Spoke tension Question



On 2007-11-07, Peter Cole <[email protected]> wrote:
> Ben C wrote:
>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>> Ben C wrote:
>>>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>>>> The most a rim can deform before spokes slack is ~1mm. That's not enough
>>>>> to permanently deform.
>>>> That ~1mm is the _change in deformation_, not the total deformation. The
>>>> rim is already precompressed.
>>> Spoke tension causes a circumferential force, load/impact a radial
>>> force, they are orthogonal.

>>
>> But the spokes are pulling radially so isn't that also a radial force?

>
> Yes, but (locally) when the spoke goes slake, that component is gone.


I was talking about the rim yielding due to the radial tension + load,
i.e. yielding that might happen _before_ the spoke above the contact
patch has gone slack.

But I see your point-- the spokes directly above the bit that's
potentially flat-spotting may be slack, but the other spokes are still
contributing a bit of compressive stress because of the circumferential
force. I hadn't even considered that.

[...]
>> Not sure what you mean by ~4x nominal spoke tension.

>
> If you calculate the stress from rim compression, you get somewhere
> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
> 4x to bring the cross section into the region of yield (but the spokes
> would snap, and/or the rim would buckle long before that).


I see.

Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
thinking of the wheel as a cylinder and the spokes collectively as a
sort of gas inside it.

36 spokes, 1500N each: 54000N
Radius (r): 0.3m
Thickness of wall (t): 0.02m

Width of rim: 0.02m
Area of rim: 2*pi*r * 0.02m = 0.037 m^2
Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2

hoop stress = pr / t = 21MPa.

Hmm, not quite right, but then the rim is actually a box section, for
one thing.

>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>> it right up to yield, then yes, there is a maximum ~1mm deep
>> deformation.

>
> No rim is that flimsy, not even the old school ones.


Yes, and certainly not if normal spoke tension brings the rim to 1/4
yield.
 
On 2007-11-07, Peter Cole <[email protected]> wrote:
> Ben C wrote:
>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>> Ben C wrote:
>>>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>>>> The most a rim can deform before spokes slack is ~1mm. That's not enough
>>>>> to permanently deform.
>>>> That ~1mm is the _change in deformation_, not the total deformation. The
>>>> rim is already precompressed.
>>> Spoke tension causes a circumferential force, load/impact a radial
>>> force, they are orthogonal.

>>
>> But the spokes are pulling radially so isn't that also a radial force?

>
> Yes, but (locally) when the spoke goes slake, that component is gone.


I was talking about the rim yielding due to the radial tension + load,
i.e. yielding that might happen _before_ the spoke above the contact
patch has gone slack.

But I see your point-- the spokes directly above the bit that's
potentially flat-spotting may be slack, but the other spokes are still
contributing a bit of compressive stress because of the circumferential
force. I hadn't even considered that.

[...]
>> Not sure what you mean by ~4x nominal spoke tension.

>
> If you calculate the stress from rim compression, you get somewhere
> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
> 4x to bring the cross section into the region of yield (but the spokes
> would snap, and/or the rim would buckle long before that).


I see.

Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
thinking of the wheel as a cylinder and the spokes collectively as a
sort of gas inside it.

36 spokes, 1500N each: 54000N
Radius (r): 0.3m
Thickness of wall (t): 0.02m

Width of rim: 0.02m
Area of rim: 2*pi*r * 0.02m = 0.037 m^2
Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2

hoop stress = pr / t = 21MPa.

Hmm, not quite right, but then the rim is actually a box section, for
one thing.

>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>> it right up to yield, then yes, there is a maximum ~1mm deep
>> deformation.

>
> No rim is that flimsy, not even the old school ones.


Yes, and certainly not if normal spoke tension brings the rim to 1/4
yield.
 
Ben C wrote:
> On 2007-11-07, Peter Cole <[email protected]> wrote:
>> Ben C wrote:
>>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>>> Ben C wrote:
>>>>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>>>>> The most a rim can deform before spokes slack is ~1mm. That's not enough
>>>>>> to permanently deform.
>>>>> That ~1mm is the _change in deformation_, not the total deformation. The
>>>>> rim is already precompressed.
>>>> Spoke tension causes a circumferential force, load/impact a radial
>>>> force, they are orthogonal.
>>> But the spokes are pulling radially so isn't that also a radial force?

