If you think I've assumed a spoke can carry compression

I haven't

You need to read the bit on the previous page about Linear Superposition:

Linear Superposition

The first issue to address is that of linear superposition. What this means is that I'm not analysing all the stresses in the wheel. I know that all the spokes start out with a uniform tension, and I don't really care about it. For the purposes of the analysis I simply ignore it, and it goes away!

Therefore, when the analysis shows a force in a spoke, the real force in the spoke is whatever the preload (the initial tension) was, plus the force calculated. If the force was tension, we end up with a more highly stressed spoke. If the calculated load was compression we end up with a less tensile spoke. That is, a reference to a 'compressive' spoke could be read as a 'less tensile' spoke. To get the true state in the wheel you need to superimpose (ie, add) the results of this analysis on the initial state.

None of this affects the analysis. If we ignore buckling (or restrain against it), a spoke under tension which is subject to (say) 100N less tension contracts just as much as an unstressed spoke subject to 100N compression (or for that matter a compressive spoke subject to 100N more compression). In the analysis I simply don't tell the computer to let anything buckle, so I can analyse a spoke with compression without worrying that it's really a spoke that started out with a tension and now has less tension.

That is to say, in all these analyses, the initial preload state of the wheel is neglected, ignored. The initial tensile load in every spoke and compression load in the rim is not included. The true stress state in a spoke is not the load these calculations show divided by the cross-section - it's the load these calculations show added to the initial load divided by the cross section. All references in the text to a 'compressive spoke' mean a 'spoke which is now stressed to a lower tension than it was when teh wheel is not externally loaded'. It's just a shorthand, becasue that's a bit of a mouthful.


Try this analogy:

What is fourteen million and twenty-seven minus six (14,000,027 - 6)?

If you have any sense for numbers, you didn't just do any arithmetic operations on 8-digit numbers, you identified that the 14 million could be set aside (neglected, ignored) and did twenty-seven minus six in your head. At the end, you put the 14 million back on, but it didn't really affect the processing you did.

So, to develop the analogy, suppose you have five boxes of widgets. All boxes start identical, and each box contains 14,000,027 widgets. There is a uniform and constant distribution of widgets.

Now, you do something, the effect of which is as follows:

Now, you can actually examine widget numbers quite usefully without doing 8-digit arithmetic, without even putting it back on at the end:

All those questions can be answered without 8-digit arithmetic, by using what is effectively linear superposition.

In particular, that remove / add process can be carried out with real, physical widgets without violating any laws of physics, even though when you do the maths you might make use of the concept of a negative widget (the change in box A is five negative widgets). You don't need any actual ant-matter widgets, even though the maths has some 'negative widgets'.

All spokes tensile

None of these compressive loads exceed the preload in the spoke. Every spoke in the wheel, in all these analyses, stays tensile at all times.

Spokes in tension don't buckle.

If you're now worrying about standing on something in tension, you need to read the semantics bit on the main page.

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