Modulus of Rigidity of Rod given Strain Energy in Rod Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
G = (τ^2)*L/(2*J*U)
This formula uses 5 Variables
Variables Used
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.
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.
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.
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)
Strain Energy in Rod or Shaft: 40 Joule --> 40 Joule No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
G = (τ^2)*L/(2*J*U) --> (1140^2)*1.33/(2*2.047E-07*40)
Evaluating ... ...
G = 105548851978.505
STEP 3: Convert Result to Output's Unit
105548851978.505 Pascal -->105548.851978505 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
105548.851978505 105548.9 Newton per Square Millimeter <-- Modulus of rigidity of rod or shaft
(Calculation completed in 00.004 seconds)

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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

Modulus of Rigidity of Rod given Strain Energy in Rod Formula

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)
G = (τ^2)*L/(2*J*U)

Define Modulus of Rigidity?

Shear modulus also known as Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. Shear Modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus.

How to Calculate Modulus of Rigidity of Rod given Strain Energy in Rod?

Modulus of Rigidity of Rod given Strain Energy in Rod calculator uses 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) to calculate the Modulus of rigidity of rod or shaft, The Modulus of Rigidity of Rod given Strain Energy in Rod formula is defined as the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus. The shear modulus of material gives us the ratio of shear stress to shear strain in a body. Modulus of rigidity of rod or shaft is denoted by G symbol.

How to calculate Modulus of Rigidity of Rod given Strain Energy in Rod using this online calculator? To use this online calculator for Modulus of Rigidity of Rod given Strain Energy in Rod, enter Torque on Rod or Shaft (τ), Length of Rod or Shaft (L), Polar Moment of Inertia of rod or shaft (J) & Strain Energy in Rod or Shaft (U) and hit the calculate button. Here is how the Modulus of Rigidity of Rod given Strain Energy in Rod calculation can be explained with given input values -> 0.105549 = (1140^2)*1.33/(2*2.047E-07*40).

FAQ

What is Modulus of Rigidity of Rod given Strain Energy in Rod?
The Modulus of Rigidity of Rod given Strain Energy in Rod formula is defined as the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus. The shear modulus of material gives us the ratio of shear stress to shear strain in a body and is represented as G = (τ^2)*L/(2*J*U) or 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). 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 & Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.
How to calculate Modulus of Rigidity of Rod given Strain Energy in Rod?
The Modulus of Rigidity of Rod given Strain Energy in Rod formula is defined as the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus. The shear modulus of material gives us the ratio of shear stress to shear strain in a body is calculated using 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). To calculate Modulus of Rigidity of Rod given Strain Energy in Rod, you need Torque on Rod or Shaft (τ), Length of Rod or Shaft (L), Polar Moment of Inertia of rod or shaft (J) & Strain Energy in Rod or Shaft (U). 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 & Strain Energy in 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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