>> Yes, but (locally) when the spoke goes slake, that component is gone.

>
> I was talking about the rim yielding due to the radial tension + load,
> i.e. yielding that might happen _before_ the spoke above the contact
> patch has gone slack.
>
> But I see your point-- the spokes directly above the bit that's
> potentially flat-spotting may be slack, but the other spokes are still
> contributing a bit of compressive stress because of the circumferential
> force. I hadn't even considered that.
>
> [...]
>>> Not sure what you mean by ~4x nominal spoke tension.

>> If you calculate the stress from rim compression, you get somewhere
>> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
>> 4x to bring the cross section into the region of yield (but the spokes
>> would snap, and/or the rim would buckle long before that).

>
> I see.
>
> Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
> thinking of the wheel as a cylinder and the spokes collectively as a
> sort of gas inside it.
>
> 36 spokes, 1500N each: 54000N
> Radius (r): 0.3m
> Thickness of wall (t): 0.02m
>
> Width of rim: 0.02m
> Area of rim: 2*pi*r * 0.02m = 0.037 m^2
> Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2
>
> hoop stress = pr / t = 21MPa.
>
> Hmm, not quite right, but then the rim is actually a box section, for
> one thing.
>
>>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>>> it right up to yield, then yes, there is a maximum ~1mm deep
>>> deformation.

>> No rim is that flimsy, not even the old school ones.

>
> Yes, and certainly not if normal spoke tension brings the rim to 1/4
> yield.


the above assumes bulk yielding. the actual deformation zone is small,
and caused by bending - leverage alone causes significant stress. 21MPa
could be 10% of yield, but that's 10% less load required to cause a flat
spot.
 
Ben C wrote:
> On 2007-11-07, Peter Cole <[email protected]> wrote:
>> Ben C wrote:
>>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>>> Ben C wrote:
>>>>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>>>>> The most a rim can deform before spokes slack is ~1mm. That's not enough
>>>>>> to permanently deform.
>>>>> That ~1mm is the _change in deformation_, not the total deformation. The
>>>>> rim is already precompressed.
>>>> Spoke tension causes a circumferential force, load/impact a radial
>>>> force, they are orthogonal.
>>> But the spokes are pulling radially so isn't that also a radial force?

>> Yes, but (locally) when the spoke goes slake, that component is gone.

>
> I was talking about the rim yielding due to the radial tension + load,
> i.e. yielding that might happen _before_ the spoke above the contact
> patch has gone slack.
>
> But I see your point-- the spokes directly above the bit that's
> potentially flat-spotting may be slack, but the other spokes are still
> contributing a bit of compressive stress because of the circumferential
> force. I hadn't even considered that.
>
> [...]
>>> Not sure what you mean by ~4x nominal spoke tension.

>> If you calculate the stress from rim compression, you get somewhere
>> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
>> 4x to bring the cross section into the region of yield (but the spokes
>> would snap, and/or the rim would buckle long before that).

>
> I see.
>
> Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
> thinking of the wheel as a cylinder and the spokes collectively as a
> sort of gas inside it.
>
> 36 spokes, 1500N each: 54000N
> Radius (r): 0.3m
> Thickness of wall (t): 0.02m
>
> Width of rim: 0.02m
> Area of rim: 2*pi*r * 0.02m = 0.037 m^2
> Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2
>
> hoop stress = pr / t = 21MPa.
>
> Hmm, not quite right, but then the rim is actually a box section, for
> one thing.
>
>>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>>> it right up to yield, then yes, there is a maximum ~1mm deep
>>> deformation.

>> No rim is that flimsy, not even the old school ones.

>
> Yes, and certainly not if normal spoke tension brings the rim to 1/4
> yield.


the above assumes bulk yielding. the actual deformation zone is small,
and caused by bending - leverage alone causes significant stress. 21MPa
could be 10% of yield, but that's 10% less load required to cause a flat
spot.
 
