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WellKnown Member
I've been thinking a little about composite wing spars and something that Billski said in another thread.
I am not trying to say how anything actually works, I am just relating my observations and tentative opinions about some VERY crude experiments I've done.
First....
What are composites?
I think when we say composites on this forum, we generally mean long strands of fiber encased in a "plastic" matrix. The fibers by themselves do a pretty good job of reacting to tension forces, but by themselves, are not good for compression loads. They will buckle under their own weight. When we bundle many of these fibers parallel together and encase them in a plastic "matrix", the matrix together with their close proximity to one another makes them able to resist buckling and we now have a structure capable of withstanding both tensile and compressive loads such as we would want in a spar "cap".
But what about shear loads?
Shear is not like loads normal to the crosssectional area of the spar (normal=perpendicular in mathspeak, i.e., tension/compression as in the spar caps described above). Here, shear is longitudinal along the spar, to put it very simplistically, parallel to the tension/compression forces, but it is different. When you push a sanding block along a piece of wood, the force that resists you is "shear" force between the block and the wood. Think of the top half of the shear web pushing the bottom half of the web toward the wing tip and the bottom half pushing the top toward the root. My first intuitive guess about a strand orientation for a shear web "weave" was a bidirectional with the strands at 90° to one another and 45° to the spar caps. So I cut out a square of aluminum screen "cloth" so that the strands were at 45° to the edges of the square(see fig. "A"). Then I clamped opposite edges of the "cloth" and put the square under a shear load and it seemed to do a pretty good job of resisting the shear load. It would deform to the shape of fig. "B", but not without some force and wrinkling, just like a solid foil sheet would have done. So I formed the opinion that 45° to the spar cap was a reasonable strand orientation for the shear web.
What about tension and compression loads?
Then I compressed one edge of the "cloth" and stretched the opposite edge so that the square then became a trapezoid as in fig. "C". This required no effort and there was no buckling or wrinkling. I concluded that my shear web "weave" was not good at withstanding tension/compression forces.
Next, I stretched it out.
I formed the square into a long rectangle so that the strands were now at about 20° to 22° to the spar caps and tried the shear force again and it did seem to react better against the shear force. Also, if I clamped the short edges on the ends, one of the long edges seemed to offer more resistance to compression force, but not a great deal more. If I unclamped the short edges at the ends, then I could easily compress a long edge and the rectangle would easily form a trapezoid, but not without a great deal of vertical expansion (see fig. "C"). I then formed the opinion that a good strand orientation for the shear web might be similar to that shown in fig. "D".
But what about what Billski said?
Billski has indeed said in several different posts that there is a problem with shear web failure where it joins or is influenced by the spar caps. Or at least thats what I think Billski said. I assumed that it was obviously because the shear web fibers are at an angle to those of the spar cap and this would cause them to stretch or shorten a comparatively greater amount than the spar cap fibers. But this is not true, the opposite is what actually happens, see fig."E". But then I remembered that the only place in a beam cross section that is not subject to normal (tension/compression) stress is at the neutral axis. From the neutral axis, stress increases from zero to a maxim at the outer sufaces of the spar caps. The neutral axis is a line drawn crossways through the beam cross section about which the beam cross section will generally balance.
This means the shear web is under combined stresses.
So, I simulated combined shear and normal stresses on the shear web cloth, i.e., I returned it to a trapezoidal shape (fig. "C") and then applied a shear load to it. This time it no longer did such a good job of resisting the shear load and also, there was a region in the center of the trapeziod where the "cloth" seemed to be trying to twist into a spiral shape. I you look at fig. "C", you can see that all of these strange deformations cannot be good for the matrix!
A good solution seemed to be...
As per Billski's recomendation in his post in the "Upsilon" thread, a good solution seemed to be to extend the spar cap down into the shear web so that the crosssectional area of the "spar cap extension" was greater in comparison to the amount of force it had to deal with than than the crosssectional area of the original spar cap needed to to be. Greater crosssectional area for a given amount of force means less stress and, since stress and strain are directly related, less strain, i.e.,less "movement" (stretching/shortening) of the spar caps and less torture for the shear web. At first, this might seem like a waste of spar material, but the only alternative is to increase the shear web material and as we've already seen, it is not suitable for reacting to normal stresses. So it would require more material and be heavier. At least thats what I think Billski was talking about. A very fanciful sketch of what I imagine a properly designed composite wing spar MIGHT look like is shown in fig."F", hopefully someone will critique it and set me straight; I have steeled myself for the news. Even if I have got anywhere close to understanding this, without an understanding of the mathematics involved, I'm still just a beagle chasing a Farrari!
