spoke tension question # 165,345,06.....

[steve]

Please forgive my ignorance but could someone please set me straight
here. Would I be correct in saying that as spoke tension increases the
strength, not fatigue, of a wheel will increase only in the radial
direction? My reasoning is that if you look at a wheel in terms of
lateral loads the angles in combination with spoke tension of apposing
spokes cause the rim to sit in a position were the lateral force of the
spokes on each side are equal. So if you apply a 50n load laterally to
the wheel, the wheel should deflect the same amount laterally
regardless of tension because of the fact that the modulous of
elasticity is linear. From my understanding this means that one spoke
loses a certain amount of tension while the other side should gain the
exact same amount, assuming we are dealing with a front wheel. But,
since there is a linear relationship for the modulous of elasticity the
spoke will stretch the same amount regardless of whether the spoke is
increasing from 400n-500n or 1000n-1100n.
There is something very wrong with my logic but I can't figure out
what it is. I suppose the compression of the rim from spoke tension
might increase the load distrubution as tension increases but that is
my only idea, and that would only apply to lateral loads and not
torsional loads which, seem to follow the same logic since a 3x wheel
is in equalibrium because of apposing spokes.

Steve Sauter

 

[jim beam]

steve wrote:
> Please forgive my ignorance but could someone please set me straight
> here. Would I be correct in saying that as spoke tension increases the
> strength, not fatigue, of a wheel will increase only in the radial
> direction?

if we're just considering the spoke, tension gives it "pseudo"
compression strength where it would otherwise have none. BUT, that
comes at the expense of "borrowing" it from the rim. and the cost of
"borrowing" too much from the rim is having it crack and/or taco.

> My reasoning is that if you look at a wheel in terms of
> lateral loads the angles in combination with spoke tension of apposing
> spokes cause the rim to sit in a position were the lateral force of the
> spokes on each side are equal. So if you apply a 50n load laterally to
> the wheel, the wheel should deflect the same amount laterally
> regardless of tension because of the fact that the modulous of
> elasticity is linear. From my understanding this means that one spoke
> loses a certain amount of tension while the other side should gain the
> exact same amount, assuming we are dealing with a front wheel. But,
> since there is a linear relationship for the modulous of elasticity the
> spoke will stretch the same amount regardless of whether the spoke is
> increasing from 400n-500n or 1000n-1100n.

that's correct.

> There is something very wrong with my logic but I can't figure out
> what it is.

you're kinda sorta on the right track. need to consider the whole wheel
though, not just spokes.

> I suppose the compression of the rim from spoke tension
> might increase the load distrubution as tension increases

in equilibrium, load distribution should be the same - for the reasons
you deduced earlier. the rim has a linear stress-strain graph until it
reaches yield.

> but that is
> my only idea, and that would only apply to lateral loads and not
> torsional loads which, seem to follow the same logic since a 3x wheel
> is in equalibrium because of apposing spokes.

 

[steve]

jim beam wrote:
>
> if we're just considering the spoke, tension gives it "pseudo"
> compression strength where it would otherwise have none. BUT, that
> comes at the expense of "borrowing" it from the rim. and the cost of
> "borrowing" too much from the rim is having it crack and/or taco.

So as the spoke increases in tension the compressive strength of the
rim increases because the rim is, in a sence, more rigid and there for
is able to distribute an applied radial force over a greater area of
the rim?
>
> >
> in equilibrium, load distribution should be the same - for the
reasons
> you deduced earlier. the rim has a linear stress-strain graph until it
> reaches yield.
>
Yes, but what happens to load distribution when a lateral force is
applied at the rim. Will a higher tensioned wheel distribute that load
better than a low tensioned wheel? and if so, why?
If I were to have two wheels, one that was tensioned to 300n and one
that was tensioned to 1000n, would lateral and torsional strength be
the same for both wheels?

