On 12/11/22 9:18 AM, Grant Saviers wrote:
A thought experiment is to consider what happens as the guys are
separated by even more than 120 degrees. As 180 degrees is approached
the tension needed in each guy to resist wind splitting the angle goes
to infinity. I think we would all agree only two guys opposing won't
resist the wind between them and the tower falls down. Conversely, a
pair of guys at the same angle each only need one half the tension.
So at some angle between them the tension in each exceeds all the wind
on one guy.
So then how to do the calculation. To simplify the compound angle
force vector calculations, I considered the tension to oppose a 1000#
force on the antenna, if the guys were at 90 degrees and horizontal
with the antenna. Then calculated the increased tension needed if the
angle to the tower was 45 degrees.
So from the thought experiment, we know the tensions at 120 degrees
are higher than at 90 degrees. Maybe somebody would calculate the
exact angle when it exceeds the wind directly on one guy.
Considering 4 guys 90 degrees apart. Wind aligned with one of the guys.
if there's *no displacement* then all the wind load is on the upwind
guy, plus its installation tension. The side guys see their installation
tension. the down wind guy sees installation tension less the wind load.
However, the tower isn't perfectly rigid nor is it rigidly attached to
the ground, so it bends slightly downwind - now the side guys see some
increased load. So the problem isn't quite a simple as it seems.
It's kind of an interesting problem, and solving it analytically (as
opposed to with some sort of systematic FEM approach, where you step the
wind direction around 360 degrees) would be "an exercise for the
ambitious student" even if you picked a model that is simple (single
beam in compression, hinged at bottom - or, fixed-free beam with simple
bending and no torsion)
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