# Composite wing spar web design - composite webs, foam webs, etc.

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#### wsimpso1

##### Super Moderator
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Some quick back of the envelope calcs for the KR2.
Wing span: 24 feet
wing area: 93 ft^2

Make the gross assumption that the wing is a rectangle. Ignore that the wing starts outside the cabin. Chord = 93 ft^2/ 24 feet = 3.875 feet
Spar load per foot = 3.875 x 14 = 54.25 lbs/ft
Moment at center fo spar = 1/2 12^2 x 54.25 = 3906 foot pounds = 48,872 in lbs.
Spar height at center = 7 inches
Cap forces = 6,981 pounds, roughly

Each main spar cap has 6 rods in it. The Secondary spar caps (front and back) have 10 rods in the top and 7 rods in the bottom. So the top has 16 rods in total and the bottom has 13 rods. The force in each top rod is 6981 pounds/16 = 436 pounds. The force in each top rod is 6981/13 = 537 pounds.

All loads at max weight, 1g, no safety factor.

The rods are 0.070 x .437 Graphite, solid rectangle. Area = 0.0306 in^2.

The static 1g stress in the top rods is 436 pounds / 0.0306 in^2 = 14,250 PSI.
The static 1g stress in the bottom rods is 537 pounds / 0.0306 in^2 = 17,500 PSI

Does this look correct ?
Using the simple approach of dividing moment by spar dept only is approximate at best, and should probably be left behind once you get past initial sizing. Issues with this: Asymmetric caps move the neutral axis of the spar section, changing y's to extreme fibers for stress calcs; Ignores effect of the web and of the wing skins.

A more accurate look is to compute neutral axis position, then y's (distance to extreme fibers from neutral axis and I for the caps, then stress is My/I. This still skips contribution of the web and the skin, but is closer;

A more accurate look is obtained by computing EA and raw y's for the caps, the webs, and all of the wraps taken around the spar putting it together, compute the neutral axis position and corrected y's, compute the EI's for the set of lamina, sum them up, then divide by E for the cap material to get a better I, then compute My/I for extreme fibers in both caps;

Then the best is to do the full up composite mechanics run.

Now let's check your numbers to see if the spar mentioned looks OK.

First we recognize that the bending moment is overstated. For elliptical lift distribution, centroid of lift is around 42% of semi-span, not 50%.

Next, I do not know if the spar height of 7" is extreme fiber to extreme fiber or from center of cap to center of cap. It matters. Bending resistance is from neutral axis to centroid of the cap, stress is neutral axis to extreme fibers in both directions.

Minimum FOS for composites is 2.0. For the KR2, I suspect that its design n1 is 4 g because that is pretty common. Many later composite airplanes use 5 or 6 g because some folks just can not resist rolling or looping the things. So, at minimum, multiply your stresses by 8 or 10 or 12. You get to pick. Using 12 gives stress in the tensile side of 210,000 psi. I suspect that with corrected numbers, you will have higher stresses in both caps. Get out the mechanics of materials text, go through the beam chapters and the section on composite beams (talking steel reinforced concrete).

As to shear web stress, on flanged beams and hollow rectangular beams, the shear stress is mostly carried on the free web, that is the part not supported by the flanges. Shear stress is slightly higher at the neutral axis than by the flanges, but it is slightly conservative to assume constant in the free section of the web and also slightly conservative to assume only the free portion of the web carries all of the shear. So tau = V/A where V is shear load, A is area of the free portion of the glass/resin part of the web. In metal, shear yield is 0.577 times tensile yield. In composites we do not have such stuff so well nailed down.

Then to finish the whole thing, the webs at the flanges are distorting with the caps, so they have not only shear stress close to that calculated in the para above, they have some tension or compression. So we end up beefing the caps and web. Full up analysis, automated by putting it into Excel makes all of this fairly easy, but you have to get through all of the undergraduate stuff mentioned above plus matrix algebra and plate theory, then the equivalent of a gradate course in composites materials mechanics to do the full up analysis. UGH! Composites are sort of like getting old, it is not for sissies!