On 2007-11-09, jim beam <[email protected]> wrote:
> Ben C wrote:
>> On 2007-11-07, Peter Cole <[email protected]> wrote:

[...]
>>>> Not sure what you mean by ~4x nominal spoke tension.
>>> If you calculate the stress from rim compression, you get somewhere
>>> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
>>> 4x to bring the cross section into the region of yield (but the spokes
>>> would snap, and/or the rim would buckle long before that).

>>
>> I see.
>>
>> Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
>> thinking of the wheel as a cylinder and the spokes collectively as a
>> sort of gas inside it.
>>
>> 36 spokes, 1500N each: 54000N
>> Radius (r): 0.3m
>> Thickness of wall (t): 0.02m
>>
>> Width of rim: 0.02m
>> Area of rim: 2*pi*r * 0.02m = 0.037 m^2
>> Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2
>>
>> hoop stress = pr / t = 21MPa.
>>
>> Hmm, not quite right, but then the rim is actually a box section, for
>> one thing.
>>
>>>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>>>> it right up to yield, then yes, there is a maximum ~1mm deep
>>>> deformation.
>>> No rim is that flimsy, not even the old school ones.

>>
>> Yes, and certainly not if normal spoke tension brings the rim to 1/4
>> yield.

>
> the above assumes bulk yielding. the actual deformation zone is small,
> and caused by bending - leverage alone causes significant stress. 21MPa
> could be 10% of yield, but that's 10% less load required to cause a flat
> spot.


70MPa is likely to be a better figure than my probably incorrect
estimate of 21MPa.

But you're right: if it's hoop compression we're talking about, that's
still there (reduced a bit but still there) even when spokes above the
contact patch have gone slack. So the limit of ~1mm doesn't apply.

In this scenario the rim flat spots with slack spokes above it but
bending is assisted by the hoop compression contributed by other spokes
whose length is changing very little.

The problem is you have to set that against the number of spokes that go
slack. With tighter spokes fewer will go slack for a given load and so
the rim will be supported better-- less bending leverage.
 
On 2007-11-09, jim beam <[email protected]> wrote:
> Ben C wrote:
>> On 2007-11-07, Peter Cole <[email protected]> wrote:

[...]
>>>> Not sure what you mean by ~4x nominal spoke tension.
>>> If you calculate the stress from rim compression, you get somewhere
>>> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
>>> 4x to bring the cross section into the region of yield (but the spokes
>>> would snap, and/or the rim would buckle long before that).

>>
>> I see.
>>
>> Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
>> thinking of the wheel as a cylinder and the spokes collectively as a
>> sort of gas inside it.
>>
>> 36 spokes, 1500N each: 54000N
>> Radius (r): 0.3m
>> Thickness of wall (t): 0.02m
>>
>> Width of rim: 0.02m
>> Area of rim: 2*pi*r * 0.02m = 0.037 m^2
>> Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2
>>
>> hoop stress = pr / t = 21MPa.
>>
>> Hmm, not quite right, but then the rim is actually a box section, for
>> one thing.
>>
>>>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>>>> it right up to yield, then yes, there is a maximum ~1mm deep
>>>> deformation.
>>> No rim is that flimsy, not even the old school ones.

>>
>> Yes, and certainly not if normal spoke tension brings the rim to 1/4
>> yield.

>
> the above assumes bulk yielding. the actual deformation zone is small,
> and caused by bending - leverage alone causes significant stress. 21MPa
> could be 10% of yield, but that's 10% less load required to cause a flat
> spot.


70MPa is likely to be a better figure than my probably incorrect
estimate of 21MPa.

But you're right: if it's hoop compression we're talking about, that's
still there (reduced a bit but still there) even when spokes above the
contact patch have gone slack. So the limit of ~1mm doesn't apply.

In this scenario the rim flat spots with slack spokes above it but
bending is assisted by the hoop compression contributed by other spokes
whose length is changing very little.

The problem is you have to set that against the number of spokes that go
slack. With tighter spokes fewer will go slack for a given load and so
the rim will be supported better-- less bending leverage.
 
