Forces on spokes

writes:

wrote:
Until all the pre-tension is used up, even a string will "support" a
compressive load

A string may support a compressive load if it is pretensioned but if
there is nothing to support the string it doesn't matter. There is no
way for a spoke under compressive load to support anything except by
its nipple's friction with the spoke hole. Any compressive load will
try to push the spoke out the outside of the rim.

What would you say if the string were replaced with a chain that was
welded to the rim? How is the link to link interface of the chain any
different from the nipple to rim interface?

The point being, the pretension in the spoke acts on the nipple to rim
interface just as it does on the links (or string or spoke).

--
Joe Riel

That article makes the simplifying assumption that if you can hang from
a rope, you can sit on it.

A foolish linearity is the hobgoblin of little minds.

Forces on a pre-tensioned wheel loaded at the axle:

http://www.astounding.org.uk/ian/wheel/index.html

Cheers,

Carl Fogel

An interesting and thorough analysis at that link, and yet I am not
sure that I believe
the final result. He concludes that the load is supported almost
exclusively by the
bottom few spokes (the ones pointing down toward the road) which are
strongly in
compression. However, long slender members such as spokes cannot
support large compressive loads because of their tendency to buckle
(bend). Also, much of the
strength of a wheel comes from the fact that all the spokes contribute
to the load at
all times. I suspect that he has not accounted fully for the
pretensioning of the spokes.
Jeff

Dear Jeff,

Actually, Ian's whole article is about accounting fully for the
pre-tensioning of the spokes.

True - his problem is not ignoring the pretensioning, sorry.

It's a subject that's been covered repeatedly. That's the nicest
online, detailed explanation that I know of.

You can find pretty much the same engineering analysis and conclusions
in "The Bicycle Wheel" by Jobst Brandt, any edition.

I certainly hope not.


And you can see experimental strain gauge confirmation in figures 10
and 11 Professor Gavin's paper he

http://www.duke.edu/~hpgavin/papers/...heel-Paper.pdf

The icicle-shapes on the graphs show the pre-tensioned spoke losing
and then regaining a large amount of tension as it rolls under the
loaded axle.

Yes, but this does not indicate that they are supporting the load at
that point, but rather that they are *not* supporting the load at that
point. The "icicles" are the spokes at the bottom getting shorter (a
strain gage measures distance) as they lose their pretensioning. The
load is being supported by all of the other spokes *except* for the few
spokes at the bottom that go slack.

Until all the pre-tension is used up, even a string will "support" a
compressive load,

I don't know what you mean by that sentence. A spoke that is
underneath the axle can't support the load whether it is pretensioned
or not because to oppose the load would require it to go into
compression.

which is why emergency repair spokes can be made of
kevlar string and why whole wheels can and have been made of them.

Spokes can be made out of anything that is strong in tension. The fact
that they can be made out of string nicely illustrates the point that
spokes are never in compression, and shows why the spokes at the bottom
of the wheel don't support any of the load.

Jeff

Someone did a test of a bicycle with a tensiometer providing constant
telemetry of spoke tension and found that the spokes under the axle
lost tension, the spokes above the axle stayed relatively close, and
the spokes at +-90o from those under the axle increased. My ignorant
conclusion based on this data was that all the spokes except those
directly under the axle contributed to sharing the load, and that the
load was shared (this part is even more controversial) by the tendencey
of the rim to distort ovally. Others on this ng will now proceed to
dismiss this data as insignificant

Not me - I agree 100%

and insist that because the spokes
under the axle are tensioned, they are able to support the weight of
the bike until the load becomes great enough that they go slack,

By being pretensioned the spokes at the bottom are trying to pull the
axle downward, not to push it back up. The pretensioning in the
bottome spokes actually increases the load that the other spokes must
support.

they don't really bother to explain convincingly (for me) why the
greatest tension rise is seen in the spokes that are _parallel_ to the
road surface.

For me personally, the tensioned spoke theory would be plausible if the
spoke nipple were somehow fixed in the rim, but because the nipple is
not fixed, there is no way for the spoke (tensioned or not) to
significantly act acgainst the rim to provide support of the weight of
the bicycle when the spoke is directly under the axle/hub.

And a spoke would be woefully inadequate to support any compressive
loads anyway.

Jeff

wrote:
On 28 Aug 2006 12:09:17 -0700, wrote:


wrote:
Experiment seems to confirm theory.

The experiment confirms that the spokes do indeed go slack as they pass
under the hub. It doesn't in anyway prove that they are supporting the
wheel through compressive loading before they go slack.

Dear SSTW,

All the spokes are accounted for in both theory and experiment.

What else besides the spokes connects the wheel to the loaded axle?

If the forces don't show up anywhere else, what supports the load?

Ian's page goes through this in patient detail--the increase in
tension in the other spokes isn't anywhere near enough to support the
load.

Then his analysis must be wrong. The load must be supported by the
spokes that are not underneath the axle, becuase those spokes are
unable to push upward against the downward force exerted by the axle.
Remember, there are only a few spokes at the bottom, and some 30 spokes
not at the bottom.

Jeff

bicycle_disciple wrote:
Hi all.

Just wanted to clear a little question.

Or a not so little question, as the case seems to be!

Thinking of a wheel spoke as a
prismatic member, what is the nature of normal forces acting on it. Is
it all in tension, all in compression or a mix of both?

Spokes are always in tension. A thin wire cannot go into compression
without buckling. Spokes are pretensioned when the wheel is built, and
the tension in any spoke increases or decreases as the wheel rotates,
with the lowest tension when the spoke is beneath the axle.
This much is uncontroversial, I think.

