Seating strings

[Phillip Ford]

>.......
>>I don't understand why you have a different number for moving down 
>>the pin and moving up the pin?  Static friction is dependent on the 
>>normal force between the string and bridge pin and the coefficient 
>>of friction.  The initial force to start an infinitesimal movement 
>>of the string should be the same whether it moves up the pin or 
>>down.
>
>The difference is the downbearing and vector force from the pin 
>tilt. Going down, the vector is in your favor. Going up, it is 
>resistance. What I was originally looking for with this spreadsheet 
>was an indication of the PSI load placed on the bridge cap by the 
>expanding cap pushing the string up the pin. I wanted ammunition for 
>my cyclic destruction scenario of cap damage. This seating thing was 
>an afterthought.

OK.  I think I see what you're saying.  In order to push the string 
up, the bridge cap has to exert enough force on the string to 
overcome the static friction and what I'm calling the Parallel force. 
 From my previous calculations, with the assumptions that I made, the 
static friction was 11.7 LB and Parallel force along the pin from the 
down bearing and side bearing was 8.0 LB.  So the bridge cap has to 
exert 19.7 LB along the bridge pin to move the string up.  Since the 
surface of the cap is presumably moving straight up that means that 
the force it has to exert on the string has to be great enough that 
the component of that force along the bridge pin is 19.7 LB or more. 
So, that means that the force P applied to the string (assuming a 15 
degree pin angle) has to be at least:

P cos 15 = 19.7 LB

P = 20.4 LB

To get some idea of the bearing stress on the cap we'll have to 
assume some bearing area.  This is easier said than done.  In theory 
since the string has a circular cross section it has a line contact 
on the bridge cap, which means that in theory the bearing stress is 
infinite (which also means that it should easily be able to indent 
the bridge cap).  In more practical terms the string and cap will 
indent a little and there will be some realistic bearing area.  I'm 
proposing that we make the width of the bearing area half the 
diameter of a large string, say 0.020 inch, and the effective length 
(the distance back from the notch) .250 inch.  I think that both of 
these numbers are generous.  In reality I think they will both be 
smaller.  But, for now, assume that bearing area is:

A = .25 x .020 = .005 IN ^ 2 (that's square inches in case the 
symbols don't come through)

So, bearing stress = 20.4/.005 = 4080 PSI

My wood handbooks say that compression perpendicular to the grain for 
maple is on the order of 1500 PSI.  So, guess what?

>...I see strings in contact with bridge caps with crushed edges, so 
>I'm assuming that string movement from play and the continual 
>moisture and temperature induced dimensional changes of everything 
>involved are partially overcoming the static friction and the down 
>vector force seats the string on the bridge.

Sounds reasonable.

>  Until reports of feeler gages going under strings on bridge caps 
>start poring in, I won't believe it happens.

I'll try to do my part on that front.

>  The easily observable fact that the notch edges of old bridges, and 
>not so old bridges, are crushed at an angle far exceeding any 
>downbearing angle the bridge ever supported means that a string 
>seated on the bridge top is quite likely not touching the notch 
>edge, and can still be measurably forced down there.

This also sounds reasonable.

Phil F

>
>Thanks for the clarification on the calcs.
>
>Ron N