Composite beam design. 1

[ADrunkenMan]

What are the basic steps for composite beam design?
Its been a while since i did any calcs for a composite beam, there are plenty of programs i can use, but i just want to know the basic steps.
Cheers

 

[RPstress]

For something like an I-beam it's usual to assume a sensible layup for the flanges (for unidirectional material maybe 80% fibres at 0, with 10% at +-45 and 10% at 90), find the allowable tension and compression stresses for that with classical laminate theory (e.g., The Laminator), and size flange thickness accordingly within whatever constraints you have on loading, depth, deflection, etc.

Keep the flange width/thickness ratio below 10 and it's highly likely to be stable. However, a check on one-edge free buckling can be made with this simple formula:
Pcr = b*( pi^2*D11/a^2 + 12*D33/b^2 )
Pcr is *load* in flange (lb or N); b is flange width; a is length; D11 and D33 are from the ABD matrix (get this from CLT analysis). If you want to use laminate Ex, Gxy, etc., then the formula becomes:
Pcr = t^3/b * (pi^2*b^2/a^2 * EfX/(12*(1-nufXY*nufYX)) + GfXY)
where the f's indicate flexural properties, which can be roughly approximated by the in-plane ones.

This formula is only good for a/b >=4, and preferably 8. It's best to check this properly with FE; I don't know of a simple code which does orthotropic laminate buckling with one edge free.

To size the web you just need to do the appropriate shear strength and shear buckling calcs assuming maybe 15/70/15 percentages for the layup. I've never seen a simple shear buckling formula for orthotropic plates (anybody else know of one?), so I tend to use ESDU 81047 or analyse a plate in FE. However, for a really quick and dirty bodge, you can use the laminate shear modulus (Gxy from CLT) times 2.6 (a real bodge from isotropic G = E/(2+2*nu); you can use the actual laminate nuxy from the CLT, but there's not much point) to get a fictitious modulus and use that with isotropic shear buckling formulas for a long simply supported plate. Note that this is only for initial ballpark sizing; you have to check buckling properly with a code.

Finally you have to blend the two to get a practical laminate. You're probably going to have to run the web plies up around the flange. Hopefully most of the 0's needed in the flange but not in the web can be dropped in quite severe ply drops (maybe 10:1 or even 5:1) around the radius. Those that can't be dropped in this distance can be dropped off in the web.

For 45's needed in the web but not the flange, those needed for strength rather than buckling must be carried around the radius and can only then be dropped off with sensible ply drops (about 18:1) across the flange width. (The shear in the 45's needs to transfer itself into building up endload in the flange 0's, so you need a good structural connection between the two.)

For the most part you can just keep the layups reasonably uniform and symmetric. For ultimate efficiency you'll need to bias the ply directions to get the best buckling behaviour. FE can help with this, but from memory I think you need the web 45's and the flange 0's towards the outside of the laminate. Some compromise between flange and web weight must be made there. (NB: not entirely sure about the 0's in the flange; oddly, I think for a properly simply supported plate (all four sides) it's most resistant to buckling with the 45's on the outside. However, I think for one edge free, like the flange, you want the 0's on the outside.) Of course, if the web and flange are strength designed and stable there's no point in this level of optimisation.

For something that's crude but easy to make, you might make the web 100% 45's, and run them all round the radius and all out right to the edge of the flange, then just pile a slab of 0's with a few 90's in it on top. This is not efficient for buckling and will give an undesirable asymmetric laminate, but it's practical and won't give too great a reduction in strength. If you do this you should do a quick check on the shear stress between the 45's and the slab of 0/90's (SAybar/I or VQ/Ib).

Note that the through-thickness shear stiffnesses can reduce the buckling allowables. it's important to include these in any final checking and tweaking for buckling. You can calculate these (e.g., ESDU 89013) or approximate them with the isotropic 5/6 of the in-plane all 0 degree material G12.

-R.