Bending Moment 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%
✖Length of Member is the measurement or extent of member (beam or column) from end to end.ⓘ Length of Member [L]			+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 using Strain Energy [M]

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Bending Moment using Strain Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member)
M = sqrt(U*(2*E*I)/L)
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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

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
Length of Member: 3000 Millimeter --> 3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = sqrt(U*(2*E*I)/L) --> sqrt(136.08*(2*20000000000*0.0016)/3)

Evaluating ... ...

M = 53879.8663695448

STEP 3: Convert Result to Output's Unit

53879.8663695448 Newton Meter -->53.8798663695448 Kilonewton Meter (Check conversion here)

FINAL ANSWER

53.8798663695448 ≈ 53.87987 Kilonewton Meter <-- Bending Moment

(Calculation completed in 00.020 seconds)

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Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

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< Strain Energy in Structural Members Calculators

Shear Force using Strain Energy

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

Strain Energy in Shear

LaTeX 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 Shear

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

Stress using Hook's Law

LaTeX Go Direct Stress = Young's Modulus*Lateral Strain

Bending Moment using Strain Energy Formula

LaTeX Go

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

How do you convert Bending Moments to Stress?

In both cases, the stress (normal for bending, and shear for torsion) is equal to a couple/moment (M for bending, and T for torsion) times the location along the cross section, because the stress isn't uniform along the cross section (with Cartesian coordinates for bending, and cylindrical coordinates for torsion)

How to Calculate Bending Moment using Strain Energy?

Bending Moment using Strain Energy calculator uses Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member) to calculate the Bending Moment, The Bending Moment using Strain Energy formula is defined as 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 is denoted by M symbol.

How to calculate Bending Moment using Strain Energy using this online calculator? To use this online calculator for Bending Moment using Strain Energy, enter Strain Energy (U), Young's Modulus (E), Area Moment of Inertia (I) & Length of Member (L) and hit the calculate button. Here is how the Bending Moment using Strain Energy calculation can be explained with given input values -> 0.05388 = sqrt(136.08*(2*20000000000*0.0016)/3).

FAQ

What is Bending Moment using Strain Energy?

The Bending Moment using Strain Energy formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend and is represented as M = sqrt(U*(2*E*I)/L) or Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member). 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 & Length of Member is the measurement or extent of member (beam or column) from end to end.

How to calculate Bending Moment using Strain Energy?

The Bending Moment using Strain Energy formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend is calculated using Bending Moment = sqrt(Strain Energy*(2*Young's Modulus*Area Moment of Inertia)/Length of Member). To calculate Bending Moment using Strain Energy, you need Strain Energy (U), Young's Modulus (E), Area Moment of Inertia (I) & Length of Member (L). With our tool, you need to enter the respective value for Strain Energy, Young's Modulus, Area Moment of Inertia & Length of Member and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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