Billski

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#### wsimpso1

##### Super Moderator
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yes but what does it weigh?.....of course looking at certified composite aircraft such as the Cirrus .....it is not lighter in weight than the Mooney. SR22 G6 Empty Weight: 2,270 lbs vs 1986 Mooney M20K 1800 lb.....The Cirrus has a parachute....but I am pretty sure it does not weigh close to 500 lb.
Not exactly an apples to apples comparison - The Cirrus cited has the IO550 engine and is a roomy airplane for four adults. The M20K has the IO360 engine and is much tighter inside, both for people and for bags. Between the Cirrus having 50% more engine, a lot more interior volume, more wing and tail area, and the BRS, yeah, it should weigh more. Should it weigh 470 pounds more? Well the engine is about 160 pounds more, the substantially bigger airframe probably accounts for 150 pounds, then the BRS... Yeah, maybe the Cirrus is 100 pounds heavier than if it were a tube fuselage aluminum wing and tail airplane.

Billski

#### proppastie

##### Well-Known Member
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Not exactly an apples to apples comparison -The Cirrus cited has the IO550 engine
Sorry Cirrus Sr 20 has IO360 Empty weight 2,126 lb (964 kg) vs K model Mooney of 1800 # Mooney has a retractable gear .....Cirrus has a parachute.....

I think the idea here is (older?) composite designs have larger FOS and apparently are not as light as people expect them to be given the difference in strength numbers of the raw fiber.

#### Mavigogun

##### Well-Known Member
A couple images to consider, mindful of previous conversation here; the last is the back side of a D-cell leading edge with floating ribs attached to the sail- alternate ways to confront structure:

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#### tdfsks

##### Well-Known Member
Minimum FOS for composites is 2.0.
All composite structures I have worked on have a much higher FOS than 2.0. This assumes that we define the FOS as the ratio between the limit loads (i.e. max loads expected in service) and the failure load (i.e. the same definition used in FAR 23 etc to define the minimum FOS of 1.5).

I think this idea of a FOS of 2.0 for composites was started by Andrew C Marshall back in the 80's with his articles in Homebuilt Aircraft magazine and his later book. However, so far as I am aware, it has no real engineering basis and probably seemed like a good number at the time given the uncertainties.

The only published rules of thumb that I am aware of (as per earlier posts) are those in JAR VLA AMC (now CS-VLA under EASA & AMC = Acceptable Means of Compliance). This requires the usual FOS = 1.5 + a factor of 1.25 for temperature (assuming white paint) + a factor of 1.2 for moisture.
So minimum factor is 1.5 x 1.25 x 1.2 = 2.25.

However, in this certified world, you also have a fatigue requirement and the stress levels required to comply with this will generally drive even larger margins. Again, in the absence of any other simplistic guidance, JAR VLA AMC allows compliance with the fatigue requirement to be assumed without further justification if cap stresses at limit loads are less than:
Glass Roving / Epoxy = 250 MPa (36 kpsi)
Carbon Roving / Epoxy = 400 MPa (58 ksi)

A typical glass roving / epoxy laminate might have a failure stress of 120 ksi range and carbon maybe 200 ksi. So after fatigue is considered it can be seen that the FOS is more like 4.

As I have pointed out in previous posts, in reality most composite structures are designed for about 1000 microstrain per 'g' in the caps, maybe as high as 1500 microstrain in some cases, but as usual the exact answer depends on a lot of issues.

These stresses might seem low compared to raw material test data but they are what they are and represent more than 50 years real world experience with composite airframes in light aircraft and gliders. The allowable for Glass Epoxy of 250 MPa in JAR VLA has increased over the years (it was 200 MPa back in the 90's) based on better understanding, more service history and a lot of research (many full scale fatigue tests). Whilst they may increase in the future as we learn more, these numbers represent the current state of knowledge. At the end of the day this is a bit of a pointless discussion without nailing down exactly what materials we are talking about and until we understand what test data is available for them and the reliability of this data.

