Wooden structure reinforced with carbon fibre

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PMD

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If you are working with wood and carbon fiber combined as tensile or compressive members, the axial stiffness is EA of an element. And load is distributed according to the fraction of stiffness for each element in the structure. Bond two elements together or laminate them is alternating plies,
Not to stray too far from the thread subject: Why do we not see more main spars made with wood as the sheer web and CF capstrips? I am assuming the length and area of the epoxy bondline would be the ultimate determinate of failure or would it go to the cap strips to call it quits?
 

BBerson

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The Carbon capstrips could be placed about 25% closer to the beam neutral axis than the wood which extends to to the spar outer extreme fiber (put carbon on underside of the spar caps).That would share the load a bit more optimally, I think
 

wsimpso1

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Why do we not see more main spars made with wood as the sheer web and CF capstrips? I am assuming the length and area of the epoxy bondline would be the ultimate determinate of failure or would it go to the cap strips to call it quits?
The short answer is that WEIGHT IS THE ENEMY. There are a whole bunch of reasons, all of them related to making the spars lighter at the required strengths.

Webs must simultaneously do a couple things:
  • Carry the shear load between the caps, and;
  • Extend or contract with the cap motion under bending deformation;
This drives a need for the the connection between caps and web(s) to be pretty darned sturdy. A successful and reasonably efficient built up wooden spar then usually has webs attached by one of these methods:
  • Bonded to the sides of the caps;
  • Bonded into a substantial kerf in the caps;
  • Attached with blocking.
This takes the strains and stresses in the epoxy into the durable range. If you simply tried to edge bond the plywood webs to the caps, the epoxy is unlikely to carry it durably unless you add the bonding area given by each of the above methods.

In composite webs, we usually laminate the web with the caps and carry the cloth onto the caps to get interlaminar shear stress significantly below epoxy strength and strains in the application.

Strength of the epoxy is higher than the wood, but much lower than the glass-epoxy, which is again substantially lower than graphite-epoxy;
The ideal lay of plywood for shear webs is with grain at +45/-45 degrees, and gets expensive that way. Composite webs are also ideally laid up at +/-45, but that costs no more than any other orientation in composites;

Plywood shear webs are not easily tailored for thickness - thicknesses are 1/16, 3/32, 1/8, so the steps for tailoring are kind of big, areas are large making laminating and clamping cumbersome unless you vacuum bag. The result is many wooden webs go untailored. Composite webs are easily tailored in 0.006 - 0.018" thick steps, and so are readily tailored to thickness where needed, thinning as you go outboard. They can be open laid up, wet vacuum bagged, or even vacuum infused;

The webs not only have to carry shear loads between the caps, but they must resist buckling under the loads discussed. This frequently drives more wooden web thickness than if buckling were not an issue or requires design and application of a bunch of web stiffeners. In composites, we just build the web with a foam core, which generally pushes buckling way out and allows tailoring the web plies based upon shear and bending inputs.

Foam cores generally run from 2 to 8 pounds per cubic foot, while birch plywood is around 40 pcf. That combined with a nicely tailored fiberglass or carbon fiber web is usually substantially lighter that wooden webs.

There are more reasons all related to wood being heavier. If anyone is certain that they can reinforce wood with modern composites and come out lighter and/or cheaper, I recommend Mechanics of Materials book of their choosing (I like Timoshenko), focusing on the beam theory sections, then bone up on matrix algebra, then get into either Tsai and Hahn or Jones for composite calculation methods.

Wooden webs work OK with wooden spars when done correctly. Glass webs work OK with glass or carbon fiber caps. Carbon fiber caps and webs work together OK too. Wood with carbon in spars has been done, but is just not as good an idea as you might think - yes, it can be done strong enough, but that usually means more weight than by doing an all composite spar.

Yes, looking at my spars, you will find some laminated wooden cores. They are located where shear plates are bolted through the web, and are meant to carry the crush loads from those bolts. Wood and phenolic are applied local to these loads only, with foam cores elsewhere. I have 388" of main spar system, and wooden cores are in 24" of that length. The other 94% of the length of these spars is either 1" or 1/2" polyurethane foam at 2 pcf.