Ben C wrote:

> But you're right: if it's hoop compression we're talking about, that's
> still there (reduced a bit but still there) even when spokes above the
> contact patch have gone slack. So the limit of ~1mm doesn't apply.
>
> In this scenario the rim flat spots with slack spokes above it but
> bending is assisted by the hoop compression contributed by other spokes
> whose length is changing very little.
>
> The problem is you have to set that against the number of spokes that go
> slack. With tighter spokes fewer will go slack for a given load and so
> the rim will be supported better-- less bending leverage.


Flat spotting is caused by striking a hole edge or some other uneven
surface, causing very local deformation. Under normal (flat surface)
loading, a 36 spoke wheel will see 1/2 the spoke change in tension in
adjacent spokes compared to the spoke directly above the contact patch
(from FEA). One could only assume that an uneven surface would cause
even more concentrated deformation.

The salient point is that when the spoke at load center becomes slack
(~1mm), the rim is no longer supported in this area, but will be still
supported by adjacent spokes. This causes a dramatic change in local
stiffness, with additional force causing proportionally greater rim
deflection.

The circumferential compression from spoke tension causes a uniform
stress across the rim cross section, estimated to be in the order of
70Mpa for a nominal wheel (36x100kgf). Bending force will superimpose an
additional compression on the outer part of the rim (tension inner)
reaching a maximum at the outer skin.

My very rough estimate of bending stress for the nominal wheel in
Jobst's book gives perhaps 20MPa for 50kg load. Given that yield is at
least 250MPa, 70Mpa static stress gives an additional >180MPa of bending
stress before yield, or ~9x load (assuming no spoke slacking). The spoke
at the load point will go slack at approximately 5x load. It's not clear
that a 50% increase in spoke tension from the nominal 100kgf wouldn't
make a wheel that was less prone to flat spotting, it would approach
yield at around the same point as spoke slack, or about 7.5x load,
whereas the nominal wheel would slack at 5x, change stiffness at that
point, and be unsupported for the further 2.5x load. It's likely that
that greater bending stress (from loss of stiffness) would exceed the
additional static rim compression stress from increasing spoke tension 50%.

For rims significantly stiffer than the nominal, the change in stiffness
at spoke slack load may not be as large, but I'd guess the difference is
small when such rims are used with fewer (and stiffer) spokes.
 
Ben C wrote:

> But you're right: if it's hoop compression we're talking about, that's
> still there (reduced a bit but still there) even when spokes above the
> contact patch have gone slack. So the limit of ~1mm doesn't apply.
>
> In this scenario the rim flat spots with slack spokes above it but
> bending is assisted by the hoop compression contributed by other spokes
> whose length is changing very little.
>
> The problem is you have to set that against the number of spokes that go
> slack. With tighter spokes fewer will go slack for a given load and so
> the rim will be supported better-- less bending leverage.


Flat spotting is caused by striking a hole edge or some other uneven
surface, causing very local deformation. Under normal (flat surface)
loading, a 36 spoke wheel will see 1/2 the spoke change in tension in
adjacent spokes compared to the spoke directly above the contact patch
(from FEA). One could only assume that an uneven surface would cause
even more concentrated deformation.

The salient point is that when the spoke at load center becomes slack
(~1mm), the rim is no longer supported in this area, but will be still
supported by adjacent spokes. This causes a dramatic change in local
stiffness, with additional force causing proportionally greater rim
deflection.

The circumferential compression from spoke tension causes a uniform
stress across the rim cross section, estimated to be in the order of
70Mpa for a nominal wheel (36x100kgf). Bending force will superimpose an
additional compression on the outer part of the rim (tension inner)
reaching a maximum at the outer skin.

My very rough estimate of bending stress for the nominal wheel in
Jobst's book gives perhaps 20MPa for 50kg load. Given that yield is at
least 250MPa, 70Mpa static stress gives an additional >180MPa of bending
stress before yield, or ~9x load (assuming no spoke slacking). The spoke
at the load point will go slack at approximately 5x load. It's not clear
that a 50% increase in spoke tension from the nominal 100kgf wouldn't
make a wheel that was less prone to flat spotting, it would approach
yield at around the same point as spoke slack, or about 7.5x load,
whereas the nominal wheel would slack at 5x, change stiffness at that
point, and be unsupported for the further 2.5x load. It's likely that
that greater bending stress (from loss of stiffness) would exceed the
additional static rim compression stress from increasing spoke tension 50%.

