Moment of Inertia using Strain Energy Calculator

✖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 [M]			+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 [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.ⓘ Moment of Inertia using Strain Energy [I]

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Moment of Inertia using Strain Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Length of Member: 3000 Millimeter --> 3 Meter (Check conversion here)
Bending Moment: 53.8 Kilonewton Meter --> 53800 Newton Meter (Check conversion here)
Strain Energy: 136.08 Newton Meter --> 136.08 Joule (Check conversion here)
Young's Modulus: 20000 Megapascal --> 20000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = L*((M^2)/(2*U*E)) --> 3*((53800^2)/(2*136.08*20000000000))

Evaluating ... ...

I = 0.00159526014109347

STEP 3: Convert Result to Output's Unit

0.00159526014109347 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00159526014109347 ≈ 0.001595 Meter⁴ <-- Area Moment of Inertia

(Calculation completed in 00.004 seconds)

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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

Moment of Inertia using Strain Energy Formula

LaTeX Go

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

What is meant by Moment of Inertia?

Moment of inertia also appears in momentum, kinetic energy, and Newton's laws of motion for a rigid body as a physical parameter that combines its shape and mass. The moment of inertia of a rotating flywheel is used in a machine to resist variations in applied torque to smooth its rotational output.

How to Calculate Moment of Inertia using Strain Energy?

Moment of Inertia using Strain Energy calculator uses Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus)) to calculate the Area Moment of Inertia, The Moment of Inertia using Strain Energy formula is defined as a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of torque (turning force). Area Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia using Strain Energy using this online calculator? To use this online calculator for Moment of Inertia using Strain Energy, enter Length of Member (L), Bending Moment (M), Strain Energy (U) & Young's Modulus (E) and hit the calculate button. Here is how the Moment of Inertia using Strain Energy calculation can be explained with given input values -> 0.001595 = 3*((53800^2)/(2*136.08*20000000000)).

FAQ

What is Moment of Inertia using Strain Energy?

The Moment of Inertia using Strain Energy formula is defined as a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of torque (turning force) and is represented as I = L*((M^2)/(2*U*E)) or Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus)). Length of Member is the measurement or extent of member (beam or column) from end to end, 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 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.

How to calculate Moment of Inertia using Strain Energy?

The Moment of Inertia using Strain Energy formula is defined as a quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of torque (turning force) is calculated using Area Moment of Inertia = Length of Member*((Bending Moment^2)/(2*Strain Energy*Young's Modulus)). To calculate Moment of Inertia using Strain Energy, you need Length of Member (L), Bending Moment (M), Strain Energy (U) & Young's Modulus (E). With our tool, you need to enter the respective value for Length of Member, Bending Moment, Strain Energy & Young's Modulus 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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