Spoke stress

I believe the misunderstanding about stresses that cause spoke
failures arises because spoke stress is invisible and not easily
measured. Stress being the tensile or compressive force per unit of
cross section area. Spoke tension is readily measured as is spoke
cross section (area) to get the stress in psi (pounds per square inch
of cross section) of the straight part of the spoke. Less evident is
what residual stresses are caused in manufacture and from lacing
wheels, the stresses that, along with operating stress, cause spokes
to fail at their ends rather than in their slender mid sections.

Spoke wire is shipped from the manufacturer on reels from which it
must be uncoiled, straightened and stress relieved before heading,
threading and, for some, swaging the shaft to be thinner than the
ends. Because all this is done at room temperature, new spokes retain
residual stress, steel being an elastic (springy) material.

Elasticity is evident in that spokes, when deformed, spring back
partially. This can be tested by manually bending a spoke. Bending
to change shape is in effect stretching the outside surface of the
bend and compressing the inside. Spring-back occurs because not all
parts of the cross section exceeded the elastic limit and partly
because after yielding, steel still has some elastic "memory", but not
enough to return to its original shape.

Partial spring-back results from the outer and inner surfaces of the
bend exceeding yield stress (plastic stretch) from which it does not
fully return. In addition, inner parts of the cross section did not
stretch as far and did not exceed yield, wanting to return to the
original shape. Spring-back succeeds only partially because the outer
surface yielded to a new home position while inner parts did not.

Partial spring-back shows there is a conflict between different depths
of the spoke wire, some in compression, some in tension, trying to
reach a neutral position. Residual stress from forming can be
thermally annealed or mechanically reduced. The example of mechanical
stress relief occurs when bulk spoke wire is uncoiled.

To swage and thread spokes, spoke wire must be straightened after
uncoiling from the spool. This is done by pulling the wire through a
slalom of rollers with ever diminishing excursions both vertically and
horizontally. This produces straight wire with no significant
residual stress, initial large excursions yielding the inner part of
the wire (as well as the outer) and subsequent smaller excursions
affecting in sequence the outer surface until all stresses have been
relieved... and giving a straight wire.

Swaging the midspan of spokes is done by forging, either by special
hammering or rolling. After swaging, spokes are headed with a single
forming stroke of a die and cut to length before rolling the thread.
The final step bends the elbow to a slightly obtuse angle (about 95°).

Heading, threading, and elbow bending leave residual stress, each
operation having some spring-back that is too small to detect
visually. Just the same, the stress is there although not
significantly high.

The final assault on spoke integrity comes after its elbow is bent to
conform to the angle required by a wheel. The most conspicuous being
the elbow bend of outbound spokes (where they exit hub flanges away
from wheel central plane,) as is evident from inspection after
unlacing a wheel. These spokes no longer have the original obtuse
angle but an acute angle, showing that the spoke elbow yielded.

After spokes are laced into a wheel, tensile stresses, at elbows and
threads, are augmented by spoke tension that is in itself not
threateningly high (about 1/3 yield) but because elbows were at yield,
they remains at yield, not being able to sustain any higher stress.
Subsequently, in use, where spoke tension is cyclically changing from
the carried load, and because cyclic stresses near yield are the cause
of fatigue failures in metals, spokes break.

Steel, even when stretched beyond yield, springs back until its stress
is zero but does not return to where it was before being stretched.
An analogy would be to be pulling a brick using a spring. Yielding
would occur when the brick slides and changes its home position from
which the spring pulls. When the spring is backed off to its former
position, its stress is lower than before the slip (yield.)

The same occurs in spokes that are at yield at their elbows.
Momentary overload affects peak stress by localized yielding, while
the bulk of the spoke remains in its elastic range. Cracks are
initiated High stress tensile locations in bends (elbows and threads)
to cause spoke failure. That this occurs most often at the elbow is
because that is the most highly stressed location resulting from both
manufacture and wheel lacing.

That this scenario occurs was demonstrated by spokes that had poorer
fatigue characteristics and were made noticeably more durable by
mechanical stress reliving (momentary overload). Stress relieving,
even on better spoke, material is worth the effort as is evident from
spoke failure reports with today's better spoke material.

Jobst Brandt

On 21 Dec 2006 03:46:58 GMT, wrote:

[snip duplicate post]

Dear Jobst,

Saying exactly the same thing twice is not really an argument.



Cheers,

Carl Fogel

In article
,
wrote:

On 21 Dec 2006 03:46:58 GMT, wrote:

[snip duplicate post]

Dear Jobst,

Saying exactly the same thing twice is not really an argument.

Leaving your misleading and incomplete essays
unanswered in a technical forum is not to be
countenanced. You are wrong, Jobst is right. Get over
it.

Answer truthfully. Do you fully comprehend Luns Tee's
essays on the geometry of residual stress in a cold
formed bend?

--
Michael Press

Michael Press wrote:
In article
,
wrote:

On 21 Dec 2006 03:46:58 GMT, wrote:

[snip duplicate post]

Dear Jobst,

Saying exactly the same thing twice is not really an argument.

Leaving your misleading and incomplete essays
unanswered in a technical forum is not to be
countenanced. You are wrong, Jobst is right.

eh?

Get over
it.

why? just accept that the emperor is fully clothed and stop rocking the
boat? buddy, the emperor is stark bollocky naked. get over it.


Answer truthfully. Do you fully comprehend Luns Tee's
essays on the geometry of residual stress in a cold
formed bend?