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<p>Ron or somebody... would you please tell me where the two numbers I
have italisized and in bold text below ?? The rest is easy enough to follow.
:)
<p>Richard Brekne
<br>I.C.P.T.G. N.P.T.F.
<br>Bergen, Norway
<p>Ron Nossaman wrote:
<blockquote TYPE=CITE>
<br>* As long as the assembly is in the press, this is true. As for the
Voodoo
<br>engineering, let's conjure up a little math and see what the ancient
Gods
<br>have to say about all this and try to ascertain who's shaking the beads
<br>here. Let's talk Engineer.
<p>When the rib (or panel) is bent, there is a neutral stress line running
<br>roughly through the center of it's height. That part is obvious, so
let's
<br>use the rib centerline as a reference for computation. Let's use Del's
<br>example rib and panel as a standard and start with a rib 1000mm long,
25mm
<br>high, and 25mm wide, with a panel 8mm thick. Let's also assume the
18000mm
<br>final radius result after assembly, because we need some sort of figure
as a
<br>benchmark and the 60' radius seems to be the most widely accepted.
So what
<br>are the final arc lengths of the assembled surfaces? Here's where the
math
<br>comes in. First, let's figure the segment angle of the formed arc.
Angle =
<br><b><i>57.29578</i></b>*(riblength/radius). That's 57.29578 times 1000/18000,
or 3.1831
<br>degrees. The formed arc segment of the top of the panel is computed
as
<br>PanelTop = <b><i>0.017453</i></b>*(radius+(ribheight/2)+PanelThickness)*angle.
In the
<br>final assembly, that comes to 1001.1221. the formula
<br>Radius-sqrt(sqr(radius)-sqr(riblength/2)) gives us a crown height of
<br>6.9458mm. I figured four decimal places ought to be adequate overkill.
Now,
<br>in order to have compression in the top of the panel after assembly,
and
<br>before string load, We have to form the assembly in a press with a
curve
<br>radius such that the arc segment defined by the neutral stress centerline
of
<br>the panel when it's in the press is the same, or greater, than the
arc
<br>segment defined by the top of the panel after removal from the press
and
<br>spring back. As it turns out, a press caul of 14487mm radius produces
an arc
<br>segment angle of 3.955, and using
<br>0.017453*(radius+(RibHeight/2)+(PanelThickness/2)*angle gives us a
panel
<br>centerline of 1001.1222, with a crown height of 8.631mm. Therefor,
if the
<br>spring back after taking the assembly out of the press accounts for
a
<br>reduction in crown of more than 1.6854mm to arrive at that 18000mm
radius,
<br>the top of the panel will be under compression. That is the case with
this
<br>particular set of rib and panel dimensions, but the principal can be
put to
<br>any set of dimensions you may have to test the premise.
<p>Now, in your example, if we knew the caul radius of the press used,
the rib
<br>and panel dimensions, and the resultant crown radius of the assembly
upon
<br>removal from the press, we could find out what we really have.
<p>If my math is incorrect, please correct me. I need all the help I can
get
<br>with math. Also, I realise that this isn't exact to the four decimal
places
<br>shown, primarily because bending the rib in an arc shortens the chord
<br>measurement from which the computations are taken. Taking this into
account,
<br>the actual figures would be minutely different, but I assumed that
a
<br>hundredth of a millimeter or so wouldn't invalidate the illustration.
<p> Ron N</blockquote>
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