Bending and deflection of composite beam

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SUMMARY

The discussion focuses on calculating the deflection of a composite beam composed of two distinct homogeneous materials. Key methods mentioned include energy methods (specifically Castigliano's Second Theorem) and the elastic curve equations, both of which require the Young's modulus (E) and moment of inertia (I) for accurate calculations. The challenge arises in determining the appropriate values for E and I, as the neutral axis shifts towards the material with the higher Young's modulus. The use of the parallel axis theorem is essential for calculating the moment of inertia for each part of the cross-section.

PREREQUISITES
  • Understanding of Young's modulus (E) and its significance in material properties
  • Familiarity with moment of inertia (I) and its role in beam deflection calculations
  • Knowledge of Castigliano's Second Theorem for energy methods in structural analysis
  • Proficiency in applying the parallel axis theorem for composite sections
NEXT STEPS
  • Study the application of Castigliano's Theorem in composite beam analysis
  • Learn how to determine the neutral axis in composite cross-sections
  • Explore advanced techniques for calculating deflection in composite materials
  • Investigate software tools for structural analysis of composite beams
USEFUL FOR

Structural engineers, mechanical engineers, and students studying composite materials and beam deflection analysis will benefit from this discussion.

Dell
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my question is regarding calculation of deflection of a composite beam, ie a beam with a cross section made up of 2 separate homogeneous materials.

the methods i know for calculating deflections in homogenous beams are energy methods(catiglianos 2nd) and the elatic curve equations(second integral of the bending moment)

my problem is that in both of these methods(and any other method) i need to use E and I, my question is what E and what I should i use here?
originally i thought i could move over to an equivalen x-section as i would do co calculate stress from bending, expanding one material and then use the E of the other mateerial.
something just doesn't seem right doing that,, (if i used the opposite i would get totally different answers)

please help, agaain the question is mainly about which E and I to use.
 
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I guess you'll have to determine where the neutral axis or centroid is in the cross section, this will be skewed towards the material with the higher young's modulus.

then to determine I, you can determine I for each of the parts of the cross section then use the parallel axis theorem to determine their moment of inertia about the centroid and add them up like any composite material.
 

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