Jeff

anonymous snipes:

Until all the pre-tension is used up, even a string will "support"
a compressive load

A string may support a compressive load if it is pretensioned but if
there is nothing to support the string it doesn't matter. There is
no way for a spoke under compressive load to support anything except
by its nipple's friction with the spoke hole. Any compressive load
will try to push the spoke out the outside of the rim.

I take it then that you don't recall adding and subtracting negative
and positive numbers in algebra. In this case, compression (-) and
tension (+) are these values, pick your norm.

You may visualize this more easily if you imagine two contestants in
a tug-of-war, one of whom is standing at the edge of a swimming pool.
If I were to push his opponent from behind, I would push the other
person into the water via the tensioned rope.

The only reason we tension spokes is because they are too thin to bear
the load in compression. The analysis of their elastic response is
done without considering either buckling or that they are tensioned.
Finite element analysis (FEA) for the bicycle wheel is performed
without introduction of tension, only external loads. The axle is a
fixed node (0,0) coordinates and the road presses against the rim.

I should mention that the rim of a bicycle wheel responds to loads as
an "elastically supported beam" the most common of these being a
railroad rail sitting on cross-ties. With the point load of a rail
wheel, the rail takes on the shape shown in Fig. 11 of Gavin's paper
and in "the Bicycle wheel". The straight line development of a
circular rim takes on this wavy form when loaded.

Jobst Brandt

The only reason we tension spokes is because they are too thin to bear
the load in compression. The analysis of their elastic response is
done without considering either buckling or that they are tensioned.
Finite element analysis (FEA) for the bicycle wheel is performed
without introduction of tension, only external loads. The axle is a
fixed node (0,0) coordinates and the road presses against the rim.

I should mention that the rim of a bicycle wheel responds to loads as
an "elastically supported beam" the most common of these being a
railroad rail sitting on cross-ties. With the point load of a rail
wheel, the rail takes on the shape shown in Fig. 11 of Gavin's paper
and in "the Bicycle wheel". The straight line development of a
circular rim takes on this wavy form when loaded.

Jobst Brandt

All very learned and no doubt correct. The specific issue being argued
is whether the few spokes directly under the axle support the load, as
the original link in this thread and Carl Fogel claim, or whether all
the other spokes support the load, as I and another poster claim.
Could you comment directly on that?

Jeff

Jeff Thomas writes:

Experiment seems to confirm theory.

The experiment confirms that the spokes do indeed go slack as they
pass under the hub. It doesn't in anyway prove that they are
supporting the wheel through compressive loading before they go
slack.

All the spokes are accounted for in both theory and experiment.

What else besides the spokes connects the wheel to the loaded axle?

If the forces don't show up anywhere else, what supports the load?

Ian's page goes through this in patient detail--the increase in
tension in the other spokes isn't anywhere near enough to support
the load.

Then his analysis must be wrong. The load must be supported by the
spokes that are not underneath the axle, because those spokes are
unable to push upward against the downward force exerted by the
axle. Remember, there are only a few spokes at the bottom, and some
30 spokes not at the bottom.

Maybe you should pluck spokes at various locations around the wheel
and nor which ones (by change in tone) are affected by placing a load
on the wheel. Let me tell you in advance what you will find (for pure
vertical loading). The only spokes affected by the load will be the
three or four spokes at the bottom directed at the road from the hub.

If the spokes at the top are supporting the wheel, as you propose,
then they would be affected by the load, but they are not. I think
you are, as many others, not visualizing these things algebraically.
The problem is much like adding debits and credits to a bank account.

Jobst Brandt

Jeff Thomas writes:

The only reason we tension spokes is because they are too thin to bear
the load in compression. The analysis of their elastic response is
done without considering either buckling or that they are tensioned.
Finite element analysis (FEA) for the bicycle wheel is performed
without introduction of tension, only external loads. The axle is a
fixed node (0,0) coordinates and the road presses against the rim.

I should mention that the rim of a bicycle wheel responds to loads as
an "elastically supported beam" the most common of these being a
railroad rail sitting on cross-ties. With the point load of a rail
wheel, the rail takes on the shape shown in Fig. 11 of Gavin's paper
and in "the Bicycle wheel". The straight line development of a
circular rim takes on this wavy form when loaded.

Jobst Brandt

All very learned and no doubt correct. The specific issue being argued
is whether the few spokes directly under the axle support the load, as
the original link in this thread and Carl Fogel claim, or whether all
the other spokes support the load, as I and another poster claim.
Could you comment directly on that?

I think you are caught in semantics. If you were to look at the
analysis of a die cast moped wheel, as depicted in "the Bicycle Wheel"
your question should answer itself. These spokes are rigid enough to
support the load in compression, yet we do not know if the wheel by
differential cooling leaves these spokes in tension or compression,
both being possible. The FEA of the wheel is unaffected by semantics.
It sees only that under load the bottom spokes are compressed to a
shorter length than the rest and that the others do not experience any
significant load.

As I have pointed out in the past, the minimal increase in tension of
the other spokes for a 36 spoke wheel sums to zero, it being a side
effect of the rim flattening at the load affected zone causing the
remaining rim diameter to increase ever so slightly.

If you were to perform a fatigue test on a bicycle wheel in a non
rotating manner bu loading and unloading the wheel, the three or four
spokes at the bottom would ultimately fail. They being the only ones
affected by the load identical to a wooden wagon wheel.

Jobst Brandt