For rims significantly stiffer than the nominal, the change in stiffness
at spoke slack load may not be as large, but I'd guess the difference is
small when such rims are used with fewer (and stiffer) spokes.
 
Ben C wrote:
> On 2007-11-09, jim beam <[email protected]> wrote:
>> Ben C wrote:
>>> On 2007-11-07, Peter Cole <[email protected]> wrote:

> [...]
>>>>> Not sure what you mean by ~4x nominal spoke tension.
>>>> If you calculate the stress from rim compression, you get somewhere
>>>> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
>>>> 4x to bring the cross section into the region of yield (but the spokes
>>>> would snap, and/or the rim would buckle long before that).
>>> I see.
>>>
>>> Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
>>> thinking of the wheel as a cylinder and the spokes collectively as a
>>> sort of gas inside it.
>>>
>>> 36 spokes, 1500N each: 54000N
>>> Radius (r): 0.3m
>>> Thickness of wall (t): 0.02m
>>>
>>> Width of rim: 0.02m
>>> Area of rim: 2*pi*r * 0.02m = 0.037 m^2
>>> Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2
>>>
>>> hoop stress = pr / t = 21MPa.
>>>
>>> Hmm, not quite right, but then the rim is actually a box section, for
>>> one thing.
>>>
>>>>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>>>>> it right up to yield, then yes, there is a maximum ~1mm deep
>>>>> deformation.
>>>> No rim is that flimsy, not even the old school ones.
>>> Yes, and certainly not if normal spoke tension brings the rim to 1/4
>>> yield.

>> the above assumes bulk yielding. the actual deformation zone is small,
>> and caused by bending - leverage alone causes significant stress. 21MPa
>> could be 10% of yield, but that's 10% less load required to cause a flat
>> spot.

>
> 70MPa is likely to be a better figure than my probably incorrect
> estimate of 21MPa.
>
> But you're right: if it's hoop compression we're talking about, that's
> still there (reduced a bit but still there) even when spokes above the
> contact patch have gone slack. So the limit of ~1mm doesn't apply.
>
> In this scenario the rim flat spots with slack spokes above it but
> bending is assisted by the hoop compression contributed by other spokes
> whose length is changing very little.
>
> The problem is you have to set that against the number of spokes that go
> slack. With tighter spokes fewer will go slack for a given load and so
> the rim will be supported better-- less bending leverage.


if the rim was infinitely stiff, the spoke tension distribution deltas
would be completely different. so, if you look at spoke slacking as a
function of rim deformation, you can start to see why modern wheels use
deeper rims and lower spoke counts with spoke tension remaining about
the same.
 
Ben C wrote:
> On 2007-11-09, jim beam <[email protected]> wrote:
>> Ben C wrote:
>>> On 2007-11-07, Peter Cole <[email protected]> wrote:

> [...]
>>>>> Not sure what you mean by ~4x nominal spoke tension.
>>>> If you calculate the stress from rim compression, you get somewhere
>>>> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
>>>> 4x to bring the cross section into the region of yield (but the spokes
>>>> would snap, and/or the rim would buckle long before that).
>>> I see.
>>>
>>> Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
>>> thinking of the wheel as a cylinder and the spokes collectively as a
>>> sort of gas inside it.
>>>
>>> 36 spokes, 1500N each: 54000N
>>> Radius (r): 0.3m
>>> Thickness of wall (t): 0.02m
>>>
>>> Width of rim: 0.02m
>>> Area of rim: 2*pi*r * 0.02m = 0.037 m^2
>>> Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2
>>>
>>> hoop stress = pr / t = 21MPa.
>>>
>>> Hmm, not quite right, but then the rim is actually a box section, for
>>> one thing.
>>>
>>>>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>>>>> it right up to yield, then yes, there is a maximum ~1mm deep
>>>>> deformation.
>>>> No rim is that flimsy, not even the old school ones.
>>> Yes, and certainly not if normal spoke tension brings the rim to 1/4
>>> yield.

