Biplane Top Wing Structure 2

[Dick40]

Retired EE, EAA Chapter member and Zenaire Zodiac pilot is struggling with top wing support's static/dynamic analysis even with my references: "Stress without Tears" by T. Rhodes and "Engineering Mechanics" by R.C. Hibbler.

My project involves the elimination of the center section cabane supports (connecting top wing and fuselage) on a biplane and only using outboard inter-wing supports
(I'll call them struts).

Current sticky point is maybe best represented by
a simple mental sketch: top and bottom wings are horizontal lines seperated near outboard ends with vertical lines representing struts. Assume all 90 degree angles for simplicity. Fuselage is at center of lower wing. Top wing contribute slightly more lift.

Finally the question:: if wing loading and total weight are known, how do I calculate the tensile or compression force on the struts? My abilities currently involve x-y force summations and taking moments. I can draw the free body diagram of either top or botom wing but stumbling on a combined drawing??

Thanks, Dick

 

[insideman]

Trying to eliminate the center section struts opens a real can of worms.

Make a free body diagram showing the front view. So many pounds for the load from the fuselage. Apportion the lift from the two wings. Figure out the strut loads. Make bending moment diagrams for both wings. Now do this for all critical flight regimes and see where it leads you.

I think you will find that the bending moments fro the top wing are simply too high.

 

[Dick40]

Thanks for your comments, old guy here needs all the help he can get <G>.

<Trying to eliminate the center section struts opens a real can of worms>---Don't I know it! Been trying for months to resolve the free body diagram. I can do free body and calculations on a low mono-wing but have a problem with the biplane free body diagram in the strut area.

My approach todate has been to take either the top or bottom wing as a seperate freebody for a specific flight regime and calculate the force on a strut. Then take the vertically opposite wing as a free body and calculate it's strut force. My question is whether to add the resultant forces or just use one value for my &quot;sizing&quot; efforts on the
strut??

Someplace in my studies, I ran across a way to analyse
the tail section of a tube fuselage as a simple truss
and one of the steps involved keeping a magnitude but reversing the direction at a particular point/joint.

I'm leaning towards considering the greater force from whichever wing rather than the combined force for my strut &quot;sizing&quot; efforts. Am I on the right track or what can I do to get on it?

Dick

PS--Regarding <bending moments from the top wing are simply too high>; this is a new design and the spar will be sized to handle them rather than just trying to use an existing biplane top wing spar. At this moment I don't foresee a problem.

 

[i278]

Just wondering...

Is this project an academic exercise, or is this something you're planning on building? If this is a proposed design, what are trying to gain from the removal of the cabane struts? Does it interfere with some other aspect of your configuration?

I haven't figured any numbers (but I'm sure I'll be spending my evening calculator-in-hand), but I have a strong feeling that you'll be more than losing the structural advantage a biplane has over a fully cantilevered monoplane.

If this comes across as overly negative, I don't mean to be; it's always good to make sure you actually need something before adding it 'because everyone else has'.

I'm sure that with careful design from the outset this configuration could be (and probably has been) made to work, but most often aircraft structural design is less about making it strong enough and more about not eating up more useful load than necessary to keep it strong enough.

If you're looking to add to your library, I'd recommend 'Design of Light Aircraft' by Richard Hiscocks. It's a good text to give you a grounding in loads determination and standard good practices in light aircraft design. It's too light on the theory for large work, and it won't help you resolve the structure you have, but it's written with the technically-competent, home-building non-professional in mind. It'll get you thinking in the right directions to successfully complete your project.

Regards

 

[Dick40]

Thanks but my project is not an academic exercise but a three year evolution towards a definitive goal.

Taking into consideration; my background, manual skills, plane building experience, finances, available time/materials/engine along with my personal preference led me to the following criteria::::

100 mph cruise, 60 hp engine, low drag, semi-monocoque, light weight, aluminum, single seat, canopied BIPLANE without a center-section cabane top wing support structure (ie: wings connected with outboard near vertical struts only)!

Every time I solicite help from a group, usually general theory or lot's of &quot;reasons why it won't work&quot; are offered.

I'm just seeking some help with free body diagrams, summation of forces and moments since college was 40 years ago <G>. Perhaps someone would like to communicate and help me offlist.

Thanks, Dick
rwripperxyz@prodigy.net (remove xyz)

 

[i278]

Fair enough, I doubt that there's been a plane ever built where the configuration wasn't strongly influenced by someone's personal preference.

So, here's what I'd sketch out for a first order sizing approximation: (I don't know where you're at with your analysis or research, so forgive me if I go over painfully obvious stuff)

I'm sure you've already figured your total lift requirement (Weight times maximum load factor). Add 50% for a minimum safety factor and then add 5% for downward horizontal tail lift. Take 60% of that total lift force and distribute it evenly along the entire upper wing span.

Consider the upper wing separately, ignoring struts and lower wing. Assume the wing is simply-supported (at the strut locations) and get your reactions. The wing should (with your references) be straightforward to solve for bending and shear.

