Composite Tube bending properties

[Lan123]

I want to find the Young's Modulus of a composite tube (Concentric) made out of three tubes of different material glued together. Once the pipe is manufactured it will bend perpendicular to the axis. Can someone tell me where I can find the relevent equations.

Also I want to to find the poisson ratio for the composite tube. Is there an equation for this?

Thanks in advance.

 

[GregLocock]

Are you trying to estimate the bending stiffness of the composite tube around its neutral axis?

If so The trick is that M/I=s/y=E/R, or more usefully s/(yE)=1/R

R is the same for all three tubes, the strain (s/E) is the same for each at a given y.

Now you know that you can easily derive an expression for the total EI of the assembly.



Cheers

Greg Locock


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[izax1]

Are the three different materials fibre reinforced composite? Are the fibres directions different for the three tubes? In order to be of any help I think some more info would be necessary.

 

[prex]

Differently from Greg, I understand that you have essentially a single tube, where three layers in the thickness are formed with different materials, right? A sketch would help much!
If I'm correct, and if I recall correctly the theory of reinf.concrete, you should do this:
-call E₁ the elastic modulus of one of the three materials
-for the remaining two materials define n₂=E₂/E₁ and n₃=E₃/E₁
-now I_c=I₁+n₂I₂+n₃I₃ and
[σ]₁=My/I_c
[σ]₂=n₂My/I_c
[σ]₃=n₃My/I_c
Concerning the Poisson's ratio, I don't know how to combine them, and I suspect this would depend on the type of induced stress (if you are dealing with simple bending, what ere you doing with Poisson?). Anyway I would average the ratii on the area of the cross sections of the tubes.

prex

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[GregLocock]

prex, that's the same, you've jumped to the answer, and formatted it nicely.

Cheers

Greg Locock


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