Dave, W6NL/HC8L wrote: "Thanks [to N7WS] for the link to the very
detailed Weber papers. They clarify the issue. ."
Yes, but as you alluded to, K5IU's analysis is only true in a
world where the wind is of constant speed, horizontal, all flows
are laminar, and the tower and antennas are statically fixed.
Analyzing towers and antennas with simple stick models, statics and
trigonometry are mathematically correct but badly miss the mark on
what happens in the real world. Not only is the wind highly
variable, but towers and antennas are very flexible and have
"geometric non-linearities," meaning the wind forces they
experience change as a function of their bending.
The current building code (TIA-222-H) requires a first-order
finite element analysis. The only second order non-linearity
that is required to be considered is the P-delta effect,
where bending moments increase as a function of tower
lean over. That's a much better approximation than simple statics
but still isn't quite right.
A few years back I discussed with Kurt K7NV (SK) about his
YagiStress program and how using simple statics don't model
antenna elements very well. We agreed there is no program readily
available that takes geometric non-linearities into account.
The finite element program I use for tower analysis can't do
it out of the box. The solution would require a time step
analysis where the wind force and drag are adjusted for each
model node as a function of its displacement.
Recently I read a paper(1) that gives an idea what is needed to
properly model the responses of a tower/antennas to the wind. It
involves "stochastic finite element" analysis where the wind is
described in a time series data set with variations in wind
velocity, azimuth and elevation. The simple brute force way is
to then run those wind numbers as a Monte Carlo against a finite
element structural model of the tower/antenna system. You end up
with a response spectra of stresses and displacements.
Because towers/antennas are flexible structures that behave in
a non-linear way, how they respond to a 100 mph gust is going
to depend on what happens in the time periods just prior to
the arrival of the gust because, on a windy day, it is already
in motion seeking equilibrium and has a mix of potential and
kinetic energy in flux. And so in some cases the tower will
be in a favorable position to handle that gust, in others, it
will not.
Therefore one cannot say a tower or antenna is rated for
exactly 100 mph. Instead, it's a pair of probability curves,
one for the load (the wind) and another for the strength of
the tower system. Then the correct answer is along the lines
of "there's a 95% chance the tower will survive a wind gust
between 95 mph and 105 mph."
So is K5IU right about balancing wind loads and alternating
booms on masts? Yes, but only for the simple assumptions
he made. I think it's highly likely that in a wind storm there
are so many other dynamics going with the tower, mast and
antenna parts moving around that the static balance
will be swamped and disappear. Really the owner of a
tower/antenna system should invest their efforts in making
all mechanical connections as resistant as possible to
dynamics like vibration, oscillations and galloping as possible.
Jim Varney, P.E., K6OK
(1) Szafran, Jacek & Juszczyk-Andraszyk, Klaudia & Kamiński,
Marcin (2020). Reliability Assessment of Steel Lattice Tower
Subjected to Random Wind Load by the Stochastic Finite-Element
Method. ASCE-ASME Journal of Risk and Uncertainty in Engineering
Systems, Part A: Civil Engineering. 6. 10.1061/AJRUA6.0001040.
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