One of the issues is the reliability of data and the policy of airworthiness authorities and DOD (as published in MIL-STD's) requires a detailed statistical analysis of the reliability of composite allowable data. Basically if you have a small number of test results or large scatter in the data you get a large knock down factor and if you have the results of many coupons (many dozens) and the data is well correlated then you may escape with a factor close to 1.0. I have run composite coupon test programs to establish allowables and it is always a balance between testing enough coupons to get a good statistical basis (and hence smaller knockdown) and the cost of doing this. However, that is another issue which is not really relevant to homebuilders other than to point out the need for conservatism in the absence of proper data.

Also one last point. The modulus of glass epoxy is 1/3 to 1/2 that of aluminium. If the stresses are too high you will have a very flexible structure and so it might be necessary to keep stresses low to ensure that the structure is stiff enough (which feeds into flutter etc).

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#### wsimpso1

##### Super Moderator
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Sorry Cirrus Sr 20 has IO360 Empty weight 2,126 lb (964 kg) vs K model Mooney of 1800 # Mooney has a retractable gear .....Cirrus has a parachute.....

I think the idea here is (older?) composite designs have larger FOS and apparently are not as light as people expect them to be given the difference in strength numbers of the raw fiber.
The Cirrus is still a much larger airframe than the Mooney, which also weighs something. Then there is comprehensive design for fatigue added into the Cirrus that was never a deliberate part of the Mooney design. And as in the previous note, The Cirrus is probably a little heavier than if it were a tube fuselage and aluminum wing. And with a Cirrus, you are not in continuous danger of owning an orphan...

Bill

#### proppastie

##### Well-Known Member
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continuous danger of owning an orphan...
makes life exciting.......look at it this way probably the greatest "Phoenix Brand" in history..... how many other brands have died and come back as many times.....

#### proppastie

##### Well-Known Member
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Obviously the big boys (Boeing Air Bus)are able to save weight or they would not be using CF....AutoReply claimed weight saving just substituting CF for Alum thickness wise. (Black Aluminum)

#### wsimpso1

##### Super Moderator
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... here is an example analysis for a composite spar generalized for any tapered wing planform. I have included both bending and shear stresses.

I have simplified it by assuming that the loading on the wing is constant over the surface (i.e. no spanwise lift distribution which is conservative).

The hand written notes derive the equations in general form.

I have then programmed these into a spreadsheet to do the calculations for each station along the wing (see last image).

I have also provided a sample manual calculation for one station.

This is about as simple as you can get to do a half decent job but there are still quite a few assumptions in this analysis. Good enough for a homebuilt if you build in some margins but more work would be required for a certified aircraft.

Also note that this analysis should be preceded by a more detailed analysis of the loads on the airplane to understand the critical case for the wing.

....

OK ... I hope this helps and feel free to ask any questions.
tdfsks,

I read the first six sheets closely.

The first pair of sheets cover the process for applying a uniform wing load per unit area to a wing, calculating shear and bending moment as a function of spanwise position. Going through the meat of this computation should be useful to many of our readers. It can be expanded to cover an elliptical pressure distribution, an elliptical lift distribution, or allow computation of Shrenck’s Approximation.

The third sheet covers computation of neutral axis, I, y’s, and axial stresses in a cross section of a beam. This appears to be straight out of a Mechanics of Materials text for homogenous and isotropic material. There appears to be no treatment for varying E among the lamina. How is that treated by you?

The fourth sheet covers computation of shear stress in a beam as a function of y position using one Young’s modulus. This appears to be straight out of a Mechanics of Materials text for homogenous and isotropic material. There appears to be no treatment for varying E and G among the lamina. How is that treated by you?

The fifth and sixth sheets are a run example, and should be useful to many of our readers.

The seventh sheet is illegible, while the first six were difficult to read. A clearer copy would be useful to those attempting to learn this topic.

Do you consider the effects of combining shear and axial stresses in the regions close to the junctions between cap and web lamina?

