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I really do think that mono-stays are an idea that deserve their day in the sun on bicycles once again. Stiffer, lighter, more aerodynamic, and much easier to change tires as an added practical benefit.

The bending stress in a tube is proportional to its diameter and its area moment of inertia (really just a way of describing the distribution of material in its cross-section). That moment of inertia (I) involves the 4th power, so a round 1.0″ x 0.035″ wall tube will have an I of 0.0123, while a 1.5″ x 0.035″ tube will have an I of 0.0432 (nearly 4 times larger).

At the same time, that 1.0″ tube will have a cross-sectional area of 0.1061 in^2, whereas the 1.5″ tube is just 0.1611 in^2.

So while the 1.5″ tube will be much stiffer – 2.33x less bending stress – in this example, it is only 1.52x heavier, so the stiffness/weight is 1.54x higher. This effect gets more pronounced if you decrease the wall thickness of the tube as you get larger (within limits, eventually you get into buckling issues when your diameter/wall thickness ratio is greater than about 50).

Obviously you need to do other stress analysis, like torsional stiffness, but it’s pretty undeniable that with proper engineering a monoleg will have better performance.

It’s so cute when undergrads try to use math. Take a step back, close the textbook, and think for a second. A traditional rear sub-frame on a bike is a tetrahedral truss. Pretty much all tension and compression, while a monostay is is a twisted cantilever. Now, you don’t even need to bother with the math to know that long, slender tubes are great at supporting tension, mediocre in compression, and utter rubish in bending and torsion. I highly recommend working out the full analysis over your semester break. A lot of the world, from bridges to bike frames, is going to make much more sense when you figure out for yourself that cantilevered really are a terribly inefficient way to support load.

I too think the monolegs are nice and practical. Good to see more of it, and of its history.
That is an clear and concise explanation there Androo, lik it. im also fond of monolegs and constructed the no-fork, discussion here: http://www.lfgss.com/thread82804.html

Ooh, I really like the look of that! Very elegant lines. Nicely done, sir. One of these days I’ll build myself a monoleg fork…but I work in composites, and forks are a little bit beyond my comfort zone at this point!

## 9 Comments

I love that Invincible. Hadn’t seen it before.

I really do think that mono-stays are an idea that deserve their day in the sun on bicycles once again. Stiffer, lighter, more aerodynamic, and much easier to change tires as an added practical benefit.

I get the aerodynamics and ease of tire changes, but I can’t see how a monostay can increase stiffness without a significant weight penalty.

The bending stress in a tube is proportional to its diameter and its area moment of inertia (really just a way of describing the distribution of material in its cross-section). That moment of inertia (I) involves the 4th power, so a round 1.0″ x 0.035″ wall tube will have an I of 0.0123, while a 1.5″ x 0.035″ tube will have an I of 0.0432 (nearly 4 times larger).

At the same time, that 1.0″ tube will have a cross-sectional area of 0.1061 in^2, whereas the 1.5″ tube is just 0.1611 in^2.

So while the 1.5″ tube will be much stiffer – 2.33x less bending stress – in this example, it is only 1.52x heavier, so the stiffness/weight is 1.54x higher. This effect gets more pronounced if you decrease the wall thickness of the tube as you get larger (within limits, eventually you get into buckling issues when your diameter/wall thickness ratio is greater than about 50).

Obviously you need to do other stress analysis, like torsional stiffness, but it’s pretty undeniable that with proper engineering a monoleg will have better performance.

It’s so cute when undergrads try to use math. Take a step back, close the textbook, and think for a second. A traditional rear sub-frame on a bike is a tetrahedral truss. Pretty much all tension and compression, while a monostay is is a twisted cantilever. Now, you don’t even need to bother with the math to know that long, slender tubes are great at supporting tension, mediocre in compression, and utter rubish in bending and torsion. I highly recommend working out the full analysis over your semester break. A lot of the world, from bridges to bike frames, is going to make much more sense when you figure out for yourself that cantilevered really are a terribly inefficient way to support load.

No need for the snark.

You must be right, though. That’s why all cars and airplanes use monoleg wheel carriers – oh wait…

I too think the monolegs are nice and practical. Good to see more of it, and of its history.

That is an clear and concise explanation there Androo, lik it. im also fond of monolegs and constructed the no-fork, discussion here: http://www.lfgss.com/thread82804.html

Ooh, I really like the look of that! Very elegant lines. Nicely done, sir. One of these days I’ll build myself a monoleg fork…but I work in composites, and forks are a little bit beyond my comfort zone at this point!

Crazy to think how far the bike has come since then !!!

What about that folding one before 1900… http://velodesign.wordpress.com/2012/06/19/bicyclette-pliante-capitaine-gerard/