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Radius of Shaft given Total Strain Energy Stored in Shaft Formula

GoRadius of shaft given shear stress at radius r from center Formula

GoRadius of shaft given shear strain energy in ring of radius r Formula

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The Radius of Shaft is the radius of the shaft subjected under torsion. Check FAQs

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

r_shaft - Radius of Shaft?𝜏 - Shear stress on surface of shaft?L - Length of Shaft?J_shaft - Polar Moment of Inertia of shaft?G - Modulus of rigidity of Shaft?U - Strain Energy in body?

Radius of Shaft given Total Strain Energy Stored in Shaft Example

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Here is how the Radius of Shaft given Total Strain Energy Stored in Shaft equation looks like with Values.

Here is how the Radius of Shaft given Total Strain Energy Stored in Shaft equation looks like with Units.

Here is how the Radius of Shaft given Total Strain Energy Stored in Shaft equation looks like.

16.7332 = \sqrt{\frac{({4E-6}^{2}) \cdot 7000 \cdot 10}{2 \cdot 4E-5 \cdot (50)}}

16.7332mm = \sqrt{\frac{({4E-6MPa}^{2}) \cdot 7000mm \cdot 10m⁴}{2 \cdot 4E-5MPa \cdot (50KJ)}}

16.7332 = \sqrt{\frac{({4E-6}^{2}) \cdot 7000 \cdot 10}{2 \cdot 4E-5 \cdot (50)}}

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Radius of Shaft given Total Strain Energy Stored in Shaft Solution

Follow our step by step solution on how to calculate Radius of Shaft given Total Strain Energy Stored in Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r shaft = \sqrt{\frac{({4E-6MPa}^{2}) \cdot 7000mm \cdot 10m⁴}{2 \cdot 4E-5MPa \cdot (50KJ)}}

Next Step Convert Units

∴

r shaft = \sqrt{\frac{({4Pa}^{2}) \cdot 7m \cdot 10m⁴}{2 \cdot 40Pa \cdot (50000J)}}

Next Step Prepare to Evaluate

∴

r shaft = \sqrt{\frac{(4^{2}) \cdot 7 \cdot 10}{2 \cdot 40 \cdot (50000)}}

Next Step Evaluate

∴

r shaft = 0.0167332005306815m

Next Step Convert to Output's Unit

∴

r shaft = 16.7332005306815mm

LAST Step Rounding Answer

∴

r shaft = 16.7332mm

Radius of Shaft given Total Strain Energy Stored in Shaft Formula Elements

Variables

Functions

Radius of Shaft

The Radius of Shaft is the radius of the shaft subjected under torsion.

Symbol: r_shaft

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Radius 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

Length of Shaft

The Length of Shaft is the distance between two ends of shaft.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Polar Moment of Inertia of shaft

Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

Symbol: J_shaft

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia of shaft

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Radius of Shaft

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

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

Go Radius of shaft given shear strain energy in ring of radius r

r shaft = \sqrt{\frac{2 \cdot π \cdot (𝜏^{2}) \cdot L \cdot ({r center}^{3}) \cdot δx}{2 \cdot G \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 Shear strain energy

U = (𝜏^{2}) \cdot \frac{V}{2 \cdot G}

Go Modulus of rigidity given shear strain energy

G = (𝜏^{2}) \cdot \frac{V}{2 \cdot U}

Go Volume given shear strain energy

V = \frac{U \cdot 2 \cdot G}{𝜏^{2}}

How to Evaluate Radius of Shaft given Total Strain Energy Stored in Shaft?

Radius of Shaft given Total Strain Energy Stored in Shaft evaluator uses Radius of Shaft = sqrt(((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Strain Energy in body))) to evaluate the Radius of Shaft, The Radius of Shaft given Total Strain Energy Stored in Shaft formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Radius of Shaft is denoted by r_shaft symbol.

How to evaluate Radius of Shaft given Total Strain Energy Stored in Shaft using this online evaluator? To use this online evaluator for Radius of Shaft given Total Strain Energy Stored in Shaft, enter Shear stress on surface of shaft (𝜏), Length of Shaft (L), Polar Moment of Inertia of shaft (J_shaft), Modulus of rigidity of Shaft (G) & Strain Energy in body (U) and hit the calculate button.

FAQs on Radius of Shaft given Total Strain Energy Stored in Shaft

What is the formula to find Radius of Shaft given Total Strain Energy Stored in Shaft?

The formula of Radius of Shaft given Total Strain Energy Stored in Shaft is expressed as Radius of Shaft = sqrt(((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Strain Energy in body))). Here is an example- 16733.2 = sqrt(((4^2)*7*10)/(2*40*(50000))).

How to calculate Radius of Shaft given Total Strain Energy Stored in Shaft?

With Shear stress on surface of shaft (𝜏), Length of Shaft (L), Polar Moment of Inertia of shaft (J_shaft), Modulus of rigidity of Shaft (G) & Strain Energy in body (U) we can find Radius of Shaft given Total Strain Energy Stored in Shaft using the formula - Radius of Shaft = sqrt(((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Strain Energy in body))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Radius of Shaft?

Here are the different ways to Calculate Radius of Shaft-

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

Can the Radius of Shaft given Total Strain Energy Stored in Shaft be negative?

Yes, the Radius of Shaft given Total Strain Energy Stored in Shaft, measured in Length can be negative.

Which unit is used to measure Radius of Shaft given Total Strain Energy Stored in Shaft?

Radius of Shaft given Total Strain Energy Stored in Shaft is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Shaft given Total Strain Energy Stored in Shaft can be measured.

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Radius of Shaft given Total Strain Energy Stored in Shaft Formula

​GoRadius of shaft given shear stress at radius r from center Formula

​GoRadius of shaft given shear strain energy in ring of radius r Formula

Radius of Shaft given Total Strain Energy Stored in Shaft Example

Radius of Shaft given Total Strain Energy Stored in Shaft Solution

Radius of Shaft given Total Strain Energy Stored in Shaft Formula Elements

Other Formulas to find Radius of Shaft

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

How to Evaluate Radius of Shaft given Total Strain Energy Stored in Shaft?

FAQs on Radius of Shaft given Total Strain Energy Stored in Shaft

Variable Name

GoRadius of shaft given shear stress at radius r from center Formula

GoRadius of shaft given shear strain energy in ring of radius r Formula