Some practical considerations for selecting tubing
for a recumbent bicycle frame.

By Mark Stonich

In this article, I'll be refering to 4130. This is the alloy number for commonly available Chrome-Molebdenum steel. The most likely source for this tubing is aircraft supply houses. Aircraft grade 4130 is seamless drawn and supplied Condition "N" (normalized).

I don't want to make it sound as though round tube frames are terribly hard to build. But, if you are thinking about building your first frame, using square tubes could make your life much simpler, giving you that much less to worry about while you're on the steep part of the learning curve. If you are building a commuter/beater, where a little extra weight doesn't matter, I think it's great. Square tubes can save a LOT of work and bother.

Advantages:

The trickiest mitering problem, with round tubes, is the difficulty of ensuring that miters, at both ends of a tube, are parallel or perpendicular to one another. With square tubing, this is pretty hard to screw up. The miter for joining 2 straight tubes, or joining the end of a round tube to the side of a square one is a simple straight cut. Joining square to round is almost as easy. First, a straight cut parallel to the axis of the round tube, and two sides are done. Then cut scrap piece of round tubing off at the angle of intersection. Now use the end of the tube, which is now elliptical, to scribe a line on the other two sides of the square. Remember, a perfectly straight, square cut isn't all that easy either.

When welding or brazing a round-to-round tubing joint, the relationship of the puddle to gravity, the angle of your torch, and your line of sight, is constantly changing. The amount of heat required varies constantly around the joint. If both tubes are square, you do 4 nice straight passes.

Jigging is often as simple as C-clamping 2 square tubes to a flat surface. And, the angle between two square tubes is easier to measure or set than between round tubes.

Positioning most braze-ons is easier, although some are designed to follow the curvature of a round tube

If you don't mind clamping directly on paint, seat mounting can be much easier with square.

Disadvantages:


Slightly less rigid for a given weight, Or, more likely, slightly heavier for a given rigidity.

You can't grab it in a Park stand, which gets to be a real pain after a few years. On my next commuter I may use a round top tube for that reason. It's also difficult to hold at odd angles for brazing or welding. Of course this is rarely a problem when welding square.

The corners of a square top tube eventually wear thru the plastic coating on bumper rack type supports, and paint on these corners seems vulnerable.

Availability-Sizes; In 4130 tubing you can get 0.035" wall square tubing up to 1". Dillsberg Aeroplane Works carries 1 1/8" in 0.049", 1 1/4" in 0.058" and 2" in 0.065" but in these sizes I think 4130 is overkill for most single recumbent designs. 4130 square tubing is about 30-40% more expensive than round tubing of equal weight.

0.035" wall thickness 4130 round tubing is available, from Dillsberg, as large as 2", but I know of no source of square 0.035" 4130 larger than 1". This rules out a really lightweight, steel, single tube frame made from square. Garelick's usually has 1" x 0.065" square mild steel in stock, but 0.049" x 1" is only occasionally available there. You might also try Discount Steel

Mild Steel or Chrome Moly?

A typical 63" wheelbase recumbent might have a 0.035" x 1 1/4" x 28" bottom tube. A 0.035" x 1 1/8" x 36" top tube and 3 - 0.035" x 1 1/8" x 8" tubes for down tube, derrailleur tube and "seat tube". For a total of 3.16 lbs, and cost about $2.80/Ft. replacing them all with 1" x 0.049" square mild steel you would end up with 4.64 lbs but at a cost of less than $3 total.

Mild steel is much more tolerant of overheating than 4130. One less worry for the novice

On my first 'bent, the yellow commuter, I used 0.049" x 1" mild steel from Garelick's for the top and bottom tubes. Lighter 4130 tubing would have cost more, been harder to work with and would probably have rusted thru by now. On this bike and Eli's commuter I used heat to put a slight upward bow in the bottom tube. Resistance to flex from pedalling forces seems unaffected, but ride is much improved.

Some Design Considerations


For a "conventional" recumbent with top and bottom tubes, and "seat" and derrailleur tubes, I think it's safe to generalize that pedalling forces deflect tubes in a combination of bending and torsion. The riders weight deflects tubes in bending and tension or compression. Because of this, multitube frames capable of resisting pedalling forces are overbuilt for supporting the riders weight. (If you still think a vertically stiff frame is a good thing, we gotta talk) You can reduce vertical stiffness, by keeping the top and bottom tubes close together, or curving top or buttom tubes and/or rear stays. Mono-tube frames are loaded in bending for both supporting the riders weight and resisting pedalling forces. With a symetrical (round or square) tube such a frame is overbuilt against pedalling forces. Not really a bad thing, just a little heavier than necessary. The optimum then seems to be using an ovalized or rectangular tube for mono-tube frames.