Billski
 

PMD

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The short answer is that WEIGHT IS THE ENEMY. There are a whole bunch of reasons, all of them related to making the spars lighter at the required strengths.

Webs must simultaneously do a couple things:
  • Carry the shear load between the caps, and;
  • Extend or contract with the cap motion under bending deformation;
This drives a need for the the connection between caps and web(s) to be pretty darned sturdy. A successful and reasonably efficient built up wooden spar then usually has webs attached by one of these methods.....etc.

Billski
Pretty close to what I was imagining, but I had thought of a wooden shear web as more of a millwork proposition with a flange top and bottom to feed the spar cap loads with sufficient bond area.

I feel I should mail you a cheque for this answer. I sure as heck owe you a lunch at OSH or S&F some day. Thanks - greatly appreciated your reply.
 

wsimpso1

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Pretty close to what I was imagining, but I had thought of a wooden shear web as more of a millwork proposition with a flange top and bottom to feed the spar cap loads with sufficient bond area.
A solid rectangular wooden spar of sufficient cross section will work and is common in strut braced fabric covered wings - Max moments are much smaller in these spars than in cantilever wings of the same dimensions.

Mill a plank of wood into a flanged beam with the grain running the the long way, and then you will quickly run up against the low shear strength wood has between growth rings.

We can get to a lot lower weight by using milled spar caps and then plywood for the webs and bonding the webs to the flats on the sides of the milled caps. Yeah, a little harder to analyze, but big weight save over solid rectangular spars.

If you want to build in wood, built up spars are the way to go. I am one of the first to recommend that builders decide what material set they want to work in before deciding on a design, as they will have to stay in love with the process long enough to finish the airplane.

As for lunch at OSH or SnF, you are on, but then I would have to catch you for beer too...

Billski
 
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AncientAviation

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Which type of bowing are you trying to protect against... the trailing edge being pulled forward (toward the middle of the wing) or the trailing edge becoming "wobbly" and "wavy" when sighting spanwise along the edge of the TE?

Greetings... this is what a builder sent me years and years ago as his solution... it was a massive inprovement.
(He also added 2x spoilers which he said was really, really helpful although may have opted for a different design)

After the degree of intelligence needed to mix wood and carbon I think something like this with HotWings suggestion of a thin bit of ply to stiffen it up would be the quickest and easiest :)
 

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AncientAviation

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If you are working with wood and carbon fiber combined as tensile or compressive members, the axial stiffness is EA of an element. And load is distributed according to the fraction of stiffness for each element in the structure. Bond two elements together or laminate them is alternating plies, and EA = E1*A1 + E2*A2. Doing a couple examples, E of spruce is about 1.57Mpsi and bidirectional graphite-epoxy is about 12 Mpsi:
  • If wood is 1 in^2 and graphite is 0.01 in^2, EA = 1.57e6*1 +12E6*0.01 = 1.57e6 + 0.12e6 = 1.69e6. It is only a little stiffer than the wood alone and the wood is carrying 93% of the load;
  • If wood is 1 in^2 and graphite is 0.1 in^2, EA = 1.57e6*1 +12E6*0.1 = 1.57e6 + 1.2e6 = 2.77e6. This thing is now 76% stiffer than the wood alone, and the wood is now carrying 57% of the load;
  • If wood is 1 in^2 and graphite is 0.25 in^2, EA = 1.57e6*1 +12E6*0.25 = 1.57e6 + 3e6 = 4.57 e6. This thing is now 291% stiffer than the wood alone, and the wood is now carrying 34% of the load;
You can look at strengths the same way. The two materials will strain together, and the first one to hit its failure strain will limit the assembly. Spruce gets to about 3%, graphite fiber usually to around 1%, so the part will fail when the graphite does, and your parts will only get to the loads the graphite can carry.

