Beam Theory Explained - How Spars Work

Discussion in 'Aircraft Design / Aerodynamics / New Technology' started by wsimpso1, Dec 29, 2017.

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  1. Jan 6, 2018 #61

    wsimpso1

    wsimpso1

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    This is just the first part of doing composites, and it is a useful exercise to go through and learn from, but it can give big errors in strength.

    Let's discuss the limitations of this simplified version:

    When you convert the width of the various materials to correct for E in them, you are correcting for E perpendicular to the cross section. In steel and concrete, that is OK because the E changes the same in all directions. In wood and in unidrectional composites, that is WAY OFF, and significant errors will result in actual strains and FOS;

    There is no attempt in this method to calculate or account for strain induced perpendicular to the long axis of the beam (in the plane of the cross section), and it matters, as that also loads the lamina (steel caps here) and the wooden core and the bond lline between them, which will also be subject to failure;

    The large widths compared to thicknesses also produced some other fundemental errors in strain state and stresses, even in a homogenous plate. Plate and shell theories were developed to take into account the attemps by the materials to change width when length is changed under loads. This model does not attempt to consider the plate theory issues;

    In fiber and matrix composites, the E's of the materials in the plane of the cross section are generally hugely different from the E's perpendicular to the cross section, and so would have to corrected differently. These differences in on-axis strain and perpendicular-axis strain generally further strains the lamina and increases the shear stresses both within and between the lamina;

    These failures of simple composite theory to adequately model fiber and matrix composites and to model plates were significant - things were not behaving as modeled and were failing at lower loads than expected. This provided the incentive to develop plate theory and composite plate theory.

    I have an intro coming, still editing. It will have its own thread.

    Billski
     
  2. Jan 6, 2018 #62

    wsimpso1

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    Choppergirl is asking a complex question here... She wants to know which truss form is better, and then it is qualified for airplane fuselages. This is related to beam theory in that the truss elements that make up the shape are talking the place of the shear web in a tall sparse beam.

    First, the short answer. The best is the lightest simple structure that can be readily built and that looks good. Allow me to elaborate. Sorry, no simple answer to explain all of the variation we see...

    There are several reasons why one truss scheme may have been used over another in any particular application, so let's get into them, starting with bridges:

    • Just to get it out of the way, some of the bridge designers out there do fancy themselves to be artists at some level, concerned about the appearance of their bridges on top of the issues of weight and cost and how many lives will be lost building the thing. It is true that the folks who have been designing them fall prey to vanity a bit. Just because it is big and immensely expensive does not mean that it should be ugly or that the folks designing them would not want to have pride in more than just the utility of it. Nope, their's is a creative profession, and they too want their stuff to look good, so that has to come into some of them;
    • Next issue is that every bid for new bridge goes through some sort of government agency or railroad company engineering division for review. If the bid is competitive on cost, but the bridge looks flimsey or looks bad to the engineering division management, the folks may select a better looking or more robust looking bid. So, after the designers make choices based upon both objective and subjective points, so does the folks who select the winning bid. So, we have more reasons for decisions than just the objective issue of cost;
    • Next in bridges, the design and construction is usually let out to bid among companies who do such things, and cost is a big deal. With bridges weighing the immense amounts that they do, keeping the weight of the steel, concrete, etc down is a huge part of keeping the cost down. So is manpower to put the bridge up. Such a big deal that custom cross sections of the steel pieces are often used on large bridges, so a certain amount of optimization of the sections and trusses occur too;
    • So, in bridges, we can expect that many of them are highly tailored to keep steel weight down. There are a several primary bridge truss forms available, and the bridge designers also can run a variety of truss depths to satisfy the strength and weight and looks topics. If they were only concerned with cost, they will play with the truss depths and truss forms, optimize the bridge design for each pattern while making strength, and select the lowest cost one, which is frequently the lightest one too.


