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Value of radius 'r' given shear strain energy in ring of radius 'r' Formula

GoValue of radius 'r' given shear stress at radius 'r' from center Formula

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Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve. Check FAQs

r center = {(\frac{U \cdot (2 \cdot G \cdot ({r shaft}^{2}))}{2 \cdot π \cdot (𝜏^{2}) \cdot L \cdot U \cdot δx})}^{\frac{1}{3}}

r_center - Radius 'r' from Center Of Shaft?U - Strain Energy in body?G - Modulus of rigidity of Shaft?r_shaft - Radius of Shaft?𝜏 - Shear stress on surface of shaft?L - Length of Shaft?δx - Length of Small Element?π - Archimedes' constant?

Value of radius 'r' given shear strain energy in ring of radius 'r' Example

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Here is how the Value of radius 'r' given shear strain energy in ring of radius 'r' equation looks like with Values.

Here is how the Value of radius 'r' given shear strain energy in ring of radius 'r' equation looks like with Units.

Here is how the Value of radius 'r' given shear strain energy in ring of radius 'r' equation looks like.

2188.8749 = {(\frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{2 \cdot 3.1416 \cdot ({4E-6}^{2}) \cdot 7000 \cdot 50 \cdot 43.36})}^{\frac{1}{3}}

2188.8749mm = {(\frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot 3.1416 \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot 50KJ \cdot 43.36mm})}^{\frac{1}{3}}

2188.8749 = {(\frac{50 \cdot (2 \cdot 4E-5 \cdot (2000^{2}))}{2 \cdot 3.1416 \cdot ({4E-6}^{2}) \cdot 7000 \cdot 50 \cdot 43.36})}^{\frac{1}{3}}

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Value of radius 'r' given shear strain energy in ring of radius 'r' Solution

Follow our step by step solution on how to calculate Value of radius 'r' given shear strain energy in ring of radius 'r'?

FIRST Step Consider the formula

r center = {(\frac{U \cdot (2 \cdot G \cdot ({r shaft}^{2}))}{2 \cdot π \cdot (𝜏^{2}) \cdot L \cdot U \cdot δx})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

r center = {(\frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot π \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot 50KJ \cdot 43.36mm})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

r center = {(\frac{50KJ \cdot (2 \cdot 4E-5MPa \cdot ({2000mm}^{2}))}{2 \cdot 3.1416 \cdot ({4E-6MPa}^{2}) \cdot 7000mm \cdot 50KJ \cdot 43.36mm})}^{\frac{1}{3}}

Next Step Convert Units

∴

r center = {(\frac{50000J \cdot (2 \cdot 40Pa \cdot ({2m}^{2}))}{2 \cdot 3.1416 \cdot ({4Pa}^{2}) \cdot 7m \cdot 50000J \cdot 0.0434m})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

r center = {(\frac{50000 \cdot (2 \cdot 40 \cdot (2^{2}))}{2 \cdot 3.1416 \cdot (4^{2}) \cdot 7 \cdot 50000 \cdot 0.0434})}^{\frac{1}{3}}

Next Step Evaluate

∴

r center = 2.1888748834864m

Next Step Convert to Output's Unit

∴

r center = 2188.8748834864mm

LAST Step Rounding Answer

∴

r center = 2188.8749mm

Value of radius 'r' given shear strain energy in ring of radius 'r' Formula Elements

Variables

Constants

Radius 'r' from Center Of Shaft

Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.

Symbol: r_center

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius 'r' from Center 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

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

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

Length of Small Element

Length of Small Element is a measure of distance.

Symbol: δx

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Small Element

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Radius 'r' from Center Of Shaft

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

r center = \frac{q \cdot r shaft}{𝜏}

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

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}

How to Evaluate Value of radius 'r' given shear strain energy in ring of radius 'r'?

Value of radius 'r' given shear strain energy in ring of radius 'r' evaluator uses Radius 'r' from Center Of Shaft = ((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*Strain Energy in body*Length of Small Element))^(1/3) to evaluate the Radius 'r' from Center Of Shaft, Value of radius 'r' given shear strain energy in ring of radius 'r' is a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Radius 'r' from Center Of Shaft is denoted by r_center symbol.

How to evaluate Value of radius 'r' given shear strain energy in ring of radius 'r' using this online evaluator? To use this online evaluator for Value of radius 'r' given shear strain energy in ring of radius 'r', enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Shear stress on surface of shaft (𝜏), Length of Shaft (L) & Length of Small Element (δx) and hit the calculate button.

FAQs on Value of radius 'r' given shear strain energy in ring of radius 'r'

What is the formula to find Value of radius 'r' given shear strain energy in ring of radius 'r'?

The formula of Value of radius 'r' given shear strain energy in ring of radius 'r' is expressed as Radius 'r' from Center Of Shaft = ((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*Strain Energy in body*Length of Small Element))^(1/3). Here is an example- 5.5E+6 = ((50000*(2*40*(2^2)))/(2*pi*(4^2)*7*50000*0.04336))^(1/3).

How to calculate Value of radius 'r' given shear strain energy in ring of radius 'r'?

With Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Shear stress on surface of shaft (𝜏), Length of Shaft (L) & Length of Small Element (δx) we can find Value of radius 'r' given shear strain energy in ring of radius 'r' using the formula - Radius 'r' from Center Of Shaft = ((Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/(2*pi*(Shear stress on surface of shaft^2)*Length of Shaft*Strain Energy in body*Length of Small Element))^(1/3). This formula also uses Archimedes' constant .

What are the other ways to Calculate Radius 'r' from Center Of Shaft?

Here are the different ways to Calculate Radius 'r' from Center Of Shaft-

Radius 'r' from Center Of Shaft=(Shear stress at radius 'r' from shaft*Radius of Shaft)/Shear stress on surface of shaft

Can the Value of radius 'r' given shear strain energy in ring of radius 'r' be negative?

No, the Value of radius 'r' given shear strain energy in ring of radius 'r', measured in Length cannot be negative.

Which unit is used to measure Value of radius 'r' given shear strain energy in ring of radius 'r'?

Value of radius 'r' given shear strain energy in ring of radius 'r' is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Value of radius 'r' given shear strain energy in ring of radius 'r' can be measured.

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Value of radius 'r' given shear strain energy in ring of radius 'r' Formula

​GoValue of radius 'r' given shear stress at radius 'r' from center Formula

Value of radius 'r' given shear strain energy in ring of radius 'r' Example

Value of radius 'r' given shear strain energy in ring of radius 'r' Solution

Value of radius 'r' given shear strain energy in ring of radius 'r' Formula Elements

Other Formulas to find Radius 'r' from Center Of Shaft

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

How to Evaluate Value of radius 'r' given shear strain energy in ring of radius 'r'?

FAQs on Value of radius 'r' given shear strain energy in ring of radius 'r'

Variable Name

GoValue of radius 'r' given shear stress at radius 'r' from center Formula