Similar things happen in bending, except the metric then becomes EI, where is E is the same, but I is second area moment of inertia...

Now if instead of laminating wood and graphite fiber, you slit the trailing edge of the ribs and put in a strip of carbon fiber to keep the trailing edge straighter than otherwise, it could be a fine fix. Lots of folks have strung a steel cable this way...

Billski

Just... WOW!
It's good to have hero's in life and I think I found another one :)

After having read that a few times I then got to the conclusion!
thanks
 

wsimpso1

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Not to stray too far from the thread subject: Why do we not see more main spars made with wood as the sheer web and CF capstrips? I am assuming the length and area of the epoxy bondline would be the ultimate determinate of failure or would it go to the cap strips to call it quits?
Carbon fiber spar caps are usually unidirectional carbon fiber. Then the carbon or glass fiber shear webs either run along one edge of the caps and warp around the outside of the caps or run between caps and wrap onto the inside surface of the caps. In both cases, two plies of web material also wraps allof the cap in +/- 45 cloth. This wrap takes up edge shear and prevents any edge splitting that might otherwise occur in the monolithic unidrectional spar cap.

To apply a wooden shear web and transfer the loads between web and caps durably is - engineering term here - difficult. Typical carbon fiber spar cap is much wider than it is thick, as this makes for lighter spars at some strength as well as facilitating bonding to the wing skins. And carbon's very high strength means that thickness is pretty darned small, leaving little faying area for bonding the web. And you simply can not just bond the top and bottom edges of the web to the inside surface of the caps - nowhere near enough area. So, we end up placing glass or carbon cloth at +/- 45 that wraps from the shear web onto the spar caps. This set of tapes has to be thick enough to carry the loads between caps and web and extend far enough beyond the web-cap boundary in both directions to transmit the load through adhesive action. Hmm, begins to sound like you have a glass or carbon fiber shear web over much of the wooden web... Also, you still need a couple plies of web material to completely wrap the caps to keep the interlaminar shear stresses from splitting the caps.

You are say 70-90% of the way to having glass or carbon web, all of the cost and lamination effort of the glass or carbon web, and you have the cost weight of the wooden web too. It is quite a bit lighter to just use a foam core instead of the wood, and make the tapes continuous, doing duty as shear web, connection to caps, and wrap of the cap edges all in one assembly operation.

We have not even gotten into issues of elastic mismatch between carbon caps and wooden web driving larger sections in each, nor the whole philosophy issue of dissimilar materials seeming wrong. Maybe another time...

Billski
 

PMD

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In general language, I think “elastic mismatch “ is the perfect description for mixing these materials.
This is true if you are considering/designing the shear web as a member contributing to bending loads in deflection. My own beam preferences and experience is in designing beams to be as much as possible totally in bending with the shear web only there to keep the compressive side in column. i.e. in this case I assume ALL of the bending loads are passed directly into the spar caps and except for rib loads that would travel a very short path through some heavier area to feed into the cap strips. I assume for some hypothetical wing that the torsional and drag loads are resolved within the skin (obviously skinned in aluminum, plywood or some other relatively rigid material) and turned into bending loads for the spar cap in vertical axis and root-to-skin for torsion and drag.
 

Hot Wings

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this is what a builder sent me years and years ago as his solution...
That solution will result in a stiffer 'fix' than my mini "I" beam solution. It may take a little longer and add a few ounces more, but we know that method works.
The mini "I" beam may have to look more like a mini "T" beam to resist twisting from asymmetrical fabric loads - which would/could significantly reduce the stiffness.

What we really need/want is a trailing edge that is designed from the start to be a little stiffer. The folded carbon (post #14) may be the lightest but not all Mitchell builders are willing to, or comfortable with, work in anything but wood.
 

Riggerrob

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What is the difference in thermal expansion of wood, versus glass, vs. carbon, vs. epoxy vs. fabric vs. steel?
 

Geraldc

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It is quite a bit lighter to just use a foam core instead of the wood, and make the tapes continuous, doing duty as shear web, connection to caps, and wrap of the cap edges all in one assembly operation.

