Length of Shaft when Strain Energy in Shaft Subjected to External Torque Calculator

✖Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.ⓘ Strain Energy in Rod or Shaft [U]			+10% -10%
✖Polar Moment of Inertia of rod or shaft is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Polar Moment of Inertia of rod or shaft [J]			+10% -10%
✖Modulus of rigidity of rod or 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 rod or shaft [G]			+10% -10%
✖Torque on Rod or Shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.ⓘ Torque on Rod or Shaft [τ]			+10% -10%

✖Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.ⓘ Length of Shaft when Strain Energy in Shaft Subjected to External Torque [L]

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Formula

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Length of Shaft when Strain Energy in Shaft Subjected to External Torque

Formula

`"L" = (2*"U"*"J"*"G")/("τ"^2)`

Example

`"1323.084mm"=(2*"40J"*"20.47E4mm⁴"*"1.05E5N/mm²")/(("1.14E6N*mm")^2)`

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Length of Shaft when Strain Energy in Shaft Subjected to External Torque Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2)
L = (2*U*J*G)/(τ^2)
This formula uses 5 Variables

Variables Used

Length of Rod or Shaft - (Measured in Meter) - Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.
Strain Energy in Rod or Shaft - (Measured in Joule) - Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.
Polar Moment of Inertia of rod or shaft - (Measured in Meter⁴) - Polar Moment of Inertia of rod or shaft is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.
Modulus of rigidity of rod or shaft - (Measured in Pascal) - Modulus of rigidity of rod or 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.
Torque on Rod or Shaft - (Measured in Newton Meter) - Torque on Rod or Shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.

STEP 1: Convert Input(s) to Base Unit

Strain Energy in Rod or Shaft: 40 Joule --> 40 Joule No Conversion Required
Polar Moment of Inertia of rod or shaft: 204700 Millimeter⁴ --> 2.047E-07 Meter⁴ (Check conversion here)
Modulus of rigidity of rod or shaft: 105000 Newton per Square Millimeter --> 105000000000 Pascal (Check conversion here)
Torque on Rod or Shaft: 1140000 Newton Millimeter --> 1140 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (2*U*J*G)/(τ^2) --> (2*40*2.047E-07*105000000000)/(1140^2)

Evaluating ... ...

L = 1.32308402585411

STEP 3: Convert Result to Output's Unit

1.32308402585411 Meter -->1323.08402585411 Millimeter (Check conversion here)

FINAL ANSWER

1323.08402585411 ≈ 1323.084 Millimeter <-- Length of Rod or Shaft

(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad

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< 14 Castigliano's Theorem for Deflection in Complex Structures Calculators

Torque given Strain Energy in Rod Subjected to External Torque

Go Torque on Rod or Shaft = sqrt(2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft/Length of Rod or Shaft)

Force Applied on Rod given Strain Energy Stored in Tension Rod

Go Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft)

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment

Go Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft)

Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment

Go Modulus of elasticity of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Area Moment of Inertia of rod or shaft)

Strain Energy Stored in Rod Subjected to Bending Moment

Go Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft)

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment

Go Length of Rod or Shaft = 2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft/(Bending Moment in Shaft or Beam^2)

Length of Shaft when Strain Energy in Shaft Subjected to External Torque

Go Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2)

Strain Energy in Rod when it is Subjected to External Torque

Go Strain Energy in Rod or Shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)

Polar Moment of Inertia of Rod given Strain Energy in Rod

Go Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft)

Modulus of Rigidity of Rod given Strain Energy in Rod

Go Modulus of rigidity of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Strain Energy in Rod or Shaft)

Strain Energy Stored in Tension Rod

Go Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft)

Cross-sectional Area of Rod given Strain Energy stored in Rod

Go Cross Sectional Area of Rod = Axial Force on Beam^2*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft)

Modulus of Elasticity of Rod given Strain Energy Stored

Go Modulus of elasticity of rod or shaft = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy in Rod or Shaft)

Length of Rod given Strain Energy Stored

Go Length of Rod or Shaft = Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Axial Force on Beam^2

Length of Shaft when Strain Energy in Shaft Subjected to External Torque Formula

Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2)
L = (2*U*J*G)/(τ^2)

Define Strain Energy?

Strain energy is a type of potential energy that is stored in a structural member as a result of elastic deformation. The external work done on such a member when it is deformed from its unstressed state is transformed into, and considered equal to the strain energy stored in it.

How to Calculate Length of Shaft when Strain Energy in Shaft Subjected to External Torque?

Length of Shaft when Strain Energy in Shaft Subjected to External Torque calculator uses Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2) to calculate the Length of Rod or Shaft, The Length of Shaft when Strain Energy in Shaft Subjected to External Torque formula is defined as total length of shaft on which we are applying external torque to observe deflections and internal energy of shaft. Length of Rod or Shaft is denoted by L symbol.

How to calculate Length of Shaft when Strain Energy in Shaft Subjected to External Torque using this online calculator? To use this online calculator for Length of Shaft when Strain Energy in Shaft Subjected to External Torque, enter Strain Energy in Rod or Shaft (U), Polar Moment of Inertia of rod or shaft (J), Modulus of rigidity of rod or shaft (G) & Torque on Rod or Shaft (τ) and hit the calculate button. Here is how the Length of Shaft when Strain Energy in Shaft Subjected to External Torque calculation can be explained with given input values -> 1.3E+6 = (2*40*2.047E-07*105000000000)/(1140^2).

FAQ

What is Length of Shaft when Strain Energy in Shaft Subjected to External Torque?

The Length of Shaft when Strain Energy in Shaft Subjected to External Torque formula is defined as total length of shaft on which we are applying external torque to observe deflections and internal energy of shaft and is represented as L = (2*U*J*G)/(τ^2) or Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2). Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation, Polar Moment of Inertia of rod or shaft is a shaft or beam's resistance to being distorted by torsion, as a function of its shape, Modulus of rigidity of rod or 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 & Torque on Rod or Shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.

How to calculate Length of Shaft when Strain Energy in Shaft Subjected to External Torque?

The Length of Shaft when Strain Energy in Shaft Subjected to External Torque formula is defined as total length of shaft on which we are applying external torque to observe deflections and internal energy of shaft is calculated using Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2). To calculate Length of Shaft when Strain Energy in Shaft Subjected to External Torque, you need Strain Energy in Rod or Shaft (U), Polar Moment of Inertia of rod or shaft (J), Modulus of rigidity of rod or shaft (G) & Torque on Rod or Shaft (τ). With our tool, you need to enter the respective value for Strain Energy in Rod or Shaft, Polar Moment of Inertia of rod or shaft, Modulus of rigidity of rod or shaft & Torque on Rod or 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 Rod or Shaft?

In this formula, Length of Rod or Shaft uses Strain Energy in Rod or Shaft, Polar Moment of Inertia of rod or shaft, Modulus of rigidity of rod or shaft & Torque on Rod or Shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of Rod or Shaft = Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Axial Force on Beam^2
Length of Rod or Shaft = 2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft/(Bending Moment in Shaft or Beam^2)

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