I'm not discussing space frames here as the math is too complex for me. They have theoretical advantages, in that all members are supposedly loaded only in tension or compression. But, they seem to have a high failure rate. John thinks this is due to stress concentrations (perhaps due to procedures or design or both), no post-weld stress relief and great quality, but very brittle materials.
I think that a bike is so light already, that to get any weight savings from a space frame you have to use very small and/or very thin tubes. You can't seem to eliminate all bending loads, which overloads the small tubes at the joints. Moultons seem well triangulated and durable, but I don't think the frame is especially light.

Tubing Comparisons

There is little empirical data out there about the magnitude of the forces that act on the tubes in a recumbent. However, given John's formulas, one can calculate the stiffness of tubes in an existing frame, for comparison purposes. Another use for the formulas is to determine whether a tube you already own is an acceptable replacement for the one you really want, which has been on back order for weeks. Jane's recumbent has a 33" x 1" x 0.035" round top tube and a 26" x 1 1/4" x 0.028" round bottom tube. Fairly light, but my son Matt finds it adequately rigid, and I'd wager not many of us push the pedals quite as hard as he does. I want to calculate whether a similar frame, using 1" x 0.035" square for both, would be at least as stiff against pedalling forces.

Using John's formulas
These formulas not only help us compare the stiffness of Round vs Square. We can use them to compare two round tubes. If I understand how this all works, resistanse to bending is in direct proportion to moment of inertia. Same with torsion in a symetrical tube (ie. round or square but not oval or rectangular). Resistance to compression or tension is in direct proportion to cross sectional area, so playing with shapes or diameters doesn't change anything here.

Weight in Lbs per foot (steel)
1" x 0.035" round 0.360 Lbs/ft
1" x 0.035" square 0.459 Lbs/ft
1.25" x 0.028" round 0.365 Lbs/ft

Formulas
moment of inertia, round tube = (pi/64)* (D^4 - d^4) moment of inertia, square tube = (1/12)* (D^4 - d^4)
pi = 3.14159

The top tube is Case 1 vs 2
round 3.1416/64 (1.00^4 - 0.93^4) = .01237 square 1/12 (1.00^4 - 0.93^4)= .02000

.02000/.01237=1.697 so the square tube is over 69% more rigid (which surprised the heck out of me) but only about 28% heavier.

The bottom tube is similar to Case 1 vs 4 round 3.1416/64 (1.25^4 - 1.194^4) = 0.02007 square 1/12 (1.00^4 - 0.93^4)= .02000

This time the square tube is less than 1% less rigid, yet is about 26% heavier

Therefore: If I copied Jane's bike in 1" x 0.035" sq., rigidity wouldn't suffer, but weight would increase by 0.474 lbs.

Comparing the two round tubes is like Case 3 vs 4 (same weight, 25% larger diameter) The larger diameter thin wall round tube is 70% stiffer yet only abt. 2% heavier. Most impressive. This may explain why Roger Sperling's frame hasn't failed. Roger is one of our "Gravitationally Challenged" riders. Yet his recumbent has 1 1/4" x 0.028" round, mild steel, top and bottom tubes. While mild steel has a lower yield strength, the rigidity of all steels is about the same. Roger's frame is so rigid that it probably hasn't flexed anywhere near the yield point of mild steel. However, thin walled mild steel dents fairly easily, and the top tube of a recumbent is under a lot of compression. One good sized ding in Roger's top tube, and you could have an example of John's "Pop Can" anology.
John mentioned that, traditionally, a ratio of 1/50 of thickness to OD has been the suggested minimum to avoid local buckling. I've never seen this 1/50 related to the quality of the steel. I think it should be. I can get 0.035 x 2.00 in 4130 for a ratio of 1/57. In mild steel I could probably dent this with my thumbs. Aermet100, when used for bikes, comes in 0.020" x 1.25" for a ratio of 1/62.5

Conclusions
Square can offer a strength to weight advantage only where you are limited in the width of your tube. My prefered seat mounting method uses an extrusion with an inside width of only 1.065". So, if I needed more stiffness than I get from a 1" x 0.035" round top tube, (which I don't) square would be the way to go.

Unless you are building a no-compromise performance machine, practical considerations may outweigh theoretical ones.

Don't let the math get you in trouble. 1 1/8" x 0.028" round is 17% stiffer than 1" x 0.035" round, but only 91% as heavy. However, are you ready to build a frame of such thin material? Localized overheating of 4130 is never a good thing. If you want to try, I have a stockpile of 1 1/4" & 1 1/8" x 0.028" round mild steel, for practice joints. Let me know if you want some.

Tubing sources
Dillsberg Aeroplane Works (717) 432-4589
114 Sawmill Rd. Dillsberg, PA 17019

Garelick Steel Co.
1900 N 2nd St Mpls MN   (612) 521- 8857

Discount Steel
2700 N 2nd St Mpls MN   (612) 522-5956

Theoretical Considerations By John Zabrieski 1995
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