Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment Calculator

✖Bending Moment in Shaft or Beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Shaft or Beam [M_b]			+10% -10%
✖Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.ⓘ Strain Energy in Rod or Shaft [U]			+10% -10%
✖Area Moment of Inertia of rod or shaft is the measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.ⓘ Area Moment of Inertia of rod or shaft [I]			+10% -10%

✖Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment [E]

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Formula

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Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment

Formula

`"E" = ("M"_{"b"}^2)*"L"/(2*"U"*"I")`

Example

`"98200.49N/mm²"=(("7.8E5N*mm")^2)*"1330mm"/(2*"40J"*"1.03E5mm⁴")`

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Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
E = (M_b^2)*L/(2*U*I)
This formula uses 5 Variables

Variables Used

Modulus of elasticity of rod or shaft - (Measured in Pascal) - Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Bending Moment in Shaft or Beam - (Measured in Newton Meter) - Bending Moment in Shaft or Beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
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.
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.
Area Moment of Inertia of rod or shaft - (Measured in Meter⁴) - Area Moment of Inertia of rod or shaft is the measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Shaft or Beam: 780000 Newton Millimeter --> 780 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1330 Millimeter --> 1.33 Meter (Check conversion here)
Strain Energy in Rod or Shaft: 40 Joule --> 40 Joule No Conversion Required
Area Moment of Inertia of rod or shaft: 103000 Millimeter⁴ --> 1.03E-07 Meter⁴ (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = (M_b^2)*L/(2*U*I) --> (780^2)*1.33/(2*40*1.03E-07)

Evaluating ... ...

E = 98200485436.8932

STEP 3: Convert Result to Output's Unit

98200485436.8932 Pascal -->98200.4854368932 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

98200.4854368932 ≈ 98200.49 Newton per Square Millimeter <-- Modulus of elasticity of rod or shaft

(Calculation completed in 00.020 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 Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment Formula

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)
E = (M_b^2)*L/(2*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 given Strain Energy Stored in Shaft Subjected to Bending Moment?

Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment calculator uses 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) to calculate the Modulus of elasticity of rod or shaft, The Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment 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 of rod or shaft is denoted by E symbol.

How to calculate Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment using this online calculator? To use this online calculator for Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment, enter Bending Moment in Shaft or Beam (M_b), Length of Rod or Shaft (L), Strain Energy in Rod or Shaft (U) & Area Moment of Inertia of rod or shaft (I) and hit the calculate button. Here is how the Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment calculation can be explained with given input values -> 0.0982 = (780^2)*1.33/(2*40*1.03E-07).

FAQ

What is Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment?

The Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment 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_b^2)*L/(2*U*I) or 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). Bending Moment in Shaft or Beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend, Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom, Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation & Area Moment of Inertia of rod or shaft is the measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.

How to calculate Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment?

The Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment 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 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). To calculate Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment, you need Bending Moment in Shaft or Beam (M_b), Length of Rod or Shaft (L), Strain Energy in Rod or Shaft (U) & Area Moment of Inertia of rod or shaft (I). With our tool, you need to enter the respective value for Bending Moment in Shaft or Beam, Length of Rod or Shaft, Strain Energy in Rod or Shaft & Area Moment of Inertia of rod or shaft 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 of rod or shaft?

In this formula, Modulus of elasticity of rod or shaft uses Bending Moment in Shaft or Beam, Length of Rod or Shaft, Strain Energy in Rod or Shaft & Area Moment of Inertia of rod or shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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