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Strain Energy for Pure Bending when Beam rotates in One End 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 = (E \cdot I \cdot \frac{{(θ \cdot (\frac{π}{180}))}^{2}}{2 \cdot L})

U - Strain Energy?E - Young's Modulus?I - Area Moment of Inertia?θ - Angle of Twist?L - Length of Member?π - Archimedes' constant?

Strain Energy for Pure Bending when Beam rotates in One End Example

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Here is how the Strain Energy for Pure Bending when Beam rotates in One End equation looks like with Values.

Here is how the Strain Energy for Pure Bending when Beam rotates in One End equation looks like with Units.

Here is how the Strain Energy for Pure Bending when Beam rotates in One End equation looks like.

111.3501 = (20000 \cdot 0.0016 \cdot \frac{{(15 \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3000})

111.3501N*m = (20000MPa \cdot 0.0016m⁴ \cdot \frac{{(15° \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3000mm})

111.3501 = (20000 \cdot 0.0016 \cdot \frac{{(15 \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3000})

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Strain Energy for Pure Bending when Beam rotates in One End Solution

Follow our step by step solution on how to calculate Strain Energy for Pure Bending when Beam rotates in One End?

FIRST Step Consider the formula

U = (E \cdot I \cdot \frac{{(θ \cdot (\frac{π}{180}))}^{2}}{2 \cdot L})

Next Step Substitute values of Variables

∴

U = (20000MPa \cdot 0.0016m⁴ \cdot \frac{{(15° \cdot (\frac{π}{180}))}^{2}}{2 \cdot 3000mm})

Next Step Substitute values of Constants

∴

U = (20000MPa \cdot 0.0016m⁴ \cdot \frac{{(15° \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3000mm})

Next Step Convert Units

∴

U = (2E+10Pa \cdot 0.0016m⁴ \cdot \frac{{(0.2618rad \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3m})

Next Step Prepare to Evaluate

∴

U = (2E+10 \cdot 0.0016 \cdot \frac{{(0.2618 \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3})

Next Step Evaluate

∴

U = 111.350126924972J

Next Step Convert to Output's Unit

∴

U = 111.350126924972N*m

LAST Step Rounding Answer

∴

U = 111.3501N*m

Strain Energy for Pure Bending when Beam rotates in One End Formula Elements

Variables

Constants

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

Angle of Twist

Angle of Twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle of Twist

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 for Pure Bending when Beam rotates in One End?

Strain Energy for Pure Bending when Beam rotates in One End evaluator uses Strain Energy = (Young's Modulus*Area Moment of Inertia*((Angle of Twist*(pi/180))^2)/(2*Length of Member)) to evaluate the Strain Energy, The Strain Energy for Pure Bending when Beam rotates in One End 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 for Pure Bending when Beam rotates in One End using this online evaluator? To use this online evaluator for Strain Energy for Pure Bending when Beam rotates in One End, enter Young's Modulus (E), Area Moment of Inertia (I), Angle of Twist (θ) & Length of Member (L) and hit the calculate button.

FAQs on Strain Energy for Pure Bending when Beam rotates in One End

What is the formula to find Strain Energy for Pure Bending when Beam rotates in One End?

The formula of Strain Energy for Pure Bending when Beam rotates in One End is expressed as Strain Energy = (Young's Modulus*Area Moment of Inertia*((Angle of Twist*(pi/180))^2)/(2*Length of Member)). Here is an example- 111.3501 = (20000000000*0.0016*((0.2617993877991*(pi/180))^2)/(2*3)).

How to calculate Strain Energy for Pure Bending when Beam rotates in One End?

With Young's Modulus (E), Area Moment of Inertia (I), Angle of Twist (θ) & Length of Member (L) we can find Strain Energy for Pure Bending when Beam rotates in One End using the formula - Strain Energy = (Young's Modulus*Area Moment of Inertia*((Angle of Twist*(pi/180))^2)/(2*Length of Member)). This formula also uses Archimedes' constant .

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 for Pure Bending when Beam rotates in One End be negative?

Yes, the Strain Energy for Pure Bending when Beam rotates in One End, measured in Energy can be negative.

Which unit is used to measure Strain Energy for Pure Bending when Beam rotates in One End?

Strain Energy for Pure Bending when Beam rotates in One End 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 for Pure Bending when Beam rotates in One End can be measured.

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Strain Energy for Pure Bending when Beam rotates in One End Formula

​GoStrain Energy in Shear Formula

​GoStrain Energy in Shear given Shear Deformation Formula

Strain Energy for Pure Bending when Beam rotates in One End Example

Strain Energy for Pure Bending when Beam rotates in One End Solution

Strain Energy for Pure Bending when Beam rotates in One End Formula Elements

Other Formulas to find Strain Energy

Other formulas in Strain Energy in Structural Members category

How to Evaluate Strain Energy for Pure Bending when Beam rotates in One End?

FAQs on Strain Energy for Pure Bending when Beam rotates in One End

Variable Name

GoStrain Energy in Shear Formula

GoStrain Energy in Shear given Shear Deformation Formula