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Length of Shaft When Strain Energy in the Shaft Subjected to External Torque Solution

STEP 0: Pre-Calculation Summary
Formula Used
length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2)
l = U*J*C/(τ^2)
This formula uses 4 Variables
Variables Used
Strain Energy - The Strain energy is defined as the energy stored in a body due to deformation. (Measured in Joule)
Polar moment of Inertia - The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. (Measured in Kilogram Meter²)
Modulus of rigidity - Modulus of rigidity 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. (Measured in Newton per Square Meter)
Torque - Torque is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ. (Measured in Newton Meter)
STEP 1: Convert Input(s) to Base Unit
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
Polar moment of Inertia: 50 Kilogram Meter² --> 50 Kilogram Meter² No Conversion Required
Modulus of rigidity: 50 Newton per Square Meter --> 50 Pascal (Check conversion here)
Torque: 50 Newton Meter --> 50 Newton Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = U*J*C/(τ^2) --> 50*50*50/(50^2)
Evaluating ... ...
l = 50
STEP 3: Convert Result to Output's Unit
50 Meter --> No Conversion Required
FINAL ANSWER
50 Meter <-- Length of Shaft
(Calculation completed in 00.016 seconds)

10+ Castigliano's Theorem Calculators

Force Applied on the Rod When Strain Energy Stored in Tension Rod is Given
axial_force = sqrt(Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Length of Rod) Go
Torque When Strain Energy in the Rod When Subjected to External Torque is Given
torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft) Go
Strain Energy Stored in the Rod Subjected to Bending Moment
strain_energy = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Moment of Inertia Go
Modulus of Elasticity of the Rod When Strain Energy Stored is Given
modulus_of_elasticity = Axial Force^2*Length of Rod/2*Cross sectional area*Strain Energy Go
Length of the Rod When Strain Energy Stored is Given
length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2 Go
Strain Energy Stored in Tension Rod
strain_energy = Axial Force^2*Length of Rod/2*Cross sectional area*Modulus Of Elasticity Go
Length of Shaft When Strain Energy in the Shaft Subjected to External Torque
length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2) Go
Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given
polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity Go
Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given
modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy Go
Strain Energy in the Rod When it is Subjected to External Torque
strain_energy = (Torque^2)*Length of Shaft/Polar moment of Inertia*Modulus of rigidity Go

Length of Shaft When Strain Energy in the Shaft Subjected to External Torque Formula

length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2)
l = U*J*C/(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 the Shaft Subjected to External Torque?

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

How to calculate Length of Shaft When Strain Energy in the Shaft Subjected to External Torque using this online calculator? To use this online calculator for Length of Shaft When Strain Energy in the Shaft Subjected to External Torque, enter Strain Energy (U), Polar moment of Inertia (J), Modulus of rigidity (C) and Torque (τ) and hit the calculate button. Here is how the Length of Shaft When Strain Energy in the Shaft Subjected to External Torque calculation can be explained with given input values -> 50 = 50*50*50/(50^2).

FAQ

What is Length of Shaft When Strain Energy in the Shaft Subjected to External Torque?
The Length of Shaft When Strain Energy in the Shaft Subjected to External Torque formula is defined as the total length of the shaft on which we are applying external torque to observe the deflections and internal energy of shaft, and is represented as l = U*J*C/(τ^2) or length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2). The Strain energy is defined as the energy stored in a body due to deformation, The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape, Modulus of rigidity 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 and Torque is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.
How to calculate Length of Shaft When Strain Energy in the Shaft Subjected to External Torque?
The Length of Shaft When Strain Energy in the Shaft Subjected to External Torque formula is defined as the total length of the shaft on which we are applying external torque to observe the deflections and internal energy of shaft, is calculated using length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2). To calculate Length of Shaft When Strain Energy in the Shaft Subjected to External Torque, you need Strain Energy (U), Polar moment of Inertia (J), Modulus of rigidity (C) and Torque (τ). With our tool, you need to enter the respective value for Strain Energy, Polar moment of Inertia, Modulus of rigidity and Torque 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, Polar moment of Inertia, Modulus of rigidity and Torque. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • strain_energy = Axial Force^2*Length of Rod/2*Cross sectional area*Modulus Of Elasticity
  • axial_force = sqrt(Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Length of Rod)
  • length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2
  • modulus_of_elasticity = Axial Force^2*Length of Rod/2*Cross sectional area*Strain Energy
  • strain_energy = (Torque^2)*Length of Shaft/Polar moment of Inertia*Modulus of rigidity
  • torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft)
  • length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2)
  • modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy
  • polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity
  • strain_energy = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Moment of Inertia
Where is the Length of Shaft When Strain Energy in the Shaft Subjected to External Torque calculator used?
Among many, Length of Shaft When Strain Energy in the Shaft Subjected to External Torque calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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