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Moment of Inertia using Strain Energy Formula

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

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

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

Moment of Inertia using Strain Energy Example

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Here is how the Moment of Inertia using Strain Energy equation looks like with Values.

Here is how the Moment of Inertia using Strain Energy equation looks like with Units.

Here is how the Moment of Inertia using Strain Energy equation looks like.

0.0016 = 3000 \cdot (\frac{{53.8}^{2}}{2 \cdot 136.08 \cdot 20000})

0.0016m⁴ = 3000mm \cdot (\frac{{53.8kN*m}^{2}}{2 \cdot 136.08N*m \cdot 20000MPa})

0.0016 = 3000 \cdot (\frac{{53.8}^{2}}{2 \cdot 136.08 \cdot 20000})

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Moment of Inertia using Strain Energy Solution

Follow our step by step solution on how to calculate Moment of Inertia using Strain Energy?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I = 3000mm \cdot (\frac{{53.8kN*m}^{2}}{2 \cdot 136.08N*m \cdot 20000MPa})

Next Step Convert Units

∴

I = 3m \cdot (\frac{{53800N*m}^{2}}{2 \cdot 136.08J \cdot 2E+10Pa})

Next Step Prepare to Evaluate

∴

I = 3 \cdot (\frac{53800^{2}}{2 \cdot 136.08 \cdot 2E+10})

Next Step Evaluate

∴

I = 0.00159526014109347m⁴

LAST Step Rounding Answer

∴

I = 0.0016m⁴

Moment of Inertia using Strain Energy Formula Elements

Variables

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

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

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

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 Moment of Inertia using Strain Energy?

Moment of Inertia using Strain Energy evaluator uses Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus)) to evaluate the Area Moment of Inertia, The Moment of Inertia using Strain Energy formula is defined as a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of torque (turning force). Area Moment of Inertia is denoted by I symbol.

How to evaluate Moment of Inertia using Strain Energy using this online evaluator? To use this online evaluator for Moment of Inertia using Strain Energy, enter Length of Member (L), Bending Moment (M), Strain Energy (U) & Young's Modulus (E) and hit the calculate button.

FAQs on Moment of Inertia using Strain Energy

What is the formula to find Moment of Inertia using Strain Energy?

The formula of Moment of Inertia using Strain Energy is expressed as Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus)). Here is an example- 0.001595 = 3*((53800^2)/(2*136.08*20000000000)).

How to calculate Moment of Inertia using Strain Energy?

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

Can the Moment of Inertia using Strain Energy be negative?

No, the Moment of Inertia using Strain Energy, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia using Strain Energy?

Moment of Inertia using Strain Energy is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Moment of Inertia using Strain Energy can be measured.

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Moment of Inertia using Strain Energy Formula

Moment of Inertia using Strain Energy Example

Moment of Inertia using Strain Energy Solution

Moment of Inertia using Strain Energy Formula Elements

Other formulas in Strain Energy in Structural Members category

How to Evaluate Moment of Inertia using Strain Energy?

FAQs on Moment of Inertia using Strain Energy

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