Brian Ratliff

I was in the bike shop yesterday and I paged through Mr. Brandt's book "The Bicycle Wheel". Anyway, I randomly found the section where he is explaining that how people usually describe the wheel holding load: that the bike "hangs" from the spokes, is wrong. He makes an argument that the wheel is supported by the spokes below the hub. Anyway, the Mechanical Engineer inside of me rebelled against his argument, especially the one where he compares spokes to a pre-stressed concrete beam in bending to argue that the bottom spokes can be both in tension and support a compressive load at the same time.

Anyone else see this in his book and find this argument odd? To me, it makes no sense logically (how can a spoke be in tension and compression at the same time?), and his pre-stressed concrete beam example is hogwash because a prestressed concrete beam (uses pre-tensioned rebar inside the beam to keep the concrete perpetually in compression) is a composite structure. He basically argues that the spoke can be in compression and tension at the same time because a prestressed concrete beam can be pulled in tension and support a tension load even while the concrete stays in compression. What he's missing is that something has to be supporting the tensile load, and if it is not the cement, then it must be the rebar inside the cement (which is holding the beam in compression) that is taking up the tensile load.

It makes it hard to trust any engineering science analysis he presents in his book or any other publications he writes - the fact that he got this wrong. Or, alternatively, am I missing something here? (God only knows how many times I've been wrong in my fundamentals! )

sancocho

see usenet

Phantoj

The rim is not very stiff; the force applied to the bottom of the wheel relieves some of the tension on the lower spokes.

search USENET (rec.bicycles.tech) on Google Groups for lots of discussion.

https://yarchive.net/bike/wheel_stresses.html

mrt10x

my wheels roll round and round

Hocam

Put your weight on your bike and pluck a spoke at directly above the hub and at one directly below the hub, then take your weight off and pluck the same two spokes again. This is most easily done by leaning on your handlebars and plucking spokes from the front wheel.

Because pitch is a function of tension, a higher pitch denotes a larger tensile force on the spoke. You'll find the spoke below the hub had a much greater change in pitch, while the difference of the upper spoke was harder to discern. The upper spoke will increase slightly in tension, but the increase is very small compared to the lower spoke.

Brian Ratliff

What I'm getting from the usenet discussions is that this is basically a semantic issue of how to go from a complex analysis of how the load is shared amongst spokes to a simplified, watered down version to tell those who don't want to get into details. Ah, screw it then. The Mechanical Engineer in me has lost interest.

BlazingPedals

It's probably best that way. Just ride and enjoy it.

biker128pedal

Each spoke is one part. The wheel is a composite structure. Tear it down and draw a free body diagram of the parts.

DiabloScott

The spoke is in tension and supporting a compressive load because it is in less tension than the rest of the spokes; the load equals the reduction in tension. None of the spokes are in compression and JB does not claim this.

BSME +18 years.

Phantoj

Good luck; it is a statically indeterminate structure.

Brian Ratliff

^^^
Eh? You can draw a free body diagram of an indeterminant structure. You just cannot solve it without introducing a constituative stress as a function of strain model.

merlinextraligh

no engineering expertise here, just a question. Couldn't you test this hypothesis by building a wheel with very flexible wire, instead of conventional spokes?

If the wheel hangs from the spokes above, then you ought to be able to use just wire; If however the wheel is supported by the spokes below, wouldn't the wire wheel collapse?

eb314

I feel like if you did this the flex-spokes wouldn't act as real spokes do since they couldn't support compression without bending. I think the wheel would just hang, but wouldn't prove that the wheel hangs with real spokes.

Brian Ratliff

Like I said, it is semantics. "Standing on the bottom spokes" I've interpreted to mean that the spokes are acting as columns. Evidently you and he do not mean this when the above statement is made. I can argue that the statement is not terribly descriptive of what is actually going on, but these kind of arguments I lose interest in.

What is interesting is an FEA model I found on the web which shows that only the bottom 2 or 4 spokes (on a 32 spoke wheel) are unloaded and the rest increase in load. Looking how the rim deforms, I can see this: it's because the rim deforms into a squished pear shape and load up spokes below the axle as well as those above it. I imagine that this effect is lessened as the rim is made stiffer and can support bending stresses to keep the rim rounder and transmit more force to the spokes above the axle and unload more spokes below the axle of the wheel. The FEA analysis probably only assumed that the rim could only support compressive stresses.

Brian Ratliff

Conventional spokes are modeled basically as wires that cannot support compressive loadings. What Brandt's point is is that since only a couple spokes see a decrease in tension and all the other spokes increase in tension, the couple bottom spokes can be said that they are holding the wheel up. If you are honest about all the forces involved though, you can see that the couple bottom spokes are unloaded slightly and play no role in opposing the force placed on the axle and the rest of the spokes on the wheel is supporting the load at the hub. From what I gather, Brandt's just wants to be different by explaining the same content as above in a simplified manner he thinks is more useful than the model of the hub "hanging from the rim" which is also not strictly correct (it assumes that the rim is perfectly stiff and does not deform).

