Greetings from Virginia's Middle Peninsula,
At the risk of boring some, I will make an attempt to describe and quantify
'stretching' for those who are interested. Forgive me if the majority have
no interest in this level of detail or consider the topic already beaten to
death. Reviewing it sure helps me, anyway.
The phenomenon that is being described, "stretch", is elastic deformation
(also deflection), a temporary change of shape that makes a material act
like a spring. Materials can stretch elastically (temporary), plastically
(permanent), or a combination of both, in any direction.
Just about any part will act like a spring under certain conditions. When a
load is applied to a part, it moves a little (deformation). Strain is
actually defined as the amount of movement per unit length of the part. If
its yield stress was not exceeded, it moves back to its original shape, and
that is called elastic deformation (deflection). In this manner, a part
(such as a boom, mast, or guy wire) acts like a spring. If it deflects too
far and its yield stress was exceeded, however, it may move back toward its
original shape, but it will retain some amount of permanent change of shape
(elastic deformation + plastic deformation) and the material suffers damage.
We want to avoid the permanent, plastic deformation! We design parts to be
strong enough so that they don't break (yield stress is not exceeded).
However, and this is the point: Just because a part won't break does *not*
mean that it will not bend elastically and be quite springy! And sometimes
more than you intended! Parts have to be designed to control their
deflection (related to springiness) as well as their ultimate strength.
Who else has tried to straighten some wire from a spool or your whip
antenna? (who else has had to use their 2m whip to unlock their car door?
<grin>) You have to bend it way back in the opposite direction (elastic),
and then carefully a little more (exceeding the part's yield stress) to get
the right amount of permanent bend (plastic) so that when you let go it has
the shape you want.
The relationship between the size of the load and the amount of deflection
(elastic movement) is controlled by the size and shape of the part and the
"Modulus of Elasticity" (modulus for short) of the material that the part is
made from. Just as the yield stresses can vary for different materials, the
modulus is also dependent on the type of material. The higher the modulus,
the *less* a part will change shape elastically. The modulus of steels is
well known, and varies very little for different steels. I don't have data
for aramid fiber. Perhaps Kurt can find this or someone will contact
Phillystran's manufacturer for this data.
Fiberglass is a composite material, and has a wildly different modulus
depending on the direction in which the load is applied compared to how the
glass strands are oriented. Quad spreaders are quite elastic in bending, but
much stiffer in tension. I have no data for these materials. Now we're
really getting complicated!
We tend to think of wire cables as fixed in length, but they will deform
with a load, and we hope they will always be elastic deformations!
A straight, solid rod is easy to analyze for strain. As you can imagine, a
lot of force is required to make it change length (high spring constant).
Plain, straight rod makes a crummy extension spring, but a spring
nonetheless! However, if you coil it, the stress is applied in a different
way, and there's much, much more length of wire per unit of length. When you
pull on a coil spring, you are actually causing the wire to twist in torsion
rather than just extend in length. You can get a lot more elastic movement
from this shape without exceeding the yield stress (lower spring constant).
Think about the shape of a piece of EHS guy wire. Its strands are twisted
into a gentle spiral. Nothing like a coil extension spring, but some small
amount of torsional loading will occur, slightly increasing increasing the
overal deflection/change in length. Also, there is less cross-sectional area
of steel as compared to a solid rod of the same diameter, also increasing
the deformation.
Now, for those of you who haven't hit delete yet, and without dragging you
through too much more mumbo-jumbo, here are a few numbers to give you a feel
for the amount of movement we're talking about:
EXAMPLE: 100 feet of *solid* steel cable, with a 400 pound tension:
DIA, TENSILE STRESS, TOTAL CHANGE IN LENGTH
1/8, 32,600 psi, 1.3 inches
3/16, 14,600 psi, 0.58 inches
1/4, 2000 psi, 0.33 inches
You see how using a part that is way oversized for stress alone helps
control deflection/deformation/'springiness'
I don't have data in my handbooks for the modulus of wire rope in tension,
but the above numbers should be a good starting point. I would venture a
guess as 10% more for EHS.
This means that when you preload your 3/16 guys, for example, they will
stretch elastically somewhere around 3/4 inch, I'd say, just due to the
change in length. Something else happens, too. Guy wires have droop, or sag,
which, due to gravity, requires more length of cable between two points
because it's not in a perfectly straight line. This introduces yet another
potential for elastic change in length. Let's now guess about 1 inch of
total change in length for our 3/16 cable. Once the sag is pulled out of
your guy, not too many turns of your turnbuckle are needed to raise the
tension!
Reducing sag and the spring effect it introduces is another reason for
proper preloading of guys. Bigger guys are heavier, will sag more, and will
require more preload. It seems to me now, after thinking about all that I
have learned about towers here on the reflector, that the 10% of breaking
strength rule of thumb helps out here.
OK, long again as usual... for those of you who are still reading... What
happens to the tension in guys and to the movement of the tower when the
wind blows on it?
As the wind forces build, the tower moves a little. This movement stretches
the upwind guy(s) elastically, adding to the preload tension on the upwind
guys and resisting the movement. However, the downwind guy(s) will *release*
their preload and lose tension, also resisting the movement. In this system,
the guy forces react synergistically to hold the tower closer to, but not
exactly in its original position. The more the guys act like springs the
more the tower will move in the wind. The more the tower moves, the more
fatal bending moment will be applied to the tower section. Therefore (I must
be getting toward the end), larger guys made from materials with with a
greater modulus will control your tower better and keep the bending forces
lower.
Thank you for the bandwidth. This post turned out longer than I wanted, but
I hope it helps someone understand some of the engineering and materials a
little better. And if so, then they will build their towers more safely.
regards,
Mark, N1LO
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