Strength of solid versus hollow axles

[[email protected]]

Recently therehave been a few posts which may confuse (or indeed
originate from) uneducated reader(s) concerning the strength of solid
versus hollow axles.

The strength of any particular cross-sectional shape can be described
by quantity called the section modulus, which is kind of a combination
of the amount of material and the distance away from the bending line
- usually taken as the centre - of the section.

If we take a typical rear axle the OD is pretty close to 0.4 inch. A
hollow axle has an ID of pretty close to 0.2 inch - giving a tube or
column with a wall thickness of almost 0.1 inch.

Using these numbers:

The solid axle will have a section modulus of 0.00627.
The hollow axle will have a section modulus of 0.00588

For front axles, which are around 0.35 OD, the numbers are:

Solid - 0.00435
Hollow - 0.00390

Now, of course, these figures mean that a solid axle is stronger.
There are other factors which affect the strength of axles, of course;
the choice of material, the heat treatment, the surface finish,
etcetera.

A particular effect which cannot be eliminated from hollow axles is
that of the roughness of the inside surface of the hole. Solid axles,
of course, do not have this, and so also do not suffer from the chance
that a crack may start at an irregularity on the inner surface. Cycle
axles of the highest prices (and, the buyer may sometimes presume, the
highest quality) are finished very well on the outside surface; but
the inside is a hidden quantity, difficult to finish and inspect.

In the real world of cycling, there are axles made from different
material and to different qualities. Of course it is possible to find
a particular hollow axle which may be stronger than another particular
solid axle - but to claim in abstract that a hollow axle is stronger
(or even no weaker than) than a solid one is clearly wrong.

 

[Bob Johnstone]

[email protected] wrote:
> The strength of any particular cross-sectional shape can be described
> by quantity called the section modulus, which is kind of a combination
> of the amount of material and the distance away from the bending line
> - usually taken as the centre - of the section.

The section modulus doesn't actually describe the strength of a beam. It
describes the stiffness.

> There are other factors which affect the strength of axles, of course;
> the choice of material, the heat treatment, the surface finish,
> etcetera.

Another important factor is whether the axle is being compressed by a
quick-release skewer. I would expect the compression from the skewer to
increase the strength of an axle in a way similar way to pre-stressed
concrete. The skewer may also provide a back-up if the axle fractures.

Bob

 

[Ian Smith]

On Sun, 24 Sep 2006, [email protected] <> wrote:

> uneducated reader(s)

Hmmm.

> The strength of any particular cross-sectional shape can be described
> by quantity called the section modulus,

No it can't. From your figures below, it is apparent you are talking
about the elastic section modulus (though you don't actually say so).
The elastic section modulus tells you about the stiffness of a section
(for a given, linear-elastic material).

It would tell you about strength only if your section were made from a
linear-elastic material with a brittle stress-limited failure mode.

Something like porcelain, for example.

Are your axles made of porcelain?

> Now, of course, these figures mean that a solid axle is stronger.

They mean it is stiffer. They do not mean it is stronger.

> A particular effect which cannot be eliminated from hollow axles is
> that of the roughness of the inside surface of the hole.

And the rest of this argument is substantially FUD. Internal
roughness can be controlled at least as well as can the stress-raiser
effect of the thread on the outside of the axle. Claiming this is a
fundamental flaw having a serious impact on strength of axle is
unjustified.

regards, Ian SMith
--
|\ /| no .sig
|o o|
|/ \|

 

[Al Gorithm]

[email protected] wrote:
> Recently therehave been a few posts which may confuse (or indeed
> originate from) uneducated reader(s) concerning the strength of solid
> versus hollow axles.
>
> The strength of any particular cross-sectional shape can be described
> by quantity called the section modulus, which is kind of a combination
> of the amount of material and the distance away from the bending line
> - usually taken as the centre - of the section.
>
> If we take a typical rear axle the OD is pretty close to 0.4 inch. A
> hollow axle has an ID of pretty close to 0.2 inch - giving a tube or
> column with a wall thickness of almost 0.1 inch.
>
> Using these numbers:
>
> The solid axle will have a section modulus of 0.00627.
> The hollow axle will have a section modulus of 0.00588
>
> For front axles, which are around 0.35 OD, the numbers are:
>
> Solid - 0.00435
> Hollow - 0.00390
>
> Now, of course, these figures mean that a solid axle is stronger.
> There are other factors which affect the strength of axles, of course;
> the choice of material, the heat treatment, the surface finish,
> etcetera.
>
> A particular effect which cannot be eliminated from hollow axles is
> that of the roughness of the inside surface of the hole. Solid axles,
> of course, do not have this, and so also do not suffer from the chance
> that a crack may start at an irregularity on the inner surface. Cycle
> axles of the highest prices (and, the buyer may sometimes presume, the
> highest quality) are finished very well on the outside surface; but
> the inside is a hidden quantity, difficult to finish and inspect.
>
> In the real world of cycling, there are axles made from different
> material and to different qualities. Of course it is possible to find
> a particular hollow axle which may be stronger than another particular
> solid axle - but to claim in abstract that a hollow axle is stronger
> (or even no weaker than) than a solid one is clearly wrong.
>
>
As everyone seems to be having a go here I'm going to step in too

