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

✖Strain Energy in body is defined as the energy stored in a body due to deformation.ⓘ Strain Energy in body [U]			+10% -10%
✖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.ⓘ Modulus of rigidity of Shaft [G]			+10% -10%
✖The Radius of Shaft is the radius of the shaft subjected under torsion.ⓘ Radius of Shaft [r_shaft]			+10% -10%
✖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.ⓘ Shear stress on surface of shaft [𝜏]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖Length of Small Element is a measure of distance.ⓘ Length of Small Element [δx]			+10% -10%

✖Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.ⓘ Value of radius 'r' given shear strain energy in ring of radius 'r' [r_center]

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Formula

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

Formula

`"r"_{"center"} = (("U"*(2*"G"*("r"_{"shaft"}^2)))/(2*pi*("𝜏"^2)*"L"*"U"*"δx"))^(1/3)`

Example

`"2188.875mm"=(("50KJ"*(2*"0.00004MPa"*(("2000mm")^2)))/(2*pi*(("0.000004MPa")^2)*"7000mm"*"50KJ"*"43.36mm"))^(1/3)`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
r_center = ((U*(2*G*(r_shaft^2)))/(2*pi*(𝜏^2)*L*U*δx))^(1/3)
This formula uses 1 Constants, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Radius 'r' from Center Of Shaft - (Measured in Meter) - Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve.
Strain Energy in body - (Measured in Joule) - Strain Energy in body is defined as the energy stored in a body due to deformation.
Modulus of rigidity of Shaft - (Measured in Pascal) - 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.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the radius of the shaft subjected under torsion.
Shear stress on surface of shaft - (Measured in Pascal) - 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.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Length of Small Element - (Measured in Meter) - Length of Small Element is a measure of distance.

STEP 1: Convert Input(s) to Base Unit

Strain Energy in body: 50 Kilojoule --> 50000 Joule (Check conversion here)
Modulus of rigidity of Shaft: 4E-05 Megapascal --> 40 Pascal (Check conversion here)
Radius of Shaft: 2000 Millimeter --> 2 Meter (Check conversion here)
Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Length of Small Element: 43.36 Millimeter --> 0.04336 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_center = ((U*(2*G*(r_shaft^2)))/(2*pi*(𝜏^2)*L*U*δx))^(1/3) --> ((50000*(2*40*(2^2)))/(2*pi*(4^2)*7*50000*0.04336))^(1/3)

Evaluating ... ...

r_center = 2.1888748834864

STEP 3: Convert Result to Output's Unit

2.1888748834864 Meter -->2188.8748834864 Millimeter (Check conversion here)

FINAL ANSWER

2188.8748834864 ≈ 2188.875 Millimeter <-- Radius 'r' from Center Of Shaft

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Expression for Strain Energy stored in a Body Due to Torsion » Value of radius 'r' given shear strain energy in ring of radius 'r'

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< 22 Expression for Strain Energy stored in a Body Due to Torsion Calculators

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

Go 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)

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

Go 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)))

Length of shaft given shear strain energy in ring of radius r

Go Length 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)*(Radius 'r' from Center Of Shaft^3)*Length of Small Element)

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

Go 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))

Shear strain energy in ring of radius 'r'

Go Strain Energy in body = (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*(Radius of Shaft^2))

Inner diameter of shaft given total strain energy in hollow shaft

Go Inner Diameter of Shaft = (((Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/((Shear stress on surface of shaft^2)*Volume of Shaft))-(Outer Diameter of Shaft^2))^(1/2)

Volume of shaft given total strain energy in hollow shaft

Go Volume of Shaft = (Strain Energy in body*(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2)))/((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2)))

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

Go 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))

Total strain energy in hollow shaft due to torsion

Go Strain Energy in body = ((Shear stress on surface of shaft^2)*((Outer Diameter of Shaft^2)+(Inner Diameter of Shaft^2))*Volume of Shaft)/(4*Modulus of rigidity of Shaft*(Outer Diameter of Shaft^2))

Radius of Shaft given Total Strain Energy Stored in Shaft

Go 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)))

Polar Moment of Inertia of Shaft given Total Strain Energy Stored in Shaft

Go Polar Moment of Inertia of shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Length of Shaft)

Length of shaft given total strain energy stored in shaft

Go Length of Shaft = (Strain Energy in body*(2*Modulus of rigidity of Shaft*(Radius of Shaft^2)))/((Shear stress on surface of shaft^2)*Polar Moment of Inertia of shaft)

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

Go 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))

Total Strain Energy Stored in Shaft

Go Strain Energy in body = ((Shear stress on surface of shaft^2)*Length of Shaft*Polar Moment of Inertia of shaft)/(2*Modulus of rigidity of Shaft*(Radius of Shaft^2))

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

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

Radius of shaft given shear stress at radius r from center

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

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

Go Modulus of rigidity of Shaft = ((Shear stress on surface of shaft^2)*Volume of Shaft)/(4*Strain Energy in body)

Volume of Shaft given Total Strain Energy in Shaft due to Torsion

Go Volume of Shaft = (Strain Energy in body*4*Modulus of rigidity of Shaft)/((Shear stress on surface of shaft^2))

Modulus of rigidity given shear strain energy

Go Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body)

Total strain energy in shaft due to torsion

Go Strain Energy in body = ((Shear stress on surface of shaft^2)*Volume of Shaft)/(4*Modulus of rigidity of Shaft)

Shear strain energy

Go Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft)

Volume given shear strain energy

Go Volume of Shaft = (Strain Energy in body*2*Modulus of rigidity of Shaft)/(Shear stress on surface of shaft^2)

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

Is strain energy a material property?

The strain energy (i.e. the amount of potential energy stored due to the deformation) is equal to the work expended in deforming the material. The total strain energy corresponds to the area under the load-deflection curve.

How to Calculate 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' calculator 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 calculate 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 calculate Value of radius 'r' given shear strain energy in ring of radius 'r' using this online calculator? To use this online calculator 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. Here is how the Value of radius 'r' given shear strain energy in ring of radius 'r' calculation can be explained with given input values -> 5.5E+6 = ((50000*(2*40*(2^2)))/(2*pi*(4^2)*7*50000*0.04336))^(1/3).

FAQ

What is 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 a line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as r_center = ((U*(2*G*(r_shaft^2)))/(2*pi*(𝜏^2)*L*U*δx))^(1/3) or 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). Strain Energy in body is defined as the energy stored in a body due to deformation, 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, The Radius of Shaft is the radius of the shaft subjected under torsion, 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, The Length of Shaft is the distance between two ends of shaft & Length of Small Element is a measure of distance.

How to calculate 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 a line segment extending from the center of a circle or sphere to the circumference or bounding surface is calculated using 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 calculate Value of radius 'r' given shear strain energy in ring of radius 'r', you need 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). With our tool, you need to enter the respective value for Strain Energy in body, Modulus of rigidity of Shaft, Radius of Shaft, Shear stress on surface of shaft, Length of Shaft & Length of Small Element and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Radius 'r' from Center Of Shaft?

In this formula, Radius 'r' from Center Of Shaft uses Strain Energy in body, Modulus of rigidity of Shaft, Radius of Shaft, Shear stress on surface of shaft, Length of Shaft & Length of Small Element. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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