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Length over which Deformation takes place using Strain Energy Formula

GoLength over which Deformation takes place given Strain Energy in Shear Formula

GoLength over which Deformation takes place given Strain Energy in Torsion Formula

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Length of Member is the measurement or extent of member (beam or column) from end to end. Check FAQs

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

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

Length over which Deformation takes place using Strain Energy Example

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With units

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Here is how the Length over which Deformation takes place using Strain Energy equation looks like with Values.

Here is how the Length over which Deformation takes place using Strain Energy equation looks like with Units.

Here is how the Length over which Deformation takes place using Strain Energy equation looks like.

3008.9136 = (136.08 \cdot \frac{2 \cdot 20000 \cdot 0.0016}{{53.8}^{2}})

3008.9136mm = (136.08N*m \cdot \frac{2 \cdot 20000MPa \cdot 0.0016m⁴}{{53.8kN*m}^{2}})

3008.9136 = (136.08 \cdot \frac{2 \cdot 20000 \cdot 0.0016}{{53.8}^{2}})

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Length over which Deformation takes place using Strain Energy Solution

Follow our step by step solution on how to calculate Length over which Deformation takes place using Strain Energy?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

L = (136.08J \cdot \frac{2 \cdot 2E+10Pa \cdot 0.0016m⁴}{{53800N*m}^{2}})

Next Step Prepare to Evaluate

∴

L = (136.08 \cdot \frac{2 \cdot 2E+10 \cdot 0.0016}{53800^{2}})

Next Step Evaluate

∴

L = 3.00891364132613m

Next Step Convert to Output's Unit

∴

L = 3008.91364132613mm

LAST Step Rounding Answer

∴

L = 3008.9136mm

Length over which Deformation takes place using Strain Energy Formula Elements

Variables

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

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

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

Other Formulas to find Length of Member

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 Length over which Deformation takes place given Strain Energy in Torsion

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

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 Shear Area given Strain Energy in Shear

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

How to Evaluate Length over which Deformation takes place using Strain Energy?

Length over which Deformation takes place using Strain Energy evaluator uses Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2)) to evaluate the Length of Member, The Length over which Deformation takes place using Strain Energy formula is defined as the length of the section of the specimen under bending whose original dimension gets distorted or changed after bending. Length of Member is denoted by L symbol.

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

FAQs on Length over which Deformation takes place using Strain Energy

What is the formula to find Length over which Deformation takes place using Strain Energy?

The formula of Length over which Deformation takes place using Strain Energy is expressed as Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2)). Here is an example- 3.008914 = (136.08*(2*20000000000*0.0016)/(53800^2)).

How to calculate Length over which Deformation takes place using Strain Energy?

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

What are the other ways to Calculate Length of Member?

Here are the different ways to Calculate Length of Member-

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

Can the Length over which Deformation takes place using Strain Energy be negative?

No, the Length over which Deformation takes place using Strain Energy, measured in Length cannot be negative.

Which unit is used to measure Length over which Deformation takes place using Strain Energy?

Length over which Deformation takes place using Strain Energy is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length over which Deformation takes place using Strain Energy can be measured.

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Length over which Deformation takes place using Strain Energy Formula

​GoLength over which Deformation takes place given Strain Energy in Shear Formula

​GoLength over which Deformation takes place given Strain Energy in Torsion Formula

Length over which Deformation takes place using Strain Energy Example

Length over which Deformation takes place using Strain Energy Solution

Length over which Deformation takes place using Strain Energy Formula Elements

Other Formulas to find Length of Member

Other formulas in Strain Energy in Structural Members category

How to Evaluate Length over which Deformation takes place using Strain Energy?

FAQs on Length over which Deformation takes place using Strain Energy

Variable Name

GoLength over which Deformation takes place given Strain Energy in Shear Formula

GoLength over which Deformation takes place given Strain Energy in Torsion Formula