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

✖The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering.ⓘ Bending Moment [M_b]			+10% -10%
✖The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.ⓘ Strain Energy [U]			+10% -10%
✖The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.ⓘ Area Moment of Inertia [I]			+10% -10%

✖The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions.ⓘ Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment [E]

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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 = Bending Moment^2*Length of Rod or Shaft/(2*Strain Energy*Area Moment of Inertia)
E = M_b^2*L/(2*U*I)
This formula uses 5 Variables

Variables Used

Modulus of Elasticity - (Measured in Pascal) - The Modulus of Elasticity is a measure of a material's stiffness, indicating how much it deforms under stress in relation to its original dimensions.
Bending Moment - (Measured in Newton Meter) - The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering.
Length of Rod or Shaft - (Measured in Meter) - The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis.
Strain Energy - (Measured in Joule) - The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape.
Area Moment of Inertia - (Measured in Meter⁴) - The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 55001 Newton Millimeter --> 55.001 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1432.449 Millimeter --> 1.432449 Meter (Check conversion here)
Strain Energy: 37.13919 Joule --> 37.13919 Joule No Conversion Required
Area Moment of Inertia: 552.5 Millimeter⁴ --> 5.525E-10 Meter⁴ (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = M_b^2*L/(2*U*I) --> 55.001^2*1.432449/(2*37.13919*5.525E-10)

Evaluating ... ...

E = 105590691568.675

STEP 3: Convert Result to Output's Unit

105590691568.675 Pascal -->105590.691568675 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

105590.691568675 ≈ 105590.7 Newton per Square Millimeter <-- Modulus of Elasticity

(Calculation completed in 00.020 seconds)

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< Castigliano's Theorem for Deflection in Complex Structures Calculators

Force Applied on Rod given Strain Energy Stored in Tension Rod

Go Axial Force on Beam = sqrt(Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Length of Rod or Shaft)

Strain Energy Stored in Tension Rod

Go Strain Energy = (Axial Force on Beam^2*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of Elasticity)

Modulus of Elasticity of Rod given Strain Energy Stored

Go Modulus of Elasticity = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy)

Length of Rod given Strain Energy Stored

Go Length of Rod or Shaft = Strain Energy*2*Cross Sectional Area of Rod*Modulus of Elasticity/Axial Force on Beam^2

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

Modulus of Elasticity = Bending Moment^2*Length of Rod or Shaft/(2*Strain Energy*Area Moment of Inertia)
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 = Bending Moment^2*Length of Rod or Shaft/(2*Strain Energy*Area Moment of Inertia) to calculate the Modulus of Elasticity, Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a relationship that quantifies the stiffness of a material by relating the strain energy stored in a shaft to the bending moment applied, reflecting its ability to deform elastically under load. Modulus of Elasticity 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 (M_b), Length of Rod or Shaft (L), Strain Energy (U) & Area Moment of Inertia (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 -> 0.000565 = 55.001^2*1.432449/(2*37.13919*5.525E-10).

FAQ

What is 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 formula is defined as a relationship that quantifies the stiffness of a material by relating the strain energy stored in a shaft to the bending moment applied, reflecting its ability to deform elastically under load and is represented as E = M_b^2*L/(2*U*I) or Modulus of Elasticity = Bending Moment^2*Length of Rod or Shaft/(2*Strain Energy*Area Moment of Inertia). The Bending Moment is the internal moment that causes a beam to bend, reflecting the distribution of forces along its length in structural engineering, The Length of Rod or Shaft is the measurement of the distance from one end of the rod or shaft to the other, crucial for structural analysis, The Strain Energy is the energy stored in a material due to deformation, which can be released when the material returns to its original shape & The Area Moment of Inertia is a property that measures an object's resistance to bending and deflection under load, crucial for structural analysis and design.

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 formula is defined as a relationship that quantifies the stiffness of a material by relating the strain energy stored in a shaft to the bending moment applied, reflecting its ability to deform elastically under load is calculated using Modulus of Elasticity = Bending Moment^2*Length of Rod or Shaft/(2*Strain Energy*Area Moment of Inertia). To calculate Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment, you need Bending Moment (M_b), Length of Rod or Shaft (L), Strain Energy (U) & Area Moment of Inertia (I). With our tool, you need to enter the respective value for Bending Moment, Length of Rod or Shaft, Strain Energy & Area 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 Rod or Shaft, Strain Energy & Area Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -

Modulus of Elasticity = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy)

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