    Now to fuselages. We have much the same issue of safely carrying the intended loads and keeping flutter way at minimum weight and cost. In a factory-built airplane, cost includes all of the time fitting pieces and welding them, being able to inspect and assure ourselves that they are strong, being able to paint it and apply fabric, etc. And factories use elaborate fixtures to build fuselages, so they can do things to optimize manpower and materials costs that we homebuilders may find very difficult (or impossible) to build and make straight. We homebuilders must use simple expendable tooling, and our man-hours may be less of an issue than the purchased cost of materials, particularly when building the fuselage may come years before buying an engine.

    Then, when we get into design of a fuselage, we have similar issues to the bridge builder. We have a fuselage profile, so the depth of our truss is fixed, which simplifies things. We have a number of truss forms available to select from, and we have a wide variety of tube diameters and wall thicknesses. The designer strives to design the lightest fuselage that is easily fixtured, welded, and inspected. Resistance to buckling of elements in compression frequently sets min tube sizes. More bays means more tubes, but the loads in each are smaller, so maybe you can reduce tube size. One truss form over another may or may not give advantage. And while we homebuilders like to think that we would be willing to do more work to save some weight, very few of us will double the hours to build a fuselage to only reduce fuselage weight by a pound. In an airplane fuselage, looks will most likely come into it only with regards to "does it look like it will do the job?" For some of us, that means it has to look like other known airplanes. For a few of us, that can mean it has to look different from the other birds out there - these folks fancy themselves artists...

    Let's remember another constraint. Out tubes come in a bunch of sizes, but they all have discrete steps in diameter and wall thickness. If one size is just a skosh too small, you have to go up to the next size for substantial wieght increase in both tube and weld. So, while one design might be best if you could get 0.700 x 0.030 tubing, but you can not get it, and have to go up to 3/4 x 0.035... So each design gets some extra weight at each element and each weld, and frequently the one that gains the least will be the lightest, not the ideal form with optimized tube sizes...

    My preference? Since weight is the enemy in airplanes, I propose a thoroughly objective scheme. Survey the design space, scheme up the various designs, size tubes and welds within the catalog of available tubes, come up with the expected total weight for each scheme, and select the lightest one. This includes the issue of crossing elements attached together or not.

    Back to the question... Should you bolt truss elements together? Usually there is little additional strength gained by doing so, at the expense of having to install structure to stand having the holes in the elements and the loads from tightening the fasteners. Yeah, you do reduce the free column length in one axis, but not in the other. In the end you have to look at each case on its own merits and make choices. In most airplane fuselages, the truss elements do not usually cross anyway, except where the crossing is also an attachment point for some significant device like a bellcrank or landing gear piece...

    Billski
     
    Last edited: Jan 6, 2018
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  3. Jan 6, 2018 #63

    Aviator168

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    That is one of the questions I had in mind when i was watching the video.
     
  4. Jan 11, 2018 #64

    Aviator168

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    Billski, thinking about your comment on composite beam analysis. Are you talking about the stress on the foam, and specially the (horizontal) shear stress at the interface between cap and foam?
     
  5. Jan 11, 2018 #65

    wsimpso1

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    Not following you... The thread is not about composites, but one on composites is now posted.

    Specific to your question, all of the core foams I know about have deflection to failure on the order of 3 to 5 times the deflections to failure of common fiber-resin combinations., and so the strength of foam is not normally an issue. Add to that the fact that we customarily "close out" edges of sandwich panels which specifically avoids having foam exposed to shear stresses that can fail the foam or peel the fiber-resin layer from the foam.

    Does this address your issue?

    Billski
     
  6. Jan 25, 2018 #66

    wsimpso1

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    Failures in Beams

    Now that we have the mechanics of beams explained, we can talk about failure modes a little and how they occur in metal beams, meaning aluminum alloys as commonly applied to airplanes, whether it is sheet metal or wrought shapes. We can also include steel, magnesium, and titanium, even though they are uncommon these days in aircraft spars and beams. The same concepts apply in all of these materials. This little post is not intended to be exhaustive, and only hits the high points. To do a good job on design of a durable airplane wing, you will need to go into depth on every one of the topics covered below, but this should give you a basic run through what occurs in our structures to cause them to be bent or broken. I hope that this helps with understanding or spars and beams...

