# Mechanics of Composite Plates, Beams, and Bigger Structures

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#### wsimpso1

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Simply bonding your web to one side of a piece of foam will improve things. Putting half of your web thickness on one side of a foam core and the other half on the other side will be more resistant to buckling and crippling - I will run a simple example of one web, one web on a foam plate, and web split and applied to both sides of the same foam plate later. Gotta run...

Billski

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#### proppastie

##### Well-Known Member
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I will run a simple example of one web, one web on a foam plate, and web split and applied to both sides of the same foam plate later.

Billski
6x6?

#### wsimpso1

##### Super Moderator
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OK, The last thing I was doing took less time than I expected, so I got some time... I ran an example in Excel. I will ship it to anyone who wants it, just send me a PM with your email addy.

I had a web 6" high carrying 12000 pounds (2000 pound airplane, 12 g design, half the weight on each wing.

With a 30,000 psi shear strength, the web needed 8 plies, for a shear web 0.068" thick, and 0.408 in^2/linear inch of web (everything after this is per linear inch of web).

Something to understand: Buckling of the whole spar will be a function of whole spar EI and L^2, just look at the Euler buckling criteria... Go into wrinkling and crippling and they get into similar stuff. In both cases, more EI is how you put buckling at bay, so let's look at EI of several sandwiches:

A plain web - no foam - will have an EI/L^2 of 1.29 lb and weigh 0.0034 lb/in.

Layup that same shear web on 1/4" divinycel foam, and gets an EI/L^2 of 19.44 lb and weighs 0.0043 l/in. It is 15.1 times stiffer than the base and its stiffness to weight ratio is 12.0 times that of the base.

Use the same amount of glass split in two, and laminated on both sides of the same 1/4" foam, and EI/L^2 is 37.49 lb, and weighs the same 0.0043 lb/in as the second example. It is 29.1 times as stiff as the base and its stiffness to weight ratio is 23.2.

Why the difference? The stiff glass on one side of the soft foam moves the neutral axis less distance from the glass than when you put stiff glass on both sides.

I also ran a second set of numbers finding the number of plies and weight to reach the same stiffness. Foam with all the glass on one side had to be 80% heavier, and no foam had to be 149% heavier. Looks like laminating a little foam in between the glass layers is the deal.

This sort of result is common.

I do not know why people want to ask about laminating on one side of a piece of foam. That leaves foam exposed where it is easily damaged. Putting the same amount of material on, but splitting it up to cover the foam makes for a stiffer, stronger, and much more buckling resistant structure, while also making it much sturdier to handling and everything else that we see in use.

Billski

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#### Aviator168

##### Well-Known Member
Question about the number of plies. Given the thickness of the total GF, how to calculate the number of plies needed?

#### proppastie

##### Well-Known Member
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Question about the number of plies. Given the thickness of the total GF, how to calculate the number of plies needed?
You play with the calculations until you get something that satisfy the strength you are looking for......You need to know the required loading.

#### Aviator168

##### Well-Known Member
You play with the calculations until you get something that satisfy the strength you are looking for......You need to know the required loading.
Say I calculated the loading of xxxxx lb, and the width of cross section of glass fiber has to be 80mm. How is the number of plies determined?

#### wsimpso1

##### Super Moderator
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Say I calculated the loading of xxxxx lb, and the width of cross section of glass fiber has to be 80mm. How is the number of plies determined?
I will run an example.

First off, let's remember that we are doing initial sizing here. The design will have to be analyzed and in all likelihood will require iteration to a final form with more plies.

Let's say you have a spar cap with a 14000 pound axial load and you want to fabricate it out of UNI Tape. In my shop and with our practices, UNI tape laminates up to 3" wide and 0.025" thick per ply when laminated with epoxy, brushed out and squeegeed out to fully straighten and compact it until it feels hard. Oh, I use foam barriers and packing tape to make a mold that sets the laminate at 3" wide. Book value on unidirectional E-glass laminate is 70,000 psi. I have tested samples in simple four point bending and gotten first fiber failure at about 80,000 psi (detected from creaking and confirmed with magnification - micro buckling on the compression side and visible tensile fractures, both in the first layer) so I know I am OK using the book values. This is my process capability in my shop and from my testing... YMMV.