How would this work?Wrap a center section with x layers then add a section at each and continue wrapping y layers then add another section at each end then wrap z layers.This gives more thickness of spar in the center section and progressively less towards the wing tips.
Edited -Sides covered with carbon at +- 45 deg
1633118378149.png
 
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wsimpso1

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This is true if you are considering/designing the shear web as a member contributing to bending loads in deflection. My own beam preferences and experience is in designing beams to be as much as possible totally in bending with the shear web only there to keep the compressive side in column. i.e. in this case I assume ALL of the bending loads are passed directly into the spar caps and except for rib loads that would travel a very short path through some heavier area to feed into the cap strips. I assume for some hypothetical wing that the torsional and drag loads are resolved within the skin (obviously skinned in aluminum, plywood or some other relatively rigid material) and turned into bending loads for the spar cap in vertical axis and root-to-skin for torsion and drag.
This set of thinking is useful for understanding the beams and for initial sizing of beams. Where FOS are high, this actually works pretty well. The problem with this is it is a shortcut. No part of the beam knows what load should go where. Build a beam with the flanges left and right and the loading still vertical, and the flanges will not be carrying the bending load and the web will not be carrying the shear load. When we build a spar, we connect the parts together and they ALL bend together and shear together. You can look this up in Timoshenko or other Mechanics of Materials books - look for beam theory, then stresses in beams.
  • All of the beam contributes to bending stiffness;
  • The neutral axis is the center of bending in the beam;
  • Bending stiffness is made up of the E*I of all of the spar pieces - E is material stiffness and I is second area moment of inertia, both of the part of the cross section we are working on;
  • The sum of EI is the bending stiffness of the beam;
  • Bending strain at any place in the beam cross section is linear with distance from the neutral axis of the beam, with maximum occurring at the spot on the cross section furthest up or down from the neutral axis;
So, in a classic flanged beam (capital I shaped or wide flange or channel) everything sees bending strain, even though folks are fond of saying the caps carry the bending.

Let's say we have a beam section 6" deep, with 1/2" thick flanges and the neutral axis is 3" from bottom. Put a pure bending load on the beam, and the beam curves - the upper cap gets a little bit shorter and has a negative strain and negative stress on it. The upper surface is 3" from neutral axis. The bottom cap gets a little bit longer and has a positive strain and positive stress on it, and is also 3" from the neutral axis. At the top of the shear web, 2-1/2" from the neutral axis, the shear web has 2-1/2/3 = 0.833 times the strain at the 3". Yeah, the web is under 83.3% of the strain that the worst spot in the cap is. If the cap and web have the same E (like in steel construction beams), the web also has 83.3% of the stress that the top fiber has... If the web has lower E than the cap (common in composite beams or even in built up wooden beams) the tensile and compressive stresses from bending are lower - stress is strain times E in each material. This is the root of "loads are distributed per the fraction of the stiffness".

Now to shear. First off, the only way to avoid external shear on a beam is to carry pure bending - place a bending moment on one end and an equal and opposite bending moment on the other end. If there are any vertical loads making the bending, then you have shear in the beam. This is rarely achieved in real beams and loading.

Shear is carried throughout the beam, but the relationship is more complicated than tensile and compressive stresses. See Timoshenko. Shear resolves to zero at the very top and very bottom of the cross section, and increases toward center of the beam. In a rectangular cross section, shear is a clean parabola with peak shear stress equal to 3/2*shear/area. On flanged beams the shear stress is quite modest in the flanges but is much higher in the web, with max shear stress at the neutral axis with maximum close to shear/web area. Just remember that shear in this sort of beam is almost as large where the web attaches to the flanges as it is everywhere else AND the tensile or compressive strains from bending are also present where the web connects to the flanges. This is where you look up Mohr's circle and/or von Mises stress in the same textbook, so you can figure out the effective total stress in the web close to the flanges.

So, the loads can be quite big and kind of complicated in the web at the flanges.

