

G = \frac{(𝜏^{2}) \cdot (({d outer}^{2}) + ({d inner}^{2})) \cdot V}{4 \cdot U \cdot ({d outer}^{2})}

Next Step Substitute values of Variables

∴

G = \frac{({4E-6MPa}^{2}) \cdot (({4000mm}^{2}) + ({1000mm}^{2})) \cdot 125.6m³}{4 \cdot 50KJ \cdot ({4000mm}^{2})}

Next Step Convert Units

∴

G = \frac{({4Pa}^{2}) \cdot (({4m}^{2}) + ({1m}^{2})) \cdot 125.6m³}{4 \cdot 50000J \cdot ({4m}^{2})}

Next Step Prepare to Evaluate

∴

G = \frac{(4^{2}) \cdot ((4^{2}) + (1^{2})) \cdot 125.6}{4 \cdot 50000 \cdot (4^{2})}

Next Step Evaluate

∴

G = 0.010676Pa

Next Step Convert to Output's Unit

∴

G = 1.0676E-08MPa

LAST Step Rounding Answer

∴

G = 1.1E-8MPa

Modulus of rigidity of shaft given total strain energy in hollow shaft Formula Elements

Variables

Modulus of rigidity of Shaft

Modulus of rigidity of Shaft 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 Shaft

Shear stress on surface of shaft

Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: 𝜏

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear stress on surface of shaft

Outer Diameter of Shaft

Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Diameter of Shaft

Inner Diameter of Shaft

The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

Symbol: d_inner

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Inner Diameter of Shaft

Volume of Shaft

The Volume of Shaft is the volume of cylindical component under torsion.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Volume of Shaft

Strain Energy in body

Strain Energy in body is defined as the energy stored in a body due to deformation.

Symbol: U

Measurement: EnergyUnit: KJ

Note: Value should be greater than 0.

Formulas to find Strain Energy in body

Other Formulas to find Modulus of rigidity of Shaft

Go Modulus of rigidity given shear strain energy

G = (𝜏^{2}) \cdot \frac{V}{2 \cdot U}

Go Modulus of rigidity of shaft given shear strain energy in ring of radius 'r'

G = \frac{2 \cdot π \cdot (𝜏^{2}) \cdot L \cdot ({r center}^{3}) \cdot δx}{2 \cdot U \cdot ({r shaft}^{2})}

Go Modulus of Rigidity of Shaft given Total Strain Energy Stored in Shaft

G = \frac{(𝜏^{2}) \cdot L \cdot J shaft}{2 \cdot U \cdot ({r shaft}^{2})}

Go Modulus of rigidity of shaft given total strain energy in shaft due to torsion

G = \frac{(𝜏^{2}) \cdot V}{4 \cdot U}

Other formulas in Expression for Strain Energy stored in a Body Due to Torsion category

Go Value of radius 'r' given shear stress at radius 'r' from center

r center = \frac{q \cdot r shaft}{𝜏}

Go Radius of shaft given shear stress at radius r from center

r shaft = (\frac{r center}{q}) \cdot 𝜏

Go Shear strain energy

U = (𝜏^{2}) \cdot \frac{V}{2 \cdot G}

Go Volume given shear strain energy

V = \frac{U \cdot 2 \cdot G}{𝜏^{2}}

How to Evaluate Modulus of rigidity of shaft given total strain energy in hollow shaft?

Modulus of rigidity of shaft given total strain energy in hollow shaft evaluator uses Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Strain Energy in body*(Outer Diameter of Shaft^2)) to evaluate the Modulus of rigidity of Shaft, Modulus of rigidity of shaft given total strain energy in hollow shaft is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Modulus of rigidity of Shaft is denoted by G symbol.

How to evaluate Modulus of rigidity of shaft given total strain energy in hollow shaft using this online evaluator? To use this online evaluator for Modulus of rigidity of shaft given total strain energy in hollow shaft, enter Shear stress on surface of shaft (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Strain Energy in body (U) and hit the calculate button.

FAQs on Modulus of rigidity of shaft given total strain energy in hollow shaft

What is the formula to find Modulus of rigidity of shaft given total strain energy in hollow shaft?

The formula of Modulus of rigidity of shaft given total strain energy in hollow shaft is expressed as Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Strain Energy in body*(Outer Diameter of Shaft^2)). Here is an example- 1.1E-14 = ((4^2)*((4^2)+(1^2))*125.6)/(4*50000*(4^2)).

How to calculate Modulus of rigidity of shaft given total strain energy in hollow shaft?

With Shear stress on surface of shaft (𝜏), Outer Diameter of Shaft (d_outer), Inner Diameter of Shaft (d_inner), Volume of Shaft (V) & Strain Energy in body (U) we can find Modulus of rigidity of shaft given total strain energy in hollow shaft using the formula - Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Strain Energy in body*(Outer Diameter of Shaft^2)).

What are the other ways to Calculate Modulus of rigidity of Shaft?

Here are the different ways to Calculate Modulus of rigidity of Shaft-

Modulus of rigidity of Shaft=(Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body)
Modulus of rigidity of Shaft=(2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)/(2*Strain Energy in body*(Radius of Shaft^2))
Modulus of rigidity of Shaft=((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Strain Energy in body*(Radius of Shaft^2))

Can the Modulus of rigidity of shaft given total strain energy in hollow shaft be negative?

No, the Modulus of rigidity of shaft given total strain energy in hollow shaft, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of rigidity of shaft given total strain energy in hollow shaft?

Modulus of rigidity of shaft given total strain energy in hollow shaft is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Modulus of rigidity of shaft given total strain energy in hollow shaft can be measured.

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Modulus of rigidity of shaft given total strain energy in hollow shaft Formula

​GoModulus of rigidity given shear strain energy Formula

​GoModulus of rigidity of shaft given shear strain energy in ring of radius 'r' Formula

Modulus of rigidity of shaft given total strain energy in hollow shaft Example

Modulus of rigidity of shaft given total strain energy in hollow shaft Solution

Modulus of rigidity of shaft given total strain energy in hollow shaft Formula Elements

Other Formulas to find Modulus of rigidity of Shaft

Other formulas in Expression for Strain Energy stored in a Body Due to Torsion category

How to Evaluate Modulus of rigidity of shaft given total strain energy in hollow shaft?

FAQs on Modulus of rigidity of shaft given total strain energy in hollow shaft

Variable Name

GoModulus of rigidity given shear strain energy Formula

GoModulus of rigidity of shaft given shear strain energy in ring of radius 'r' Formula