Billski

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#### Exian

##### Well-Known Member
Asymmetric caps move the neutral axis of the spar section, changing y's to extreme fibers for stress calcs; Ignores effect of the web and of the wing skins.

A more accurate look is to compute neutral axis position,
I have a question about that :
I may be wrong but aren't composite spar caps asymmetric so the neutral axis remains at the middle of the spar because of the difference in tension and compression young modulus?(for positive g case, minimise spar cap stresses)
So considering the middle of the spar to calculate spar cap stress in not so wrong (if designer did it right only)?

That is how I designed my plane spar caps taking into account material properties measured at my workplace...
Tension 170 GPa (60% fiber in volume)
Compression 140 GPa

#### lr27

##### Well-Known Member
If uni fiberglass shear webs are only getting 5kpsi or so allowables, I should think plywood webs would be much lighter for the same load. Assuming you had a good way to attach them to the spar caps and room for a slightly thicker web.
-----
I don't know whether Drela is really a structures guy, but he HAS done some testing which ought to be enlightening if we can find it on tne web*. He does tend,to be thorough, and his workmanship is excellent. I suspect that he mostly designs for stiffness, since in that case, at least a lot of times, a stiff enough structure will also be strong enough. He has been closely involved with a number of human powered aircraft, where light weight is crucial.

*For example, as I recall, he did some testing on foam wings without other materials as shear webs. He was comparing the use of spar caps with "weblets" to prevent buckling, as opposed to just using thicker caps. I seem to recall that the tablets weren't any better. He also did some testing on extruded polystyrene foam. I think Highload 60.

BTW, what's this about silicone in foam? Do we know which types have it? Shouldn't Sky Pups be disintegrating in the air?

#### wsimpso1

##### Super Moderator
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If uni fiberglass shear webs are only getting 5kpsi or so allowables, I should think plywood webs would be much lighter for the same load. Assuming you had a good way to attach them to the spar caps and room for a slightly thicker web.
Well, you would still have to design the structures, check them for failures at the FOS you decide is needed, validate them with tests...

I don't know whether Drela is really a structures guy, but he HAS done some testing which ought to be enlightening if we can find it on tne web*. He does tend,to be thorough, and his workmanship is excellent. I suspect that he mostly designs for stiffness, since in that case, at least a lot of times, a stiff enough structure will also be strong enough. He has been closely involved with a number of human powered aircraft, where light weight is crucial.

*For example, as I recall, he did some testing on foam wings without other materials as shear webs. He was comparing the use of spar caps with "weblets" to prevent buckling, as opposed to just using thicker caps. I seem to recall that the tablets weren't any better. He also did some testing on extruded polystyrene foam. I think Highload 60.
I have read his stuff on structures tests for the RC folks. He makes the standard extension to design the web to carry only the shear - this is a serious underdesign of the web (It also sees extension or compression from bending of the wing), and his test data clearly showed that the spar did not behave per plan. He can afford to make those errors, as the aircraft he was writing about are neither intended for many hours nor are they carrying humans aloft nor are they any danger to people and stuff on the ground if they do break up in flight. Read and believe his aerodynamics. Follow him at your own risk on structures...

BTW, what's this about silicone in foam? Do we know which types have it? Shouldn't Sky Pups be disintegrating in the air?
Nope it is a standard caution. Remember that the foam is not just giving us our shapes, it is also providing support against buckling, and that is required. Plastic foams not specifically intended as structural components are intended as dock flotation and building insulation and packaging/cushioning. Silicones might be present in them to help with processing. If there are ANY silicones or waxes on our foam, the glass/epoxy will not bond to it. We KNOW that the plastic foam products sold by Wicks and AS&S are silicone free. We know that Dow flotation billet is silicone free. We can not say that about other products. Substitutions can be a very bad idea.

Why should Sky Pups be disintegrating? What do you know?

Billski

#### tdfsks

##### Well-Known Member
I read the first six sheets closely.

The first pair of sheets cover the process for applying a uniform wing load per unit area to a wing, calculating shear and bending moment as a function of spanwise position. Going through the meat of this computation should be useful to many of our readers. It can be expanded to cover an elliptical pressure distribution, an elliptical lift distribution, or allow computation of Shrenck’s Approximation.