If you have located your struts somewhat inboard of the tip, you may have noticed that the maximum bending moment at the center-span is lower than it would be if the struts were right at the tips. If moving the struts inboard is an option for you, you will be able to find an optimum point along the span where your spar bending moments are a minimum. Probably a good idea to keep things light.

On to the struts. The upper wing reaction loads are the strut tension loads. If that seems a little odd intuitively, our frame of reference is that the struts are fixed to the lower wing; so they just sit there on the lower wing until the upper wing pulls up on them. The lower wing resists until equilibrium is reached. Hope that makes sense.

Now the trick with the struts is that although we assumed the wing to strut connection was pinned as far as the wing is concerned, in fact the connection will have to be rigid (able to transfer moment). Obviously, if the top and bottom of the strut were pinned, the upper wing would be free to flop side-to-side. So, go back to the FBD of the upper wing and now sum moments about the strut attach point, as though the point were fixed. Take that moment and apply it to the upper end of the strut (along with the tension). Now that you've brought over that moment, assume the strut is simply-supported and find the reactions at the lower end. Your references should allow you to now solve the strut beam for bending, shear, tension, and compression.

The lower wing is now approached in a similar manner. Apply the remaining 40% lift evenly along the entire lower span, including the fuselage. (so, yes, the fuselage picks up that load directly and you don't need to worry about it right now) Once again, we transfer the strut reaction loads over to the wing as point loads, and assume that the connection is rigid just long enough the transfer any moment at the end of the strut over to the lower wing as a point moment. The wing is then analyzed as a cantilevered beam with a distributed load, a point load, and a point moment. Once again, this should be a reasonable task.

A couple things to keep in mind:

1. This is exactly what I called it: a first order approximation. This is sufficient to start sizing out structure so that you can begin the long task of refining your aerodynamics assessment, your loads calculations, and your structure.

2. The wing loading we assumed for this is not accurate. You'll need to find another source to figure the actual loads distribution, that's why I had recommended 'Design of Light Aircraft' above. Anything that presents Shrenk's approximate method, though, will be sufficient--as long as it specifically addresses biplane lift.

3. This only covers one possible load case. This work will have to be redone for every potentially critical case. Also note that the load case that results in the highest loads for one component (the 'critical case' or 'design case' for that component) will most likely not be the design case for other components.

4. I have neglected wing and strut weight in this example, mostly because at this point we have no idea what they weigh. For loads during aerial maneuvers this is often a conservative approximation, but during load cases like a hard landing, nearly all the load is caused by the mass of components being decelerated.

5. Don't forget that vertical loads are not the only ones that need considering. There are both fore and aft loads, as well as torsional ones. Neither are small enough that they can be neglected.

I'm not going to try to convince you to change your proposed configuration, but I think that when you start working the numbers and gain a sense of what are the prime drivers of your stress distributions, you'll definitely gain an appreciation of why other designers would shy away from removing those cabane struts!

I also encourage you to build your collection of reference material (although it sounds as though you're well on your way), and I'm sure you've noticed that the EAA publishes a lot of good stuff geared toward the competent-though-inexperienced homebuilder.

I hope this is helpful, it's off the top of my head so others may be able to point out errors or better methods.

I wish you success in your project.

Regards

 

[Dick40]

Now that is a great reply!! Thanks.

Before I disappear for a couple of weeks now digesting this, let me shed a little more light on my efforts todate
<G>.

My first order approximation attempt has lasted a very unproductive year probably due to a poor grounding in Statics/Strength of Materials and a lack of a definitive method to approach those darn struts. Yesterday I did find a 1943 reference text with an example of strut/wire bracing/cabane calculations buuut haven't been able to figure out the unshown calculation steps. What the authors think is obvious, forces me back to that old college text once again. Alas to no avail however.

Currently some of my initial (more than likely subject to later revision) assumptions are: do structural first then approach aerodynamics, top overhangs bottom wing, zero stagger, identical chords, perpendicular struts (actually probably will be canted outwards in later calculations for transverse strength), top wing provides 54% of lift, 800# gross, single wing panel construction weight around 35#, upward acceleration of 4 G's.

I hadn't considered a safety factor or tail lift factor yet. Good point however. In my mind, the 800# gross and 4 g's allow me to use the existing spar configuration from a proven and flying, lighter-grossed plane stressed at +/-6 g's (upon which I'm basing my design). After almost two years of flip-flopping back and forth between different design configurations (for which I bought plans and studied) while attempting comparison/eyeball engineering, popular demand forced me into my present more analytical approach.

Not believing I have the smarts or patience to design totally from scratch, my approach is to take an existing low wing and make it into a biplane. Please no hate mail .

Besides my shelf full, I have access to a great library
with many historical texts and published magazines where I spend some time.

Off to sharpen my pencil, Dick

 

[i278]

So am I right in guessing that you're trying to avoid cabane struts so that you can use the fuselage design unaltered? (i.e. not adding structural pickup points for the struts?)