 

[jim beam]

steve wrote:
> jim beam wrote:
> >
>> if we're just considering the spoke, tension gives it "pseudo"
>> compression strength where it would otherwise have none. BUT, that
>> comes at the expense of "borrowing" it from the rim. and the cost of
>> "borrowing" too much from the rim is having it crack and/or taco.
>
> So as the spoke increases in tension the compressive strength of the
> rim increases because the rim is, in a sence, more rigid and there for
> is able to distribute an applied radial force over a greater area of
> the rim?

no. you can "borrow" spoke load capacity at the expense of rim load
capacity, and that makes the spokes able to sustain compressive load
where they otherwise couldn't, BUT this is a zero sum equation.
whatever is "borrowed" for the spokes is no longer available as capacity
in the rim, hence the rim is closer to yield [and its fatigue threshold].

> >
> > in equilibrium, load distribution should be the same - for the
> reasons
>> you deduced earlier. the rim has a linear stress-strain graph until it
>> reaches yield.
>>
> Yes, but what happens to load distribution when a lateral force is
> applied at the rim. Will a higher tensioned wheel distribute that load
> better than a low tensioned wheel? and if so, why?

no, distribution remains the same until equilibrium is lost.

> If I were to have two wheels, one that was tensioned to 300n and one
> that was tensioned to 1000n, would lateral and torsional strength be
> the same for both wheels?

where would the strength increase come from? load is a vector quantity,
strength is scalar.

 

[steve]

jim beam wrote:
> steve wrote:
> > jim beam wrote:
>
> no. you can "borrow" spoke load capacity at the expense of rim load
> capacity, and that makes the spokes able to sustain compressive load
> where they otherwise couldn't, BUT this is a zero sum equation.
> whatever is "borrowed" for the spokes is no longer available as capacity
> in the rim, hence the rim is closer to yield [and its fatigue threshold].

It sounds like you are saying that spokes only get there load capacity
by taking it from the rim. There for the rim is the limiting factor to
spoke tension. as spoke tension increases load capacity of the rim
decreases. So what makes a spoked wheel stronger than a rim by itself
if the rim has all the load capacity that a spoked wheel will have?

> > Yes, but what happens to load distribution when a lateral force is
> > applied at the rim. Will a higher tensioned wheel distribute that load
> > better than a low tensioned wheel? and if so, why?
>
> no, distribution remains the same until equilibrium is lost.

I don't know if I quite understand what you are saying. Do you mean
that distribution remains the same regardless of the lateral load
applied to the wheel as long as the wheel doesn't collapse?

> > If I were to have two wheels, one that was tensioned to 300n and one
> > that was tensioned to 1000n, would lateral and torsional strength be
> > the same for both wheels?
>
> where would the strength increase come from? load is a vector quantity,
> strength is scalar.

So my interpretation of what you just said is that spoke tension is
independent of the strength of the wheel in terms of lateral and
torsional loads. If that is the case then the only reason for high
spoke tension is to increase fatigue life of the wheel.
Thanks for your time.

Steve Sauter

 

[jim beam]

steve wrote:
> jim beam wrote:
>> steve wrote:
>>> jim beam wrote:
> >
>> no. you can "borrow" spoke load capacity at the expense of rim load
>> capacity, and that makes the spokes able to sustain compressive load
>> where they otherwise couldn't, BUT this is a zero sum equation.
>> whatever is "borrowed" for the spokes is no longer available as capacity
>> in the rim, hence the rim is closer to yield [and its fatigue threshold].
>
> It sounds like you are saying that spokes only get there load capacity
> by taking it from the rim.

spokes only get their compression capacity from the rim, not tensile.

> There for the rim is the limiting factor to
> spoke tension. as spoke tension increases load capacity of the rim
> decreases.

correct.

> So what makes a spoked wheel stronger than a rim by itself
> if the rim has all the load capacity that a spoked wheel will have?

an unsupported rim fails by buckling - a function of the length between
load points. how does the distance between load points compare for a
spoked vs. unspoked rim? [this ties in with modern high profile rims
and lower spoke counts.]

