# Question(s) about Steel Tube Fuselage Design

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#### bmcj

##### Well-Known Member
HBA Supporter
BMCJ, although I really don't have a solid feel for what statically indeterminate means, I do recall the term from Ryerson. I also understand that the more members I add, the greater the complexity of load calculations. That in itself may not be a good reason for having fewer frame members, but ultimately, it would be good to have a pretty firm understanding of what each frame member is doing. And I guess that means statically determining each load value and direction.
Sorry if I made it overly complicated. To give you a simple example of statically indeterminate, imagine a block of concrete hanging by three cables, one attached at each end, and the third at the midpoint. You don't know how much weight each cable is supporting. The middle cable might support the entire weight and the ends are slack, or the ends might carry the load and the middle slack, or any combination in between. That is statically indeterminate.

What really happens here is that the cables supporting the load may or may not stretch enough to allow the others to share the load more equally. To make the calculations for this, you now need to know how each cable will stretch.

The good news is that if your structure is strong enough without the extra tubes, then the extra tubes will not hurt your strength, they'll just add more weight and maybe a little more strength.

Bruce

#### Starman

##### Well-Known Member
I have vacilated many times about whether I'd go with the Warren truss (what I affectionately call zig-zag) or just diagonally braced truss with the diags all going the same way. The Renegade biplane has all the side diags oriented as you said, from top to bottom as you progress aftwards, making them all in tension in a hard pull up. Great for positive G's, as this biplane is capable of 10 G's +.

I thought I had some logic for trying a Warren approach, but I'm not sure if there really is an advantage to it. Thanks for the compliment about the 3D models, but Rhino can take most of the credit. I like the software more every time I use it, despite a few axes gaffs.
I don't think it matters whether its a Warren truss or the other way you describe, half of the tubes will be in tension and the other half will be in compression whether they are vertical or not; but being vertical though does make the compression side shorter and therefore stiffer.

#### Tom Kay

##### Well-Known Member
Guys;

I put an update in the Replica Fighters section. With the tube fuselage work I've been fine-tuning, it seemed more specific to that forum, and less appropriate to this one (general questions about fuse frame design).

So, if willing, please have a look there.

Bruce, your example of statically indeterminate is very understandable.

Thanks, Tom.

#### Autodidact

##### Well-Known Member
Some fuselage trusses (these were culled from the Flying and Glider manuals):

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#### Autodidact

##### Well-Known Member
This is where it gets interesting. I saw the fuse truss of the Bristol Bulldog in this months issue of Aeroplane Monthly and noticed that all of its fuselage diagonals are going the "wrong" way. Also, in the first pic of the previous post, one of the rear (near the tail) diagonals of the Gere Sport biplane is also seemingly "wrong".

I can only speculate (one of the great passtimes of the world :gig about the reasons for this: in the Gere Sport, all of the tubes from the seat back rearward are of consistent size (fairly standard practice, I think), i.e., same size longerons and same size for the verticals and diagonals. But the loads on the tubes decrease as you go back so that a diagonal tube that is strong enough in tension near the seat back may also be strong enough to handle a lighter load in compression near the tail. This is only conjecture, though. I don't know what the actual reasoning was.

The Bulldog has all of its diagonals in compression for positve G. It is not welded steel tube; "...high tensile steel strip was rolled into various profiles which were riveted together along their length to form spars, longerons and stringers, internal struts and other components. These were then joined by riveted gusset plates." - Derek James, Areoplane Monthly, March 2010. My only guess here is that the riveted joints were stronger in compression than tension since the tubes can press against one another taking at least some of the stress that would otherwise be withstood solely by the rivets. At least that is the only thing I can think of.

For example, if you produced a joint (maybe silver soldered or something) that was weaker in tension than the actual tubing itself, then you might be better off putting the tube in compression if the joint is weaker in tension than the buckling strength of the tube. There may also be the question of fatigue; if the tubes are crushed together, taking some of the stress off of the rivets, then rivets in single shear might not work loose as easily.

It is my understanding that a properly welded tubing joint is stronger in tension than the tube is, i.e., the tube will fail in tension before the weld does.

Bristol Bulldog:

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#### Autodidact

##### Well-Known Member
Here is the formula for buckling in a long, slender column from Schaum's, Strength of Materials (pull up full size and magnify):

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#### Tom Kay

##### Well-Known Member
Auotdidact;

This is great. Thanks for the examples. I'll study the tube frames a bit closer.

I see lots of similarity between your tube Moment of Inertia calculation and one that I saw on the web a few months ago. But I want to ask, since there appear to be differences, about the "second" moment of inertia. In the other calc, it's just refered to as "Moment of Inertia."

The best way I can show this is to post it. I don't need to ask about the number .78539, as this is a quick way to obtain the area of a circle using diameter squared, rather than using radius (not much time saved, but my Grandpa always used this method in his naval architecture days, A= D squared X .7854).

