Re: [ATM] wire spiders

["Donald Good" <donald.good@comcast.net>]

Tony said:

> Think of it this way. Wire is very strong when the force is applied 
> along the long axis (in tension) and has little resistance to forces 
> applied 90 degrees to that (limp noodle). So.....the closer you are to 
> taking the loads in tension the stronger the spider will be.

But by laws of mechanics:
A wire can only support loads in tension.
Transverse loads are zero.
The sum of the tension vectors (1 per wire) plus the weight and torque
vectors (associated with the diagonal and mount) is zero.


Arjan said:

...
> The differential tension is given by:
>   T=E*A*(dL-dL')/L
...
> Conclusions:
> -1- It is against gut feeling that the amount of force calculated in te
example is independent of the amount of
> pretension in the wires. But I don't know what I did wrong ... anyone?
> -2- The force needed is relatively small, at least for the first mm. This
could have consequences for collimation
> for use between zenith and horizon.
...

As derived, dL and dL' should have opposite signs because one is stretch and
the other is shrink.  Therefore if dL is positive and dL' is negative, then
-dL' is positive and the absolute value for (dL-dL') is larger.  From this
and the assumption that mutual angle 30deg means P=15deg in your example, I
get F=88N.  If the values used for dL and dL' are both positive, then the
absolute value for (dL-dL') is much smaller and the result is 0.6N.

Pretension does not matter up to a point.  If a wire is slack, its tension
(and E) is effectively zero and remains zero until the slack is taken up.
But E does not jump immediately to E = 2.10^11 N/m^2.  At first the
directions of the bonds between the atoms in the steel have a lot of
randomness.  When the slack is taken up and the wire just starts to stretch,
the bonds become more aligned and E rapidly increases to its nominal value.
E then stays mostly (but not totally) constant over its useful range until
the wire begins to fail by permanent deformation or breaking.

You can upload your spreadsheet to your section of the atmlist file area.

Don

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