Inner diameter of shaft given total strain energy in hollow shaft 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%
✖Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_outer]			+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 Volume of Shaft is the volume of cylindical component under torsion.ⓘ Volume of Shaft [V]			+10% -10%

✖The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.ⓘ Inner diameter of shaft given total strain energy in hollow shaft [d_inner]

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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)
d_inner = (((U*(4*G*(d_outer^2)))/((𝜏^2)*V))-(d_outer^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

d_inner = (((U*(4*G*(d_outer^2)))/((𝜏^2)*V))-(d_outer^2))^(1/2) --> (((50000*(4*40*(4^2)))/((4^2)*125.6))-(4^2))^(1/2)

Evaluating ... ...

d_inner = 252.345531991204

STEP 3: Convert Result to Output's Unit

252.345531991204 Meter -->252345.531991204 Millimeter (Check conversion here)

FINAL ANSWER

252345.531991204 ≈ 252345.5 Millimeter <-- Inner Diameter of Shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Expression for Strain Energy stored in a Body Due to Torsion » Inner diameter of shaft given total strain energy in hollow shaft

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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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)

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

LaTeX Go

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 d_inner 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 (d_outer), Shear stress on surface of shaft (𝜏) & 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 d_inner = (((U*(4*G*(d_outer^2)))/((𝜏^2)*V))-(d_outer^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 (d_outer), Shear stress on surface of shaft (𝜏) & 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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