Engineering: Buckling Limit of Frame Tubing

In the last post, I began to address Yoshi’s interest in understanding how Seven Cycles goes about determining bicycle frame tube diameter and tube wall thickness.

I’ve already discussed a bit about how we adjust ride characteristics; I then talked about how we think about ride characteristics.  Here I’ll address one of the most fundamental engineering parameters of any thin wall shell structure—like a bicycle frame tube, for example:  unstable shell bucking.

The concept of shell bucking is simple.  And the simplest example of unstable shell bucking is seen in the result of holding a soda can at both ends and twisting the ends in opposite directions—the can buckles.  It buckles because the can is an unstable shell.  In the case of a soda can, this instability is fine—in fact it’s a good feature—because the can engineers did not optimize the design around an open and empty can.  The can is designed to function when full.  When it’s full, it is not unstable.  When it’s empty, it’s very unstable.

As you can see, addressing a tube’s buckling limit is one of the most important engineering decisions for designing the lightest and safest frame possible.

This buckling limit holds true with any frame material.  Monolithic metals are somewhat straight forward—at least on paper—and carbon fiber, as always, is a lot more complicated, but the buckling limit remains true.

Again, the idea is very simple:  make sure no tube is so thin that it creates a potentially unstable shell buckling situation.  Unfortunately, the math that goes into ensuring this doesn’t happen is not very simple at all.  Seishi Yamada, Professor at the Toyohashi University of Technology explains this complexity:

“Partly due to the major discrepancies between observed buckling loads and the predictions from classical theory, the buckling of shells has excited extraordinary interest…  Indeed, the list of contributions to the understanding of the behavior of shells almost reads as a Pantheon of the 20th century's leading mechanicians and applied physicists.  …despite the immense effort put into its understanding, added to the growth in our ability to undertake sophisticated non-linear calculations, most shell design still relies more upon empirical evidence than it does upon the fruits of the many ingenious theoretical solutions.”

For all the importance of shell buckling, most frame builders don’t actually have to grapple with this issue.  I would estimate that well over 90% of the high end frames sold in the US begin with stock tubes developed by a tube supplier, not the frame builder.  Reynolds, True Temper, Dedacciai, Columbus, Easton, Advanced Composites, and a handful of other tubing companies research and manage the unstable buckling limit issues.  The frame builder, then, chooses from some options provided by the tube supplier.

Unfortunately, not every tube supplier has figured out all the complexities of shell buckling.  This 20-year old photo is a perfect example of what happens when a tube set is engineered beyond the edge of stable.

Seven, on the other hand, develops all our titanium, much of steel, and all of our carbon tube sets from scratch, so the buckling limit is one of the fundamental parameters from which we begin—we design around this threshold on every frame we build.  Because of this, Seven has never had a single shell buckling failure.

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Note about the photo:  I was going to Photoshop out the brand name but I decided not to for three reasons:

1. Joe Breeze is a legend and has nothing to worry about with a 20-year old photo.  Joe is one of the founders and early innovators in the mountain bike world.  He was the quiet one in the original group of down hillers.  He is a really important figure in mountain biking and this frame is not a reflection of him or his skill.  It’s actually an example of how the tube supplier did not do their job.  And it is an example of how the frame builder could not have known that the tube set was in the unstable buckling state.
2. The photo was taken 20-years ago.  This bike model is long gone.  This tube set isn’t even close to existing anymore.  In fact, Joe’s taken his bike design and bike line in a very different direction that is not relevant to this old bike design.
3. I suck at Photoshop.

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Back to the story:  Yoshi next asked about comparing 6-4 titanium to 3-2.5 titanium.  This is also a great question.  A bit trickier.  I’ll get to that next time.  First I have to find a company that still builds frames using 6-4 titanium.

Comments

[Halvor Hansen]

Dear Sir,

I believe that the presence of the Rock Shox Mag-something fork in this photo places it after 1992, which makes it less than or equal to 18 years of age.

Cheers,

[Wicked FAT]

Late 92/early 1993.
-ControlTech seatpost,
-Dia-compe ss-7 brake levers,
-986 rear brakes on the Cracknfail in the background.
-no neon
- threaded headsets