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Osmania University (OU), Hyderabad
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## Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy
C = (τ^2)*l/J*U
This formula uses 4 Variables
Variables Used
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)
Length of Shaft - The Length of Shaft is the distance between two ends of shaft. (Measured in Meter)
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)
Strain Energy - The Strain energy is defined as the energy stored in a body due to deformation. (Measured in Joule)
STEP 1: Convert Input(s) to Base Unit
Torque: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Length of Shaft: 50 Meter --> 50 Meter No Conversion Required
Polar moment of Inertia: 50 Kilogram Meter² --> 50 Kilogram Meter² No Conversion Required
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
C = (τ^2)*l/J*U --> (50^2)*50/50*50
Evaluating ... ...
C = 125000
STEP 3: Convert Result to Output's Unit
125000 Pascal -->125000 Newton per Square Meter (Check conversion here)
FINAL ANSWER
125000 Newton per Square Meter <-- Modulus of rigidity
(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

### Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given Formula

modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy
C = (τ^2)*l/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 the Rod When Strain Energy in the Rod is Given?

Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given calculator uses modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy to calculate the Modulus of rigidity, The Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given 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 and is denoted by C symbol.

How to calculate Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given using this online calculator? To use this online calculator for Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given, enter Torque (τ), Length of Shaft (l), Polar moment of Inertia (J) and Strain Energy (U) and hit the calculate button. Here is how the Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given calculation can be explained with given input values -> 125000 = (50^2)*50/50*50.

### FAQ

What is Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given?
The Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given 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 C = (τ^2)*l/J*U or modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy. 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, The Length of Shaft is the distance between two ends of shaft, The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape and The Strain energy is defined as the energy stored in a body due to deformation.
How to calculate Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given?
The Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given 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 = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy. To calculate Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given, you need Torque (τ), Length of Shaft (l), Polar moment of Inertia (J) and Strain Energy (U). With our tool, you need to enter the respective value for Torque, Length of Shaft, Polar moment of Inertia and Strain Energy 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 Modulus of rigidity?
In this formula, Modulus of rigidity uses Torque, Length of Shaft, Polar moment of Inertia and Strain Energy. 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 Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given calculator used?
Among many, Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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