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Stress analysis of a simple wing

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Battson

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Is there a simple formula which one can use to analyse the stress within a simple wing, of constant chord, shape, and with zero twist or washout?
Perhaps there is a simplified form of the Schrenk approximation which removes the form factors and rate of twist variables?

I really just want to know how the stress born by the wing varies with distance along the wing. Specifically I am interested in strut-braced wings. I would prefer to refer to an accepted text online, if at all possible.

I have had a hard time finding a credible source of knowledge in this area, short of purchasing texts. I am betting I haven't looked in the right places.
 

Hot Wings

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There is nothing special about a wing. It a structure just like a bridge or a building. They use the same formulas to analyze the various loads, such as bending and torsion.

Before you can do this you need to figure out what loads are that the wing needs to handle. A good online place to start is the LAA's website. Once this is all figured out a copy of Bhrun's Analysis and design of Airplane Structures can be found on the internet in PDF form.

There really is no substitute for buying a few books! There is a sticky here on HBA with some pretty good recommendations. And unfortunately there is nothing 'simple' about this process if it's done well.
 

PTAirco

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Imagine wanting to learn how to design a biplane. In the mid80s. No internet. Nothing in libraries. "Real" engineers scoffing at you. Still, I found enough by digging a lot. You can't do this kind of thing without buying a few books. The internet also makes that part easy, not to mention you can ask questions and find answers.

Which books is the next question and if you do a search here, you'll find lot of recommendations.
 

Floydr92

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Theres no single simple formula, but luckily all the formulae you need are quite simple. Keep everything static, and calculate external forces and reaction forces, so this is the distributed loads on the wing surface (lift and drag), and the reaction forces at the spar root and strut brace. A bit of trig, then for a statically determinate structure all you need to know is the four following 'equations' or statements...
Sum of forces in the X axis equal 0
Sum of forces in the Y axis equal 0
Sum of forces in the Z axis equal 0
Sum of moments equal 0

Very rime consuming and fiddly even for a simple structure. Miss out a negative and every other calculation done after with that data point is wrong.

Hence the easier route, is probably to learn CAD and run a simulation. (Or build a wing and wire up a load of strain gauges). Its just one of those things that as an engineer you should know how to calculate by hand, but in reality you should utilise the tools at your disposal (computer) to save time and eliminate errors.

Edit: as a thought, if you want to calculate by hand i would suggest you first analyse a rib and calculate the forces acting on it which transfer to the spar, so you then add all the X and Y reaction forces to a diagram of a spar and now you are just working with a beam, becomes quite simple.
 
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wsimpso1

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Bhrun is good, but I can do this stuff with Theory of Wing Sections (Abbott and von Doenhoff), Mechanics of Materials (Timoshencko and Gere) and knowing that lift is elliptically distributed. TOWS gets into how the air load is applied distributed along the span, and MOM has a chapter on truss design (a strut braced wing is a simple truss) and chapters covering beam loading, shear and bending moment calculation, beam stresses and deflection. Oh, and Excel. You can do all of this in Excel.

Billski
 

Swampyankee

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Boy, Timoshenko brings back memories: Strength of Materials (I don't have that book -- I sold it; I don't like doing structures) and Theory of Elasticity. That was actually fun. Of course, it wasn't structures.

Calculating stresses is most definitely not trivial. It may be straightforward, but even in the simplest wing, the loading is complex: what is the load distribution in a 35 fps vertical gust? Or for maximum aileron deflection, or for maximum flaps. What is the load distribution tanks full vs tanks empty? Are you reacting the gear loads through the wing? What's the wing's inertial loading in the landing gear's design case sink rate? Will the wing's deflection change the airfoil properties? Do you need to walk on the wing? If you overestimate the stresses, the wing will be a bit heavy; if you underestimate the stresses you may be lucky enough to have visible cracks; else, your estate may get to see film at 11. Worse, you could overestimate some of the stresses and underestimate others and have a wing that is both too heavy and too weak.

This is why I didn't do structures. Structures guys get to explain why the shiny new static test wing failed 20% before it should have.
 

Battson

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Thanks for the references to online materials so far. I will have a look at that tonight, and I appreciate you sharing the knowledge.

I already have the engineering structures text books, materials, etc and the degree to match... I was hoping to avoid having to go back to first principles and calculate it all from scratch, although I can if I want to. So, in the politest way possible, suggesting that approach isn't the help I am looking for :)

In well-explored fields of engineering like structural design, there are always tried and tested assumptions you can apply safely, to save you lots of time doing the math from scratch. That is what I am after. Thanks in advance.
 

autoreply

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Simple. Use max lift and devide that equilly, proportional to wing area. This always overestimates torsion and bending loads.