14000 lb / 70000 lb/in^2 = 0.200 in^2 of laminate. Since the lamina is 3" wide, 0.200 in^2/3 in = 0.067" thick. One ply is 0.025", 0.067/0.025 = 2.67 plies. I can not make 0.67 plies, so I need three (3) plies or about 0.075" thick, 0.225 in^2, and 15750 pounds strength in this basic sizing.

If you really want to get critical, you could build the cap to have a 3" wide by three ply laminate at that station, then saw cut and sand down to 0.200 in^2/0.075 = 2.67" wide at this station. I urge against this at the initial sizing as you will be putting this basic size in, and then iterating the number of plies until you have a successful design, and caps almost always get bigger.

When you arrive at your span-wise schedule, you will find that you have a lot of plies at the root, and then the cap thickness reduces quickly as you move away from the root. Sometimes, you may find that you are tapering thickness faster than the one ply per inch rule-of-thumb that some use, and that reduces your thickness taper rate. Remember also that you want to carry each ply an inch or two past where you last calculated you need it...

Then at some point along the span, you find your needed cap is less than 2 plies thick. On a freestanding channel spar, I do not go below 2 plies (0.050") thick on caps - the parts get too wobbly for good fixturing and assembly. I also do not use less than two plies of woven cloth or one ply of knitted cloth (when vacuum bagged) in the shear web and around either side of caps and cores. Where the needed cap calculates out to less than two plies, I will taper the shear core from 1" down to 3/8" and taper the cap width down to 2" or even 1-1/2".

On massive core parts with the spar on the same core as the rest of the part, I will go down to one ply of UNI tape in caps, but stay with a minimum of two plies of woven cloth or one ply of knitted cloth for shear webs. YMMV on what is robust in your shop and airplane...

Use of Graphlite rods in your caps will require a straightforward extension in the math and in rule-of-thumb category too. Jim Marske has his advice on this topic. Words to the wise...

I hope that this helps.

Billski

#### Pops

##### Well-Known Member
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Thanks. The only composite parts that I have make are nose bowls, wheel pants, wing tips, fuel tanks,etc, all non-structural. This is a good class room for me. I would never think that I knew enough to make a structural part, but its fun to learn.

#### Aviator168

##### Well-Known Member
14000 lb / 70000 lb/in^2 = 0.200 in^2 of laminate. Since the lamina is 3" wide, 0.200 in^2/3 in = 0.067" thick. One ply is 0.025", 0.067/0.025 = 2.67 plies. I can not make 0.67 plies, so I need three (3) plies or about 0.075" thick, 0.225 in^2, and 15750 pounds strength in this basic sizing.
Thanks for pointing it out Billski. But it also points to the root of my question. Since each thread of fiber is round and you can't possibly stack them perfectly, so the number of plies calculated this way might be less than the cross section area of the lamina.

Edit. Anyway to get the book values of GF and CF?

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#### wsimpso1

##### Super Moderator
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Thanks for pointing it out Billski. But it also points to the root of my question. Since each thread of fiber is round and you can't possibly stack them perfectly, so the number of plies calculated this way might be less than the cross section area of the lamina.

Edit. Anyway to get the book values of GF and CF?
Rant mode on! Please use a level of care in writing your questions that reflects the level of care you would like in the response. Sentence fragments, your own abbreviations, not explaining your points - they all make it difficult to understand what you are getting at and is demotivating to those of us trying to help you. This is the third post on this topic and I finally think I understand your question, which tries my patience. OK, rant mode off.

