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

STEP 0: Pre-Calculation Summary
Formula Used
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)))
rshaft = sqrt((2*pi*(𝜏^2)*L*(rcenter^3)*δx)/(2*G*(U)))
This formula uses 1 Constants, 1 Functions, 7 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
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., sqrt(Number)
Variables Used
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.
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.
Length of Small Element - (Measured in Meter) - Length of Small Element is a measure of distance.
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.
Strain Energy in body - (Measured in Joule) - Strain Energy in body is defined as the energy stored in a body due to deformation.
STEP 1: Convert Input(s) to Base Unit
Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Radius 'r' from Center Of Shaft: 1500 Millimeter --> 1.5 Meter (Check conversion here)
Length of Small Element: 43.36 Millimeter --> 0.04336 Meter (Check conversion here)
Modulus of rigidity of Shaft: 4E-05 Megapascal --> 40 Pascal (Check conversion here)
Strain Energy in body: 50 Kilojoule --> 50000 Joule (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rshaft = sqrt((2*pi*(𝜏^2)*L*(rcenter^3)*δx)/(2*G*(U))) --> sqrt((2*pi*(4^2)*7*(1.5^3)*0.04336)/(2*40*(50000)))
Evaluating ... ...
rshaft = 0.00507400014385834
STEP 3: Convert Result to Output's Unit
0.00507400014385834 Meter -->5.07400014385834 Millimeter (Check conversion here)
FINAL ANSWER
5.07400014385834 5.074 Millimeter <-- Radius of Shaft
(Calculation completed in 00.004 seconds)

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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)

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

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

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 and has units of in-lbf in US Customary units and N-m in SI units.

How to Calculate Radius of shaft given shear strain energy in ring of radius r?

Radius of shaft given shear strain energy in ring of radius r calculator uses 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))) to calculate the Radius of Shaft, Radius of shaft 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 of Shaft is denoted by rshaft symbol.

How to calculate Radius of shaft given shear strain energy in ring of radius r using this online calculator? To use this online calculator for Radius of shaft given shear strain energy in ring of radius r, enter Shear stress on surface of shaft (𝜏), Length of Shaft (L), Radius 'r' from Center Of Shaft (rcenter), Length of Small Element (δx), Modulus of rigidity of Shaft (G) & Strain Energy in body (U) and hit the calculate button. Here is how the Radius of shaft given shear strain energy in ring of radius r calculation can be explained with given input values -> 1266.157 = sqrt((2*pi*(4^2)*7*(1.5^3)*0.04336)/(2*40*(50000))).

FAQ

What is Radius of shaft given shear strain energy in ring of radius r?
Radius of shaft 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 rshaft = sqrt((2*pi*(𝜏^2)*L*(rcenter^3)*δx)/(2*G*(U))) or 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))). 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, Radius 'r' from Center Of Shaft is a radial line from the focus to any point of a curve, Length of Small Element is a measure of distance, 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 & Strain Energy in body is defined as the energy stored in a body due to deformation.
How to calculate Radius of shaft given shear strain energy in ring of radius r?
Radius of shaft 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 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))). To calculate Radius of shaft given shear strain energy in ring of radius r, you need Shear stress on surface of shaft (𝜏), Length of Shaft (L), Radius 'r' from Center Of Shaft (rcenter), Length of Small Element (δx), Modulus of rigidity of Shaft (G) & Strain Energy in body (U). With our tool, you need to enter the respective value for Shear stress on surface of shaft, Length of Shaft, Radius 'r' from Center Of Shaft, Length of Small Element, Modulus of rigidity of Shaft & Strain Energy in body 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 of Shaft?
In this formula, Radius of Shaft uses Shear stress on surface of shaft, Length of Shaft, Radius 'r' from Center Of Shaft, Length of Small Element, Modulus of rigidity of Shaft & Strain Energy in body. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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(((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)))
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