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To all,
The following information and discussion are intended to clarify my
previous comments about guy tensions and tower loads at two different wind
attack angles and the apparent conflict between Tom (N4KG) and myself on
this subject.
I think that we may have been comparing an apple to an orange because, as
stated before, I agree with what the math says for the planer determination
of force components that Tom described in his previous mail.
The main difference between the apple and the orange in this subject is the
elongation of the guys.
Preface:
I had really hoped to avoid getting into a discussion of this magnitude,
because it has the tendency to open up so many doors for discussion that
the whole thing could resemble a perpetual motion device, and result in far
more confusion than useful information for the reflector subscribers.
The following information and discussion is offered to all that are
interested in the subject
As mentioned before I spent a fair chunk of time looking at loaded towers
with a linear FEA program. The software can analyze 2 or 3 dimensional
structures. Additionally, I spent a lot of time trying to make sure that
the guy
elements in the models were as accurate as possible for stretch (or
elongation)
for the information at hand. There is more data to be gathered here, but I
am pretty comfortable with the data used.
There are two FEA models in this discussion. Both are of the same tower
configuration. Model #1 is with the wind aligned with one set of guys (a 2
dimensional model). Model #2 is with the wind bisecting a pair of guy sets
(a 3 dimensional model).
My objective in the discussion is not to present these analyses as a final
solution to the tower design, but to show what they revealed about the
behavior of the entire system that lead to my previous abbreviated
comments.
Description of the tower:
I wasn't trying to copy one of the Rohn configurations, but evaluate one of
many options I might want to have during the building of the station.
Antennas usually move around when another tower goes up and the station
gets closer to it's final configuration.
The closest comparable Rohn configuration can be found in the ham
catalogue, dwg C902041 R3 (110 Mph basic wind speed), P/N 25G110D090 (90'
tower).
The differences are that I didn't put the antenna loads only in one place
at the top of the tower, and used 4 sets of guys instead of 3. This was
because I wanted to have a lower antenna at the middle of the tower and got
higher safety margins with 4 guys.
This is probably very similar to something that is already out there or
something close to what others might want to have.
Tower: Rohn 25G, 88.66' to top of tower.
The top section is a modified 25AG with the taper removed and fit with
custom flat plate that holds the bearing.
Guys:
Set #1 1/4" EHS attached at 88.37'
Set #2 3/16" EHS attached at 66.71'
Set #3 3/16" EHS attached at 44.66'
Set #4 3/16" EHS attached at 23.63'
The guy anchors were 72' away from tower footing on flat level ground.
That's 81% of tower height. The tower base was rigidly connected to the
ground to duplicate burying it in a concrete footing.
The unequal guy spacing is mostly due to selecting the next closest
horizontal brace location to attach the guy brackets. The guy braces rarely
allow one to place the brackets at the nice nominal locations suggested or
wished for.
Loads on the tower:
All applied loads were determined using 50 Psf effective wind pressure.
Antenna & mast Loads:
2.8 SqFt antenna 9' above top of tower on 2" dia mast. (Like a 105BA)
5.0 SqFt antenna 1' above top of tower on 2" dia mast. (Like a 402BA)
2.8 SqFt antenna mounted just above the middle guy. (Like a 105BA)
Note: Please don't quarrel with the surface areas and antenna names used.
That is the subject of another discussion. Let's not complicate this one!
The input loads from the top antennas and the mast were determined from a
separate model of the mast and antennas, as they would be supported by the
tower.
Then, the reactions from that model were used as input loads on the tower
model. One at the tower top and the other 10 Ft down where the rotor was
located. Those who are quick with a calculator will see that it is a 20'
long mast, 10' in the tower, with 1 Ft hanging out above the top antenna. I
had already tried a shorter bury in the tower and didn't like it. That is
also another discussion.
Guy Loads:
The guy weights and wind loads were separately calculated and applied to
the tower as discrete point loads. The wind & weight loads applied are
larger than actual for ease of calculation.
The 10% guy pretensions were added to the guy loads calculated by the
software.
Tower Loads:
The wind load on tower was uniformly applied using the Rohn surface area
from my old specs (.254 SqFt/ Ft).
The tower section elements were configured to have a cross-sectional
area and density that would create the correct vertical loads when an
acceleration
of -1G was applied to the model. This is the easiest method of having the
software include the tower section weight in the analysis.
The guy pretension loads were calculated and applied as discreet point
loads.
