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Bending Moment using Strain Energy Formula

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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. Check FAQs

M = \sqrt{U \cdot \frac{2 \cdot E \cdot I}{L}}

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

Bending Moment using Strain Energy Example

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

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

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

53.8799 = \sqrt{136.08 \cdot \frac{2 \cdot 20000 \cdot 0.0016}{3000}}

53.8799kN*m = \sqrt{136.08N*m \cdot \frac{2 \cdot 20000MPa \cdot 0.0016m⁴}{3000mm}}

53.8799 = \sqrt{136.08 \cdot \frac{2 \cdot 20000 \cdot 0.0016}{3000}}

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Bending Moment using Strain Energy Solution

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

FIRST Step Consider the formula

M = \sqrt{U \cdot \frac{2 \cdot E \cdot I}{L}}

Next Step Substitute values of Variables

∴

M = \sqrt{136.08N*m \cdot \frac{2 \cdot 20000MPa \cdot 0.0016m⁴}{3000mm}}

Next Step Convert Units

∴

M = \sqrt{136.08J \cdot \frac{2 \cdot 2E+10Pa \cdot 0.0016m⁴}{3m}}

Next Step Prepare to Evaluate

∴

M = \sqrt{136.08 \cdot \frac{2 \cdot 2E+10 \cdot 0.0016}{3}}

Next Step Evaluate

∴

M = 53879.8663695448N*m

Next Step Convert to Output's Unit

∴

M = 53.8798663695448kN*m

LAST Step Rounding Answer

∴

M = 53.8799kN*m

Bending Moment using Strain Energy Formula Elements

Variables

Functions

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Bending Moment using Strain Energy?

Bending Moment using Strain Energy evaluator uses Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member) to evaluate the Bending Moment, The Bending Moment using Strain Energy formula is defined as 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 is denoted by M symbol.

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

FAQs on Bending Moment using Strain Energy

What is the formula to find Bending Moment using Strain Energy?

The formula of Bending Moment using Strain Energy is expressed as Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member). Here is an example- 0.05388 = sqrt(136.08*(2*20000000000*0.0016)/3).

How to calculate Bending Moment using Strain Energy?

With Strain Energy (U), Young's Modulus (E), Area Moment of Inertia (I) & Length of Member (L) we can find Bending Moment using Strain Energy using the formula - Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member). This formula also uses Square Root (sqrt) function(s).

Can the Bending Moment using Strain Energy be negative?

Yes, the Bending Moment using Strain Energy, measured in Moment of Force can be negative.

Which unit is used to measure Bending Moment using Strain Energy?

Bending Moment using Strain Energy is usually measured using the Kilonewton Meter[kN*m] for Moment of Force. Newton Meter[kN*m], Millinewton Meter[kN*m], Micronewton Meter[kN*m] are the few other units in which Bending Moment using Strain Energy can be measured.

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Bending Moment using Strain Energy Formula

Bending Moment using Strain Energy Example

Bending Moment using Strain Energy Solution

Bending Moment using Strain Energy Formula Elements

Other formulas in Strain Energy in Structural Members category

How to Evaluate Bending Moment using Strain Energy?

FAQs on Bending Moment using Strain Energy

Variable Name