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

STEP 0: Pre-Calculation Summary
Formula Used
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)
L = 2*U*E*I/(Mb^2)
This formula uses 5 Variables
Variables Used
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.
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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Strain Energy in Rod or Shaft: 40 Joule --> 40 Joule No Conversion Required
Modulus of elasticity of rod or shaft: 98000 Newton per Square Millimeter --> 98000000000 Pascal (Check conversion here)
Area Moment of Inertia of rod or shaft: 103000 Millimeter⁴ --> 1.03E-07 Meter⁴ (Check conversion here)
Bending Moment in Shaft or Beam: 780000 Newton Millimeter --> 780 Newton Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
L = 2*U*E*I/(Mb^2) --> 2*40*98000000000*1.03E-07/(780^2)
Evaluating ... ...
L = 1.32728468113083
STEP 3: Convert Result to Output's Unit
1.32728468113083 Meter -->1327.28468113083 Millimeter (Check conversion here)
FINAL ANSWER
1327.28468113083 1327.285 Millimeter <-- Length of Rod or Shaft
(Calculation completed in 00.020 seconds)

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

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

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)
L = 2*U*E*I/(Mb^2)

Define Strain Energy?

Strain energy is a type of potential energy that is stored in a structural member as a result of elastic deformation. The external work done on such a member when it is deformed from its unstressed state is transformed into, and considered equal to the strain energy stored in it.

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

Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment calculator uses 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) to calculate the Length of Rod or Shaft, The Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as the total length of the shaft that is subjected to bending Moment. Length of Rod or Shaft is denoted by L symbol.

How to calculate Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment using this online calculator? To use this online calculator for Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment, enter Strain Energy in Rod or Shaft (U), Modulus of elasticity of rod or shaft (E), Area Moment of Inertia of rod or shaft (I) & Bending Moment in Shaft or Beam (Mb) and hit the calculate button. Here is how the Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment calculation can be explained with given input values -> 1.3E+6 = 2*40*98000000000*1.03E-07/(780^2).

FAQ

What is Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment?
The Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as the total length of the shaft that is subjected to bending Moment and is represented as L = 2*U*E*I/(Mb^2) or 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). Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation, 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, 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 is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
How to calculate Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment?
The Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment formula is defined as the total length of the shaft that is subjected to bending Moment is calculated using 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). To calculate Length of Shaft given Strain Energy Stored in Shaft Subjected to Bending Moment, you need Strain Energy in Rod or Shaft (U), Modulus of elasticity of rod or shaft (E), Area Moment of Inertia of rod or shaft (I) & Bending Moment in Shaft or Beam (Mb). With our tool, you need to enter the respective value for 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 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 Length of Rod or Shaft?
In this formula, Length of Rod or Shaft uses 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. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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
  • 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)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!