Modeling Notes:
The guy elements in the model were solid steel rods with unique diameters
to match the stretch of the cables. They were modeled with material that
has no mass to prevent the -1G gravity load from duplicating the guy
weights, that were previously applied. The guy weights that would occur,
due to the gravity load, would be wrong because the guy cross section was
sized for stretch, not actual material area.
All tower elements in the model were beam elements, having rigid
connections between each other. The moment of inertia for the tower section
was not listed in the older Rohn specs I had when the models were run. I
calculated my own values. My new Rohn specs now give the value and agree
with the one used in these models.
All guy elements were truss type elements, having freely rotating pinned
type connections.
The models assume the tower is perfectly straight and plumb to the flat
footing plane.
Known inaccuracies in the models:
The way in which the guys were modeled does not account for sag. The sag
lowers the angles between the guys and the tower. This will cause the guys
to apply slightly more vertical load to the tower than these analyses will
predict. The guys, as modeled, don't get any straighter when loaded, so a
real world installation would allow slightly more tower deflection than
these models predict.
The cross sectional area used for the tower is greater than the actual load
bearing area, because it includes the bracing. This will cause the analysis
to understate the vertical elastic deformation of the tower.
This small error will result in the predicted lateral tower deflections to
be less than actual.
The guys are constrained at ground level. A real installation would have a
small amount of anchor rod stretch.
Design allowables:
Guys:
1/4" EHS breaking strength = 6000 Lbs, safe workiing load (Limit Load) =
3000 Lbs
3/16" EHS breaking strength = 3990 Lbs, safe working load (Limit Load)1995
Lbs
(Taken from Texas Towers catalogue)
Tower:
At the time these models were run, I had an old set of Rohn specs that
stated the max safe bending moment for the tower section was 5130 Ft-Lbs
The new Rohn dwg C630625 R9 (per EIA-222-E) in a catalogue I got this week
from Champion Radio, states the value at 6720 Ft-Lbs, with a note that the
value allows for 1/3 increase in allowable stress. I'll use the 6720 Ft-Lb
criteria.
Minimum yield strength = 50000 Psi (Rohn dwg C630625 R9)
Analytical Results: S.F. = Safety Factor
Model #1: Wind in line with 1 set of guys.
Lateral displacement at top of tower = 3.31"
Guy load Guy #1 = 1913 Lb S.F. = 1.57
Guy Load Guy #2 = 979 Lb S.F. = 2.04
Guy Load Guy #3 = 956 Lb S.F. = 2.09
Guy Load Guy #4 = 740 Lb S.F. = 2.70
Tower bending moment @ Guy #2 =1188 Ft-Lb S.F. = 5.66
Tower bending moment @ Guy #3 =297 Ft-Lb S.F. = 22.62
Tower bending moment @ Guy #4 =382 Ft-Lb S.F. = 17.59
Tower bending moment @ Base = 1556 Ft-Lb S.F. = 4.32
Tower Compression load @ Base = 5703 Lbs
Lateral load @ base = 197 Lb
Combined stress at base (compression + moment) = 16533 Psi S.F. =
3.02
Model #2: Wind bisecting 2 guy sets.
Lateral displacement at top of tower = 6.59"
Guy load Guy #1 = 1892 Lb S.F. = 1.58
Guy Load Guy #2 = 1014 Lb S.F. = 1.97
Guy Load Guy #3 = 941 Lb S.F. = 2.12
Guy Load Guy #4 = 706 Lb S.F. = 2.83
Tower bending moment @ Guy #2 =1475 Ft-Lb S.F. = 4.56
Tower bending moment @ Guy #3 =302 Ft-Lb S.F. = 22.25
Tower bending moment @ Guy #4 =390 Ft-Lb S.F. = 17.23
Tower bending moment @ Base = 2306 Ft-Lb S.F. = 2.91
Tower Compression load @ Base = 7511 Lbs
Lateral load @ base = 229 Lb
Combined stress at base (compression + moment) = 23193 Psi S.F. =
2.16
Comparison:
Comparing the changes from Model #1 to Model #2,
The top of tower displacement increased 199%
Guy load #1 decreased 1%
Guy load #2 increased 3.5%
Guy load #3 decreased 1.5%
Guy load #4 decreased 4.6%
Net change in total load in 1 guy set = 35 Lb .7% decrease
Tower moment @ guy #2 increased 24.2%
Tower moment @ guy #3 increased 1.7%
Tower moment @ guy #4 increased 2.1%
Tower moment @ base increased 48.2%
Tower compression @ base increased 31.7%
Lateral load @ base increased 16.2%
Tower stress @ base increased 40.2%
Discussion:
Due to the increased deflection in the top of the tower, and the difference
in geometry between the two top sets of guys, the 2nd set of guys carried a
larger portion of the top load.