    Beam Sizing

    Initial sizing establishes the cap size based upon bending resolved into axial loads and the shear web is sized to just carry the shear uniformly spread on the free part of the web. The web is under strength until either the web is beefed up a lot (the heavy way) or the web and the caps are both beefed up some (the light way). Either way, the caps end up over strength and the web ends up being no better than you designed it, maybe less if any buckling mode shows up.

    Beam Deformation and Stress

    When a beam is carrying a moment, plane sections remain plane. All parts of the beam deform when the beam is bent, and the deformation at any spot goes with how far above or below the neutral axis that spot is. Throw in shear, and we skew those plane sections too. But the deformations of the parts of the beam are all related to each other, and they all increase or decrease together as the g- loading changes. Stresses are linear with the strains seen from the deformation.

    Beam Failure

    From zero to a particular load, the deflections and strains and stresses and loads all change together linearly. At that particular load, some portion of the beam reaches a limit, and the deflection increases markedly. This can be yielding, fracture, or any of the buckling modes. The web and caps are no longer moving together like they were. Deflection vs load will definitely increase. Failure has commenced and it may collapse completely if the load stays high.

    Spar Caps

    The big possibilities for failure within the design limits in the caps are crippling/buckling and fatigue around attachment points, either between parts of the spar or to the rest of the airplane. Even at significant overload of the spar, you are not likely to yield the cap as the initial failure unless the web has been hugely oversized. Crippling and buckling is covered in texts on elastic stability and by the standard airplane structures textbooks.
    If the spar has separate sheet metal webs and/or laminated caps, they are usually riveted together. The rivet holes are common starting points for cracks. If instead, you have a machined spar, like many Beechcraft have, the machined surfaces and cutouts and attaching holes are initiation points for cracks. In either case, they should see thorough review for stress concentration and fatigue. Careful deburring, setting rivets to fully fill the holes and preloading the assembly are your manufacturing priorities. Elastic stability and classic stress analysis with stress concentrations are your big design tools.

    Shear Web

    This is the place where we expect to have problems. What does happen when you overload the spar? Well, the caps should be somewhat overbuilt in the first place, so mostly they just take this in stride, at least until the web gives up.

    Web carries shear and it also carries tensile or compressive stress as they deform with the adjacent caps. If you want some insight into stresses in the web, I like Mechanics of Materials by Timoshenko and Gere, look at the stresses in beams chapter. There are other books that work well too. Mohr’s circle will allow you to collect various stressors and figure out what the total stress state is at any one place. This all contributes to yielding of the web. Once the load causes the web to yield, the relationship between the caps and web is disrupted, increases deflection vs load, stresses in everything increase and the wing changes shape, with folding or other collapse of the wing occurring if the loads are continued. Yielding is pretty easily forecast from classical analysis or from FEA, and should be precluded until significantly above limit loads, and hopefully until above 1.5 times max g.

    Now we move into buckling. First we have to improve our view of shear load. The classic buckling circumstance is where the web becomes unstable in any of a bunch of modes. If you were to look at a little square element of the shear web between the caps that has two sides parallel to the caps, it sees shear as loads along two adjacent edges towards one corner and loads along the other two edges towards the opposite corner. That may be hard to imagine, so let’s transform it. Mohr’s circle helps in understanding this stuff too. Cut out a different square element with the faces at 45 degrees. This element is cut from the same place in the wing and with the wing under the same load. It now has tension pulling two faces (that are across from each other), and compression pushing on the other two faces.

    We are trying to stretch the web one way and compress it at 90 degrees to the tension. When the loads get to the place where the web becomes unstable, the web will have wrinkles parallel to the tension load. The compression direction loses much of its ability to carry its part of the load, while the tensile direction is now carrying more load. The web’s stiffness in shear will decrease sharply and its ability to carry an imposed shear load is dependent upon the tensile direction only. The caps now can move axially relative to each other and overall load may increase a little before the load drops away.