>> the above assumes bulk yielding. the actual deformation zone is small,
>> and caused by bending - leverage alone causes significant stress. 21MPa
>> could be 10% of yield, but that's 10% less load required to cause a flat
>> spot.

>
> 70MPa is likely to be a better figure than my probably incorrect
> estimate of 21MPa.
>
> But you're right: if it's hoop compression we're talking about, that's
> still there (reduced a bit but still there) even when spokes above the
> contact patch have gone slack. So the limit of ~1mm doesn't apply.
>
> In this scenario the rim flat spots with slack spokes above it but
> bending is assisted by the hoop compression contributed by other spokes
> whose length is changing very little.
>
> The problem is you have to set that against the number of spokes that go
> slack. With tighter spokes fewer will go slack for a given load and so
> the rim will be supported better-- less bending leverage.


if the rim was infinitely stiff, the spoke tension distribution deltas
would be completely different. so, if you look at spoke slacking as a
function of rim deformation, you can start to see why modern wheels use
deeper rims and lower spoke counts with spoke tension remaining about
the same.
 
On 2007-11-09, Peter Cole <[email protected]> wrote:
> Ben C wrote:
>
>> But you're right: if it's hoop compression we're talking about, that's
>> still there (reduced a bit but still there) even when spokes above the
>> contact patch have gone slack. So the limit of ~1mm doesn't apply.
>>
>> In this scenario the rim flat spots with slack spokes above it but
>> bending is assisted by the hoop compression contributed by other spokes
>> whose length is changing very little.
>>
>> The problem is you have to set that against the number of spokes that go
>> slack. With tighter spokes fewer will go slack for a given load and so
>> the rim will be supported better-- less bending leverage.

>
> Flat spotting is caused by striking a hole edge or some other uneven
> surface, causing very local deformation. Under normal (flat surface)
> loading, a 36 spoke wheel will see 1/2 the spoke change in tension in
> adjacent spokes compared to the spoke directly above the contact patch
> (from FEA).


Is that from Jobst's FEA? I think Ian was saying he had to guesstimate a
bit how the load distributes, since it depends on the tyre which is
difficult to model.

> One could only assume that an uneven surface would cause even more
> concentrated deformation.


Generally yes, although I suppose if the tyre were striking a concave
deformation that approximated its own radius the deformation might be
less concentrated.

> (~1mm), the rim is no longer supported in this area, but will be still
> supported by adjacent spokes. This causes a dramatic change in local
> stiffness, with additional force causing proportionally greater rim
> deflection.
>
> The circumferential compression from spoke tension causes a uniform
> stress across the rim cross section, estimated to be in the order of
> 70Mpa for a nominal wheel (36x100kgf). Bending force will superimpose an
> additional compression on the outer part of the rim (tension inner)
> reaching a maximum at the outer skin.
>
> My very rough estimate of bending stress for the nominal wheel in
> Jobst's book gives perhaps 20MPa for 50kg load. Given that yield is at
> least 250MPa, 70Mpa static stress gives an additional >180MPa of bending
> stress before yield, or ~9x load (assuming no spoke slacking). The spoke
> at the load point will go slack at approximately 5x load. It's not clear
> that a 50% increase in spoke tension from the nominal 100kgf wouldn't
> make a wheel that was less prone to flat spotting, it would approach
> yield at around the same point as spoke slack, or about 7.5x load,
> whereas the nominal wheel would slack at 5x, change stiffness at that
> point, and be unsupported for the further 2.5x load. It's likely that
> that greater bending stress (from loss of stiffness) would exceed the
> additional static rim compression stress from increasing spoke tension 50%.


Why does loss of stiffness result in greater bending stress?

I think you get greater bending moment (and therefore stress) as a
result of losing the support of some of the spokes as they go slack
(railroad ties). Is that what you mean or are you talking about
something else?

> For rims significantly stiffer than the nominal, the change in stiffness
> at spoke slack load may not be as large, but I'd guess the difference is
> small when such rims are used with fewer (and stiffer) spokes.
 