With a solid skin (alu, composite, wood), it's a safe and conservative assumption that the spar takes all bending loads and the skin all torsional loads, if the moduli are well matched.
A wood spar with a CFRP skin is the best way to trash a structural design though.

With the above assumptions, both torsion and bending will be a bit less than calculated. I'd check for the FWD component of the lift separately. Any solid-skinned airfoil shape can take that bending load, it's LE buckling you want to check, as well as shear buckling of the D-section.
 

wsimpso1

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The reason for calculating the operating envelope and then wing moment and shear diagrams for the significant point in the envelope is so that we can design a structure that will:

Stand up to the loadings;
Be light enough for flight;
Is able to be built.

Jarno gave a huge simplification that will result in the wing being somewhat over specified, but safe. Given that calculations of actual wing loading with deflected ailerons is kind of fussy, rectangular wing with uniformly distributed airloads is not a huge reach and only a little overstated. That assumption allows you to have a uniformly loaded beam to generate your shear and moment diagram around.

Next simplifier is that a strut braced wing is simply supported at the fuselage. Only linear reactions, no moments at the root.

Another simplifier is that there is a place along the wing that minumizes the maximum bending moment. I forget exactly where that is along the semi-span, but it is available or you can derive it. It is based upon eliptical lift distribution. You can go through all of the calculus or break the wing into segments and numerically integrate it. Excel is your friend.

All of this being said, there is no substitute for doing the shear and bending moment calculations and diagrams. Just to help you out some more, aerodynamic pitching moment of the wing accumulates as torsion along the wing in the same manner as the bending moment does if you use a V or double strut. If you instead use a single strut, the torsion accumulates in the same fashion as bending moment does in a cantilever wing.

Have fun.

Billski
 

Swampyankee

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Didn't KR-2 use wood spar with a CFRP skin?
I think they're glass, not carbon.

Carbon is a great reinforcement, but designing in composites is probably harder than designing in aluminum: with composites part of the design process is actually designing the material, as composites tend to be highly anisotropic, so if you want to design a structure that needs to react both bending and torsional loads (like a wing spar ;)), you'll need to have spanwise fibers for the bending and angled fibers for the shear. Take a look at this: Hand Lay-Up GFRP Composite Marine Propeller Blade

Obviously, you also don't want to mold in any of the bolt holes.
 

TFF

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Battson, is this a new project or trying to figure out the margin on the Bearhawk wing?
 

autoreply

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I think they're glass, not carbon.

Carbon is a great reinforcement, but designing in composites is probably harder than designing in aluminum: with composites part of the design process is actually designing the material, as composites tend to be highly anisotropic, so if you want to design a structure that needs to react both bending and torsional loads (like a wing spar ;)), you'll need to have spanwise fibers for the bending and angled fibers for the shear. Take a look at this: Hand Lay-Up GFRP Composite Marine Propeller Blade

Obviously, you also don't want to mold in any of the bolt holes.
It's not always as hard as it's described by some. As long as the structure is straightforward and well designed, you can simply have 45/-45 and 0/90 (or UD) and only use the fibers in that direction for the calculations. So beef shear web up till you have enough 45/-45 to resist shear loads. Beef up spar caps for loads (and max deflection), beef up wing skin (it's probably too thick already for flight loads) for wing torsion and presto.

Spanwise loads, notably with flaps and ailerons deflected can be annoying. There too, if you simply use the 2D local Cl of that airfoil (flap or aileron deflected) you have conservative loads.

Mark Langford uses CF-foam-FG for the wing skin on his KR-2. Seems to work fine.
It's either overweight or understrength. Simply look at ultimate elongation at yield. Either the wood/glass doesn't take much load (and thus is dead weight), or the carbon fails before the rest of the wing...
 

Battson

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Battson, is this a new project or trying to figure out the margin on the Bearhawk wing?
Trying to learn more about the existing BH wing, particularly to learn about how much shear stress and bending it is handling at design limits.
 

Lendo

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Battson, Jim Marske's Carbon Rod Spar Manual has a simple format for Wing loads, but doesn't include the simple 'Cantilevered Beam Buckling formula' easily found on the Internet. I believe this might be what your looking for and worth looking at.
It won't be anything like Billski's 'Geek' Spread-sheets, but is pretty simple to use in Excel. I break my semi span up into 2" sections, I thought I was going to extremes, but some designers go to 1" -I'm led to believe!
George (down under)
 
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