Take all of this further, like with a composite wing skin structure bonded to the mains spar, and now the skin is also part of the bending structure, interacts in the shear distribution, and now has a lot of contribution to resisting torsion (torsional stiffness is sum of GJ), while the spar contributes and twists right along with the skins. To solve all of this simultaneously take matrix algebra or FEA.

This is all complex enough when it is all 2024-T3 aluminum, but make the spar caps out of unidirectional carbon-epoxy with E=22Mpsi, web of carbon fiber-epoxy at +/-45 and E of 9 Mpsi, and skins made of glass fiber-epoxy at +/-45 and E of 1.4 Mpsi. Excel is my friend to do these calcs.

This topic in a single material is usually is covered inside a one semester class taught in the sophomore year. To do it in composites, the class is a semester length class taught to seniors and grad students who have also passed matrix algebra, and have a working knowledge of not only beam theory, but also plate theory, and practice at manipulating all this stuff.

This is why design of composite structures is usually not done by amateurs...

Billski
 

ragflyer

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Classic mechanics of materials books such as Timoshenko and others Billski reccomends are great (invaluable) to understand structural theory. As practical design references though these books have very limited use except in the analysis of simple structural problems. The reason is these books are written to apply to the most generalized cases of problems which is great when one is learning the basics of analysis but not so much in analyzing complex weight optimized structures. I found these books invaluable in college. But real world design problems include all kinds of exceptions that move us away form ideal theory. Also we do not have a workable/accurate theory for a number of conditions such as buckling, post buckling behaviour etc. which are difficult to avoid when you design for low structural weight.

This is why engineers typically use semi-empirical methods for actual real world problems (now days FEA + semi-empirical methods/tests to validate). Now the trouble with semi-empirical methods are they apply in only a narrow range of application- materials, dimension ratios etc. This is why if I am designing an airplane I would focus on airplane structural books (Bruhn, ANC-18 etc.). Of course the theory is the same whether you are building a bridge or a wing (in a general sense they are both beams) but the domain specific books will include semi-empirical techniques/curves based on numerous carefully crafted tests and design gotchas that will be more applicable based on the application/material etc.

What does this mean then?
1. If you are designing a built up wooden spar, there are well established curves (in ANC 18) that are based on the testing of a large number of built up wing spars in the typical ranges of dimensions of wood caps and plywood webs. This makes the calculations relatively simple and accurate. Try using the technique in mechanics book and compared it to what you get by using ANC-18. Big difference in accuracy and speed to result. The semi-empirical curves take into account the non uniform distribution of stresses across the web and caps and the redistribution of stresses that occurs post buckling etc.

2. If you are designing a metal spar use the curves in Bruhn. These semi-empercal curves take into account web buckling, semi-tension field redistribution of stress in the caps, stiffness and web. Again these are based on tests of hundreds of spars with various dimensions of caps and web thickness.

3. For composite or hybrid spars (multiple materials ), while there are semi- empirical methods they are very limited because of virtually infinite combinations of material, lay up schedule etc. The best approach in my opinion is to use past experience and/or calculations using very simple theory plus significant FOS and testing to failure to ensure safe outcomes. There are way too many failure modes to trust just a pure calculation based approach even if it is based on the most sophisticated theory unless there is prior data on that exact same combination.
 

One Sky Dog

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For the trailing edge deflection. Carbon arrow shafts are cheap light and stiff ,bonded to the wood trailing edge inside will put the wood in compression and the arrow shaft in tension. The combined <O shape will increase the E which will increase the resistance to bending from the fabric. It would be easy to mock up and test compared to the built up trailing edge truss. I built an Ez-Riser in 1976 and flew it 40 hrs. My first aerial vehicle.
 

wsimpso1

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What is the difference in thermal expansion of wood, versus glass, vs. carbon, vs. epoxy vs. fabric vs. steel?
You can look them up on the internet pretty quickly. Carbon fiber has a negative thermal expansion coefficient along the length of the fibers and varies by the facility... It is usually published by the supplier.
 
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