>
>>> Yes, but what happens to load distribution when a lateral force is
>>> applied at the rim. Will a higher tensioned wheel distribute that load
>>> better than a low tensioned wheel? and if so, why?
>> no, distribution remains the same until equilibrium is lost.
>
> I don't know if I quite understand what you are saying. Do you mean
> that distribution remains the same regardless of the lateral load
> applied to the wheel as long as the wheel doesn't collapse?

if the spokes don't go slack, the loading distribution is the same
regardless. if the spokes do go slack, the rim alone in the slack zone
determines ability to support load. slack spokes wheels or rims are not
as weak at is commonly supposed:

http://home.comcast.net/~carlfogel/download/205lbs.jpeg

>
>>> If I were to have two wheels, one that was tensioned to 300n and one
>>> that was tensioned to 1000n, would lateral and torsional strength be
>>> the same for both wheels?
>> where would the strength increase come from? load is a vector quantity,
>> strength is scalar.
>
> So my interpretation of what you just said is that spoke tension is
> independent of the strength of the wheel in terms of lateral and
> torsional loads. If that is the case then the only reason for high
> spoke tension is to increase fatigue life of the wheel.

excess tension decreases rim fatigue life. build to the spoke tension
specified by the rim manufacturer.

 

[Peter Cole]

steve wrote:

> It sounds like you are saying that spokes only get there load capacity
> by taking it from the rim. There for the rim is the limiting factor to
> spoke tension. as spoke tension increases load capacity of the rim
> decreases. So what makes a spoked wheel stronger than a rim by itself
> if the rim has all the load capacity that a spoked wheel will have?

A spoked wheel can be very accurately modeled by a beam (rim) on an
elastic bed (spokes). Visualize a railroad track. When spoke tension
goes to zero under load it's the same as removing ties -- the track has
a longer unsupported span.


> So my interpretation of what you just said is that spoke tension is
> independent of the strength of the wheel in terms of lateral and
> torsional loads. If that is the case then the only reason for high
> spoke tension is to increase fatigue life of the wheel.

The reason for spoke tension is to support the rim. The radial stiffness
of the wheel is the sum of the rim stiffness and the spoke stiffness.
When spokes go slack under load (those closest to the road), the wheel
is left with rim stiffness alone. Imagine what would happen if your car
springs got much softer during heavy loads. Lateral and torsional loads
are not typically significant in bicycles, radial loads are. The primary
tradeoff in wheel design is radial strength vs. weight.

 

[jim beam]

Peter Cole wrote:
> steve wrote:
>
>> It sounds like you are saying that spokes only get there load capacity
>> by taking it from the rim. There for the rim is the limiting factor to
>> spoke tension. as spoke tension increases load capacity of the rim
>> decreases. So what makes a spoked wheel stronger than a rim by itself
>> if the rim has all the load capacity that a spoked wheel will have?
>
> A spoked wheel can be very accurately modeled by a beam (rim) on an
> elastic bed (spokes). Visualize a railroad track. When spoke tension
> goes to zero under load it's the same as removing ties -- the track has
> a longer unsupported span.
>
>
>> So my interpretation of what you just said is that spoke tension is
>> independent of the strength of the wheel in terms of lateral and
>> torsional loads. If that is the case then the only reason for high
>> spoke tension is to increase fatigue life of the wheel.
>
> The reason for spoke tension is to support the rim. The radial stiffness
> of the wheel is the sum of the rim stiffness and the spoke stiffness.

but that spoke stiffness comes at the expense of rim pre-load. if you
have an aluminum beam in simple bending, it will yield [the one side in
compression, the other in tension] when the material farthest from its
neutral plane reaches its elastic stress limit.

now, if you pre-load another section of that same beam material in axial
compression, then bend, it will still yield when the material reaches
its limit, but superimposing compressive axial load means the tensile
side will be farther removed from tensile yield, but the compressive
will be closer to compressive yield. therefore, because the beam
material will still yield at the same elastic stress limit, the
compressive side of the beam has had it's available load capacity
reduced by the same amount as the tensile side has increased - and it
will fail sooner.

***very important point to note: an aluminum beam like this has the same
compressive strength as tensile strength.*** pre-loading only has
benefit for materials like concrete that have no tensile strength. in
that case, compressing the concrete [by using steel tensors] gives a
"pseudo" tensile strength to the concrete by "borrowing" from it's
compressive strength - at the expense of reduced compressive load capacity.

in terms of stress/strain graphs: [use fixed space font]

stress
|
|
|
|
--------x------- strain
x |
x |
x |
x |

becomes:

stress
|
| x
| x
| x
--------x------- strain
x |
|
|
|

> When spokes go slack under load (those closest to the road), the wheel
> is left with rim stiffness alone. Imagine what would happen if your car
> springs got much softer during heavy loads. Lateral and torsional loads
> are not typically significant in bicycles, radial loads are.

lateral loads can be significant enough to increase spoke tension to
levels that yield hub holes and untrue a wheel where spokes have not
been sufficiently seated.

