Strain Energy in Bending Calculator

✖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 of Member [L]			+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%

✖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 in Bending [U]

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Formula

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Strain Energy in Bending

Formula

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

Example

`"135.6769N*m"=((("53.8kN*m")^2)*"3000mm"/(2*"20000MPa"*"0.0016m⁴"))`

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Strain Energy in Bending Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
Length of Member - (Measured in Meter) - Length of Member is the measurement or extent of member (beam or column) from end to end.
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.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 53.8 Kilonewton Meter --> 53800 Newton Meter (Check conversion here)
Length of Member: 3000 Millimeter --> 3 Meter (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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = ((M^2)*L/(2*E*I)) --> ((53800^2)*3/(2*20000000000*0.0016))

Evaluating ... ...

U = 135.676875

STEP 3: Convert Result to Output's Unit

135.676875 Joule -->135.676875 Newton Meter (Check conversion here)

FINAL ANSWER

135.676875 ≈ 135.6769 Newton Meter <-- Strain Energy

(Calculation completed in 00.004 seconds)

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Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

Rudrani Tidke has created this Calculator and 100+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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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

Strain Energy in Bending Formula

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

What is Strain Energy?

When a body is subjected to external force it undergoes deformation. The energy stored in the body due to deformation is known as strain energy.

What is the difference between Strain Energy and Resilience?

Strain energy is elastic — that is, the material tends to recover when the load is removed. Where Resilience is typically expressed as the modulus of resilience, which is the amount of strain energy the material can store per unit of volume without causing permanent deformation.

How to Calculate Strain Energy in Bending?

Strain Energy in Bending calculator uses Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia)) to calculate 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 calculate Strain Energy in Bending using this online calculator? To use this online calculator 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. Here is how the Strain Energy in Bending calculation can be explained with given input values -> 135.6769 = ((53800^2)*3/(2*20000000000*0.0016)).

FAQ

What is Strain Energy in Bending?

The Strain Energy in Bending formula is defined as the energy stored in a body due to deformation caused by bending and is represented as U = ((M^2)*L/(2*E*I)) or Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia)). 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, Length of Member is the measurement or extent of member (beam or column) from end to end, 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.

How to calculate Strain Energy in Bending?

The Strain Energy in Bending formula is defined as the energy stored in a body due to deformation caused by bending is calculated using Strain Energy = ((Bending Moment^2)*Length of Member/(2*Young's Modulus*Area Moment of Inertia)). To calculate Strain Energy in Bending, you need Bending Moment (M), Length of Member (L), Young's Modulus (E) & Area Moment of Inertia (I). With our tool, you need to enter the respective value for Bending Moment, Length of Member, Young's Modulus & Area Moment of Inertia 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 Strain Energy?

In this formula, Strain Energy uses Bending Moment, Length of Member, Young's Modulus & Area Moment of Inertia. We can use 5 other way(s) to calculate the same, which is/are as follows -

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

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