The small decrease in total guy loads occurs because the tower is working
harder to help react the loads, as evidenced by the tower moment increases.
Notice also that because of the base moment, there are additional lateral
footing reactions required to carry the moment.
If the tower base was free to rotate (on a ball socket), the base moment
would go to zero and the guy loads would increase a bit.
Due to the known inaccuracies in the models, the tower deflections and
moments shown above are best case.
I took a look at 3 other tower configurations (different tower sections &
antennas & guying arrangements) in the archives and found that they all
exhibit similar behavior.
If the guys had been modeled with infinitely high stiffness (no stretch),
the results would have been EXACTLY as Tom (N4KG) mentioned. Guy loads
equal and tower compression double. And I'll add, no base moment.
The tower moment in the top span would still be there due to the tower
reacting the load from the bottom of the mast.
I hope this helps clear things up.
73, Kurt
--
YagiStress - The Ultimate Software for Yagi Mechanical Design
Visit http://www.freeyellow.com/members3/yagistress
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<HTML>
<B>To all,</B>
<BR>The following information and discussion are intended to clarify my
previous comments about guy tensions and tower loads at two different wind
attack angles and the apparent conflict between Tom (N4KG) and myself on
this subject.
<BR>I think that we may have been comparing an apple to an orange because,
as stated before, I agree with what the math says for the planer determination
of force components that Tom described in his previous mail.
<BR>The main difference between the apple and the orange in this subject
is the elongation of the guys.
<BR>
<P><B><U>Preface:</U></B>
<BR>I had really hoped to avoid getting into a discussion of this magnitude,
because it has the tendency to open up so many doors for discussion that
the whole thing could resemble a perpetual motion device, and result in
far more confusion than useful information for the reflector subscribers.
<BR>The following information and discussion is offered to all that are
interested in the subject
<P>As mentioned before I spent a fair chunk of time looking at loaded towers
<BR>with a linear FEA program. The software can analyze 2 or 3 dimensional
structures. Additionally, I spent a lot of time trying to make sure that
the guy
<BR>elements in the models were as accurate as possible for stretch (or
elongation)
<BR>for the information at hand. There is more data to be gathered here,
but I am pretty comfortable with the data used.
<P>There are two FEA models in this discussion. Both are of the same tower
configuration. Model #1 is with the wind aligned with one set of guys (a
2 dimensional model). Model #2 is with the wind bisecting a pair of guy
sets (a 3 dimensional model).
<BR> My objective in the discussion is not to present these analyses
as a final solution to the tower design, but to show what they revealed
about the behavior of the entire system that lead to my previous abbreviated
comments.
<BR>
<P><B><U>Description of the tower:</U></B>
<BR>I wasn't trying to copy one of the Rohn configurations, but evaluate
one of many options I might want to have during the building of the station.
Antennas usually move around when another tower goes up and the station
gets closer to it's final configuration.
<BR>The closest comparable Rohn configuration can be found in the ham catalogue,
dwg C902041 R3 (110 Mph basic wind speed), P/N 25G110D090 (90' tower).
<BR>The differences are that I didn't put the antenna loads only in one
place at the top of the tower, and used 4 sets of guys instead of
3. This was because I wanted to have a lower antenna at the middle of the
tower and got higher safety margins with 4 guys.
<BR>This is probably very similar to something that is already out there
or something close to what others might want to have.
<P><B>Tower:</B> Rohn 25G, 88.66' to top of tower.
<BR>The top section is a modified 25AG with the taper removed and fit with
custom flat plate that holds the bearing.
<P><B>Guys:</B>
<BR>Set #1 1/4" EHS attached at 88.37'
<BR>Set #2 3/16" EHS attached at 66.71'
<BR>Set #3 3/16" EHS attached at 44.66'
<BR>Set #4 3/16" EHS attached at 23.63'
<P>The guy anchors were 72' away from tower footing on flat level ground.
That's 81% of tower height. The tower base was rigidly connected to the
ground to duplicate burying it in a concrete footing.