Also, you probably meant R's not D's, as your arrows refer to radii, just guessing.

So just to clear up, are the two formulae refering to different moments? IE, first, second MOI? Or is there only one MOI that's used in these types of calcs?

I also have similar examples from the same guy about rectangular tubes. Let me know if you need them.

Thanks again, Tom.

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#### Autodidact

##### Well-Known Member
Oops, busted!:nervous: Jeez I screw up so much sometimes I wonder if I know anything at all! The D's are correct, it's my drawing that's wrong. In the formula I posted, diameter is correct, not radius - I should have drawn my tube cross section with diameters indicated not radii. If you were to write the radii^4 as (diameter/two)^4, then since the bottom of the fraction is raised to the fourth power as is the numerator, it will always equal 16 (i.e., 2^4). You can then factor 1/16 out of the terms inside the parenthesis and multiply this 1/16 times 0.7854; or, since 0.7854 equals pi/4 you would have pi/4 times 1/16 which is pi/64 and the terms inside the parenthesis are now diameters^4 instead of radii^4. See, simple , eh? Maybe the pic below will help clarify.

Also, don't get confused about the pi/4 (0.7854) term; it works with radii when calculating the "second moment" and it works with diameters when calculating the area of a circle. It's the calculus used in the derivation of the moment of inertia (second moment) that causes the odd contradiction.

Oh, and the "first moment" (not first moment of inertia) is just a plain moment like a torque (force times distance) only with an element of area times its distance from some point. The terms "second moment" and "moment of inertia" are used interchangably; they mean the same thing. It is called the "second moment" because it is an element of mass or an element of area times its distance^2 from some point. Squaring a term makes it a "second degree" term. In calculus, the element of area, or "da" can be broken down into two elements of length multiplied together, i.e., "da" is actually "dy" times "dx", thats for a rectangular area; for a circular area you use polar coordinates and after you do the integration (just for the proof, you don't have to integrate just to use the formulas) it ends up with the diameters to the fourth power even though it is still defined as the "second moment" or the "moment of inertia". Just take my word for it :grin:!

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#### Tom Kay

##### Well-Known Member
Oh, I'll take your word for it! My calculus is rustier than most of the square nails still left on earth.

Anyway, thanks. I'll keep your examples on file and dust them off when I get brave, although it deosn't look that tough to figure out tube buckling with that example.

Cheers, Tom.

#### bmcj

##### Well-Known Member
HBA Supporter
I've heard it called the Gere Sport, but never the Richard Gere Sport. The designer's name was George Gere. Maybe you have to be an officer and a gentleman to fly it. :gig:

A Google search for Gere Sport should find something.

#### GESchwarz

##### Well-Known Member
Weld material is cast metal thus is relatively brittle and not as strong as the surrounding drawn or extruded material. That is why a good weld joint is designed to maximize weld length with scarf or fish mouth cuts. Never rely on a simple butt joint for a member that is going to experience a lot of tension. The structure should never be designed to cause a weld to have to take bending moments, as the weld will surely tear on the tension side. Gussets are another way to increase weld length and add strength to the joint.

#### Autodidact

##### Well-Known Member
Not agreeing OR disagreeing with Gary as the pics below seem to support contradictory positions; from what I can tell, welding is a broad and complex subject, mysterious and the subject of lots of misunderstanding. I hope to get good enough to weld an aircraft fuselage someday:

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#### GESchwarz

##### Well-Known Member
I don't know what is so contradictory in these photos. All of the failures occured very predictably at the welds. The cracks did not proagate down the centerline of the because that is where the weld material is thickest. In these samples the weld cracked at the weakest point, at the thinest section of weld material.

If you are looking for a crack to follow down the centerline of a weld, you’ll find that sort of failure on very thick joints where the parts being joined are thicker than the weld joint itself.

Another reason a crack may not occur in the weld itself but very near it is due to the geometry of the part which determines where the greatest strain is.

#### Autodidact

##### Well-Known Member
I don't know what is so contradictory in these photos. All of the failures occured very predictably at the welds.
In pic #2, the failure did not occur at the weld - it is at a distance from the weld approx. equal to the with of the weld - the picture shows this very clearly. Was the tube weakened by heat? I have read that brittleness can be taken out of a welded joint by "normalizing" it with additional heating, but I suspect that it is only to a degree and the weld will always be brittle to an extent, since it is as you say, "cast" metal. I have read repeatedly that a properly welded joint is often (there's that mystery again) stronger than the material that is welded together. I agree with you in that a welded tube joint should not be subjected to bending moments; the whole point of a truss seems to be to avoid bending moments in the individual members.

Gary, your earlier statement seemed to suggest that a welded tube joint should not be put in tension. Scarf and fishmouth joints are seen where longerons are extended to the rear with a smaller size tube inserted into the larger forward longeron. On the Tiger Moth, the square tube welded joints are supplemented with gusset plates, but on most round tube welded fuselage trusses there are often (except at wing, tail, landing gear, etc. attach points) no gussets even where the tubing will be subject to tension loads.
Are round tube joints considered strong enough to hold in tension?