Aren't there some high performance wheels which use Kevlar fibers as spokes?

Phantoj

I thought you weren't interested in this anymore.

The unloading of the couple of bottom spokes is actually the means that does act to oppose the force placed on the axle.

I.e. you end up with a hub that has an even tension on all of its eyelets except the bottom two or three with a low tension. Therefore, the net force acting on the hub from all the spokes is a vertical (up) one equal in magnitude to the amount of slackening the bottom spokes have sustained.

rmfnla

I've disagreed with stuff Jobst has written before.

Just because you put it into a book doesn't make it right.

Phantoj

He has extreme views on hydration, or lack of same.

ken cummings

If the spokes under the hub were (God{ess} forbid) to loose all tension and try to accept tension they would start to turn in the holes in the hub thus shedding any compressive load. One of those composite 3 or 4 spoke wheels could and may just go into compressive loading. Sounds like a good project for an undergraduate student with access to several strain gages.

Brian Ratliff

I am interested in mechanical engineering stuff, not semantics.

I very much doubt that the spoke tensions remain equal around the hub except for the bottom four. This would imply a discontinuity in your rim deflection, which definitely does not happen. You will see a continuously variable level of tension as you test spokes around the rim. From the FEA on the website I saw, the tensile force was at a minium at bottom dead center at below the nominal pretension value, and as you traveled toward top dead center, the tensile force first increases to cross over the nominal pretension, then reaches a maximum around 1/5th of the way toward the top and gradually decreases to a constant value above the preload tension. The rim becomes somewhat pear shaped.

This is what I meant when I said that the bottom spokes don't contribute. If the force slackens by exactly the amount of the net force, it means the spoke's only contribution to the wheel is to offset the preload of the other spokes. If you dropped all the prestress loads on all the spokes to zero, you could remove these bottom few spokes and the loads on the rest of the spokes are completely unaffected.

Brian Ratliff

The interesting part about the above is the "frame of reference" argument that Brandt's makes. From an observer, the wheel appears as if the bottom spokes are carrying the load - which gives rise to his comments. However, to get there, he has to subtract the hydrostatic forces - the preload in the spokes - from the equation. The statement makes my inner Engineer bristle because he kinda looks like he assumes the spokes are effectively in compression. As I said in the previous post, if you do, in fact, decrease the preload of all the spokes to zero, you could cut the bottom couple spokes out of the wheel without any affect. So, semantically, I believe it is wrong to say that the wheel stands on it's lower spokes just because, if you can cut them out and the forces of the remaining spokes (with no preload) are unchanged, then the wheel is doing quite the opposite of "standing" on it's lower spokes.

From a structural standpoint though, you don't describe load bearing members by what the deflection looks like from an observer's standpoint. Rather, you "cut" the load bearing member to expose the forces across the cross sectional area. When you do this, you cannot just subtract and discard the preload tensile forces the spokes see. You can calculate them out separately, because forces can be superimposed, but you have to add them back in at the end of the day.

What he does get right is that this is all pretty non-intuitive. The wrongly made assumption that has people assuming that more than just the spokes at the very bottom go slack, that only the spokes above the axle are holding the axle up, is the assumption that the rim does not deform - that it is a rigid body. If this were the case, then yes, logically only the spokes in the top half of the wheel resist the load. But this is not a good assumption, though it gets better when you talk about these deep cross-section rims like the Zipp 404 and Velocity Deep V.

Phantoj

The bending stiffness of the rim is considered. You can see the stress in the rim: https://www.astounding.org.uk/ian/wheel/3c_rim.html

Brian Ratliff

My bad, I missed this. A stiffer rim would transmit that bending stress further up the wheel. As you made the rim stiffer and stiffer in the bending direction, you'd get a closer to a rigid body rim, where the whole bottom half of the wheel has slack spokes and the wheel is truely "hanging" from it's spokes (i.e. with the preload of the spokes set to zero, you could cut out the spokes in the entire bottom half of the wheel and the stress on the top spokes would remain unchanged).

Treefox

There's some interesting discussion out on the internet of 'spontaneous' collapse of Spinergy Rev-X wheels along the lines of what your discussing at the end there. They've got four pairs of tensioned carbon fins acting as spokes. (and I think went a long way towards giving carbon its 'explosion!!!!11!' reputation in the late 1990's)

Phantoj

Jobst has something to say about the Rev-X: https://yarchive.net/bike/spinergy.html

Had some buddies with 'em, but didn't really see the appeal. I do have some Spinergy Spox MTB wheels sitting around - these were good wheels with Vectran fiber spokes, but I've got no bike to put them on.