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

✖The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.ⓘ Strain Energy [U]			+10% -10%
✖The Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, crucial for analyzing the strength and stability of structural components.ⓘ Polar Moment of Inertia [J]			+10% -10%
✖The Modulus of Rigidity is a measure of a material's ability to resist deformation under shear stress, indicating its stiffness and structural integrity in mechanical applications.ⓘ Modulus of Rigidity [G]			+10% -10%
✖The Torque is a measure of the rotational force applied to an object, influencing its ability to rotate around an axis or pivot point.ⓘ Torque [τ]			+10% -10%

✖The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.ⓘ Length of Shaft when Strain Energy in Shaft Subjected to External Torque [L]

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Download Castigliano's Theorem for Deflection in Complex Structures Formulas PDF PDF Image

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*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2)
L = (2*U*J*G)/(τ^2)
This formula uses 5 Variables

Variables Used

Length of Rod or Shaft - (Measured in Meter) - The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.
Strain Energy - (Measured in Joule) - The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.
Polar Moment of Inertia - (Measured in Meter⁴) - The Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, crucial for analyzing the strength and stability of structural components.
Modulus of Rigidity - (Measured in Pascal) - The Modulus of Rigidity is a measure of a material's ability to resist deformation under shear stress, indicating its stiffness and structural integrity in mechanical applications.
Torque - (Measured in Newton Meter) - The Torque is a measure of the rotational force applied to an object, influencing its ability to rotate around an axis or pivot point.

STEP 1: Convert Input(s) to Base Unit

Strain Energy: 37.13919 Joule --> 37.13919 Joule No Conversion Required
Polar Moment of Inertia: 553 Millimeter⁴ --> 5.53E-10 Meter⁴ (Check conversion here)
Modulus of Rigidity: 105591 Newton per Square Millimeter --> 105591000000 Pascal (Check conversion here)
Torque: 55005 Newton Millimeter --> 55.005 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (2*U*J*G)/(τ^2) --> (2*37.13919*5.53E-10*105591000000)/(55.005^2)

Evaluating ... ...

L = 1.43354100307323

STEP 3: Convert Result to Output's Unit

1.43354100307323 Meter -->1433.54100307323 Millimeter (Check conversion here)

FINAL ANSWER

1433.54100307323 ≈ 1433.541 Millimeter <-- Length of Rod or Shaft

(Calculation completed in 00.004 seconds)

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< Castigliano's Theorem for Deflection in Complex Structures Calculators

Force Applied on Rod given Strain Energy Stored in Tension Rod

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

Strain Energy Stored in Tension Rod

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

Modulus of Elasticity of Rod given Strain Energy Stored

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

Length of Rod given Strain Energy Stored

Go Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/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*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^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*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2) to calculate the Length of Rod or Shaft, Length of Shaft when Strain Energy in Shaft Subjected to External Torque formula is defined as a method to evaluate the necessary length of a shaft based on the strain energy it can store when subjected to external torque, ensuring structural integrity and performance in mechanical designs. 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 (U), Polar Moment of Inertia (J), Modulus of Rigidity (G) & Torque (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 -> 1.4E+6 = (2*37.13919*5.53E-10*105591000000)/(55.005^2).

FAQ

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

Length of Shaft when Strain Energy in Shaft Subjected to External Torque formula is defined as a method to evaluate the necessary length of a shaft based on the strain energy it can store when subjected to external torque, ensuring structural integrity and performance in mechanical designs and is represented as L = (2*U*J*G)/(τ^2) or Length of Rod or Shaft = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2). The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape, The Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, crucial for analyzing the strength and stability of structural components, The Modulus of Rigidity is a measure of a material's ability to resist deformation under shear stress, indicating its stiffness and structural integrity in mechanical applications & The Torque is a measure of the rotational force applied to an object, influencing its ability to rotate around an axis or pivot point.

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 formula is defined as a method to evaluate the necessary length of a shaft based on the strain energy it can store when subjected to external torque, ensuring structural integrity and performance in mechanical designs is calculated using Length of Rod or Shaft = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/(Torque^2). To calculate Length of Shaft when Strain Energy in Shaft Subjected to External Torque, you need Strain Energy (U), Polar Moment of Inertia (J), Modulus of Rigidity (G) & Torque (τ). With our tool, you need to enter the respective value for Strain Energy, Polar Moment of Inertia, Modulus of Rigidity & 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 Rod or Shaft?

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

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

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