Length over which Deformation takes place using Strain Energy Calculator

✖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.ⓘ Strain Energy [U]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Area Moment of Inertia is a moment about the centroidal axis without considering mass.ⓘ Area Moment of Inertia [I]			+10% -10%
✖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.ⓘ Bending Moment [M]			+10% -10%

✖Length of Member is the measurement or extent of member (beam or column) from end to end.ⓘ Length over which Deformation takes place using Strain Energy [L]

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Formula

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Length over which Deformation takes place using Strain Energy

Formula

`"L" = ("U"*(2*"E"*"I")/("M"^2))`

Example

`"3008.914mm"=("136.08N*m"*(2*"20000MPa"*"0.0016m⁴")/(("53.8kN*m")^2))`

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Length over which Deformation takes place using Strain Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2))
L = (U*(2*E*I)/(M^2))
This formula uses 5 Variables

Variables Used

Length of Member - (Measured in Meter) - Length of Member is the measurement or extent of member (beam or column) from end to end.
Strain Energy - (Measured in Joule) - 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.
Young's Modulus - (Measured in Pascal) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a moment about the centroidal axis without considering mass.
Bending Moment - (Measured in Newton Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Strain Energy: 136.08 Newton Meter --> 136.08 Joule (Check conversion here)
Young's Modulus: 20000 Megapascal --> 20000000000 Pascal (Check conversion here)
Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required
Bending Moment: 53.8 Kilonewton Meter --> 53800 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (U*(2*E*I)/(M^2)) --> (136.08*(2*20000000000*0.0016)/(53800^2))

Evaluating ... ...

L = 3.00891364132613

STEP 3: Convert Result to Output's Unit

3.00891364132613 Meter -->3008.91364132613 Millimeter (Check conversion here)

FINAL ANSWER

3008.91364132613 ≈ 3008.914 Millimeter <-- Length of Member

(Calculation completed in 00.004 seconds)

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Cummins College of Engineering for Women (CCEW), Pune

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< 19 Strain Energy in Structural Members Calculators

Strain Energy in Torsion given Angle of Twist

Go Strain Energy = (Polar Moment of Inertia*Modulus of Rigidity*(Angle of Twist*(pi/180))^2)/(2*Length of Member)

Strain Energy for Pure Bending when Beam rotates in One End

Go Strain Energy = (Young's Modulus*Area Moment of Inertia*((Angle of Twist*(pi/180))^2)/(2*Length of Member))

Bending Moment using Strain Energy

Go Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member)

Torque given Strain Energy in Torsion

Go Torque SOM = sqrt(2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity/Length of Member)

Shear Force using Strain Energy

Go Shear Force = sqrt(2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/Length of Member)

Strain Energy in Shear given Shear Deformation

Go Strain Energy = (Area of Cross-Section*Modulus of Rigidity*(Shear Deformation^2))/(2*Length of Member)

Length over which Deformation takes place using Strain Energy

Go Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2))

Modulus of Elasticity with given Strain Energy

Go Young's Modulus = (Length of Member*(Bending Moment^2)/(2*Strain Energy*Area Moment of Inertia))

Moment of Inertia using Strain Energy

Go Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus))

Strain Energy in Bending

Go Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia))

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

Go Strain Energy = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Modulus of Rigidity)

Shear Modulus of Elasticity given Strain Energy in Torsion

Go Modulus of Rigidity = (Torque SOM^2)*Length of Member/(2*Polar Moment of Inertia*Strain Energy)

Polar Moment of Inertia given Strain Energy in Torsion

Go Polar Moment of Inertia = (Torque SOM^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)

Shear Modulus of Elasticity given Strain Energy in Shear

Go Modulus of Rigidity = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Strain Energy)

Shear Area given Strain Energy in Shear

Go Area of Cross-Section = (Shear Force^2)*Length of Member/(2*Strain Energy*Modulus of Rigidity)

Strain Energy in Shear

Go Strain Energy = (Shear Force^2)*Length of Member/(2*Area of Cross-Section*Modulus of Rigidity)

Length over which Deformation takes place given Strain Energy in Torsion

Go Length of Member = (2*Strain Energy*Polar Moment of Inertia*Modulus of Rigidity)/Torque SOM^2

Length over which Deformation takes place given Strain Energy in Shear

Go Length of Member = 2*Strain Energy*Area of Cross-Section*Modulus of Rigidity/(Shear Force^2)

Stress using Hook's Law

Go Direct Stress = Young's Modulus*Lateral Strain

Length over which Deformation takes place using Strain Energy Formula

Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2))
L = (U*(2*E*I)/(M^2))

What are the four basic forms of deformation of solid bodies?

Four basic forms of deformations or displacements of structures or solid bodies and these are:
TENSION, COMPRESSION, BENDING & TWISTING.

How does Shear Deformation take place?

Shearing forces cause shearing deformation. An element subject to shear does not change in length alone but undergoes a change in shape, this is how a shear deformation takes place.

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

Length over which Deformation takes place using Strain Energy calculator uses Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2)) to calculate 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 calculate Length over which Deformation takes place using Strain Energy using this online calculator? To use this online calculator 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. Here is how the Length over which Deformation takes place using Strain Energy calculation can be explained with given input values -> 3.008914 = (136.08*(2*20000000000*0.0016)/(53800^2)).

FAQ

What is Length over which Deformation takes place using Strain Energy?

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 and is represented as L = (U*(2*E*I)/(M^2)) or Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2)). 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, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Area Moment of Inertia is a moment about the centroidal axis without considering mass & 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.

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

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 is calculated using Length of Member = (Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/(Bending Moment^2)). To calculate Length over which Deformation takes place using Strain Energy, you need Strain Energy (U), Young's Modulus (E), Area Moment of Inertia (I) & Bending Moment (M). With our tool, you need to enter the respective value for Strain Energy, Young's Modulus, Area Moment of Inertia & Bending Moment and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Length of Member?

In this formula, Length of Member uses Strain Energy, Young's Modulus, Area Moment of Inertia & Bending Moment. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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