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Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment Solution

STEP 0: Pre-Calculation Summary
Formula Used
moment_of_inertia = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Strain Energy
I = (M^2)*l/E*U
This formula uses 4 Variables
Variables Used
Bending moment - The Bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. (Measured in Newton Meter)
Length of Shaft - The Length of Shaft is the distance between two ends of shaft. (Measured in Meter)
Modulus Of Elasticity - Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it. (Measured in Kilonewton per Square Meter)
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
Bending moment: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Length of Shaft: 50 Meter --> 50 Meter No Conversion Required
Modulus Of Elasticity: 10 Kilonewton per Square Meter --> 10000 Pascal (Check conversion here)
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = (M^2)*l/E*U --> (50^2)*50/10000*50
Evaluating ... ...
I = 625
STEP 3: Convert Result to Output's Unit
625 Kilogram Meter² --> No Conversion Required
FINAL ANSWER
625 Kilogram Meter² <-- Moment of Inertia
(Calculation completed in 00.015 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

Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment Formula

moment_of_inertia = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Strain Energy
I = (M^2)*l/E*U

Define Moment of Inertia?

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.

How to Calculate Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment?

Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment calculator uses moment_of_inertia = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Strain Energy to calculate the Moment of Inertia, The Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. Moment of Inertia and is denoted by I symbol.

How to calculate Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment using this online calculator? To use this online calculator for Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment, enter Bending moment (M), Length of Shaft (l), Modulus Of Elasticity (E) and Strain Energy (U) and hit the calculate button. Here is how the Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment calculation can be explained with given input values -> 625 = (50^2)*50/10000*50.

FAQ

What is Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment?
The Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration and is represented as I = (M^2)*l/E*U or moment_of_inertia = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Strain Energy. The Bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend, The Length of Shaft is the distance between two ends of shaft, Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it and The Strain energy is defined as the energy stored in a body due to deformation.
How to calculate Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment?
The Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration is calculated using moment_of_inertia = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Strain Energy. To calculate Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment, you need Bending moment (M), Length of Shaft (l), Modulus Of Elasticity (E) and Strain Energy (U). With our tool, you need to enter the respective value for Bending moment, Length of Shaft, Modulus Of Elasticity 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 Moment of Inertia?
In this formula, Moment of Inertia uses Bending moment, Length of Shaft, Modulus Of Elasticity 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 Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment calculator used?
Among many, Moment of Inertia of Shaft When Strain Energy Stored in Shaft Subjected to Bending Moment calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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