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 00.004 seconds)

Credits

Created by Rudrani Tidke
Cummins College of Engineering for Women (CCEW), Pune
Rudrani Tidke has created this Calculator and 100+ more calculators!
Verified by Alithea Fernandes
Don Bosco College of Engineering (DBCE), Goa
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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

Bending Moment using Strain Energy Formula

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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