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

STEP 0: Pre-Calculation Summary
Formula Used
modulus_of_elasticity = (Bending moment^2)*Length of Shaft/Strain Energy*Moment of Inertia
E = (M^2)*l/U*I
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)
Strain Energy - The Strain energy is defined as the energy stored in a body due to deformation. (Measured in Joule)
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)
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
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
Moment of Inertia: 1.125 Kilogram Meter² --> 1.125 Kilogram Meter² No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
E = (M^2)*l/U*I --> (50^2)*50/50*1.125
Evaluating ... ...
E = 2812.5
STEP 3: Convert Result to Output's Unit
2812.5 Pascal -->2.8125 Kilonewton per Square Meter (Check conversion here)
FINAL ANSWER
2.8125 Kilonewton per Square Meter <-- Modulus Of Elasticity
(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 Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given Formula

modulus_of_elasticity = (Bending moment^2)*Length of Shaft/Strain Energy*Moment of Inertia
E = (M^2)*l/U*I

Define Modulus of Elasticity?

Modulus of elasticity is the measure of the stress–strain relationship on the object. Modulus of elasticity is the prime feature in the calculation of the deformation response of concrete when stress is applied. Elastic constants are those constants which determine the deformation produced by a given stress system acting on the material.

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

Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given calculator uses modulus_of_elasticity = (Bending moment^2)*Length of Shaft/Strain Energy*Moment of Inertia to calculate the Modulus Of Elasticity, The Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given formula is defined as the measure of the stress–strain relationship on the object. Modulus of elasticity is the prime feature in the calculation of the deformation response of concrete when stress is applied. Modulus Of Elasticity and is denoted by E symbol.

How to calculate Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given using this online calculator? To use this online calculator for Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given, enter Bending moment (M), Length of Shaft (l), Strain Energy (U) and Moment of Inertia (I) and hit the calculate button. Here is how the Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given calculation can be explained with given input values -> 2.8125 = (50^2)*50/50*1.125.

FAQ

What is Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given?
The Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given formula is defined as the measure of the stress–strain relationship on the object. Modulus of elasticity is the prime feature in the calculation of the deformation response of concrete when stress is applied and is represented as E = (M^2)*l/U*I or modulus_of_elasticity = (Bending moment^2)*Length of Shaft/Strain Energy*Moment of Inertia. 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, The Strain energy is defined as the energy stored in a body due to deformation and Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
How to calculate Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given?
The Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given formula is defined as the measure of the stress–strain relationship on the object. Modulus of elasticity is the prime feature in the calculation of the deformation response of concrete when stress is applied is calculated using modulus_of_elasticity = (Bending moment^2)*Length of Shaft/Strain Energy*Moment of Inertia. To calculate Modulus of Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given, you need Bending moment (M), Length of Shaft (l), Strain Energy (U) and Moment of Inertia (I). With our tool, you need to enter the respective value for Bending moment, Length of Shaft, Strain Energy and Moment of Inertia 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 Elasticity?
In this formula, Modulus Of Elasticity uses Bending moment, Length of Shaft, Strain Energy and Moment of Inertia. 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 Elasticity When Strain Energy Stored in the Shaft Subjected to Bending Moment is Given calculator used?
Among many, Modulus of Elasticity 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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