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Modulus of Elasticity with given Strain Energy Formula

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Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain. Check FAQs

E = (L \cdot \frac{M^{2}}{2 \cdot U \cdot I})

E - Young's Modulus?L - Length of Member?M - Bending Moment?U - Strain Energy?I - Area Moment of Inertia?

Modulus of Elasticity with given Strain Energy Example

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Here is how the Modulus of Elasticity with given Strain Energy equation looks like with Values.

Here is how the Modulus of Elasticity with given Strain Energy equation looks like with Units.

Here is how the Modulus of Elasticity with given Strain Energy equation looks like.

19940.7518 = (3000 \cdot \frac{{53.8}^{2}}{2 \cdot 136.08 \cdot 0.0016})

19940.7518MPa = (3000mm \cdot \frac{{53.8kN*m}^{2}}{2 \cdot 136.08N*m \cdot 0.0016m⁴})

19940.7518 = (3000 \cdot \frac{{53.8}^{2}}{2 \cdot 136.08 \cdot 0.0016})

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Modulus of Elasticity with given Strain Energy Solution

Follow our step by step solution on how to calculate Modulus of Elasticity with given Strain Energy?

FIRST Step Consider the formula

E = (L \cdot \frac{M^{2}}{2 \cdot U \cdot I})

Next Step Substitute values of Variables

∴

E = (3000mm \cdot \frac{{53.8kN*m}^{2}}{2 \cdot 136.08N*m \cdot 0.0016m⁴})

Next Step Convert Units

∴

E = (3m \cdot \frac{{53800N*m}^{2}}{2 \cdot 136.08J \cdot 0.0016m⁴})

Next Step Prepare to Evaluate

∴

E = (3 \cdot \frac{53800^{2}}{2 \cdot 136.08 \cdot 0.0016})

Next Step Evaluate

∴

E = 19940751763.6684Pa

Next Step Convert to Output's Unit

∴

E = 19940.7517636684MPa

LAST Step Rounding Answer

∴

E = 19940.7518MPa

Modulus of Elasticity with given Strain Energy Formula Elements

Variables

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Young's Modulus

Length of Member

Length of Member is the measurement or extent of member (beam or column) from end to end.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Member

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.

Symbol: M

Measurement: Moment of ForceUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Bending Moment

Strain Energy

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.

Symbol: U

Measurement: EnergyUnit: N*m

Note: Value can be positive or negative.

Formulas to find Strain Energy

Area Moment of Inertia

Area Moment of Inertia is a moment about the centroidal axis without considering mass.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Other formulas in Strain Energy in Structural Members category

Go Stress using Hook's Law

σ = E \cdot ε L

Go Shear Force using Strain Energy

V = \sqrt{2 \cdot U \cdot A \cdot \frac{G Torsion}{L}}

Go Strain Energy in Shear

U = (V^{2}) \cdot \frac{L}{2 \cdot A \cdot G Torsion}

Go Length over which Deformation takes place given Strain Energy in Shear

L = 2 \cdot U \cdot A \cdot \frac{G Torsion}{V^{2}}

How to Evaluate Modulus of Elasticity with given Strain Energy?

Modulus of Elasticity with given Strain Energy evaluator uses Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia)) to evaluate 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 evaluate Modulus of Elasticity with given Strain Energy using this online evaluator? To use this online evaluator 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.

FAQs on Modulus of Elasticity with given Strain Energy

What is the formula to find Modulus of Elasticity with given Strain Energy?

The formula of Modulus of Elasticity with given Strain Energy is expressed as Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia)). Here is an example- 0.019941 = (3*(53800^2)/(2*136.08*0.0016)).

How to calculate Modulus of Elasticity with given Strain Energy?

With Length of Member (L), Bending Moment (M), Strain Energy (U) & Area Moment of Inertia (I) we can find Modulus of Elasticity with given Strain Energy using the formula - Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia)).

Can the Modulus of Elasticity with given Strain Energy be negative?

Yes, the Modulus of Elasticity with given Strain Energy, measured in Stress can be negative.

Which unit is used to measure Modulus of Elasticity with given Strain Energy?

Modulus of Elasticity with given Strain Energy is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Modulus of Elasticity with given Strain Energy can be measured.

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Modulus of Elasticity with given Strain Energy Formula

Modulus of Elasticity with given Strain Energy Example

Modulus of Elasticity with given Strain Energy Solution

Modulus of Elasticity with given Strain Energy Formula Elements

Other formulas in Strain Energy in Structural Members category

How to Evaluate Modulus of Elasticity with given Strain Energy?

FAQs on Modulus of Elasticity with given Strain Energy

Variable Name