Torque given Strain Energy in Rod 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 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 Rod or Shaft [L]			+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 given Strain Energy in Rod Subjected to External Torque [τ]

⎘ Copy

👎

Formula

Reset

👍

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

Torque given Strain Energy in Rod Subjected to External Torque Solution

STEP 0: Pre-Calculation Summary

Formula Used

Torque = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Rod or Shaft)
τ = sqrt(2*U*J*G/L)
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.
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.

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)
Length of Rod or Shaft: 1432.449 Millimeter --> 1.432449 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ = sqrt(2*U*J*G/L) --> sqrt(2*37.13919*5.53E-10*105591000000/1.432449)

Evaluating ... ...

τ = 55.0259620677254

STEP 3: Convert Result to Output's Unit

55.0259620677254 Newton Meter -->55025.9620677254 Newton Millimeter (Check conversion here)

FINAL ANSWER

55025.9620677254 ≈ 55025.96 Newton Millimeter <-- Torque

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Machine Design » Castigliano's Theorem for Deflection in Complex Structures » Torque given Strain Energy in Rod Subjected to External Torque

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 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

Torque given Strain Energy in Rod Subjected to External Torque Formula

Torque = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Rod or Shaft)
τ = sqrt(2*U*J*G/L)

Define Torque?

Torque is the measure of the force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics. Similarly, torque is what causes an angular acceleration. Hence, torque can be defined as the rotational equivalent of linear force. The point where the object rotates is called the axis of rotation.

How to Calculate Torque given Strain Energy in Rod Subjected to External Torque?

Torque given Strain Energy in Rod Subjected to External Torque calculator uses Torque = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Rod or Shaft) to calculate the Torque, Torque given Strain Energy in Rod Subjected to External Torque formula is defined as a method to evaluate the torque applied to a rod based on the strain energy stored within it. This concept is crucial in mechanical design for understanding how materials respond to external forces. Torque is denoted by τ symbol.

How to calculate Torque given Strain Energy in Rod Subjected to External Torque using this online calculator? To use this online calculator for Torque given Strain Energy in Rod Subjected to External Torque, enter Strain Energy (U), Polar Moment of Inertia (J), Modulus of Rigidity (G) & Length of Rod or Shaft (L) and hit the calculate button. Here is how the Torque given Strain Energy in Rod Subjected to External Torque calculation can be explained with given input values -> 5.5E+7 = sqrt(2*37.13919*5.53E-10*105591000000/1.432449).

FAQ

What is Torque given Strain Energy in Rod Subjected to External Torque?

Torque given Strain Energy in Rod Subjected to External Torque formula is defined as a method to evaluate the torque applied to a rod based on the strain energy stored within it. This concept is crucial in mechanical design for understanding how materials respond to external forces and is represented as τ = sqrt(2*U*J*G/L) or Torque = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Rod or Shaft). 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 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.

How to calculate Torque given Strain Energy in Rod Subjected to External Torque?

Torque given Strain Energy in Rod Subjected to External Torque formula is defined as a method to evaluate the torque applied to a rod based on the strain energy stored within it. This concept is crucial in mechanical design for understanding how materials respond to external forces is calculated using Torque = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Rod or Shaft). To calculate Torque given Strain Energy in Rod Subjected to External Torque, you need Strain Energy (U), Polar Moment of Inertia (J), Modulus of Rigidity (G) & Length of Rod or Shaft (L). With our tool, you need to enter the respective value for Strain Energy, Polar Moment of Inertia, Modulus of Rigidity & Length 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.

Home

FREE PDFs

🔍 Search