    Once this buckling starts, if nothing else was done to the spar, it can collapse. Theory of Elastic Stability is the topic to study for these phenomena and the classic airplane design texts have sections on crippling calculations. You can put in short light stiffeners perpendicular to the caps, which constrains the wrinkles. This and other methods can be applied. This whole topic is Elastic Stability, and can be handled using Tension Field Theory.

    Understand that these wrinkles can happen at stresses that calculate out well below yield. In addition, you are likely to get zero symptoms of the impending collapse until you get to the onset of the buckling load. If you are applying load to a test wing with a large stiff frame, a hydraulic cylinder, and a whiffletree, the instability will be reached and you will see a drop in load while wing deflection will increase. If you were applying a dead load, the wing may collapse.

    Fatigue and Cracks

    If we cycle metal many times, from big positive to big negative loads (called fully reversed loading), over many, many cycles, cracks will initiate and grow. Eventually these cracks get large enough that the remaining metal is unable to carry the next load cycle and we get a catastrophic failure. Endurance limits have been estimated for many useful alloys, and methods for applying this information are also in the design textbooks.
    Our big protection against premature fatigue cracking is good shop practice, designing surfaces to avoid stress concentrations, and designing to have lower stresses where we will have a lot of cycles.

    Generally our FOS ends up somewhat bigger than intended because we cannot get ideal sized materials – we usually end up with more metal than we need. The combination of conservative design and conservative flying really goes a long ways toward making fatigue failures fairly rare. When fatigue cracks do develop, they take a while to show up, we find them during annual inspection, and we fix them.

    Riveted Joints

    Several years ago, a Boeing jetliner was videoed going through a wing test. In these planes the machined wing skins serve as spar caps, riveted to webs connecting the top and bottom skins. At some point, the wing broke. The riveted joints between upper skin and webs had broken. So you have an example… There is shear flow across one cap, down the web and then across the other cap. All of this shear flow has to be carried by rivets across joints between pieces of a built up spar. If you build up a wing with extruded or machined caps riveted to sheet metal webs, the riveted joints had better be sized conservatively to carry the shear flow between caps and web. Your mechanics of materials text or airplane structural design text should provide the tools to calculate shear flow in your beams and design riveted joints that are capable.

    Riveted joints are all over the place in metal wings. Not only do we attach the caps to the webs, we attach the wings to the carry through or to other segments of the wing, attach a multitude of ribs to the spar and then to the skins, and the ribs collect the difference in air load between bottom and top skins and apply it to the webs. Then we do other things, like hang landing gear, fuel pumps, actuators for flaps and ailerons on the spars, and we do it mostly with rivets in metal wings. All of these joints are putting holes in it, then carrying preload from these joints and g loads of the parts, so the spar sees all sorts of loading through rivets.

    Riveted joints and the rivets themselves, by their very nature, are loaded with stress concentrations. To make them resistant to fatigue, rivets must be properly set. Most of us know that the joint must be tight and the shop head properly formed, but some of us do not realize what this good practice does in the joints. When a rivet is properly set, the rivet is in tension longitudinally and the material around the rivet is in compression in the same direction, and the rivet has been upset so that it completely fills the hole. The preload on the joint from rivets must be greater than the maximum load that is attempting to separate the parts. In this way, the rivet does not see any cyclic loading, and thus is unlikely to see fatigue from loads trying to separate the joint. In addition, this preload on the rivet plus the rivet holes being completely filled with upset rivet shaft prevent any shearing movement in the joint.

    If the rivet has inadequate preload and allows the joint to open and close, the rivet and the joint materials may show fretting and will be subject to fatigue. If the rivet either does not have enough friction to prevent shear motion of the joined parts or the rivet did not completely fill the hole or both, then the joint will “work” in shear, subjecting the rivet and joined materials to fretting and fatigue.

    Corrosion

    When oxygen and water and various other chemicals cause oxidation or dissolution of our metal parts, there is less strong metal to carry loads, stress concentrations are created, and failures will occur. Enough said?

