Modulus of Elasticity with given Strain Energy Calculator

✖Length of Member is the measurement or extent of member (beam or column) from end to end.ⓘ Length of Member [L]			+10% -10%
✖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.ⓘ Bending Moment [M]			+10% -10%
✖Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.ⓘ Strain Energy [U]			+10% -10%
✖Area Moment of Inertia is a moment about the centroidal axis without considering mass.ⓘ Area Moment of Inertia [I]			+10% -10%

✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Modulus of Elasticity with given Strain Energy [E]

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Formula

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Modulus of Elasticity with given Strain Energy

Formula

`"E" = ("L"*("M"^2)/(2*"U"*"I"))`

Example

`"19940.75MPa"=("3000mm"*(("53.8kN*m")^2)/(2*"136.08N*m"*"0.0016m⁴"))`

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Modulus of Elasticity with given Strain Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia))
E = (L*(M^2)/(2*U*I))
This formula uses 5 Variables

Variables Used

Young's Modulus - (Measured in Pascal) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Length of Member - (Measured in Meter) - Length of Member is the measurement or extent of member (beam or column) from end to end.
Bending Moment - (Measured in Newton Meter) - 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.
Strain Energy - (Measured in Joule) - Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force.
Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a moment about the centroidal axis without considering mass.

STEP 1: Convert Input(s) to Base Unit

Length of Member: 3000 Millimeter --> 3 Meter (Check conversion here)
Bending Moment: 53.8 Kilonewton Meter --> 53800 Newton Meter (Check conversion here)
Strain Energy: 136.08 Newton Meter --> 136.08 Joule (Check conversion here)
Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = (L*(M^2)/(2*U*I)) --> (3*(53800^2)/(2*136.08*0.0016))

Evaluating ... ...

E = 19940751763.6684

STEP 3: Convert Result to Output's Unit

19940751763.6684 Pascal -->19940.7517636684 Megapascal (Check conversion here)

FINAL ANSWER

19940.7517636684 ≈ 19940.75 Megapascal <-- Young's Modulus

(Calculation completed in 00.004 seconds)

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< 19 Strain Energy in Structural Members Calculators

Strain Energy in Torsion given Angle of Twist

Go Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member)

Strain Energy for Pure Bending when Beam rotates in One End

Go Strain Energy = (Young's Modulus*Area Moment of Inertia*((Angle of Twist*(pi/180))^2)/(2*Length of Member))

Bending Moment using Strain Energy

Go Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member)

Torque given Strain Energy in Torsion

Go Torque SOM = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Member)

Shear Force using Strain Energy

Go Shear Force = sqrt(2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/Length of Member)

Strain Energy in Shear given Shear Deformation

Go Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)

Length over which Deformation takes place using Strain Energy

Go Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2))

Modulus of Elasticity with given Strain Energy

Go Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia))

Moment of Inertia using Strain Energy

Go Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus))

Strain Energy in Bending

Go Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia))

Strain Energy in Torsion given Polar MI and Shear Modulus of Elasticity

Go Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity)

Shear Modulus of Elasticity given Strain Energy in Torsion

Go Modulus of Rigidity = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Strain Energy)

Polar Moment of Inertia given Strain Energy in Torsion

Go Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)

Shear Modulus of Elasticity given Strain Energy in Shear

Go Modulus of Rigidity = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Strain Energy)

Shear Area given Strain Energy in Shear

Go Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)

Strain Energy in Shear

Go Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)

Length over which Deformation takes place given Strain Energy in Torsion

Go Length of Member = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/Torque SOM^2

Length over which Deformation takes place given Strain Energy in Shear

Go Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2)

Stress using Hook's Law

Go Direct Stress = Young's Modulus*Lateral Strain

Modulus of Elasticity with given Strain Energy Formula

Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia))
E = (L*(M^2)/(2*U*I))

What is a High Modulus of Elasticity?

In identical products, the higher the modulus of elasticity of the material, the greater the rigidity; doubling the modulus of elasticity doubles the rigidity of the product. The greater the rigidity of a structure, the more force must be applied to produce a given deformation.

Define Stress & Strain Energy.

The stress definition in engineering says that stress is the force applied to an object divided by its cross-section area.
The strain energy is the energy stored in any body due to its deformation, also known as Resilience.

How to Calculate Modulus of Elasticity with given Strain Energy?

Modulus of Elasticity with given Strain Energy calculator uses Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia)) to calculate the Young's Modulus, The Modulus of Elasticity with given Strain Energy formula is defined as a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it. Young's Modulus is denoted by E symbol.

How to calculate Modulus of Elasticity with given Strain Energy using this online calculator? To use this online calculator for Modulus of Elasticity with given Strain Energy, enter Length of Member (L), Bending Moment (M), Strain Energy (U) & Area Moment of Inertia (I) and hit the calculate button. Here is how the Modulus of Elasticity with given Strain Energy calculation can be explained with given input values -> 0.019941 = (3*(53800^2)/(2*136.08*0.0016)).

FAQ

What is Modulus of Elasticity with given Strain Energy?

The Modulus of Elasticity with given Strain Energy formula is defined as a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it and is represented as E = (L*(M^2)/(2*U*I)) or Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia)). Length of Member is the measurement or extent of member (beam or column) from end to end, 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, Strain Energy is the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force & Area Moment of Inertia is a moment about the centroidal axis without considering mass.

How to calculate Modulus of Elasticity with given Strain Energy?

The Modulus of Elasticity with given Strain Energy formula is defined as a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it is calculated using Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia)). To calculate Modulus of Elasticity with given Strain Energy, you need Length of Member (L), Bending Moment (M), Strain Energy (U) & Area Moment of Inertia (I). With our tool, you need to enter the respective value for Length of Member, Bending Moment, 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.

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