Inner diameter of shaft given total strain energy in hollow shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
dinner = (((U*(4*G*(douter^2)))/((๐œ^2)*V))-(douter^2))^(1/2)
This formula uses 6 Variables
Variables Used
Inner Diameter of Shaft - (Measured in Meter) - The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.
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.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
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.
Volume of Shaft - (Measured in Cubic Meter) - The Volume of Shaft is the volume of cylindical component under torsion.
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)
Outer Diameter of Shaft: 4000 Millimeter --> 4 Meter (Check conversion here)
Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Volume of Shaft: 125.6 Cubic Meter --> 125.6 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dinner = (((U*(4*G*(douter^2)))/((๐œ^2)*V))-(douter^2))^(1/2) --> (((50000*(4*40*(4^2)))/((4^2)*125.6))-(4^2))^(1/2)
Evaluating ... ...
dinner = 252.345531991204
STEP 3: Convert Result to Output's Unit
252.345531991204 Meter -->252345.531991204 Millimeter (Check conversion here)
FINAL ANSWER
252345.531991204 โ‰ˆ 252345.5 Millimeter <-- Inner Diameter of Shaft
(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur
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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)

Inner diameter of shaft given total strain energy in hollow shaft Formula

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)
dinner = (((U*(4*G*(douter^2)))/((๐œ^2)*V))-(douter^2))^(1/2)

What is the difference between strain energy and resilience?

Strain energy is elastic that is, the material tends to recover when the load is removed. Resilience is typically expressed as the modulus of resilience, which is the amount of strain energy the material can store per unit of volume without causing permanent deformation.

How to Calculate Inner diameter of shaft given total strain energy in hollow shaft?

Inner diameter of shaft given total strain energy in hollow shaft calculator uses 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) to calculate the Inner Diameter of Shaft, Inner diameter of shaft given total strain energy in hollow shaft is defined as a chord that runs through the center point of the circle. It is the longest possible chord of any circle. Inner Diameter of Shaft is denoted by dinner symbol.

How to calculate Inner diameter of shaft given total strain energy in hollow shaft using this online calculator? To use this online calculator for Inner diameter of shaft given total strain energy in hollow shaft, enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Outer Diameter of Shaft (douter), Shear stress on surface of shaft (๐œ) & Volume of Shaft (V) and hit the calculate button. Here is how the Inner diameter of shaft given total strain energy in hollow shaft calculation can be explained with given input values -> 2.5E+8 = (((50000*(4*40*(4^2)))/((4^2)*125.6))-(4^2))^(1/2).

FAQ

What is Inner diameter of shaft given total strain energy in hollow shaft?
Inner diameter of shaft given total strain energy in hollow shaft is defined as a chord that runs through the center point of the circle. It is the longest possible chord of any circle and is represented as dinner = (((U*(4*G*(douter^2)))/((๐œ^2)*V))-(douter^2))^(1/2) or 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). 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, Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular 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 & The Volume of Shaft is the volume of cylindical component under torsion.
How to calculate Inner diameter of shaft given total strain energy in hollow shaft?
Inner diameter of shaft given total strain energy in hollow shaft is defined as a chord that runs through the center point of the circle. It is the longest possible chord of any circle is calculated using 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). To calculate Inner diameter of shaft given total strain energy in hollow shaft, you need Strain Energy in body (U), Modulus of rigidity of Shaft (G), Outer Diameter of Shaft (douter), Shear stress on surface of shaft (๐œ) & Volume of Shaft (V). With our tool, you need to enter the respective value for Strain Energy in body, Modulus of rigidity of Shaft, Outer Diameter of Shaft, Shear stress on surface of shaft & Volume of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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