Rim Strength

Having looked at spoke forces (on the main analysis page), I can look at rim stresses. While spokes just have an axial force, the rim has axial (push/pull) and flexural (bending) forces. What are they?

This shows a graph of the axial force in the rim, superimposed on the rim.

If you read the summary text, you can see that the maximum value is -47.37, and the minimum is -119.4. That is, the rim is in compression all the way round, and really quite low compression. We applied 1000N, our most compressive spoke picked up 350N, but the most any part of the rim sees is 120. Add the fact that the spoke has a cross-section of only 3.14mm2, but our rim has one of 82mm2, and you'll see that the stresses are wildly different (average stresses of 111.8 N/mm2 in the spoke, and only 1.5 N/mm2 in the rim). Explains why spokes are steel, even when rims are aluminium!

This is bending in the rim.

The extreme value is clearly at the middle of the contact patch, and from the summary we can see it has magnitude 4551 Nmm. This gives rise to some more stress in the rim material. At a position 'y' from the bending axis, the stress due to bending is equal to M x y / I. The extreme value of y is at the edge of the section, in this case 5mm from the bending axis. The I value was used in the analysis is 1187 mm4. Our bending stress is therefore 4551 x 5 / 1187 = 19.2 N/mm2. So bending stress is significantly higher than axial stress (but remember that there's preload stress on the rim arising from the spoke force). Also, round most of the rim the flexural stresses are much smaller (an order of magnitude at least, as you can see from the graph).

Total peak stress in the rim from applying 1000N to the wheel is therefore 1.5 + 19.2 = 20.7 N/mm2. (Actually, that's not true, because peak axial is not coincident with peak flexural. Peak stress is actually closer to 20.1 N/mm2.) The most basic of aluminium alloys has a yield stress at least around 100 N/mm2, so we're well within allowable limits with this (as long as our preload is not too extreme).


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