Deflection of cantilever beam having two Young's modulas

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SUMMARY

The discussion focuses on deriving the formula for the deflection of a cantilever beam composed of two materials with different Young's moduli and moments of inertia when subjected to a point load at the free end. A participant successfully derived the formula using basic governing equations and validated it with MATLAB, confirming the accuracy of both results. The importance of specifying the geometry and material properties of the beam is emphasized, as each material has a distinct Young's modulus. The conversation highlights the need for clarity in the beam's construction to ensure accurate calculations.

PREREQUISITES
  • Understanding of cantilever beam mechanics
  • Knowledge of Young's modulus and moment of inertia
  • Familiarity with MATLAB for validation of engineering formulas
  • Basic principles of composite materials in structural engineering
NEXT STEPS
  • Research the governing equations for deflection in composite cantilever beams
  • Learn how to implement MATLAB for structural analysis simulations
  • Explore the effects of varying Young's moduli on beam performance
  • Study the geometric considerations for beams with multiple materials
USEFUL FOR

Structural engineers, mechanical engineers, and students working on projects involving composite materials in beam design will benefit from this discussion.

cvnaditya
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what is the formula for the cantilever beam having two different young's modulas and moment of inertia, when a point load is acting on the free end.

i have been trying but unable to get the formula. if the formula i can validate my project work and complete it
 
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cvnaditya said:
what is the formula for the cantilever beam having two different young's modulas and moment of inertia, when a point load is acting on the free end.

i have been trying but unable to get the formula. if the formula i can validate my project work and complete it
I'm afraid this description of the beam and the materials composing it is a little vague.

Are we talking something like a leaf spring, with two different materials lapped together? Is one portion of the length of the beam one material, and the rest of the beam composed of another material?

You should try to be as specific as possible about the construction of your beam. Pictures always help.
 
Each material has only one Young's Modulus value. If there are two involved, then there must be two materials and the geometry of the two becomes significant.
 
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SteamKing said:
I'm afraid this description of the beam and the materials composing it is a little vague.

Are we talking something like a leaf spring, with two different materials lapped together? Is one portion of the length of the beam one material, and the rest of the beam composed of another material?

You should try to be as specific as possible about the construction of your beam. Pictures always help.
Yes, your right one length one material and rest of the length will be another material...

I derived the formula using basic govering equation yesterday and verified it with MATLAB program for cantilever beam. Both the results are correct, it is used for having two different materials and moment of inertia for a cantilever beam.
Capture.PNG
 
OldEngr63 said:
Each material has only one Young's Modulus value. If there are two involved, then there must be two materials and the geometry of the two becomes significant.
yes sir, i have posted formula. i hope it is correct and useful.
 

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