The third sheet covers computation of neutral axis, I, y’s, and axial stresses in a cross section of a beam. This appears to be straight out of a Mechanics of Materials text for homogenous and isotropic material. There appears to be no treatment for varying E among the lamina. How is that treated by you?

The fourth sheet covers computation of shear stress in a beam as a function of y position using one Young’s modulus. This appears to be straight out of a Mechanics of Materials text for homogenous and isotropic material. There appears to be no treatment for varying E and G among the lamina. How is that treated by you?

The fifth and sixth sheets are a run example, and should be useful to many of our readers.

The seventh sheet is illegible, while the first six were difficult to read. A clearer copy would be useful to those attempting to learn this topic.

Do you consider the effects of shear and and axial stresses in the regions close to the junctions between cap and web lamina?
Billski,

Firstly, my apologies for the quality of the uploaded images. My originals were clear ... looks like the forum software reduced the resolution on upload. I will attach a PDF to this post containing a copy of the original files at original resolution.

The calculations I presented were an attempt to dumb this down to something that can be presented in a forum that the average homebuilder could work with to design a spar. I did say there were a lot of assumptions and approximations and you have picked up on some of them. However, I think the calculation method I have presented should produce a spar that is safe enough. Admittedly this is a long way from what we would do in the professional engineering world but professional engineers take years to learn their more refined methods (and the analysis time increases from hours to days and weeks).

I made the assumption of a uniform loading on the wing and this is quite conservative. The use of an elliptical or Schrenk distribution moves the load inboard and would reduce the bending moment by at least 10% - perhaps more. Also the shear force calculated by assuming a constant distribution is always conservative at any point along the wing (only exact at the root). Yes the methods can be extended to include one of the spanwise loading methods (elliptical, Schrenk, lifting line etc) but the maths would get way too messy for this forum. So better we are conservative. I have also neglected the inertial relief of the wing (i.e. the weight of the wing which directly opposes lift at any station and hence reduces the bending and shear). That would likely reduce bending moment and shear by another 10% (rough guess). Both these effects would be included in a more detailed analysis.

In calculating the section properties of the spar I made a few assumptions. First, I ignored the contribution of the web to bending. I don't think this is a bad assumption because the fibres in the web will be orientated at 45 degrees and the elastic modulus of a laminate with the fibres at 45 deg will be something like 1/6th of a laminate with all the fibres at 0 deg. The web could be included in the section properties calculations if desired by factoring its thickness by the ratio of web to cap elastic moduli. I chose to conservatively ignore the small benefit I would gain from this to simplify the calculations.

Up till this point I have tried to avoid the complication of laminate analysis. However, the previous paragraph raises the question of how we know that a laminate of +/-45 deg uni has a stiffness of say 1/6 of a laminate in which the uni is all placed at 0 deg ? When analyzing general composite laminates you always have the properties of the material in each ply at 0 and 90 deg to the fibre directions + the shear properties. If we stack these plies on top of one another at various angles, the first question is what is the elastic modulus of the laminate in any direction ? The next question is, if we apply a load to the laminate in some direction, or perhaps in different directions at the same time and perhaps some shear, what are the stresses and strains in each of the plies in their respective fibre directions ? There are methods of analyzing laminates to answer these questions. This is way beyond what can be covered in a post on a forum. All I can do is refer to a text book on composite laminate theory such as the classic "Composites Design" by Stephen W Tsai but in reality there are dozens of such books. In practice, laminate analysis is always done using software, either commercially available or home brewed. The 1/6th modulus quoted above was taken from a graph in the composites design manual of a major aerospace company but I could have used laminate design software as well.

