Why aren’t bicycles made with small i-beams?
Doesn’t an i-section give you the greatest strength/weight ratio?
Perhaps because the loading is at the ends of the members, rather than along their lengths?
Tubes would have at least two advantages:
(1) Resist deformation in all directions.
(2) No sharp edges for when parts of the cyclist’s body hit the cycle.
(3) Expedite fabrication, assembly, and design.
I’m not sure an I-beam has a greater strength to weight ratio than a round tube, but even if it does, strength isn’t the only concern here. The proper amount of stiffness (too stiff is not desirable) is a key factor. Fabrication techniques, particularly joints, may also weigh in significantly.
I find it hard to imagine any less material going into a bicycle frame than we already have with butted aluminum tube frames, which some find too stiff already. I think making a frame from aluminum I-beams would increase the weight dramatically, and offer no gain in performance.
Another thing. Even in accidents, frames don’t generally break or deform along the tube. Rather, as the OP suspected, they usually fail at the joints, i.e., the welds. At least this has been my experience and that of those with whom I have chatted about frame failures over the years.
God, I can only imagine the bruises…
I-beams are very stiff (per amount of material used) in one direction, but not so hot in the other. I’m no expert in bicycle design, so I really couldn’t tell you what is desirable and what’s not in terms of directional stiffness properties.
Not an optimal cite, I realize, but here’s what the wikipedia entry has to say: I-beams:
Note that a tube is the best compromise shape for dealing with bending in any direction. This gibes with my memory from doing the math for this stuff back in my materials classes ages ago, but don’t have time right now to replicate it.
Sounds similar to the Kirk Precision frames which were made of magnesium.
These had an I-shaped cross section, its not easy to see from the following pictures
http://www.firstflightbikes.com/KirkPrecision.html
There was a rider in my club who had one, extremely stiff and strong, but also heavy compared to higher quality tubes and it had something of a dead feel to it.
They had an initial wave of enthusiasm, and the hope was that by being one piece castings, this manufacturing process would make them cheap too, but once club riders got them, they tended to be dissappointed.
IIRC they put them into mountain bikes, but they didn’t really catch on, the straight edges didn’t make for very comfortable carrying up steep inclines.
I also believe that their stiffness actually worked against them as they had a tendency to crack around the bottom bracket.
I-beams aren’t great in resisting torsional bending (twisting about the center axis), while tubes are great in resistying this. I’d think that tubes were far superior to I-beams, even not considering aesthetics and bruising issues.
Related question - I recall hearing that a tube resists deformation better than a solid cylinder – is this correct? If true, what’s the mechanism behind this?
zoid – who should have paid a LOT more attention in school :rolleyes:
I heard that too; I don’t think it’s the case that a tube is stronger than a solid cylinder of the same diamtere and material (in fact, how can it be, since the solid cylinder incorporates everything that the tube contains?).
But rather: for x amount of bending (a feat which requires more force with a solid cylinder), the cylinder will suffer more structural damage than the tube. I guess this is because the solid material in the centre is acting as a lever to tear apart the edge on the outside radius of the bend.
An I-beam is very strong when suspended between two points and the load placed on top of it (the top of the beam in compression, the bottom of the beam in tension).
But I dont see a place on the frame of a bike where this type of load occurs.
The load points on a bike frame seem to occur at the joint intersections with the connecting tubes to be solely in tension or compression,
A couple of points:
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Bending resistance goes as the moment of inertia w.r.t. the axis about which the moment is applied. So, for a bending load an I-beam is very strong (for its mass) since the material is concentrated far from the axis about which the load is applied (and moment of inertia goes as the fourth power of distance from the centroid). Likewise, a tube is very strong (for its mass) for a torsional load, since it has its material far from the axis about which that load is applied (actually, a triangular cross-section is even more resistant to a torsional load, IIRC).
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For a complicated geometry, you need to look at all the load paths, to see what kinds of stresses are put on the bike, and how much stiffness you require - or how much flexibility you can allow. For example, a racing bicycle needs to be stiff about the bottom bracket, so that rider pedalling loads are transmitted efficiently; a mountain bike needs to be strong for vertical loads applied at the wheels, since those are loads that might be seen when encountering bumps. A city bike may be made more complient, since comfort and step-over height may be greater concerns that stiffness.
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So, a bicycle sees bending, torsional, compression, and tensile loads depending on which frame member is being considered. Something as simple as a handlebar may only see predominantly one load type (think of a handlebar as a cantilever beam, and a seatstay mostly as a compressed beam), but the downtube (going from the head tube to the bottom bracket) is going to see a complicated load history.
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To simplify the consideration of a bicyle frame design, try to imagine how an object could be built that would connect the major load points (bottom bracket, saddle, headset, rear dropouts) and use the least amount of material. Regarding the OP, there really isn’t a place where an I-beam would be the most sensible cross-section.
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Stiffness and weight are only a couple of the design constraints facing a bicycle manufacturer - others are materials availability & cost, ease of manufacture (cutting, bending, bonding/welding/brazing), resistance to fatigue cycling, resistance to impacts or stresses near the elastic limit, corrosion resistance, etc.
Hope this helps.
For equal mass, a tube resists bending, torsion, or compression better that a solid bar - meaning it will carry a greater load before yielding. This is because the material is concentrated far from the central axis, which reduces the stress for a given load (for bending or torsion) or reduces the ease of buckling (for compression). For tensile loads, to first order a tube and a bar (of equal masses) are equally strong. Hope that helps.
(4) Can be ovalized to emphasize strenght in one direction, vibration dampening in another direction.
Bingo. One of the tests that you do on a frame you might be thinking of buying is you check it for stiffness by applying torsion to deflect the head tube from being in line with the seat tube. The torsoinal rigidity of the top tube and the down tube are coming into play. With I-Beams you would probably permanently bend the frame with such a maneuver, for a frame of equivalent weight. Don’t forget, the rider is applying lots of torque between those two members, what with all the pedaling and hadndlebar work. When I am on the power part of the pedal stroke I am often twisting the handlebars the opposite way to maximize the power.
QED.
And another point. We want are frames stiff, but not TOO stiff. An I beam would make it stiff in all the wrong ways and none of the right ones. I want flexibility in the vertical axis to lessen the harshness of the ride. I beam lessens this. I want extreme rigidity with regards to torsion between the head and seat tube. Flexing this only takes my hard fought mechanical energy and turns it into waste heat. I beam decreases rigidity in this regard.
I have seen a lot of frame failures, and almost always at the joints. That is why frames are made with “Butted” tubing (thicker at the ends of the members) and why the joins are surrounded by reinforcements. Even the filigree on those enforcements is meant to avoid a sharp demarcation that might snap the tube.
/rider
One more note. There are basicly three modes in which frames fail:
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Frame fails shortly after purchase. This is a manufacturing defect, not a design problem.
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Fram fails after lotsa miles. Simple metal fatigue. Lightweight bike frames don’t last forever. Even then might be repariable.
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Frame fails after collision. Usually not reparable, because one or more frame members has been bent.
So you see, bike frames (at least road bike) don’t just go around failing. We don’t need them stronger, we need them to be light and have the right riding characteristics. Tubes win.
And as a practical matter, a lot of the stuff besides the frame that you need to make a bike is designed to work with tubular frames. Offhand: seat post, bottom bracket assembly, head tube bearings, handlebar gooseneck, brake mounting system, cable stays, etc.
Man I am making a lot of typos, but hopefully sense!