    Welded Joints

    Aluminum alloy structural assemblies are usually best made by riveting. Got that? Here is why – aluminum alloys of useful strength are heat treated in some manner. The temper, as it is called, is designated with the suffix on the alloy. If you start with –T4 or -T6 and weld it, it is now –O (annealed) adjacent to the weld. Annealed aluminum is 5-8 kpsi yield strength… While some alloys will recover some of their strength, you had better design to what the material will give you after welding and natural aging. This is not to say that the part could not be designed to work, it is just that it will either have to be beefier or you have to find someone who can re-heat treat the structure. Good luck with that. In most of the world’s stuff, we just rivet aluminum alloys. Same with magnesium, but you had better have a great plan for coating it against corrosion and then detailed inspections…

    Now 4130 steel can be welded and come out OK, but not many wing spars for little airplanes are made of steel and for good reason – you can make sheet aluminum wings of adequate strength and at lower weight. Enough said here?

    Conclusion

    So, now you have the basics of how metal spars are likely to fail and why. Designed so that the entire beam will go to 1.5 times max g without yielding and flown so that loads stay below limits, you are highly unlikely to ever fail the spar, either in the short term or over the long haul. But if the caps and web were just beefed enough to prevent yield at max g, they will be far more exposed to fatigue than many of us like.
    If the riveted joints and the rivets themselves are either poorly designed or poorly executed, you have many places where these joints could fail. Makes you want to be very thorough in designing the wing and then very thorough in setting all of those rivets, doesn’t it. It should also make you want to select a design with a good history in use and no unexplained in-flight breakups of any airframes…

    Well, I hope that this does you some good.

    Billski
     
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  7. Jan 25, 2018 #67

    BoKu

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    I think Billski is talking about what is sometimes called the "method of composite sections." That's what you use when your beam cross-section isn't a rectangle or ellipse or torus for which there is a simple expression for the moment of inertia. Instead, you break your cross-section down into a bunch of elements (rectangles, ellipses, etc) for which there _are_ simple expressions for Mi, then sum the moments of inertia of the various elements to get the moment of inertia of the whole cross-section.

    --Bob K.
     
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  8. Jan 26, 2018 #68

    proppastie

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    I read different things as to what that is, I know what I have decided but am interested as to what is "standard" or others do. As example. I have seen FOS 1.5 x limit + 15%. or 1.5 x ultimate, and if ultimate is considered 1.5 x yield then 3 x yield. All these are for metal, I also see FOS of 2 (not 1.5) for composite or wood.
     
  9. Feb 1, 2018 #69

    wsimpso1

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    Uhhh. More complicated than you think. First off, 14 CFR Part 23 is available here:

    https://www.ecfr.gov/cgi-bin/text-i...5c130073e1d26&mc=true&node=pt14.1.23&rgn=div5

    While Part 23 is not THE LAW for us homebuilders, it is still a pretty good idea. It was largely written in the blood... Please take the lessons.

    First, Part 23.2235 says that your structure has to carry limit loads without interfering with safe operation or detrimental permanent deformation, and says that it must carry ultimate loads. In metal, that generally means max g without yield and 1.5x max g without breaking. The 1.5 times max g for ultimate is based upon the common relation of many airplane metals having an ultimate strength around 1.5 times the yield strength. Well, some do, some do not, and buckling/folding/collapse can be running at stresses much lower than yield. But there is more...

    The very next section says that there must be Inspection or other procedures that will detect issues before they the can result in failures. Most of us do one inspection cycle per year. If you have a fatigue crack starting, and it is undetectable at one condition inspection, it still has to be safe to fly with until the next condition inspection. That is kind of hard to do unless you can largely prevent fatigue cracks in the first place. Make fatigue unlikely, and then hope that when it does show up, it is slow enough for you to find it before catastrophe strikes.

    Then there is the whole idea that you have spent years building this thing, do you really want to make it so light that you have to do dye penetrant inspections of the spar on an annual basis? On a spar that you have corrosion protected with epoxy primer and buried inside multiple layers of other structures? That will require immense work to replace? Not me...

