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Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
length_of_shaft = Strain Energy*Modulus Of Elasticity*Moment of Inertia/(Bending moment^2)
l = U*E*I/(M^2)
This formula uses 4 Variables
Variables Used
Strain Energy - The Strain energy is defined as the energy stored in a body due to deformation. (Measured in Joule)
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)
Moment of Inertia - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis. (Measured in Kilogram Meter²)
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)
STEP 1: Convert Input(s) to Base Unit
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
Modulus Of Elasticity: 10 Kilonewton per Square Meter --> 10000 Pascal (Check conversion here)
Moment of Inertia: 1.125 Kilogram Meter² --> 1.125 Kilogram Meter² No Conversion Required
Bending moment: 50 Newton Meter --> 50 Newton Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = U*E*I/(M^2) --> 50*10000*1.125/(50^2)
Evaluating ... ...
l = 225
STEP 3: Convert Result to Output's Unit
225 Meter --> No Conversion Required
FINAL ANSWER
225 Meter <-- Length of Shaft
(Calculation completed in 00.017 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

Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given Formula

length_of_shaft = Strain Energy*Modulus Of Elasticity*Moment of Inertia/(Bending moment^2)
l = U*E*I/(M^2)

Define Strain Energy?

Strain energy is a type of potential energy that is stored in a structural member as a result of elastic deformation. The external work done on such a member when it is deformed from its unstressed state is transformed into, and considered equal to the strain energy stored in it.

How to Calculate Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given?

Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given calculator uses length_of_shaft = Strain Energy*Modulus Of Elasticity*Moment of Inertia/(Bending moment^2) to calculate the Length of Shaft, The Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given formula is defined as the total length of the shaft that is subjected to bending Moment. Length of Shaft and is denoted by l symbol.

How to calculate Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given using this online calculator? To use this online calculator for Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given, enter Strain Energy (U), Modulus Of Elasticity (E), Moment of Inertia (I) and Bending moment (M) and hit the calculate button. Here is how the Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given calculation can be explained with given input values -> 225 = 50*10000*1.125/(50^2).

FAQ

What is Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given?
The Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given formula is defined as the total length of the shaft that is subjected to bending Moment and is represented as l = U*E*I/(M^2) or length_of_shaft = Strain Energy*Modulus Of Elasticity*Moment of Inertia/(Bending moment^2). The Strain energy is defined as the energy stored in a body due to deformation, 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, Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis and 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.
How to calculate Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given?
The Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given formula is defined as the total length of the shaft that is subjected to bending Moment is calculated using length_of_shaft = Strain Energy*Modulus Of Elasticity*Moment of Inertia/(Bending moment^2). To calculate Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given, you need Strain Energy (U), Modulus Of Elasticity (E), Moment of Inertia (I) and Bending moment (M). With our tool, you need to enter the respective value for Strain Energy, Modulus Of Elasticity, Moment of Inertia and Bending moment 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 Length of Shaft?
In this formula, Length of Shaft uses Strain Energy, Modulus Of Elasticity, Moment of Inertia and Bending moment. 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 Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given calculator used?
Among many, Length of the Shaft When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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