I don't know the specifics of the design you're working with, of course, but I would suspect that, in general terms, you'll find that you won't be able to use the lower wing spar configuration as designed. If you're only increasing the gross weight by the same factor as you're reducing the load factor (i.e. the orignal design MGW was 550 lb), then indeed the total load on the wing stays the same. However, now you're taking 60-ish percent of the load that used to be distributed along the wing and concentrating it way outboard, wherever the strut is. This will increase bending loads at the wing root.

Unless you're shortening the span to keep the wing area roughly the same. With a shortened lower wing, even though you're putting a concentrated load outboard on the wing, it may be close enough to where the resolved load used to be for the original monoplane wing. Then it may all work out. (Am I making any sense at all?)

Needless to say, don't assume your existing lower wing is adequate; create bending and shear diagrams for both the original and proposed designs. If the proposed design will have higher loads (stresses) than the original, you'll have to look at reinforcing the affected areas to take the increase.

Also, if you calculate that wing root bending will increase, you'll have to look very critically at the wing-to-fuselage connection. If it is the type that takes the bending moment out of the wing and transfers it through the fuselage to the other wing, obviously that structure will have to be strengthened accordingly. If, on the other hand, the mount only takes shear from the wing and leaves bending contained in the wing structure, you'll probably be okay.

One more thing: don't forget to check gust loads, especially if your minimum possible wing loading is going to decrease from the original design. Lighter wing loading will increase accelerations due to gusts.

As you mentioned: a real can of worms. Once again, good luck.

Regards

 

[Dick40]

Help, help, help. Weather is great for flying and I'm sitting here tearing out my remaining hair trying to get a moment diagram constructed for my top wing. Just going in circles and have no one to check me (hint-hint-hint).

Let me defer answering your last helpful email and
assuming I've got you feeling sorry for me, here's the currently frustrating situation.

Top wing unformily loaded at 26#/ft. with struts spaced at 10ft apart and inboard of wing tips by 3 ft. Viewed straight on, I've arbitarily identified the folowing points:
(a) is left wing tip, (b) is left strut, (c) is midspan of top wing, (d) is right strut and (e) is right wing tip.

Using your advice, I started with a uniformily loaded, simply supported (at the struts) wing with no overhang. Therefore as defined above, (a) and (b) are the same as are (d) and (e). Strut reactions were found to be 208# from [26#/ft x 16ft]/2. Summing Fy (shear) and M (moment) at an arbitary section between (c) and (d), the expected straight line shear curve with max values of +208# at (a) and -208 at (e) with zero at midspan (c) and max moment at parabolic curve midspan of 832#ft. If this is incorrect I'm even more goofed up then I realize. Is it right?

Then I tried to do the same with the wing tips outboard the struts! ie: overhang. After many sectioning attempts that just didn't work out, for whatever reason,I expected curve and values as follows: shear graph with a diagonal line going down from zero at the left (a) to a negative to (b). A positve diagonal at (b) going down thru zero at (c) midspan to a negative at (d). Another positive to zero tween (d) and (e). Couldn't even guess what M graph would be <G>.

My last attempt was: sectioning at distance (x) [from (a) to a point tween (c) & (d) yielded following equations;
shear,V =416-26x and M =-13xx +416x -3328. Since I've section at a lot of differents points, I obviously don't understand something??? I even tried to add up sectioning results at (b), (c) and (d) to no avail.

I've read and reread the applicable parts of my texts. I really don't want to have to sign up at some junior college
for a refresher course.

Help, Dick
PS If this is going into too much detail for this forum, just let me know (nicely <G>).

 

[Dick40]

Hold the help! Found another text that appears to clarify my problem. (hopefully) Thanks, Dick

 

[Dick40]

Okay, I've got the support reactions at the top wing struts and shears and bending forces for the top wing.

But don't understand the following steps:::
[[ So, go back to the FBD of the upper wing and now sum moments about the strut attach point, as though the point were fixed.]]---I did the bending moments about the wing tips. Am I now to take moments about both struts and seperately??

[[Take that moment and apply it to the upper end of the strut (along with the tension). Now that you've brought over that moment, assume the strut is simply-supported and find the reactions at the lower end. Your references should allow you to now solve the strut beam for bending, shear, tension, and compression.]]--Am I somehow taking the vertical strut and rotating it 90* so as to have a simple beam??

Dick

 

[i278]

<Am I now to take moments about both struts and seperately??>

Yes. You'll have the lift on the 3 ft outboard of the strut cancel the moment of the lift on the 3 ft immediately inboard of the strut. So, figure out your reaction moments (at the struts) using only the inboard 4 ft of span loaded, to make things a little easier. Note that with a more realistic span loading this doesn't work out so nicely, and you'd have to look at the entire loading along the span.

<Am I somehow taking the vertical strut and rotating it 90* so as to have a simple beam??>

You bet. Orient it however you want, it's still just a simply supported beam under tension and bending. You can draw your FBD of it however you can best keep track of force and moment directions.

Cheers

 

[airplanenut]

You need them (cabanes)- it is that easy.