    So, what does this mean? Well, if you are designing this bird, you will want to load it to max g's somewhere in your test sequence, either on a test rig or in flight. Can you really precisely hit 3.8 (or 4.2 or 6) g's in a symmetric pull up? Do you really want to find out that that your built structure permanently wrinkles at less, requiring an emergency landing (or bail out), design mods and a building a new wing or even whole airplane? Do you really want to find out that the built structure collapses a little before ultimate load, with similar consequences?

    Naw, I bet you would want your metal wing spars to be:

    Better than yield at max op g's;
    Better than ultimate at 1.5x max op g's;
    Pretty much fatigue proof under your operation and duty cycle.

    Let's look at that adjusted criteria. Since being right at limit load for min yield is unlikely, if you do a good job of basic analysis for stresses, buckling, crippling, etc, the first criteria can be met.

    The second is harder. This is NOT multiplying limit load by 1.5 in your static analysis and making sure that your stresses are lower than ultimate stress. Once some part of your structure gets past yield:

    Deformation increases a bunch. Look at stress strain curves - they are nearly vertical in pre-yield, then go almost horizontal once post-yield. Yep, the shape changes a bunch at very little increase in load once you get to yield;

    Phenomena such as plastic hinges, etc, result in large deformation, exposing your structure to many buckling and folding modes once yield occurs;
    Who says your spar will deform in a direction that unloads the airplane and removes load? Many of us are using laminar flow foils with a lot of wing ahead of the spar;
    Control systems become interfered with when the wing undergoes large deformation, and may increase loads or prevent us from unloading the structure.

    So how to prevent structure fold up at 1.5 times max g? Unless you are willing to run non-linear FEA with accurate post yield material models and all buckling modes turned on, all of the way to 1.5 x max g, and then follow with physical test of full size articles to that load, you can not say that you have put that one out of reach.

    The third is fatigue. If you fly it gently, you might prevent fatigue cracks, but even jetliners have seen fatigue cracking. Nope, good shop practice, and increased margins are your way to putting fatigue cracks at bay.

    Since our simple sheet metal wings are likely to fold when the spar yields, and you want the wing to keep from collapsing at ultimate loads, I put to you that the designer of little airplanes should probably design to just be safe from yield and all buckling modes up at 1.5 times your max g condition.

    Now going into wood and composites, those are thread drift, but I will bite. Composites generally do not have post-yield behavior. Fibers are breaking or crushing when you get to strength level stresses. Nope, put failures above 2.0 x max g in composites. And wood? I have not studied wood. Maybe someone else can help.

    Billski
     
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  10. Feb 1, 2018 #70

    PiperCruisin

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    I would be interested to see if there are any proceedings available to see how they came up with these recommendations in the FAR.

    I do a lot of structural analysis (sometimes aircraft, mostly other things). I agree with Billski. There are "standard" practices, but reality is much more complicated. While Ultimate/Yield is about 1.5 (not always and varies a lot), plastic hinges (see shape factor), tension sections, and local buckling have significant impact on the ultimate load capacity of the structure.

    A FOS of 2.0 on composites (and wood?) probably comes from their variable nature and little to now warning before catastrophic failure. Some regulator probably said, "Oooh, scary stuff I don't understand. Let's add an arbitrary 0.5." Not that I really disagree, but "2.0" screams not a lot of probabilistic analysis going on here.

    Fatigue, my bailiwick, is (hear me out) generally not as big of a concern in aircraft design because most of the load cycles are much lower than the ultimate they are designed for. There are exceptions. Pressurized fuselages go from zero-max-zero on every flight so the ratio of ultimate to cyclic stress range is relatively high, but cycle count is not super high. Airliner design loading is also lower. This means that the ratio of ultimate to normal flight vibrations is higher than something rated to 6g (unless they are doing a lot of yanking and banking). This does not mean one should not be concerned about fatigue. I talked to a guy who was a helicopter mechanic and he said most of his job was watching cracks grow. And think about all the ADs out there to inspect for cracks.
     