<P>The unequal guy spacing is mostly due to selecting the next closest
horizontal brace location to attach the guy brackets. The guy braces rarely
allow one to place the brackets at the nice nominal locations suggested
or wished for.
<P><B><U>Loads on the tower:</U></B>
<BR>All applied loads were determined using 50 Psf effective wind
pressure.
<P><B>Antenna & mast Loads:</B>
<BR>2.8 SqFt antenna 9' above top of tower on 2" dia mast. (Like
a 105BA)
<BR>5.0 SqFt antenna 1' above top of tower on 2" dia mast. (Like
a 402BA)
<BR>2.8 SqFt antenna mounted just above the middle guy.
(Like a 105BA)
<P>Note: Please don't quarrel with the surface areas and antenna names
used. That is the subject of another discussion. Let's not complicate this
one!
<P>The input loads from the top antennas and the mast were determined from
a separate model of the mast and antennas, as they would be supported by
the tower.
<BR>Then, the reactions from that model were used as input loads on the
tower model. One at the tower top and the other 10 Ft down where the rotor
was located. Those who are quick with a calculator will see that it is
a 20' long mast, 10' in the tower, with 1 Ft hanging out above the top
antenna. I had already tried a shorter bury in the tower and didn't like
it. That is also another discussion.
<P><B>Guy Loads:</B>
<BR>The guy weights and wind loads were separately calculated and applied
to the tower as discrete point loads. The wind & weight loads applied
are larger than actual for ease of calculation.
<BR>The 10% guy pretensions were added to the guy loads calculated by the
software.
<P><B>Tower Loads:</B>
<BR>The wind load on tower was uniformly applied using the Rohn surface
area from my old specs (.254 SqFt/ Ft).
<P>The tower section elements were configured to have a cross-sectional
<BR>area and density that would create the correct vertical loads when
an acceleration
<BR>of -1G was applied to the model. This is the easiest method of having
the software include the tower section weight in the analysis.
<P>The guy pretension loads were calculated and applied as discreet point
loads.
<BR>
<P><B><U>Modeling Notes:</U></B>
<BR>The guy elements in the model were solid steel rods with unique diameters
to match the stretch of the cables. They were modeled with material that
has no mass to prevent the -1G gravity load from duplicating the guy weights,
that were previously applied. The guy weights that would occur, due to
the gravity load, would be wrong because the guy cross section was sized
for stretch, not actual material area.
<P>All tower elements in the model were beam elements, having rigid connections
between each other. The moment of inertia for the tower section was not
listed in the older Rohn specs I had when the models were run. I calculated
my own values. My new Rohn specs now give the value and agree with the
one used in these models.
<P>All guy elements were truss type elements, having freely rotating pinned
type connections.
<P>The models assume the tower is perfectly straight and plumb to the flat
footing plane.
<P><B><U>Known inaccuracies in the models:</U></B>
<BR>The way in which the guys were modeled does not account for sag. The
sag lowers the angles between the guys and the tower. This will cause the
guys to apply slightly more vertical load to the tower than these analyses
will predict. The guys, as modeled, don't get any straighter when loaded,
so a real world installation would allow slightly more tower deflection
than these models predict.
<P>The cross sectional area used for the tower is greater than the actual
load bearing area, because it includes the bracing. This will cause the
analysis to understate the vertical elastic deformation of the tower.
<BR>This small error will result in the predicted lateral tower deflections
to be less than actual.
<P>The guys are constrained at ground level. A real installation would
have a small amount of anchor rod stretch.
<BR>
<P><B><U>Design allowables:</U></B>
<P><B>Guys:</B>
<BR>1/4" EHS breaking strength = 6000 Lbs, safe workiing load (Limit Load)
= 3000 Lbs
<P>3/16" EHS breaking strength = 3990 Lbs, safe working load (Limit Load)1995
Lbs
<BR>(Taken from Texas Towers catalogue)
<P><B>Tower:</B>
<BR>At the time these models were run, I had an old set of Rohn specs that
<BR>stated the max safe bending moment for the tower section was
5130 Ft-Lbs
<BR>The new Rohn dwg C630625 R9 (per EIA-222-E) in a catalogue I got this
week from Champion Radio, states the value at 6720 Ft-Lbs, with a note
that the value allows for 1/3 increase in allowable stress. I'll use the
6720 Ft-Lb criteria.
<P>Minimum yield strength = 50000 Psi (Rohn dwg C630625 R9)
<BR>
<P><B><U> Analytical Results:</U></B> S.F.
