Torque given Strain Energy in Rod Subjected to External Torque Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
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 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.
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.
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.
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)
Length of Rod or Shaft: 1330 Millimeter --> 1.33 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τ = sqrt(2*U*J*G/L) --> sqrt(2*40*2.047E-07*105000000000/1.33)
Evaluating ... ...
τ = 1137.03214785826
STEP 3: Convert Result to Output's Unit
1137.03214785826 Newton Meter -->1137032.14785826 Newton Millimeter (Check conversion here)
FINAL ANSWER
1137032.14785826 1.1E+6 Newton Millimeter <-- Torque on 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

Torque given Strain Energy in Rod Subjected to External Torque Formula

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)
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 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) to calculate the Torque on Rod or Shaft, The Torque given Strain Energy in Rod Subjected to External Torque formula is defined as 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. Torque on Rod or Shaft 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 in Rod or Shaft (U), Polar Moment of Inertia of rod or shaft (J), Modulus of rigidity of rod or shaft (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 -> 1.1E+9 = sqrt(2*40*2.047E-07*105000000000/1.33).

FAQ

What is Torque given Strain Energy in Rod Subjected to External Torque?
The Torque given Strain Energy in Rod Subjected to External Torque formula is defined as 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 and is represented as τ = sqrt(2*U*J*G/L) or 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). 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 & Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.
How to calculate Torque given Strain Energy in Rod Subjected to External Torque?
The Torque given Strain Energy in Rod Subjected to External Torque formula is defined as 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 is calculated using 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). To calculate Torque given Strain Energy in Rod 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) & Length of Rod or Shaft (L). 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 & 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.
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