Of course a solid axle of the same diameter is going to be "stronger "
than one with a hole drilled down the middle of it , but the question
here is of strength and stiffness and weight.
A spindle with hole down the middle will be lighter than a solid one
of the same diameter and it will have very similar stiffness. Although
it wont be as "strong".
To get the idea lets look at handle bars, they are about 7/8" diameter
and are hollow, if they were solid they would be "stronger" but would
be incredibly heavy. If they were made of a solid bar that weighed the
same as the 7/8" tube they would be about 10 mm diameter and very bendy.
So we make them from 7/8 tube. Horses for courses.
Al

 

[normanwisdom]

I've had 2 solid axles break (both back wheel), but no hollow ones.

cheers
Jacob

 

[[email protected]]

On Sun, 24 Sep 2006 14:03:29 GMT, Bob Johnstone
<[email protected]> wrote:

>[email protected] wrote:
>> The strength of any particular cross-sectional shape can be described
>> by quantity called the section modulus, which is kind of a combination
>> of the amount of material and the distance away from the bending line
>> - usually taken as the centre - of the section.
>
>The section modulus doesn't actually describe the strength of a beam. It
>describes the stiffness.
>
>> There are other factors which affect the strength of axles, of course;
>> the choice of material, the heat treatment, the surface finish,
>> etcetera.
>
>Another important factor is whether the axle is being compressed by a
>quick-release skewer. I would expect the compression from the skewer to
>increase the strength of an axle in a way similar way to pre-stressed
>concrete. The skewer may also provide a back-up if the axle fractures.
>

Well, it doesn't.

Compression of a long slender colum subject to bending forces
increases the likelyhood of bending and failure.

Concrete is not steel; nor is it (usually) hollow.

 

[[email protected]]

On 24 Sep 2006 10:51:09 -0700, "normanwisdom" <[email protected]>
wrote:

>I've had 2 solid axles break (both back wheel), but no hollow ones.
>

It's not because they were solid as opposed to hollow, but because
they were either of lower quality steel, poorer finish, or subject to
loads that the hollow ones weren't.

All else being equal, solid is stronger.

"All else" includes not having one made of "foam rubber".

 

[AT]

<[email protected]> wrote in message
news:[email protected]...
> Recently therehave been a few posts which may confuse (or indeed
> originate from) uneducated reader(s) concerning the strength of solid
> versus hollow axles.
>
> The strength of any particular cross-sectional shape can be described
> by quantity called the section modulus, which is kind of a combination
> of the amount of material and the distance away from the bending line
> - usually taken as the centre - of the section.
>
> If we take a typical rear axle the OD is pretty close to 0.4 inch. A
> hollow axle has an ID of pretty close to 0.2 inch - giving a tube or
> column with a wall thickness of almost 0.1 inch.
>
> Using these numbers:
>
> The solid axle will have a section modulus of 0.00627.
> The hollow axle will have a section modulus of 0.00588
>
> For front axles, which are around 0.35 OD, the numbers are:
>
> Solid - 0.00435
> Hollow - 0.00390
>
........Snip ........................

To add my twopenneth to this topic.

The reason why a hollow bar or beam will be close in stiffness to a solid
one is due to the fact that, in bending, the stress will be concentrated at
the top and bottom of the beam. If you bend a measuring ruler so that the
middle is higher than the ends, the top part will be in tension and the
lower will be in compression. Assuming that the upper half of the
cross-section mirrors the lower half then halfway up the cross-section will
be a neutral axis where no stress occurs. If the cross-section is irregular
then the neutral axis moves according to the concentration of material.

Using this principle we can see that in the centre of a solid axle, there is
hardly any stress in bending therefore it makes sense to concentrate the
material at the outer edges where the greatest stress occurs, it also saves
a lot of weight. This is why I-beams used in construction are shaped as they
are, the material is used more efficiently. The clamping of the QR lever
onto the axle induces axial compressive stress and does not gain strength in
the way that pre-stressed concrete does.