I also made the assumption that the tension and compressive moduli of the caps were the same; at least within the strain limits that we are using as allowables. In reality they will be different with the compression modulus being less than the tensile modulus. The tensile modulus is always nonlinear with modulus reducing as strain increases due to microcracking of the matrix, failure of some fibres and breakdown of the interfacial bonds between the fibres and the matrix. However the initial modulus is acceptable for this analysis because we are using a low strain allowable at limit loads. Data on compression modulus is both hard to measure reliably and not commonly available for most materials. Data that is published only ever provides an initial modulus and that indicates that it might be 5-15% lower than the tensile modulus but is highly dependent on the reinforcement style, materials and how the modulus were measured. I have no idea how the compression modulus behaves at higher strains. Anyway if we had data for the tension and compression moduli, and wanted to include the effects of that in the analysis, the width of the cap can be factored by the ratio of the modulus. This will complicate the maths and I chose not to do it. Ignoring the effects of moduli will shift the position of the neutral axis and thus alter the stress distribution between caps. The practical reality is that a amateur designer is unlikely have have compression and tensile moduli for his spar cap material and so I felt this complication was best avoided. Throughout this discussion I have preached conservatism and here is one of the reasons why.

Finally to the questions on the shear web. Yes there is some major assumptions here.

First, to the question of the differences in the E/G between web and cap. Yes ... this will change the distribution of stress. However I am not so sure that this is all that significant because I have not included the shear webs in my calculation of section properties (I & Q) resulting in a constant shear in the webs which is close to the average value (it would be even closer if this was calculated based on the clear distance between caps as you suggested instead of the full depth of the spar). Even if we factored the web or cap size for modulus we would still have a section with massive caps and thin webs and the shear stress is always going to be roughly constant through the depth in such a case so I am not so sure that the complication is warranted. At the end of the day, if we assume that the shear is all carried by the web, this is conservative and further refinements will only allow the cap to carry some of the shear and improve the accuracy of the calculation of bond line shear stress between the cap and the web. Again, I have sacrificed accuracy to develop a simple method to hopefully give amateur designers of homebuilt's something to work with rather than nothing at all.

OK now to the final issue. The question of how we handle the complex stress state of the web near the cap. At this point it is carrying shear and tension/compression due to bending as you point out. This needs to be handled via the laminate analysis that I discussed earlier. The +/-45 deg laminate needs to be analysed with a shear stress and in-plane tension or compression stress and the ply stresses recovered. The plies will have a complex state of loading and failure can be checked using one of the ply failure criteria such as Hill, Tsai-Hill, Tsai-Wu, Hoffman etc. See a textbook such as Tsai "Composites Design" - some laminate analysis software will do this for you as well. The axial stress in the web can be calculated from the strain in the caps and using the axial modulus of the web. However, I know from experience that this is unlikely to be an issue if you stick to the allowable I provided for the web.

Now, just to cover off one other point. The main reason for assymmetery on the beam design is because of the difference in the tensile and compressive strain allowables in the cap (compressive allowable is approx 3/4 of the tensile allowable) ... the compressive cap in the positive 'g' cases is bigger to ensure that its strains are lower. The negative limit load is usually half that for positive 'g' and we can live with the improper distribution of cap sizes for negative load factors ... same for a wooden spar. For an aerobatic aircraft designed for say +/-9 g then you would need to size both caps for the lower compressive strain allowable.

Lets discuss further as required.

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#### proppastie

##### Well-Known Member
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Tension 170 GPa (60% fiber in volume)
Compression 140 GPa
170 Mpa 140 Mpa ????

#### wsimpso1

##### Super Moderator
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Log Member
170 Mpa 140 Mpa ????
MPa is a megaPascal. One Pascal is one N per square meter, which makes it a really small unit. There are 6890 Pascal per psi, so you can interpret what 170 and 140 MPa are...

#### tdfsks

##### Well-Known Member
170 Mpa 140 Mpa ????
I took these to be elastic modulus and if so GPa would be the correct unit. However, these convert to 24,600,000 Psi (24.6 Msi) and 20,300,000 psi (20.3 Msi) and are high numbers for modulus ..... well high for standard carbon uni but they are in the range that might be expected for a high modulus carbon. We would need to know what material they are for and how they were measured to comment further.