On 2007-11-09, Peter Cole <[email protected]> wrote:
> Ben C wrote:
>
>> But you're right: if it's hoop compression we're talking about, that's
>> still there (reduced a bit but still there) even when spokes above the
>> contact patch have gone slack. So the limit of ~1mm doesn't apply.
>>
>> In this scenario the rim flat spots with slack spokes above it but
>> bending is assisted by the hoop compression contributed by other spokes
>> whose length is changing very little.
>>
>> The problem is you have to set that against the number of spokes that go
>> slack. With tighter spokes fewer will go slack for a given load and so
>> the rim will be supported better-- less bending leverage.

>
> Flat spotting is caused by striking a hole edge or some other uneven
> surface, causing very local deformation. Under normal (flat surface)
> loading, a 36 spoke wheel will see 1/2 the spoke change in tension in
> adjacent spokes compared to the spoke directly above the contact patch
> (from FEA).


Is that from Jobst's FEA? I think Ian was saying he had to guesstimate a
bit how the load distributes, since it depends on the tyre which is
difficult to model.

> One could only assume that an uneven surface would cause even more
> concentrated deformation.


Generally yes, although I suppose if the tyre were striking a concave
deformation that approximated its own radius the deformation might be
less concentrated.

> (~1mm), the rim is no longer supported in this area, but will be still
> supported by adjacent spokes. This causes a dramatic change in local
> stiffness, with additional force causing proportionally greater rim
> deflection.
>
> The circumferential compression from spoke tension causes a uniform
> stress across the rim cross section, estimated to be in the order of
> 70Mpa for a nominal wheel (36x100kgf). Bending force will superimpose an
> additional compression on the outer part of the rim (tension inner)
> reaching a maximum at the outer skin.
>
> My very rough estimate of bending stress for the nominal wheel in
> Jobst's book gives perhaps 20MPa for 50kg load. Given that yield is at
> least 250MPa, 70Mpa static stress gives an additional >180MPa of bending
> stress before yield, or ~9x load (assuming no spoke slacking). The spoke
> at the load point will go slack at approximately 5x load. It's not clear
> that a 50% increase in spoke tension from the nominal 100kgf wouldn't
> make a wheel that was less prone to flat spotting, it would approach
> yield at around the same point as spoke slack, or about 7.5x load,
> whereas the nominal wheel would slack at 5x, change stiffness at that
> point, and be unsupported for the further 2.5x load. It's likely that
> that greater bending stress (from loss of stiffness) would exceed the
> additional static rim compression stress from increasing spoke tension 50%.


Why does loss of stiffness result in greater bending stress?

I think you get greater bending moment (and therefore stress) as a
result of losing the support of some of the spokes as they go slack
(railroad ties). Is that what you mean or are you talking about
something else?

> For rims significantly stiffer than the nominal, the change in stiffness
> at spoke slack load may not be as large, but I'd guess the difference is
> small when such rims are used with fewer (and stiffer) spokes.
 
On Oct 30, 12:55 am, Jas51 <[email protected]> wrote:
> Using the rim taco-method of setting spoke tension, should a tire be
> mounted and inflated beforehand? Ive always brung the spokes up to tension
> with no tire mounted, but the 160 psi thread got me wondering. What's the
> proper technique?


yes set the wheels without pressure. the tube acts like an air bladder
so the pressure will be distributed evenly. if there is a problem on
set up and it is pressurized, it is only going to make it worse
regards,
carlos
www.bikingthings.com
Get Faster, Enjoy Cycling, Get Fit, Live Better.
 
On Oct 30, 12:55 am, Jas51 <[email protected]> wrote:
> Using the rim taco-method of setting spoke tension, should a tire be
> mounted and inflated beforehand? Ive always brung the spokes up to tension
> with no tire mounted, but the 160 psi thread got me wondering. What's the
> proper technique?


yes set the wheels without pressure. the tube acts like an air bladder
so the pressure will be distributed evenly. if there is a problem on
set up and it is pressurized, it is only going to make it worse
regards,
carlos
www.bikingthings.com
Get Faster, Enjoy Cycling, Get Fit, Live Better.