Composites are lamina and laminates comprised of fibers fully encapsulated with cured resin. When I or anyone else talks strength and stiffness of composites, we are working in terms of cured composites in lamina and in laminates. No fiber characteristics here. Please re-read my post that you cited - I talked of strength testing of sample parts built to reflect my capabilities for making these parts, and commented YMMV. Why may your parts be different from mine? Fibers, cloth weave, resin, post-cure, resin content, all can be different in your parts than in mine. That produces different ply thickness, different Young's modulus, and different total part stress at failure. This is why you should work out consistent processes and test your stuff some way.

When you design, you need some idea of the various moduli and strengths with your lamina so that you can get to cross section areas and then ply counts. Once you have ply counts established with known cloths, if your resin content is off, then your parts work out to different thickness, which translates to differences in weight, bulk, strength and even stiffnesses. If you are resin rich, the parts are heavy, but about the same load carrying capability. If your parts are resin lean, all of your strengths can be reduced, as can your moduli. Your fiber straightness and resin content need to be pretty consistent. That is one of the reasons I love vacuum bagging - we pretty well know what we are going to get - fibers are straight, everything is wet, consistent minimum amount of resin, and you know how thick a laminate will end up. Same with our process for achieving relatively low resin content without bubbles in our spar caps made with UNI tape.

In the end, what you are building and what you used for analysis have to gybe or you can get surprises of the bad kind.

Billski

#### proppastie

##### Well-Known Member
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In my design (metal) I carry the required buildup forward to the next outboard rib station. I was taught that one always ties together structure with bulkheads and or ribs. Given the nature of composites perhaps that is not as critical but it certainly would not hurt.

#### wsimpso1

##### Super Moderator
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In my design (metal) I carry the required buildup forward to the next outboard rib station. I was taught that one always ties together structure with bulkheads and or ribs. Given the nature of composites perhaps that is not as critical but it certainly would not hurt.
Good practice in metal and in composites to carry each layer of structure a little ways past where you need it. Going to the next rib in composites can be a long ways, so we need a better rule. In composites we usually take each ply some number of inches past where you needed any of that ply. Some carry the ply to the next place where a ply reduction would start, which results in an extra ply everywhere except at the root. Going further is the publicly shared Scaled Composites approach where you figure out what you need and then "throw in another ply for Grandma".

As to tying everything together, sheet metal has a lot of exposure to buckling and crippling. Closing out a structure so it is a closed box is really good practice. You might be tempted to not close out structures when you have cored skins and ribs that are so stiff. I say, close them all out anyway. Big issue is the parts will then hold their shape much better if you see some post-cure effects down the road. Leave a shape open, and it can distort more easily.

There may be places where some builders get away with it, but I have seen ugly access panels and panel edges too.

Billski

#### User27

##### Well-Known Member
This is an excellent thread - thanks very much for writing it, sorry it has taken me so long to find it!!
I always had a tough time in structures classes (but that was a few years ago), reading a completely different take on the same subject it really helpful!!!

#### atypicalguy

##### Active Member
HBA Supporter
The big reason for doing it in Excel is you can automate the process so iterating and then optimizing the design is easy. Come up with one spreadsheet to determine the shear, bending, torsion, chord, depth at the spar, first guess at cap and web plies for a bunch of wing stations. Copy the results to another spreadsheet, then drag down the data for one station at a time, let it draw depth, width, ply counts, then it builds stiffness and load vectors, solves for strain, decomposes laminate strains, and checks failure. Then you can optimize by intervening with different ply counts pretty simply. But if you want to solve using a calculator, you have to put all of the data in for every change in ply count... UGH! For something you may have to do hundreds of times. No, just go through Gaussian Elimination carefully once, and then let it do the work for you.

Billski
Awhile ago I was building a solid truly elliptical hydrofoil and wanted to predict the bend using an elliptical load case. I found a guy on the r/c forum who was doing a spreadsheet to predict this with wings. There are some approximations of moment of inertia for airfoil cross sections that I found in a paper (see link), so I chimed in and he put them into his spreadsheet. I am not sure the load case is 100%, but it worked pretty well I think FYI: RC Groups - View Single Post - Wing spreadsheet by Cap