Concrete is weak in tension but strong in compression therefore
pre-stressing induces compression at the top and bottom of the beam prior to
loading. Placing a load onto a pre-stressed beam creates a tensile stress
underneath which is balanced by the compressive stress already introduced
into the beam.

Hope this clarifies the matter,

AT

 

[Mark Thompson]

> All else being equal, solid is stronger.

Remember something about mutually beneficial relationships between a
fungus-type-thing and oak trees. The fungus-type-thing would eat the
inside of the oak tree, and the oak tree benefited from being hollow, and
thus being able to withstand higher winds that would otherwise knock 'em
down.

I'm not sure this helps much, as hollow oak trees probably aren't ideal for
making axles thobut.

Mark.

 

[[email protected]]

On 26 Sep 2006 11:10:27 GMT, Mark Thompson
<pleasegivegenerously@warmmail*_turn_up_the_heat_to_reply*.com> wrote:

>> All else being equal, solid is stronger.
>
>Remember something about mutually beneficial relationships between a
>fungus-type-thing and oak trees. The fungus-type-thing would eat the
>inside of the oak tree, and the oak tree benefited from being hollow, and
>thus being able to withstand higher winds that would otherwise knock 'em
>down.

The tree would bend more, and reduce the stress on the roots.

This example does not apply to cycle axles because

a) the trunk of the tree was not breaking

b) cycle axles don't have roots.

>
>I'm not sure this helps much, as hollow oak trees probably aren't ideal for
>making axles thobut.

Neither is foam rubber.

 

[Roger Thorpe]

Are solid axle the same diameter as Q/R ones now? Certainly in the past
the solid axles were thinner.
Is axle breakage still a problem? In my experience the cause of axle
bending or failure was the long distance from the dropouts to the
bearing on the drive side giving a long lever arm and therefore bending
moment. The main cause of actual breakage was the stress raiser caused
by a thread with a sharp profile or the effective change in section
caused by the cone.

--
Roger Thorpe

My email address is spamtrapped. You can work it out!

 

[[email protected]]

On Tue, 26 Sep 2006 16:14:22 +0100, Roger Thorpe
<[email protected]> wrote:

>Are solid axle the same diameter as Q/R ones now? Certainly in the past
>the solid axles were thinner.

Axle sizes vary, but both solid and hollow ones are available in all
the common sizes. Stating that "in the past solid ones were thinner"
is erroneous.

>Is axle breakage still a problem?

It can be, if the axle is insufficient to bear the loads it
encounters. The strongest axles are those well made, of good quality
steel - and solid.

>In my experience the cause of axle
>bending or failure was the long distance from the dropouts to the
>bearing on the drive side giving a long lever arm and therefore bending
>moment. The main cause of actual breakage was the stress raiser caused
>by a thread with a sharp profile or the effective change in section
>caused by the cone.

Breakages in the middle of the axle happen(ed) as well.

 

[David Martin]

[email protected] wrote:

> Breakages in the middle of the axle happen(ed) as well.

You neglect the difference in loading between solid and hollow axle. A
solid axle is under tension, ahollow axle under compression.

...d

 

[Roger Thorpe]

[email protected] wrote:

> On Tue, 26 Sep 2006 16:14:22 +0100, Roger Thorpe
> <[email protected]> wrote:
>
>
>>Are solid axle the same diameter as Q/R ones now? Certainly in the past
>>the solid axles were thinner.
>
>
> Axle sizes vary, but both solid and hollow ones are available in all
> the common sizes. Stating that "in the past solid ones were thinner"
> is erroneous.
>

My bikeshop experience is about twenty years old, before the real
mountain bike boom. At that time "good" hubs were almost always Q/R. I
think that I might have seen a couple of pairs of track hubs, but
failures in good gear was rare.
Most people rode on variations or copies of the Maillard 'Atom' hubs and
for them there was only one standard size for front nuts and one for
rear nuts (excluding Sturmey Archer and continental sizes).
At that time, for the standard medium quality equipment, most stuff was
interchangeable, there were two standard diameters each for front and
rear axles, So it's not quite erroneous to say that in the past solid
ones were thinner.
My experience was that the solid axles broke more often than q/r ones.


