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Strain Energy in Bending Formula

GoStrain Energy in Shear Formula

GoStrain Energy in Shear given Shear Deformation Formula

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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. Check FAQs

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

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

Strain Energy in Bending Example

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

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

Here is how the Strain Energy in Bending equation looks like.

135.6769 = (({53.8}^{2}) \cdot \frac{3000}{2 \cdot 20000 \cdot 0.0016})

135.6769N*m = (({53.8kN*m}^{2}) \cdot \frac{3000mm}{2 \cdot 20000MPa \cdot 0.0016m⁴})

135.6769 = (({53.8}^{2}) \cdot \frac{3000}{2 \cdot 20000 \cdot 0.0016})

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Strain Energy in Bending Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

U = (({53800N*m}^{2}) \cdot \frac{3m}{2 \cdot 2E+10Pa \cdot 0.0016m⁴})

Next Step Prepare to Evaluate

∴

U = ((53800^{2}) \cdot \frac{3}{2 \cdot 2E+10 \cdot 0.0016})

Next Step Evaluate

∴

U = 135.676875J

Next Step Convert to Output's Unit

∴

U = 135.676875N*m

LAST Step Rounding Answer

∴

U = 135.6769N*m

Strain Energy in Bending Formula Elements

Variables

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

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

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

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

Other Formulas to find Strain Energy

Go Strain Energy in Shear

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

Go Strain Energy in Shear given Shear Deformation

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

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

U = (T^{2}) \cdot \frac{L}{2 \cdot J \cdot G Torsion}

Go Strain Energy in Torsion given Angle of Twist

U = \frac{J \cdot G Torsion \cdot {(θ \cdot (\frac{π}{180}))}^{2}}{2 \cdot L}

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 Length over which Deformation takes place given Strain Energy in Shear

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

Go Shear Area given Strain Energy in Shear

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

How to Evaluate Strain Energy in Bending?

Strain Energy in Bending evaluator uses Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia)) to evaluate the Strain Energy, The Strain Energy in Bending formula is defined as the energy stored in a body due to deformation caused by bending. Strain Energy is denoted by U symbol.

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

FAQs on Strain Energy in Bending

What is the formula to find Strain Energy in Bending?

The formula of Strain Energy in Bending is expressed as Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia)). Here is an example- 135.6769 = ((53800^2)*3/(2*20000000000*0.0016)).

How to calculate Strain Energy in Bending?

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

What are the other ways to Calculate Strain Energy?

Here are the different ways to Calculate Strain Energy-

Strain Energy=(Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)
Strain Energy=(Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)
Strain Energy=(Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity)

Can the Strain Energy in Bending be negative?

Yes, the Strain Energy in Bending, measured in Energy can be negative.

Which unit is used to measure Strain Energy in Bending?

Strain Energy in Bending is usually measured using the Newton Meter[N*m] for Energy. Joule[N*m], Kilojoule[N*m], Gigajoule[N*m] are the few other units in which Strain Energy in Bending can be measured.

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Strain Energy in Bending Formula

​GoStrain Energy in Shear Formula

​GoStrain Energy in Shear given Shear Deformation Formula

Strain Energy in Bending Example

Strain Energy in Bending Solution

Strain Energy in Bending Formula Elements

Other Formulas to find Strain Energy

Other formulas in Strain Energy in Structural Members category

How to Evaluate Strain Energy in Bending?

FAQs on Strain Energy in Bending

Variable Name

GoStrain Energy in Shear Formula

GoStrain Energy in Shear given Shear Deformation Formula