Length of shaft given total strain energy stored in 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%
✖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%
✖Polar Moment of Inertia of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of shaft [J_shaft]			+10% -10%

✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of shaft given total strain energy stored in shaft [L]

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Length of shaft given total strain energy stored in shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
L = (U*(2*G*(r_shaft^2)))/((𝜏^2)*J_shaft)
This formula uses 6 Variables

Variables Used

Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of 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.
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.
Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to 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)
Radius of Shaft: 2000 Millimeter --> 2 Meter (Check conversion here)
Shear stress on surface of shaft: 4E-06 Megapascal --> 4 Pascal (Check conversion here)
Polar Moment of Inertia of shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (U*(2*G*(r_shaft^2)))/((𝜏^2)*J_shaft) --> (50000*(2*40*(2^2)))/((4^2)*10)

Evaluating ... ...

L = 100000

STEP 3: Convert Result to Output's Unit

100000 Meter -->100000000 Millimeter (Check conversion here)

FINAL ANSWER

100000000 ≈ 1E+8 Millimeter <-- Length of Shaft

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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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)

Length of shaft given total strain energy stored in shaft Formula

LaTeX Go

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 Length of shaft given total strain energy stored in shaft?

Length of shaft given total strain energy stored in shaft calculator uses 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) to calculate the Length of Shaft, Length of shaft given total strain energy stored in shaft is defined as the measurement or extent of something from end to end. Length of Shaft is denoted by L symbol.

How to calculate Length of shaft given total strain energy stored in shaft using this online calculator? To use this online calculator for Length of shaft given total strain energy stored in shaft, enter Strain Energy in body (U), Modulus of rigidity of Shaft (G), Radius of Shaft (r_shaft), Shear stress on surface of shaft (𝜏) & Polar Moment of Inertia of shaft (J_shaft) and hit the calculate button. Here is how the Length of shaft given total strain energy stored in shaft calculation can be explained with given input values -> 1E+11 = (50000*(2*40*(2^2)))/((4^2)*10).

FAQ

What is Length of shaft given total strain energy stored in shaft?

Length of shaft given total strain energy stored in shaft is defined as the measurement or extent of something from end to end and is represented as L = (U*(2*G*(r_shaft^2)))/((𝜏^2)*J_shaft) or 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). 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 & Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

How to calculate Length of shaft given total strain energy stored in shaft?

Length of shaft given total strain energy stored in shaft is defined as the measurement or extent of something from end to end is calculated using 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). To calculate Length of shaft given total strain energy stored in shaft, 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) & Polar Moment of Inertia of shaft (J_shaft). 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 & Polar Moment of Inertia of shaft 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 Length of Shaft?

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

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)

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