fiber angle and bending stiffness

It isn't, because it depends on more than the angle of the fibers. Fiber-matrix composites are highly anisotropic and the exact values depend very strongly on not only the fiber angle, but the fiber makeup (tape, weave, roving, etc.) and the order the fibers are layed up.

You might be able to do it empiracaly...I think any good building reference should have the bending stiffness for various types of woods. Then you could correlate to the fiber angle of the various woods.

Wood (and other natural fiber-matrix composites) have an added complexity that even fibers that are nominally all the same direction actually have a spread of a few degrees off nominal. This significantly boosts the off-axis properties with a negligable decrease in on-axis properties, but it's difficult to analyze.

Tom.

Well, I wasn't looking for exact, absolute values, but rather for the relation of how changing the angle changes stiffness, assuming everything else to remain the same (fiber makeup, shape etc).

This is for discussing data measured on wood from wind-sheltered and wind-exposed poplar trees where we find a lower elastic modulus (bending) in the exposed trees, despite higher wood density!

I was wondering if the decreased angle of the cellulose microfibrils in the cell walls could be responsible. Since the matrix of the cell walls in the wind-exposed wood is actually stiffer, I really can't think of too many other factors that could cause the marked decrease in modulus.

...good thinking, but different types of wood differ in too many factors other than fiber angle with significant impact on the mechanical properties.

HEY! It's *great* that you mention this. When looking at microscopic images of plant cell walls, I was sometimes thinking what mechanical impact the scattering of the fibrils around the average orientation might have on the mechanics. However, I never pursued this aspect and I never saw it being mentioned anywhere in the (botanical/biomechanical) literature. Do you know of any papers / textbooks that discuss this? (No matter whether Engineering or Biology)

"koehlerl" wrote

The graph at the top of pg. 4 in this paper shows something like what you're talking about:

Wierd. Is that possibly an evolutionary adaptation where trees exposed to more wind are more flexible, thereby more able to resist very high winds?

That could certainly do it, although without knowing the angles I don't know if it's trending right. You can easily get an order of magnitude difference in bulk modulus in a fiber-matrix composite by changing the fiber orientation (assuming significant difference in modulus between fiber and matrix).

Unfortunately not. The only place I'm aware of research on it is aerospace composites, and that's both proprietary and (usually) classified. However, some Googling on "fiber orientation composite modulus" shows an enourmous number of academic papers, so there may be something out there.

Good luck! Tom.

Yeah - only that the loading in that graph is is tension. I was stupid enough to follow local lab tradition and measure my wood samples in bending. While bending may be closer to the "real-world" challenge a tree faces by wind load, it is quite an unfortunate mixture of tensional and compressional loading when it comes to analyzing the relation of mechanical properties and wood (ultra-)structure. Thus my posting in this NG: I was hoping somebody would know of work discussing fiber angle and bending stiffness.

Not quite. Trees under wind exposure actually grow thicker stems and the increase in second moment of area overrides the decrease in modulus so that the bending stiffness of the trunk is higher in wind-exposed trees. Still, there should be an (evolutionary) advantage in this "strategy". It could probably be found by looking the cost of energy required for building the wood and at efficiency in damping wind sway?

Cellulose fibrils in tension: E=120 GPa Matrix: roughly E=10 GPa The changes in angle are from about 15 Degrees to about 18 Degrees The bending modulus of exposed trees is lower by a factor of around 0.86 ...just in case you'd have time to comment on this more specifically.

Thanks! I naturally goggled first, before addressing this news group. However, it looks like you suggest just the right search terms here. I basically got links to paper and lumber quality research returned by goggle.

Thanks again for your support! Lo