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)
rcenter = ((U*(2*G*(rshaft^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
rcenter = ((U*(2*G*(rshaft^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 ... ...
rcenter = 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 00.004 seconds)

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

Value of radius 'r' given shear stress at radius 'r' from center
​ LaTeX ​ 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
​ LaTeX ​ 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 given shear strain energy
​ LaTeX ​ Go Modulus of rigidity of Shaft = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Strain Energy in body)
Shear strain energy
​ LaTeX ​ Go Strain Energy in body = (Shear stress on surface of shaft^2)*(Volume of Shaft)/(2*Modulus of rigidity of Shaft)

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

​LaTeX ​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)
rcenter = ((U*(2*G*(rshaft^2)))/(2*pi*(𝜏^2)*L*U*δx))^(1/3)

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 rcenter 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 (rshaft), 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 rcenter = ((U*(2*G*(rshaft^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 (rshaft), 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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