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  11. Feb 1, 2018 #71

    BJC

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    Variability of fabrication, especially in HBA, is significant. Given some workmanship that I have seen, even a factor of 2 may not be enough.

    I think that the probabilist analysis was “Somebody is probably going to do a lousy job on these wet layups.”


    BJC
     
  12. Feb 1, 2018 #72

    wsimpso1

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    Official story is FOS of 1.5 and then 1.33 for water intrusion, which becomes 2.0.
     
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  13. Feb 1, 2018 #73

    wsimpso1

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    Someone else thinks so too...
     
  14. Feb 1, 2018 #74

    proppastie

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    I guess buckling can also occur at at load between yield load and ultimate load....so should one only test to yield load then that test is all one is sure about and a save ultimate load should not be assumed from just that test.

    We normally do not test one off homebuilds to destruction. And given that deformation is allowed in an ultimate load test, that would be something a homebuilder might balk at.
     
    Last edited: Feb 1, 2018
  15. Feb 2, 2018 #75

    wsimpso1

    wsimpso1

    wsimpso1

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    Thread drift... I feel that there should be shear web of more substantial stuff than foam tying the caps together. That being said, you can go calculate shear flow and determine if and where you might be able to tolerate using foam as a shear web, then do the composite ABBD including the foam, solve for strains in all of the lamina, then check to see if everything is expected to survive...

    Billski
     
  16. Feb 2, 2018 #76

    wsimpso1

    wsimpso1

    wsimpso1

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    I can not help but think that my point was missed here...

    We homebuilders really only want to build once. Spars are expensive time consuming things to make, and then we bury them under ribs and skins and such. So we probably want to make sure they are adequate against everything, including fatigue. Skins and ribs can be striped off and redone much more easily... So, design your metal spars to have a FOS of 1.5 over yield at max positive g. You can analyze it well, then proof test it and know that it is good. If you feel you must live closer to the edge, then you need to be prepared for all of the other stuff, like non linear FEA, test to 1.5 times max g, fatigue analysis, and so on.

    I think it is better to have a few more pounds of very specific strengthening and know that when I fall out of a loop, it will hold together through the recovery and then let me fly home and look for damage.

    Billski
     
  17. Feb 11, 2018 #77

    Lendo

    Lendo

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    Bill, A big thread Topic, aren't you glad you started it?
    For an introduction to Spars, I purchased the Jim Marske manual and employed the Beam Buckling formula for the beam fixed at one end and free at the other. These are available on the Internet. I used 6G at 1.5 or did I use 2 - can't remember.
    I remember someone suggesting to include the down ward weight on the wing by the Horizontal Tail to the weight the wings carry.
    I did my calculation every 2 inches along the span, some people do it for every inch. It's a very interesting exercise.
    The whole process is complex, but not difficult.
    George
     
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  18. Feb 12, 2018 #78

    PiperCruisin

    PiperCruisin

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    DeepStall will find this a funny question/observation. Why do we rarely concern ourselves with the connections, especially between the wing and the fuselage (rarely documented in any real detail)? Beams are relatively trivial and structures tend to fail at the joints. Besides, as Billski points out, a bit more positive margin in the spar is not going to cost that much in terms of weight. Better off giving up a bonbons.

    Maybe the connections should be a separate thread. Sorry, tired of hearing about beams.
     
  19. Feb 12, 2018 #79

    Aviator168

    Aviator168

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    I second that. Flap/wing connections and aileron connections.
     
  20. Feb 13, 2018 #80

    wsimpso1

    wsimpso1

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    Anyone can be a critic. All you gotta do is be negative. If you are not interested in a topic, you really do not need to read on it...

    There is a lot of commentary and uninformed talk about spar design. I elected to put out the basics without jargon or much math to help folks with understanding. At a minimum, more folks will be able to sort the garbage from reality on the topic.

    You think that leaves something else to be talked about? Feel free to start a thread talking about attachments and hard points. Heck, if you start from a position of knowledge in both theory and practice, I might even contribute...

    Billski
     
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