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Strain Energy in Torsion given Angle of Twist 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 = \frac{J \cdot G Torsion \cdot {(θ \cdot (\frac{π}{180}))}^{2}}{2 \cdot L}

U - Strain Energy?J - Polar Moment of Inertia?G_Torsion - Modulus of Rigidity?θ - Angle of Twist?L - Length of Member?π - Archimedes' constant?

Strain Energy in Torsion given Angle of Twist Example

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Here is how the Strain Energy in Torsion given Angle of Twist equation looks like with Values.

Here is how the Strain Energy in Torsion given Angle of Twist equation looks like with Units.

Here is how the Strain Energy in Torsion given Angle of Twist equation looks like.

570.6694 = \frac{0.0041 \cdot 40 \cdot {(15 \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3000}

570.6694N*m = \frac{0.0041m⁴ \cdot 40GPa \cdot {(15° \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3000mm}

570.6694 = \frac{0.0041 \cdot 40 \cdot {(15 \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3000}

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Strain Energy in Torsion given Angle of Twist Solution

Follow our step by step solution on how to calculate Strain Energy in Torsion given Angle of Twist?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U = \frac{0.0041m⁴ \cdot 40GPa \cdot {(15° \cdot (\frac{π}{180}))}^{2}}{2 \cdot 3000mm}

Next Step Substitute values of Constants

∴

U = \frac{0.0041m⁴ \cdot 40GPa \cdot {(15° \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3000mm}

Next Step Convert Units

∴

U = \frac{0.0041m⁴ \cdot 4E+10Pa \cdot {(0.2618rad \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3m}

Next Step Prepare to Evaluate

∴

U = \frac{0.0041 \cdot 4E+10 \cdot {(0.2618 \cdot (\frac{3.1416}{180}))}^{2}}{2 \cdot 3}

Next Step Evaluate

∴

U = 570.669400490482J

Next Step Convert to Output's Unit

∴

U = 570.669400490482N*m

LAST Step Rounding Answer

∴

U = 570.6694N*m

Strain Energy in Torsion given Angle of Twist 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

Polar Moment of Inertia

Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Modulus of Rigidity

Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

Symbol: G_Torsion

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

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 Bending

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

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 Torsion given Angle of Twist?

Strain Energy in Torsion given Angle of Twist evaluator uses Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member) to evaluate the Strain Energy, The Strain Energy in Torsion given Angle of Twist formula is defined as the energy stored in a body due to torsional deformation. Strain Energy is denoted by U symbol.

How to evaluate Strain Energy in Torsion given Angle of Twist using this online evaluator? To use this online evaluator for Strain Energy in Torsion given Angle of Twist, enter Polar Moment of Inertia (J), Modulus of Rigidity (G_Torsion), Angle of Twist (θ) & Length of Member (L) and hit the calculate button.

FAQs on Strain Energy in Torsion given Angle of Twist

What is the formula to find Strain Energy in Torsion given Angle of Twist?

The formula of Strain Energy in Torsion given Angle of Twist is expressed as Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member). Here is an example- 570.6694 = (0.0041*40000000000*(0.2617993877991*(pi/180))^2)/(2*3).

How to calculate Strain Energy in Torsion given Angle of Twist?

With Polar Moment of Inertia (J), Modulus of Rigidity (G_Torsion), Angle of Twist (θ) & Length of Member (L) we can find Strain Energy in Torsion given Angle of Twist using the formula - Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(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 in Torsion given Angle of Twist be negative?

Yes, the Strain Energy in Torsion given Angle of Twist, measured in Energy can be negative.

Which unit is used to measure Strain Energy in Torsion given Angle of Twist?

Strain Energy in Torsion given Angle of Twist 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 Torsion given Angle of Twist can be measured.

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Strain Energy in Torsion given Angle of Twist Formula

​GoStrain Energy in Shear Formula

​GoStrain Energy in Shear given Shear Deformation Formula

Strain Energy in Torsion given Angle of Twist Example

Strain Energy in Torsion given Angle of Twist Solution

Strain Energy in Torsion given Angle of Twist Formula Elements

Other Formulas to find Strain Energy

Other formulas in Strain Energy in Structural Members category

How to Evaluate Strain Energy in Torsion given Angle of Twist?

FAQs on Strain Energy in Torsion given Angle of Twist

Variable Name

GoStrain Energy in Shear Formula

GoStrain Energy in Shear given Shear Deformation Formula