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#### wsimpso1

##### Super Moderator
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Billski,

Firstly, my apologies for the quality of the uploaded images. My originals were clear ... looks like the forum software reduced the resolution on upload. I will attach a PDF to this post containing a copy of the original files at original resolution.

The calculations I presented were an attempt to dumb this down to something that can be presented in a forum that the average homebuilder could work with to design a spar. I did say there were a lot of assumptions and approximations and you have picked up on some of them. However, I think the calculation method I have presented should produce a spar that is safe enough. Admittedly this is a long way from what we would do in the professional engineering world but professional engineers take years to learn their more refined methods (and the analysis time increases from hours to days and weeks).

I made the assumption of a uniform loading on the wing and this is quite conservative. The use of an elliptical or Schrenk distribution moves the load inboard and would reduce the bending moment by at least 10% - perhaps more. Also the shear force calculated by assuming a constant distribution is always conservative at any point along the wing (only exact at the root). Yes the methods can be extended to include one of the spanwise loading methods (elliptical, Schrenk, lifting line etc) but the maths would get way too messy for this forum. So better we are conservative. I have also neglected the inertial relief of the wing (i.e. the weight of the wing which directly opposes lift at any station and hence reduces the bending and shear). That would likely reduce bending moment and shear by another 10% (rough guess). Both these effects would be included in a more detailed analysis.

In calculating the section properties of the spar I made a few assumptions. First, I ignored the contribution of the web to bending. I don't think this is a bad assumption because the fibres in the web will be orientated at 45 degrees and the elastic modulus of a laminate with the fibres at 45 deg will be something like 1/6th of a laminate with all the fibres at 0 deg. The web could be included in the section properties calculations if desired by factoring its thickness by the ratio of web to cap elastic moduli. I chose to conservatively ignore the small benefit I would gain from this to simplify the calculations.

Up till this point I have tried to avoid the complication of laminate analysis. However, the previous paragraph raises the question of how we know that a laminate of +/-45 deg uni has a stiffness of say 1/6 of a laminate in which the uni is all placed at 0 deg ? When analyzing general composite laminates you always have the properties of the material in each ply at 0 and 90 deg to the fibre directions + the shear properties. If we stack these plies on top of one another at various angles, the first question is what is the elastic modulus of the laminate in any direction ? The next question is, if we apply a load to the laminate in some direction, or perhaps in different directions at the same time and perhaps some shear, what are the stresses and strains in each of the plies in their respective fibre directions ? There are methods of analyzing laminates to answer these questions. This is way beyond what can be covered in a post on a forum. All I can do is refer to a text book on composite laminate theory such as the classic "Composites Design" by Stephen W Tsai but in reality there are dozens of such books. In practice, laminate analysis is always done using software, either commercially available or home brewed. The 1/6th modulus quoted above was taken from a graph in the composites design manual of a major aerospace company but I could have used laminate design software as well.

I also made the assumption that the tension and compressive moduli of the caps were the same; at least within the strain limits that we are using as allowables. In reality they will be different with the compression modulus being less than the tensile modulus. The tensile modulus is always nonlinear with modulus reducing as strain increases due to microcracking of the matrix, failure of some fibres and breakdown of the interfacial bonds between the fibres and the matrix. However the initial modulus is acceptable for this analysis because we are using a low strain allowable at limit loads. Data on compression modulus is both hard to measure reliably and not commonly available for most materials. Data that is published only ever provides an initial modulus and that indicates that it might be 10-15% lower than the tensile modulus but is highly dependent on the reinforcement style. I have no idea how the compression modulus behaves at higher strains. Anyway if we had data for the tension and compression moduli, and wanted to include the effects of that in the analysis, the width of the cap can be factored by the ratio of the modulus. This will complicate the maths and I chose not to do it. Ignoring the effects of moduli will shift the position of the neutral axis and thus alter the stress distribution between caps. The practical reality is that a amateur designer is unlikely have have compression and tensile moduli for his spar cap material and so I felt this complication was best avoided. Throughout this discussion I have preached conservatism and here is one of the reasons why.