And mathematics is the rub here.
Heres what Raymer says about compsite structural design: "To do it right requires tensor calculus equations and a pretty good computer program." Tensor calculus! This is the mathematics of Relativity, Quantum Physics, Finite Element Analysis, Computational Fluid Dynamics, etc. Another book! Here's what Wikipedia says: "For the anisotropic material, it requires the mathematics of a second order tensor and up to 21 material property constants. For the special case of orthogonal isotropy, there are three different material property constants for each of Young's Modulus, Shear Modulus, and Poisson's ratio  a total of 9 constants to describe the relationship between forces/moments and strains/curvatures."
Billski, in his rather long and informative post in the "Upsilon" thread, has made it clear that he does not favor simplified methods, specifically, Martin Hollmann's methods, over the more rigorous methods covered in books which no doubt require proficiency in understanding tensors. Raymer does recomend Hollmann, but with a caveat: "A good technical introduction to composite materials is provided in [Composite Airframe Structures by M. Niu]. For homebuilders, Hollmann provides an excellent overview of composites." I am not qualified to judge Hollmann's methods. Even if I had read his book, I would not be qualified to do that until I would have mastered tensors and read the more rigorous treatments. I will say this, if Hollmann's methods can lead to a strong enough, safe enough, albeit somewhat heavier than necessary wing structure, then this is not the worst case scenario, for the nondegreed among us who have no tensor calculus, which would be no wing at all. And I can see a time coming when, in a last ditch effort to avoid learning tensor calculus, I will probably buy some of Hollmann's books. But I can also see that having read Hollmann's "overview", curiosity will probably get the best of me (it always does) and I will crack open my Tensor Calculus.
I am not trying to say how anything actually works, I am just relating my observations and tentative opinions about some VERY crude experiments I've done.
First....
What are composites?
I think when we say composites on this forum, we generally mean long strands of fiber encased in a "plastic" matrix. The fibers by themselves do a pretty good job of reacting to tension forces, but by themselves, are not good for compression loads. They will buckle under their own weight. When we bundle many of these fibers parallel together and encase them in a plastic "matrix", the matrix together with their close proximity to one another makes them able to resist buckling and we now have a structure capable of withstanding both tensile and compressive loads such as we would want in a spar "cap".
But what about shear loads?
Shear is not like loads normal to the crosssectional area of the spar (normal=perpendicular in mathspeak, i.e., tension/compression as in the spar caps described above). Here, shear is longitudinal along the spar, to put it very simplistically, parallel to the tension/compression forces, but it is different. When you push a sanding block along a piece of wood, the force that resists you is "shear" force between the block and the wood. Think of the top half of the shear web pushing the bottom half of the web toward the wing tip and the bottom half pushing the top toward the root. My first intuitive guess about a strand orientation for a shear web "weave" was a bidirectional with the strands at 90° to one another and 45° to the spar caps. So I cut out a square of aluminum screen "cloth" so that the strands were at 45° to the edges of the square(see fig. "A"). Then I clamped opposite edges of the "cloth" and put the square under a shear load and it seemed to do a pretty good job of resisting the shear load. It would deform to the shape of fig. "B", but not without some force and wrinkling, just like a solid foil sheet would have done. So I formed the opinion that 45° to the spar cap was a reasonable strand orientation for the shear web.
What about tension and compression loads?
Then I compressed one edge of the "cloth" and stretched the opposite edge so that the square then became a trapezoid as in fig. "C". This required no effort and there was no buckling or wrinkling. I concluded that my shear web "weave" was not good at withstanding tension/compression forces.
Next, I stretched it out.
