Roger,
here's a link to some good information on tower stresses:
http://www.heightstowers.com/tower_specs_and_tutor.htm
http://www.google.com/search?q=antenna+element+bending+moment+formula&hl=en&lr
=&ie=ISO88591
The "I" value for a circular pipe is
I= Pi (Do^4Di^4)/(64)
where Do=outer diameter of pipe
Di= inner diameter of pipe
For your 2.000", 0.25" wall pipe this gives I = 0.54
The yield strength of 6061T6 is 35,000 PSI.
The bending moment when the mast will yield is 0.54(35,000) = 19,000 PSI
Let's say you have an antenna with a 6 sq. ft. wind area at the top of the 20
ft. mast. The wind is gusting to 80 mph. The force per sq. foot is about 16
lb. There are more accurate numbers then the 9 lb/sq ft I use at 60 mph. This
is conservative and is from an old ARRL antenna handbook. For 80 mph the force
per sq foot is (80/60)^0.5 X 9 lb. The wind force on the antenna is 96 lb. The
bending moment at the base of the mast is (96lb)(20') = 1920 lbft. Muliply
by 12 to get PSI, (1920 lbft)(12 in/ft) = 23,000 PSI (is this correct?).
This mast will fail. It can stand a gust to 72 mph. The highest recorded wind
velocity for your area can be found by a google search. This must be adjusted
for antenna height and the terrain. The links above contain some information
on this. Physical Design of Yagi's has all of this. I can't find my copy right
now. Before using the formula's I have put down here one should (must) double
check using a good written source. I could be in error.
There is also icing to take into consideration in some areas of the world.
Altogether this mast thing is just an engineering calculation. When performed
with worst case numbers you can be sure that your antennas will stay in the
air.
Dave WX7G
http://72.14.253.104/search?q=cache:fJ4kX54h3aAJ:www.arraysolutions.com/images/KT9OMpartI.pdf+antenna+mast+bending+moment+formula&hl=en&gl=us&ct=clnk&cd=3&;
ie=UTF8
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