> The primary
> tradeoff in wheel design is radial strength vs. weight.

make that just "strength vs. weight".

 

[Peter Cole]

jim beam wrote:
> Peter Cole wrote:
>> steve wrote:
>>
>>> It sounds like you are saying that spokes only get there load capacity
>>> by taking it from the rim. There for the rim is the limiting factor to
>>> spoke tension. as spoke tension increases load capacity of the rim
>>> decreases. So what makes a spoked wheel stronger than a rim by itself
>>> if the rim has all the load capacity that a spoked wheel will have?
>>
>> A spoked wheel can be very accurately modeled by a beam (rim) on an
>> elastic bed (spokes). Visualize a railroad track. When spoke tension
>> goes to zero under load it's the same as removing ties -- the track
>> has a longer unsupported span.
>>
>>
>>> So my interpretation of what you just said is that spoke tension is
>>> independent of the strength of the wheel in terms of lateral and
>>> torsional loads. If that is the case then the only reason for high
>>> spoke tension is to increase fatigue life of the wheel.
>>
>> The reason for spoke tension is to support the rim. The radial
>> stiffness of the wheel is the sum of the rim stiffness and the spoke
>> stiffness.
>
> but that spoke stiffness comes at the expense of rim pre-load. if you
> have an aluminum beam in simple bending, it will yield [the one side in
> compression, the other in tension] when the material farthest from its
> neutral plane reaches its elastic stress limit.

The failure mode of rims is fatigue, yield is not of interest.

>> When spokes go slack under load (those closest to the road), the wheel
>> is left with rim stiffness alone. Imagine what would happen if your
>> car springs got much softer during heavy loads. Lateral and torsional
>> loads are not typically significant in bicycles, radial loads are.
>
> lateral loads can be significant enough to increase spoke tension to
> levels that yield hub holes and untrue a wheel where spokes have not
> been sufficiently seated.

So you say. If you look at the geometry of deformation of spoke holes at
the hub, you'll see it falls off dramatically with increasing tension,
which is why almost all the deformation occurs during initial tensioning.

>> The primary tradeoff in wheel design is radial strength vs. weight.
>
> make that just "strength vs. weight".

That may be true of a rim, where there are multiple critical loads, but
the load on a wheel is almost entirely radial, lateral loads being less
than a tenth of that.

 

[jim beam]

Peter Cole wrote:
> jim beam wrote:
>> Peter Cole wrote:
>>> steve wrote:
>>>
>>>> It sounds like you are saying that spokes only get there load capacity
>>>> by taking it from the rim. There for the rim is the limiting factor to
>>>> spoke tension. as spoke tension increases load capacity of the rim
>>>> decreases. So what makes a spoked wheel stronger than a rim by itself
>>>> if the rim has all the load capacity that a spoked wheel will have?
>>>
>>> A spoked wheel can be very accurately modeled by a beam (rim) on an
>>> elastic bed (spokes). Visualize a railroad track. When spoke tension
>>> goes to zero under load it's the same as removing ties -- the track
>>> has a longer unsupported span.
>>>
>>>
>>>> So my interpretation of what you just said is that spoke tension is
>>>> independent of the strength of the wheel in terms of lateral and
>>>> torsional loads. If that is the case then the only reason for high
>>>> spoke tension is to increase fatigue life of the wheel.
>>>
>>> The reason for spoke tension is to support the rim. The radial
>>> stiffness of the wheel is the sum of the rim stiffness and the spoke
>>> stiffness.
>>
>> but that spoke stiffness comes at the expense of rim pre-load. if you
>> have an aluminum beam in simple bending, it will yield [the one side
>> in compression, the other in tension] when the material farthest from
>> its neutral plane reaches its elastic stress limit.
>
> The failure mode of rims is fatigue, yield is not of interest.

it sure is. rim buckling is by /far/ the most common wheel failure mode.

