Definition:
The modulus of elasticity is a constant of
proportionality between stress and relative extension
(change in length per unit length) for a thin rod exposed
to a tensile force.
The definition assumes that we are dealing with an
isotropic material
Bamboo is a natural fiber and the modulus varies across a
section, decreasing as you move from the hard primary
fibers and towards the center.
For a hexagonal bamboo section, the modulus is not
defined.
The classical theory of bending is based on the
assumption that plane sections remain plane and normal to
the deflected central line.
That assumption is not fulfilled for a section of a
bamboo fly rod.
Plane sections are transformed into curved surfaces.
It therefore follows, that trying to obtain a value for
the modulus by measuring the deflections due to bending
is bound to fail.
If we want a more accurate calculation, we would have to
look at the section as build from thin hexagonal rings,
each having its own modulus of elasticity and moment of
inertia.
And that is just one of the problems we run into if we
try to use a modulus that isn't constant over the
section.
But to get started on the calculations I assumed we had a
constant modulus. Trying to guess what value Garrison
would have used, he liked numbers that made calculations
on his slide rule easy, I settled for E=10,000,000
lbs./square inch. Actually I did quite a lot of
calculation before found the value of E.
Calculating the actual stress curves for Garrison's rod
showed, that they all had similar forms.
For details see The
Stress Profile.
Diagram 1.
The diagram shows a typical stress curve for a Garrison
rod. Some rods have a constant stress for the whole
length, but most of the rods have a reduction in stresses
starting 30" below the top eye.
Diagram 2.
Diagram 2. shows how the curve changes, when we use
different values for the modulus. The top curve is
calculated for E = 8,000,000 lbs./sq.in. and the bottom
curve for E = 12,000,000 lbs./sq.in.
This does not prove that Garrison used a value of
10,000,000 lbs./sq.in. for E. Neither does it prove that
Garrison calculated the stresses for the deflected curve.
What it shows is that Garrison had a technique for
calculating his tapers, which he used for all his rods.
I think, the simple form of the stress curve we get by
using a constant modulus is a much better tool for
designing new rods, than a correct but strange looking
curve, that would make comparison of rods much more
difficult.
How do we find the value of the constant stress?
I have found a marvelous way of doing it, but this page
is too small to contain it.
Loads on the Rod
This page was modified August 11, 2001
Copyright © 1998,
Falka Gregersen. All rights
reserved.
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