Strain Energy in Rod when it is Subjected to External Torque Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
U = (τ^2)*L/(2*J*G)
This formula uses 5 Variables
Variables Used
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.
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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Torque on Rod or Shaft: 1140000 Newton Millimeter --> 1140 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1330 Millimeter --> 1.33 Meter (Check conversion here)
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)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
U = (τ^2)*L/(2*J*G) --> (1140^2)*1.33/(2*2.047E-07*105000000000)
Evaluating ... ...
U = 40.209086468002
STEP 3: Convert Result to Output's Unit
40.209086468002 Joule --> No Conversion Required
FINAL ANSWER
40.209086468002 40.20909 Joule <-- Strain Energy in 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

Strain Energy in Rod when it is Subjected to External Torque Formula

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)
U = (τ^2)*L/(2*J*G)

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 Strain Energy in Rod when it is Subjected to External Torque?

Strain Energy in Rod when it is Subjected to External Torque calculator uses 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) to calculate the Strain Energy in Rod or Shaft, The Strain Energy in Rod when it is Subjected to External Torque formula is defined as type of potential energy that is stored in structural member as result of elastic deformation. Strain Energy in Rod or Shaft is denoted by U symbol.

How to calculate Strain Energy in Rod when it is Subjected to External Torque using this online calculator? To use this online calculator for Strain Energy in Rod when it is Subjected to External Torque, enter Torque on Rod or Shaft (τ), Length of Rod or Shaft (L), Polar Moment of Inertia of rod or shaft (J) & Modulus of rigidity of rod or shaft (G) and hit the calculate button. Here is how the Strain Energy in Rod when it is Subjected to External Torque calculation can be explained with given input values -> 40.20909 = (1140^2)*1.33/(2*2.047E-07*105000000000).

FAQ

What is Strain Energy in Rod when it is Subjected to External Torque?
The Strain Energy in Rod when it is Subjected to External Torque formula is defined as type of potential energy that is stored in structural member as result of elastic deformation and is represented as U = (τ^2)*L/(2*J*G) or 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). 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, Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom, 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.
How to calculate Strain Energy in Rod when it is Subjected to External Torque?
The Strain Energy in Rod when it is Subjected to External Torque formula is defined as type of potential energy that is stored in structural member as result of elastic deformation is calculated using 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). To calculate Strain Energy in Rod when it is Subjected to External Torque, you need Torque on Rod or Shaft (τ), Length of Rod or Shaft (L), Polar Moment of Inertia of rod or shaft (J) & Modulus of rigidity of rod or shaft (G). With our tool, you need to enter the respective value for Torque on Rod or Shaft, Length of Rod or Shaft, Polar Moment of Inertia of rod or shaft & Modulus of rigidity of 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 Strain Energy in Rod or Shaft?
In this formula, Strain Energy in Rod or Shaft uses Torque on Rod or Shaft, Length of Rod or Shaft, Polar Moment of Inertia of rod or shaft & Modulus of rigidity of rod or shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • 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)
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