but the torsional strength

Ahh that makes sense. I get the math behind that one – a hollow and solid bolt of the same outer diameter will ahave different max shear stress because the hollow one loses the strength coming from the inner bit, which is minor but not neglible. I’d you increase the radius of the hollow boot but keep the same thickness the max shear shear stress is lower due to the radius. So it’s all part and parcel of the same effect.

stiffness of the tube

That one I never got my head around. I’m not alone judging by the number of arguments about it if you Google the question!

Think about a drink can, paper tube, etc. As long as the walls don’t collapse, they are very resistant to bending (i.e. stiff). If you take the same amount of material and make it into a solid rod or wire, it will be very bendy. That’s why bike frames are made of tubes, not bars. It’s also why aluminium frames have a reputation for being stiff compared to steel. It’s not that aluminium itself is stiffer, just that it’s less dense so it can be used to make a larger diameter tube. The larger diameter tube is stiffer due to the shape, not the material. A thick walled aluminium tube of a smaller diameter would be much flexier.

I think it is the same amount of material thing. If you take a rod and cylinder of the same diameter, will they be equally stiff?

I know it is true because people smarter than me say so but it is thr “proof” that i have teobke finding and grasping.

people mention the effect of the gap between top and bottom of the tube referring back to the karate block breaker – who need just such a gap. The sidewalls of the tube will contribute in the same way as an open web truss etc, etc. Except it is curved and subject to outwards and inward s stress which affects it s ability to resist.

I suspect the physics involved is so complicated that you just have to ‘believe’

I suspect the physics involved is so complicated that you just have to ‘believe’

FFS, it’s not that complicated.

Glad to hear it. Maybe you can explain the stress and vector on each part of tube, using a square hollow bar as an analogue perhaps.

Think about it conceptually instead of leaping straight into the maths – the maths is just a formal expression of the underlying concept.

Imagine you have a solid bar 10 mm in diameter and you bend it into a circle with a diameter of 1000 mm. The outside circumference of the bar must be 31.4 mm longer than the inside (10 mm x pi). The metal on the outside must stretch and the material on the inside must compress to account for a 1% difference.

Now imagine that you take that same bar and use it to make a tube with a diameter of 100 mm and then try to bend that into a circle of the same 1000 mm diameter. In this case, the stretching and compression of the metal has to account for a 10% difference, so it will take much more force to bend it because it must be stretched much more. This is why larger diameter tubes are much stiffer than solid bars of the same mass as long as they don’t crumple. As soon as they crumple, they lose most of their stiffness.

Have a search for something called section modulus, that should answer your questions

That makes sense hols, thanks. I really couldn’t get my head around the “tube of infinite radius with infinity thin walls” being 2 or 4 times stiffer (can’t recall which now) than the solid bar of same mass. Of course an infinitly thin wall would crumple under any sort of point load…

I had always conceptually looked at round bar as rounded off squares. You can imagine the square inside it and it is easy to think of a load acting on the ‘slices’ as if they were beams. Even though the middle third of the beam is basically along for the ride, it prevents the top third from deflecting into space etc.

If you hollow out a square bar, it is easy to visualize a load placed on the top. The load will travel laterally to the sides, which will carry the load via compression and tension in each side. Redistribution of the material to make a taller vertical member accounts for the stiffness. As long as the load is centred and the middle of the vertical members don’t bulge outward and the top is strong enough to transfer the stress to the sides it is all really easy to imagine

But how is the load distributed in a cylinder? Is the top 1/4 the equivalent of a peaked roof carrying the stress to the 1/4 on each side which act as vertical ‘beams’ and if so how does the curve affect stiffness of the vertical members. Or is a cyclinder a top semi circle which wants to flatten laterally under stress and cannot because the lower semi circle acts as a tension member to hold the bottom edges of the top semi circle in place, therefore acts a bit like a beam shaped like an upside down u.

That’s the part I cannot grasp about hollow tubes of the non square variety.

I was working on one of my old bikes today when I realised just how relevant this topic is in a bike forum.

On my bike there were 11 threaded parts with holes through them.

The obvious ones were the canti mounts = 4, chainring bolts = 5.

If we count the ISIS crank bolts, that’s another 2, although they are capped.

If you have QR axles with cup and cone bearings, add 2 more.

All of those get cranked up pretty tight.

And then there’s the cable adjusters which even have a slot in them – I didn’t count those because they’re used finger tight. 🙂

I also noticed last night that Shimano SPD-SL cleat bolts are hollow.