Deflection of cantilever beam having two Young's modulas

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Discussion Overview

The discussion centers on deriving a formula for the deflection of a cantilever beam composed of two different materials, each with its own Young's modulus and moment of inertia, under a point load applied at the free end. The scope includes theoretical considerations and practical applications relevant to project work.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire about the specific construction of the beam, suggesting that clarity regarding the materials and their arrangement is crucial for deriving the correct formula.
  • One participant notes that each material has a single Young's modulus, implying that the presence of two Young's moduli indicates the involvement of two distinct materials.
  • A participant claims to have derived a formula using governing equations and verified it with MATLAB, asserting that both results are correct for a cantilever beam with two different materials and moments of inertia.
  • Another participant expresses hope that the posted formula is correct and useful, indicating a level of uncertainty about its validity.

Areas of Agreement / Disagreement

Participants express differing views on the clarity of the beam's description and the implications of having two materials. There is no consensus on the formula itself, as some participants are still seeking clarification and validation.

Contextual Notes

The discussion highlights the need for specific details regarding the beam's construction and the significance of geometry in deriving the formula. There are unresolved aspects related to the assumptions made about the materials and their arrangement.

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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