Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Calculator

✖Bending Moment in Shaft or Beam 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 in Shaft or Beam [M_b]			+10% -10%
✖Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.ⓘ Length of Rod or Shaft [L]			+10% -10%
✖Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of elasticity of rod or shaft [E]			+10% -10%
✖Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.ⓘ Strain Energy in Rod or Shaft [U]			+10% -10%

✖Area Moment of Inertia of rod or shaft is the measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.ⓘ Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment [I]

⎘ Copy

👎

Formula

✖

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment

Formula

`"I" = ("M"_{"b"}^2)*"L"/(2*"E"*"U")`

Example

`"103210.7mm⁴"=(("7.8E5N*mm")^2)*"1330mm"/(2*"98000N/mm²"*"40J")`

Calculator

LaTeX

Reset

👍

Download Mechanical Formula PDF PDF Image

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft)
I = (M_b^2)*L/(2*E*U)
This formula uses 5 Variables

Variables Used

Area Moment of Inertia of rod or shaft - (Measured in Meter⁴) - Area Moment of Inertia of rod or shaft is the measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.
Bending Moment in Shaft or Beam - (Measured in Newton Meter) - Bending Moment in Shaft or Beam 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 Rod or Shaft - (Measured in Meter) - Length of Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom.
Modulus of elasticity of rod or shaft - (Measured in Pascal) - Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Strain Energy in Rod or Shaft - (Measured in Joule) - Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Shaft or Beam: 780000 Newton Millimeter --> 780 Newton Meter (Check conversion here)
Length of Rod or Shaft: 1330 Millimeter --> 1.33 Meter (Check conversion here)
Modulus of elasticity of rod or shaft: 98000 Newton per Square Millimeter --> 98000000000 Pascal (Check conversion here)
Strain Energy in Rod or Shaft: 40 Joule --> 40 Joule No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (M_b^2)*L/(2*E*U) --> (780^2)*1.33/(2*98000000000*40)

Evaluating ... ...

I = 1.03210714285714E-07

STEP 3: Convert Result to Output's Unit

1.03210714285714E-07 Meter⁴ -->103210.714285714 Millimeter⁴ (Check conversion here)

FINAL ANSWER

103210.714285714 ≈ 103210.7 Millimeter⁴ <-- Area Moment of Inertia of rod or shaft

(Calculation completed in 00.020 seconds)

You are here -

Home » Engineering » Mechanical » Machine Design » Castigliano's Theorem for Deflection in Complex Structures » Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 14 Castigliano's Theorem for Deflection in Complex Structures Calculators

Torque given Strain Energy in Rod Subjected to External Torque

Go Torque on Rod or Shaft = sqrt(2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft/Length of Rod or Shaft)

Force Applied on Rod given Strain Energy Stored in Tension Rod

Go Axial Force on Beam = sqrt(Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Length of Rod or Shaft)

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment

Go Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft)

Modulus of Elasticity given Strain Energy Stored in Shaft Subjected to Bending Moment

Go Modulus of elasticity of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Area Moment of Inertia of rod or shaft)

Strain Energy Stored in Rod Subjected to Bending Moment

Go Strain Energy in Rod or Shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft)

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment

Go Length of Rod or Shaft = 2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft*Area Moment of Inertia of rod or shaft/(Bending Moment in Shaft or Beam^2)

Length of Shaft when Strain Energy in Shaft Subjected to External Torque

Go Length of Rod or Shaft = (2*Strain Energy in Rod or Shaft*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)/(Torque on Rod or Shaft^2)

Strain Energy in Rod when it is Subjected to External Torque

Go Strain Energy in Rod or Shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Modulus of rigidity of rod or shaft)

Polar Moment of Inertia of Rod given Strain Energy in Rod

Go Polar Moment of Inertia of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of rigidity of rod or shaft)

Modulus of Rigidity of Rod given Strain Energy in Rod

Go Modulus of rigidity of rod or shaft = (Torque on Rod or Shaft^2)*Length of Rod or Shaft/(2*Polar Moment of Inertia of rod or shaft*Strain Energy in Rod or Shaft)

Strain Energy Stored in Tension Rod

Go Strain Energy in Rod or Shaft = ((Axial Force on Beam^2)*Length of Rod or Shaft)/(2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft)

Cross-sectional Area of Rod given Strain Energy stored in Rod

Go Cross Sectional Area of Rod = Axial Force on Beam^2*Length of Rod or Shaft/(2*Strain Energy in Rod or Shaft*Modulus of elasticity of rod or shaft)

Modulus of Elasticity of Rod given Strain Energy Stored

Go Modulus of elasticity of rod or shaft = Axial Force on Beam^2*Length of Rod or Shaft/(2*Cross Sectional Area of Rod*Strain Energy in Rod or Shaft)

Length of Rod given Strain Energy Stored

Go Length of Rod or Shaft = Strain Energy in Rod or Shaft*2*Cross Sectional Area of Rod*Modulus of elasticity of rod or shaft/Axial Force on Beam^2

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment Formula

Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft)
I = (M_b^2)*L/(2*E*U)

Define Moment of Inertia?

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.

How to Calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment calculator uses Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft) to calculate the Area Moment of Inertia of rod or shaft, The Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. Area Moment of Inertia of rod or shaft is denoted by I symbol.

How to calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment using this online calculator? To use this online calculator for Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment, enter Bending Moment in Shaft or Beam (M_b), Length of Rod or Shaft (L), Modulus of elasticity of rod or shaft (E) & Strain Energy in Rod or Shaft (U) and hit the calculate button. Here is how the Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment calculation can be explained with given input values -> 1E+17 = (780^2)*1.33/(2*98000000000*40).

FAQ

What is Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

The Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration and is represented as I = (M_b^2)*L/(2*E*U) or Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft). Bending Moment in Shaft or Beam 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 Rod or Shaft is defined as the total length of the rod or the shaft according to Castiglano's theorom, Modulus of elasticity of rod or shaft is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it & Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation.

How to calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment?

The Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration is calculated using Area Moment of Inertia of rod or shaft = (Bending Moment in Shaft or Beam^2)*Length of Rod or Shaft/(2*Modulus of elasticity of rod or shaft*Strain Energy in Rod or Shaft). To calculate Moment of Inertia of Shaft when Strain Energy Stored in Shaft Subjected to Bending Moment, you need Bending Moment in Shaft or Beam (M_b), Length of Rod or Shaft (L), Modulus of elasticity of rod or shaft (E) & Strain Energy in Rod or Shaft (U). With our tool, you need to enter the respective value for Bending Moment in Shaft or Beam, Length of Rod or Shaft, Modulus of elasticity of rod or shaft & Strain Energy in Rod or Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search