Finally to the questions on the shear web. Yes there is some major assumptions here.

First, to the question of the differences in the E/G between web and cap. Yes ... this will change the distribution of stress. However I am not so sure that this is all that significant because I have not included the shear webs in my calculation of section properties (I & Q) resulting in a constant shear in the webs which is close to the average value (it would be even closer if this was calculated based on the clear distance between caps as you suggested instead of the full depth of the spar). Even if we factored the web or cap size for modulus we would still have a section with massive caps and thin webs and the shear stress is always going to be roughly constant through the depth in such a case so I am not so sure that the complication is warranted. At the end of the day, if we assume that the shear is all carried by the web, this is conservative and further refinements will only allow the cap to carry some of the shear and improve the accuracy of the calculation of bond line shear stress between the cap and the web. Again, I have sacrificed accuracy to develop a simple method to hopefully give amateur designers of homebuilt's something to work with rather than nothing at all.

OK now to the final issue. The question of how we handle the complex stress state of the web near the cap. At this point it is carrying shear and tension/compression due to bending as you point out. This needs to be handled via the laminate analysis that I discussed earlier. The +/-45 deg laminate needs to be analysed with a shear stress and in-plane tension or compression stress and the ply stresses recovered. The plies will have a complex state of loading and failure can be checked using one of the ply failure criteria such as Hill, Tsai-Hill, Hoffman etc. See a textbook such as Tsai "Composites Design" - some laminate analysis software will do this for you as well. The axial stress in the web can be calculated from the strain in the caps and using the axial modulus of the web. However, I know from experience that this is unlikely to be an issue if you stick to the allowable I provided for the web.

Now, just to cover off one other point. The main reason for assymmetery on the beam design is because of the difference in the tensile and compressive strain allowables in the cap (compressive allowable is approx 3/4 of the tensile allowable) ... the compressive cap in the positive 'g' cases is bigger to ensure that its strains are lower. The negative limit load is usually half that for positive 'g' and we can live with the improper distribution of cap sizes for negative load factors ... same for a wooden spar. For an aerobatic aircraft designed for say +/-9 g then you would need to size both caps for the lower compressive strain allowable.

Lets discuss further as required.
Thanks for sending the docs along as a .pdf, much clearer now what you are doing...

E = 70 Mpsi? Steel is 30 Mpsi, most unidirectional graphite epoxy materials are in the 20 to 26 Mpsi range. Tungsten carbide is about 80 Mpsi. What fiber-resin team has E = 70 Mpsi? Unidirectional E-glass in epoxy I get at around 4.4 Mpsi, unidirectional S-glass is about 5.5 Mpsi... Must be some sort of a typo, but if you slipped a decimal point, I do not know what you had either. Working with more rational E, the spar caps under these rules would have to be a LOT bigger to pass your allowable strains...

Billski

#### proppastie

##### Well-Known Member
Log Member
I took these to be elastic modulus a
That is how I designed my plane spar caps taking into account material properties measured at my workplace...
(60% fiber in volume)
When he says 60% fiber volume I assume he is talking the allowable for the matrix as tested in his shop... simple typo and/or limit design to a conservative number is a possible answer?

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#### wsimpso1

##### Super Moderator
Staff member
Log Member
60% fiber volume means that of the cured composite, it is 60% fibers by volume and 40% resin by volume. Theoretical maximum on hexagonally close packed circular cylinders 90.7%.

#### lr27

##### Well-Known Member
snip
Why should Sky Pups be disintegrating? What do you know?

Billski
I think we can at least trust Drela's test data.

Sky Pup spars use blue Styrofoam as the sheer web in most of the spar and also for some of the fuselage. If silicone was common in Dow building insulation foam, we'd have heard about Sky Pups falling apart, I think. OTOH, if I was building one I'd want to know that silicone in the foam was extremely unlikely. I guess one could compare adhesive strength or something. Or ask Dow with a properly worded question.