I am looking at designing a wing for a light airplane. I am planning on using +6/-4 G load factors. Initially I am assuming a box beam centered on the aerodynamic centre of the wing. Later. I may look at a front I beam spar with a D-cell leading edge and a front longeron for taking torsional and drag loads. In any case, I am assuming a single main spar that would take all loads and at most an aft, auxilliary spar to mount control surfaces and possible flaps to. I am considering a single spar wing in order to save weight. I am applying the above load factors to the wing lift loads and to the chordwise vectors of the lift loads in the PHAA, PLAA, NHAA ans NLAA conditions. Are there any maneuvering load factors that are normally applied to wing drag loads or to the wing pitching moment that is produced by the wings camber and lift production? Also, when combining bending, shear and torsional loads which occur simultaneously, is an interaction formula that divides actual bending, shear and torsional stresses by their corresponding allowable stresses normally used, the sum of these adding up to a value less than or equal to one? What is a good source of information on the design of "thin shell" torsion boxes (as used in a D-cell) built of wood? It should detail proper design practices, allowable shear loads, effective widths of skin between flanges, etc.

Yours is far from a simple question to answer in this type of limited format. I'll start from the bottom and try to be brief. Regarding texts, there are two classics which, although written many years ago, are still the best and most understandable around. The first is "Aircraft Structures" by Peery (see if you can find the original version, not the rewritten one) and the second is "Design of Aircraft Structures" by Bruhn (I don't have my copy of the latter in front of me so I'm not 100% sure that that is the exact title). Both are relatively advanced educational texts with plenty of examples and worked out problems. I have used both as reference often, even though I've now been doing this for well over twenty years. With today's programing capabilities one can take many of the worked out problems and write pretty detailed programs in packages like MathCAD, to make trade studies quick and configuration changes simple, with only simple modifications of variable values. As far as the loading is concerned, as with many similar static-linear problems, the stresses are additive. If one wished to do so, one could calculate the stress values in any part of the structure for any critical loading condition and then, once you establish magnitude and direction, you can combine the axial and shear stresses using techniques similar to those of a simple Mohr's Circle. Today most of the work we do is done through FEA so the manual methods are used only to check and verify the modeling and its output, however the manual techniques are time tested and proven. Critical attention must be paid to areas such as those evidenced in bolted connections since here the yield point set up in the material due to the stress concetrations of the bolt (or rivet) holes may be the driving criteria, rather than the ultimate strength of the part in that section. In our work we tend to check primarily the worst case conditions. For a normal wing, this is a combination of loading that represents the ultimate load, along with the loads encountered at Vne. This includes drag (times a safety load factor), pitching moment of the wing panel at the Vne condition, plus the additional pitching moment and drag that is created by a full deflection of the control surface(s) at the Vne condition. Other conditions (such as bolted or riveted areas as mentioned above) are checked as needed. You should also examine how each of those loads affects the wing seperately since the different load cases will affect the fatigue life of the structure in a slightly different manner. Fatigue is cumulative and is not necessarily taken care of simply by the standard load factors. Here is where you start analyzing the wing's seperate components (the most loaded ones). Also, don't forget gust loading - this is very important and you'd be surprised how many designers forget this step. Keep in mind that a wing can have several potential failure modes including not only the basic material failure (either complete or yield) but also panel or beam buckling (structural instability), fatigue (embrittlement) and stress concetration yielding or cracking. Some of these can be simply taken care of by proper design techniques, others need to be analyzed for seperately and specifically.

Bill: Thanks for your informative reply. I have Bruhn (1949, revised 1950) and Peery (1950). I also have several other smilar textbooks. I tend to buy th eoldre ones because they are the only ones that have wood design values and light aluminum structures were pretty much optimized in the 1930's. They were uncertain, at that time, however about how to handle combined loadings. That's why I was wondering if, these days, Fb actual/Fb allowable+Vactual/Vallowable+Tshear actual'Tshear allowable <=1 was an acceptable formula to use? I will use a safety factor of 1.5 for all loads as appropriate to be well below yield stresses, wood modulus stresses, etc. I also will apply a generous +and- load factor to the appropriate loads. As I see it lift related loads are usually factored and drag and wing pitching moment loads are not. I wanted some confirmation of that. Bruhn and Peery tend to "bury" the maneuvering load factors in "airplane coefficients" etc. and Bruhn's loading calc's. near the end of the book are a bit elaborate for a rectangular wing for a light plane. He made his example for many stations to account for tapered or elliptical wings. Many of the spaces in his tables become zero's for a simple straight wing, etc. I also think that it would be just as effective to find the loads for the critical load cases and just multiply them by 6 (G's) and ad additional safety factor to get the "design" loads (to make sure your structure doesn't yield or fail in actual use. I was going to start by looking at a wood structure which doesn't "fatigue" as metal ones do. The metal connections and fasteners though would need to be looked at for that. Later I was going to analyze an aluminum structure. I would then choose the one that seemed lightest, safest and most practical to build overall. With some personal judgement built in. I also would look at gust loads because this is a lightly loaded wing for an ultralight. Are pitching moments ever factored (above the ordinary 1.5 safety factor) dur to gust loads or for any other reason. How commonly is this done? This would be a cantilever wing with a single box spar for all loads as an initial assumption. Thanks, BDD

Regarding your question - I have never seen that particular equation however, that does not mean its inapplicable, it's just that I've never done the work in that form. Maybe someone else can pipe in here. Regarding the loading, in virtually all cases now we design to ultimate. If you look at the requirements set forth by the FARs, and their history of evolution, you'll see that the 1.5 factor was selected early on since that was the ratio of yield to ultimate strength for several steel materials used early on. Today though, that factor and reasoning is no longer applicable since many of our higher strength materials have a ratio that is much smaller than that. Therefore, if you design to ultimate, you'll be virtually guaranteed that nothing will yield at the limit load condition. You of course need to be familiar with the materials you are using to make sure that condition holds. That argument holds especially for the case of composites, where there is really no actual yield point. However, for laminate structures the FARs require a factor of 2.0 to account for the manufacturing uncertainties and the somewhat spread out nature of the material property statistical database. I have heard that with today's techniques and materials (there is now an FAA approaved material property database for glass and graphite) the higher factor requirement may be removed, however to date I've had no confirmation of this. Regarding the gust loading, that applies primarily to the normal loads imposed upon the wing. Since the pattern of load (chordwise) is relatively consistent irregardless of the load, the pitching moment tends to be unaffected. This of course is not actually true since there are variations due to localized flow effects, but for design purposes I have never seen the moment modified beyond the standard safety facors and the Vne condition. If I were to take a stab at your design configuration, I think that you'll find that the lightest structure will most likely be out of aluminum. I would probably guess that a light and efficient typical "I" beam spar, or similar, will deliver the best performance. Couple this with an aluminum skin covered "D" section and a Warren Truss arrangement of the ribs between the main and aft spars. Cover the whole thing in fabric or Mylar. I've done only a little bit of design work with wood, only because there does not seem to be much call for it. Most folks that start out that way seem to find that quality spar material is hard to find and tends to be quite pricey. The ones I've talked to seem to go either the way of aluminum, or bite the bullet and do the extra work required to go the way of composites.