>
>>Is axle breakage still a problem?
>
>
> It can be, if the axle is insufficient to bear the loads it
> encounters. The strongest axles are those well made, of good quality
> steel - and solid.
>
>
>>In my experience the cause of axle
>>bending or failure was the long distance from the dropouts to the
>>bearing on the drive side giving a long lever arm and therefore bending
>>moment. The main cause of actual breakage was the stress raiser caused
>>by a thread with a sharp profile or the effective change in section
>>caused by the cone.
>
>
> Breakages in the middle of the axle happen(ed) as well.

You may be right, but I honestly can't remember seeing one break anwhere
else than at the cone.

When you say tat the strongest axle of the same diameter is the solid
one you are right of course, but what is surprising and counterintuitive
is how small the contribution made by the core is. A hollow axle will be
weaker, but not much.


--
Roger Thorpe

My email address is spamtrapped. You can work it out!

 

[Rob Morley]

In article <[email protected]>
<[email protected]> wrote:
> On Tue, 26 Sep 2006 16:14:22 +0100, Roger Thorpe
> <[email protected]> wrote:
>
> >Are solid axle the same diameter as Q/R ones now? Certainly in the past
> >the solid axles were thinner.
>
> Axle sizes vary, but both solid and hollow ones are available in all
> the common sizes. Stating that "in the past solid ones were thinner"
> is erroneous.
>
I think you'll find that solid axles were usually 3/8" and hollow axles
were usually 10mm.

 

[[email protected]]

On 26 Sep 2006 08:46:22 -0700, "David Martin"
<[email protected]> wrote:

>
>[email protected] wrote:
>
>> Breakages in the middle of the axle happen(ed) as well.
>
>You neglect the difference in loading between solid and hollow axle. A
>solid axle is under tension, ahollow axle under compression.
>
>..d

Are you absolutely sure about this?

Completely, positively, absolutely sure?

You must look up Bierce's definition of "positive".

 

[Roger Thorpe]

Roger Thorpe wrote:


> When you say tat the strongest axle of the same diameter is the solid
> one you are right of course, but what is surprising and counterintuitive
> is how small the contribution made by the core is. A hollow axle will be
> weaker, but not much.
>
>
Just to back up this point. For a simple circular section beam:

stress/radius = bending moment/'second moment of area'

The stress we're talking about is the stress at the surface, where it is
maximum.
The bending moment is the load. let's take this as a constant.
The second moment of area is a sort of shape factor and is a constant x
the fourth power of the radius.
Taking the bending moment as 1 and the constant as 1 then we can do some
sums(Ignoring the units to keep things simple)and find that the strength
is 'second moment of area'/radius.

For a solid axle of diameter 9.5 mm (radius 4.75)the strngth is
4.75^4 / 4.75 = 107
for the same axle with a 5mm axial hole the strength is
(4.75^4 - 2.5^4)/4.75 = 99
the strength is reduced by 7.5%

but increase the diameter slightly to a 9.8 mm axle with the same 5mm
bore then the strength is
(4.9^4 -2.5^4)/4.9 = 109
now we're a bit sronger than the solid one, but 21% lighter.


Isn't it marvellous - we're all correct!

Roger

--
Roger Thorpe

My email address is spamtrapped. You can work it out!

 

[Alan Braggins]

Mark Thompson wrote:
>
>I'm not sure this helps much, as hollow oak trees probably aren't ideal for
>making axles thobut.

Nor internal combustion engine pistons, but my grandfather told the story
of a buyer at an auction soon after the war finding his newly acquired lorry
had oak pistons when the engine siezed - not very long after he had bought it,
but long enough that he wasn't able to get his cash back.

 

[Sandy Morton]

In article <[email protected]>, Alan
Braggins <[email protected]> wrote:
> Nor internal combustion engine pistons, but my grandfather told the
> story of a buyer at an auction soon after the war finding his newly
> acquired lorry had oak pistons when the engine siezed - not very
> long after he had bought it, but long enough that he wasn't able to
> get his cash back.

Nylon stockings were almost as good and were much easier to fit.

--
T h e - e x t e n d e r ! ! ! !

 

[Rob Morley]

In article <[email protected]>
Alan Braggins <[email protected]> wrote:
> Mark Thompson wrote:
> >
> >I'm not sure this helps much, as hollow oak trees probably aren't ideal for
> >making axles thobut.
>
> Nor internal combustion engine pistons, but my grandfather told the story
> of a buyer at an auction soon after the war finding his newly acquired lorry
> had oak pistons when the engine siezed - not very long after he had bought it,
> but long enough that he wasn't able to get his cash back.
>
http://groups.google.com/group/uk.rec.engines.stationary/tree/browse_frm
/thread/e2bc4708a968a926/3d60ee418fa61834

http://tinyurl.com/pfpzs