>
>>> When spokes go slack under load (those closest to the road), the
>>> wheel is left with rim stiffness alone. Imagine what would happen if
>>> your car springs got much softer during heavy loads. Lateral and
>>> torsional loads are not typically significant in bicycles, radial
>>> loads are.
>>
>> lateral loads can be significant enough to increase spoke tension to
>> levels that yield hub holes and untrue a wheel where spokes have not
>> been sufficiently seated.
>
> So you say. If you look at the geometry of deformation of spoke holes at
> the hub, you'll see it falls off dramatically with increasing tension,
> which is why almost all the deformation occurs during initial tensioning.

yield after tensioning can be sufficient to have spokes go completely
slack. i know this because i took the trouble to experiment - i built a
virgin hub, tensioned, trued [perfectly] and rode around the block once.
it was /way/ out of true on return, and some spokes were completely
slack. you should do that experiment yourself if you don't believe me.

>
>>> The primary tradeoff in wheel design is radial strength vs. weight.
>>
>> make that just "strength vs. weight".
>
> That may be true of a rim, where there are multiple critical loads, but
> the load on a wheel is almost entirely radial, lateral loads being less
> than a tenth of that.

1. lateral loads can be sufficient to... oh, see above.
2. if not the rim, then what else??? fudge.

 

[jim beam]

jim beam wrote:
> Peter Cole wrote:
>> jim beam wrote:
>>> Peter Cole wrote:
>>>> steve wrote:
>>>>
>>>>> It sounds like you are saying that spokes only get there load capacity
>>>>> by taking it from the rim. There for the rim is the limiting factor to
>>>>> spoke tension. as spoke tension increases load capacity of the rim
>>>>> decreases. So what makes a spoked wheel stronger than a rim by itself
>>>>> if the rim has all the load capacity that a spoked wheel will have?
>>>>
>>>> A spoked wheel can be very accurately modeled by a beam (rim) on an
>>>> elastic bed (spokes). Visualize a railroad track. When spoke tension
>>>> goes to zero under load it's the same as removing ties -- the track
>>>> has a longer unsupported span.
>>>>
>>>>
>>>>> So my interpretation of what you just said is that spoke tension is
>>>>> independent of the strength of the wheel in terms of lateral and
>>>>> torsional loads. If that is the case then the only reason for high
>>>>> spoke tension is to increase fatigue life of the wheel.
>>>>
>>>> The reason for spoke tension is to support the rim. The radial
>>>> stiffness of the wheel is the sum of the rim stiffness and the spoke
>>>> stiffness.
>>>
>>> but that spoke stiffness comes at the expense of rim pre-load. if
>>> you have an aluminum beam in simple bending, it will yield [the one
>>> side in compression, the other in tension] when the material farthest
>>> from its neutral plane reaches its elastic stress limit.
>>
>> The failure mode of rims is fatigue, yield is not of interest.
>
> it sure is. rim buckling is by /far/ the most common wheel failure mode.
>
>>
>>>> When spokes go slack under load (those closest to the road), the
>>>> wheel is left with rim stiffness alone. Imagine what would happen if
>>>> your car springs got much softer during heavy loads. Lateral and
>>>> torsional loads are not typically significant in bicycles, radial
>>>> loads are.
>>>
>>> lateral loads can be significant enough to increase spoke tension to
>>> levels that yield hub holes and untrue a wheel where spokes have not
>>> been sufficiently seated.
>>
>> So you say. If you look at the geometry of deformation of spoke holes
>> at the hub, you'll see it falls off dramatically with increasing
>> tension, which is why almost all the deformation occurs during initial
>> tensioning.
>
> yield after tensioning can be sufficient to have spokes go completely
> slack. i know this because i took the trouble to experiment - i built a
> virgin hub, tensioned,

oops, omission. make that "tensioned without 'stress relief'"

> trued [perfectly] and rode around the block once.
> it was /way/ out of true on return, and some spokes were completely
> slack. you should do that experiment yourself if you don't believe me.
>
>>
>>>> The primary tradeoff in wheel design is radial strength vs. weight.
>>>
>>> make that just "strength vs. weight".
>>
>> That may be true of a rim, where there are multiple critical loads,
>> but the load on a wheel is almost entirely radial, lateral loads being
>> less than a tenth of that.
>
> 1. lateral loads can be sufficient to... oh, see above.
> 2. if not the rim, then what else??? fudge.