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#### GESchwarz

##### Well-Known Member
The only thing "wrong" with a simple butt joint is that the total weld length is so small.

I certainly did not mean to say that welds should not be placed in tension.

The heat-effected zone surrounding the weld is weaker than the uneffected metal.

All forms of joining, whether it be welds, adhesive bonds, rivets, ecetera, are all vulnerable to stress concentrations caused by asymetric loading as in bending and peel. A good designer will avoid placing asymetric loads on his joints.

The crack in your attached photo initiated at the point of greatest strain, which was more nearly perpindicular to the fulcrum of the bend which is the crotch of the joint. This is a case of where the geometry of the part determined where the failure would occur.

#### Tom Kay

##### Well-Known Member
Hi;

I have another design-related tube fuselage question, but I'll just add it to this thread, instead of starting another one.

I am curious if curved fuselage longeron tubes are weaker (mostly in compression) than straight longeron tubes.

Please have a look at the sketch and also make the following assumptions:

1. Tubes are 4130 welded.

2. Assume that all cross pieces and diagonals are there. I just left them off to uncomplicate the drawing.

3. Assume the tube section that's circled in red is in compression. This would mean it's the lower longeron, during a hard pull up.

In many ways, the curved fuselage looks nicer, and may conform more closely to a streamlined final shape. But, I wonder if it's riskier because each little section of curved longeron is already curved, and therefore already artificially "buckled" even before a compressive load is applied.

The straight tubes haven't got any pre-compression curvature built-in, so maybe they would withstand more compression before they even approach buckling.

Bottom line question is, is one design more accepted in the homebuilt world than the other?

Bonus question: Is one design easier to make than the other, when working with steel tubing? With the wood Murphy Renegade fuselage mockup that I made (3/4" square pine longerons) it was very easy to curve them to make the rear half like the left drawing, but is it easy to get that much smooth, gradual curve out of steel without bending it around some huge mandrel?

If this were your project, which approach would you favour, and why?

Thanks, Tom.

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#### GESchwarz

##### Well-Known Member
I also have curved longerons in my steel tube fuselage. I was able to get just the curve I wanted simply by putting the tube in the table vice with the jaws open just a little wider than the diameter of the tube itself. I then put the tube between the jaws where I wanted the bend to start and began pulling the tube a little at a time, each time moving the tube through the vice a little bit to bend some more. After a few pulls on the tube, lay the tube over the curve template to see how you are conforming to the desired curve. I wouldn't use this method for tight radius curves but for a large radius curve like a fuselage longeron, it works real nice.

#### orion

##### Well-Known Member
Depends on your covering. If for instance you were covering with a molded shape then making a curved substructure is not necessary and just adds work. Precise conformity is not necessarily a requirement since the attachment of said shell will be through brackets, which can be designed, adjusted and mounted as needed to meet the shell's inner surface.

If on the other hand you were covering with a simpler material like a thin ply, sheet metal or fabric and were trying to achieve a particular shape then yes, the curved substructure makes more sense. But now you have two issues to consider: First, the curved shape is inherently less stable that a straight tube so you'll need to use curved column design requirements. This can get a bit tricky but is doable.

Second, you'll need to figure out how you're going to put that curve into that part - after all, it is a steel tube. You can either roll it or you can simply force it into a jig (assuming the walls are thin enough to allow you to do that) and weld it in place. But if you force it into the jig you are pre-stressing the tube, which can cause problems down the road. The severity of this however is your own call - I know some designers who adamantly oppose this kind of shaping (they prefer to roll it to the proper shape first), and some who don't think it's all that big a deal, especially if in a lightly loaded part of the weldment.

#### BBerson

##### Light Plane Philosopher
HBA Supporter
A tube can easily be forced into a curve and held in the jig. But when welded the weld heat will relax the stress in the weld area and the longeron will straighten itself somewhat between welds.

#### GarandOwner

##### Well-Known Member
........... But if you force it into the jig you are pre-stressing the tube, which can cause problems down the road. The severity of this however is your own call - I know some designers who adamantly oppose this kind of shaping (they prefer to roll it to the proper shape first), and some who don't think it's all that big a deal, especially if in a lightly loaded part of the weldment.

Actually we do this quite frequently, it is a common practice and not really a hard thing to design for. When you plasticly deform something (permanent deformation) they material has already yielded. So its strength is greatly deminished. What you want is too aleviate these internal stresses. Hot forming is best way to do this, because the stresses are releaved as your part cools (normalization). If you cold form your part, you can "simply" heat treat it. By heating your part above the recrystallization temperature of the metal, and air cooling (normalization) the crystaline structure of the metal will change and your part will keep its deformed shape, but will no longer be stressed.