Youngs Modulus for Piano wire

[John Delacour]

At 9:48 pm +0200 27/8/06, Ric Brekne wrote:

>Well, I had rather hoped to be able to avoid stretching a few 
>samples of wire across the room and hanging weights to measure 
>deflections and then figure the relevant numbers out... At least at 
>this point.

You mean you want someone else to do it for you :-)   Well here's a 
simple way to do it.  Hang a wire (preferably straightened) from as 
high a point as you have available, say the upstairs window-sill. 
Rig up a rigid and immovable whatnot (technical term) as below so 
that the wire just touches the crossbar.  Attach a weight to the 
wire.  Tape a card to the crossbar and another card to the wire 
overlapping the first card. Carefully push a needle through the top 
card into the card behind it.  Remove the weight and replace it with 
just enough weight to hold the wire straight (just pull it tight). 
Push the needle through the top card at the same point so that you 
now have two needle pricks in the back card.  Measure the wire from A 
to B.  Measure the distance between the two pin pricks.  End of 
practical.  Tidy up.


>I just need a reliable ball park figure in order to proceed with my project.

31,000 lbs per sq. mm.

Youngs Modulus is the force that would be required to stretch the 
wire to double its length if it were to continue obeying Hooke's law 
-- in other words if it were infinitely elastic.  Hooke's law states 
that if you pull a wire with F and it stretches L, then a force of 2F 
will stretch it 2L, 3F 3L etc.  In other words there is a linear 
relationship between the force and the extension.

Here are the data and the result in a Perl script, which is easy to 
understand even if you've never heard of Perl.


#!/usr/bin/perl
$wire_number = 15;
$wire_diameter = 0.875; #mm.
$pi = 3.1415926;
$xsection_area = $wire_diameter**2 * $pi / 4;
$free_length = 2420; #mm.
$load = 42; #lbs.
$extension = 5.5; #mm.
$E = 1/$xsection_area * $free_length / $extension * $load;
printf "%0.0f\n", $E;
# --=> 30732

I used a No. 15 wire (not Ršslau in this case) at the end of which I 
made an English eye and passed the wire through a hole is a brass 
plate so that it would hang from the finishing coils of the eye and 
nothing would stretch at that point.  When the work was done I 
measured on the bench from the pin prick in the card (B) to the 
hanging point (A) to get 2,420 mm.  The distance between the two pin 
pricks in the back card was 5.5 mm.  If 42 lbs. stretched the wire 
5.5mm. then to stretch it to double its length I would need 18,480 
lbs and therefore to stretch a wire of 1 sq. mm. cross-section I 
would need 30,732 lbs. or, to be fussy, allowing for a generous error 
of 0.1mm in my measurement of the pin-pricks the figure will be 
somewhere between 30,184 and 31,301lbs.

ERGO, 31,000 lbs is the proper choice in this case.  There are likely 
to be variations according to the gauge number but I think the figure 
is more likely to go down than up as the wire gets thicker.  To test 
the fatter wires with any reasonable accuracy I would need a much 
higher house

JD




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