I formed the square into a long rectangle so that the strands were now at about 20° to 22° to the spar caps and tried the shear force again and it did seem to react better against the shear force. Also, if I clamped the short edges on the ends, one of the long edges seemed to offer more resistance to compression force, but not a great deal more. If I unclamped the short edges at the ends, then I could easily compress a long edge and the rectangle would easily form a trapezoid, but not without a great deal of vertical expansion (see fig. "C"). I then formed the opinion that a good strand orientation for the shear web might be similar to that shown in fig. "D".
But what about what Billski said?
Billski has indeed said in several different posts that there is a problem with shear web failure where it joins or is influenced by the spar caps. Or at least thats what I think Billski said. I assumed that it was obviously because the shear web fibers are at an angle to those of the spar cap and this would cause them to stretch or shorten a comparatively greater amount than the spar cap fibers. But this is not true, the opposite is what actually happens, see fig."E". But then I remembered that the only place in a beam cross section that is not subject to normal (tension/compression) stress is at the neutral axis. From the neutral axis, stress increases from zero to a maxim at the outer sufaces of the spar caps. The neutral axis is a line drawn crossways through the beam cross section about which the beam cross section will generally balance.
This means the shear web is under combined stresses.
So, I simulated combined shear and normal stresses on the shear web cloth, i.e., I returned it to a trapezoidal shape (fig. "C") and then applied a shear load to it. This time it no longer did such a good job of resisting the shear load and also, there was a region in the center of the trapeziod where the "cloth" seemed to be trying to twist into a spiral shape. I you look at fig. "C", you can see that all of these strange deformations cannot be good for the matrix!
A good solution seemed to be...
As per Billski's recomendation in his post in the "Upsilon" thread, a good solution seemed to be to extend the spar cap down into the shear web so that the crosssectional area of the "spar cap extension" was greater in comparison to the amount of force it had to deal with than than the crosssectional area of the original spar cap needed to to be. Greater crosssectional area for a given amount of force means less stress and, since stress and strain are directly related, less strain, i.e.,less "movement" (stretching/shortening) of the spar caps and less torture for the shear web. At first, this might seem like a waste of spar material, but the only alternative is to increase the shear web material and as we've already seen, it is not suitable for reacting to normal stresses. So it would require more material and be heavier. At least thats what I think Billski was talking about. A very fanciful sketch of what I imagine a properly designed composite wing spar MIGHT look like is shown in fig."F", hopefully someone will critique it and set me straight; I have steeled myself for the news. Even if I have got anywhere close to understanding this, without an understanding of the mathematics involved, I'm still just a beagle chasing a Farrari!
And mathematics is the rub here.
Heres what Raymer says about compsite structural design: "To do it right requires tensor calculus equations and a pretty good computer program." Tensor calculus! This is the mathematics of Relativity, Quantum Physics, Finite Element Analysis, Computational Fluid Dynamics, etc. Another book! Here's what Wikipedia says: "For the anisotropic material, it requires the mathematics of a second order tensor and up to 21 material property constants. For the special case of orthogonal isotropy, there are three different material property constants for each of Young's Modulus, Shear Modulus, and Poisson's ratio  a total of 9 constants to describe the relationship between forces/moments and strains/curvatures."
Billski, in his rather long and informative post in the "Upsilon" thread, has made it clear that he does not favor simplified methods, specifically, Martin Hollmann's methods, over the more rigorous methods covered in books which no doubt require proficiency in understanding tensors. Raymer does recomend Hollmann, but with a caveat: "A good technical introduction to composite materials is provided in [Composite Airframe Structures by M. Niu]. For homebuilders, Hollmann provides an excellent overview of composites." I am not qualified to judge Hollmann's methods. Even if I had read his book, I would not be qualified to do that until I would have mastered tensors and read the more rigorous treatments. I will say this, if Hollmann's methods can lead to a strong enough, safe enough, albeit somewhat heavier than necessary wing structure, then this is not the worst case scenario, for the nondegreed among us who have no tensor calculus, which would be no wing at all. And I can see a time coming when, in a last ditch effort to avoid learning tensor calculus, I will probably buy some of Hollmann's books. But I can also see that having read Hollmann's "overview", curiosity will probably get the best of me (it always does) and I will crack open my Tensor Calculus.
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