= Safety Factor
<BR>
<BR><B>Model #1:</B> Wind in line with 1 set of guys.
<BR>
<BR>Lateral displacement at top of tower = 3.31"
<P>Guy load Guy #1 = 1913
Lb
S.F. = 1.57
<BR>Guy Load Guy #2 = 979
Lb
S.F. = 2.04
<BR>Guy Load Guy #3 = 956
Lb
S.F. = 2.09
<BR>Guy Load Guy #4 = 740
Lb
S.F. = 2.70
<P>Tower bending moment @ Guy #2 =1188
Ft-Lb
S.F. = 5.66
<BR>Tower bending moment @ Guy #3 =297
Ft-Lb
S.F. = 22.62
<BR>Tower bending moment @ Guy #4 =382
Ft-Lb
S.F. = 17.59
<BR>Tower bending moment @ Base = 1556
Ft-Lb
S.F. = 4.32
<P>Tower Compression load @ Base = 5703 Lbs
<P>Lateral load @ base = 197 Lb
<P>Combined stress at base (compression + moment) = 16533
Psi
S.F. = 3.02
<BR>
<BR><B>Model #2:</B> Wind bisecting 2 guy sets.
<BR>
<BR>Lateral displacement at top of tower = 6.59"
<P>Guy load Guy #1 = 1892
Lb
S.F. = 1.58
<BR>Guy Load Guy #2 = 1014
Lb
S.F. = 1.97
<BR>Guy Load Guy #3 = 941
Lb
S.F. = 2.12
<BR>Guy Load Guy #4 = 706
Lb
S.F. = 2.83
<P>Tower bending moment @ Guy #2 =1475
Ft-Lb
S.F. = 4.56
<BR>Tower bending moment @ Guy #3 =302
Ft-Lb
S.F. = 22.25
<BR>Tower bending moment @ Guy #4 =390
Ft-Lb
S.F. = 17.23
<BR>Tower bending moment @ Base = 2306
Ft-Lb
S.F. = 2.91
<P>Tower Compression load @ Base = 7511 Lbs
<P>Lateral load @ base = 229 Lb
<P>Combined stress at base (compression + moment) = 23193
Psi
S.F. = 2.16
<BR>
<BR><B><U>Comparison:</U></B>
<BR>Comparing the changes from Model #1 to Model #2,
<P>The top of tower displacement increased 199%
<P>Guy load #1 decreased 1%
<BR>Guy load #2 increased 3.5%
<BR>Guy load #3 decreased 1.5%
<BR>Guy load #4 decreased 4.6%
<P>Net change in total load in 1 guy set = 35 Lb .7% decrease
<P>Tower moment @ guy #2 increased 24.2%
<BR>Tower moment @ guy #3 increased 1.7%
<BR>Tower moment @ guy #4 increased 2.1%
<BR>Tower moment @ base increased 48.2%
<P>Tower compression @ base increased 31.7%
<P>Lateral load @ base increased 16.2%
<P>Tower stress @ base increased 40.2%
<BR>
<BR><B><U>Discussion:</U></B>
<BR>Due to the increased deflection in the top of the tower, and the difference
in geometry between the two top sets of guys, the 2nd set of guys carried
a larger portion of the top load.
<BR>The small decrease in total guy loads occurs because the tower is working
harder to help react the loads, as evidenced by the tower moment increases.
<P>Notice also that because of the base moment, there are additional lateral
footing reactions required to carry the moment.
<P>If the tower base was free to rotate (on a ball socket), the base moment
would go to zero and the guy loads would increase a bit.
<P>Due to the known inaccuracies in the models, the tower deflections and
moments shown above are best case.
<BR>
<BR>I took a look at 3 other tower configurations (different tower sections
& antennas & guying arrangements) in the archives and found that
they all exhibit similar behavior.
<P>If the guys had been modeled with infinitely high stiffness (no stretch),
the results would have been EXACTLY as Tom (N4KG) mentioned. Guy
loads equal and tower compression double. And I'll add, no base moment.
<BR>The tower moment in the top span would still be there due to the tower
reacting the load from the bottom of the mast.
<BR>
<BR>I hope this helps clear things up.
<P>73, Kurt
<P>--
<BR>YagiStress - The Ultimate Software for Yagi Mechanical Design
<BR>Visit <A
HREF="http://www.freeyellow.com/members3/yagistress";>http://www.freeyellow.com/members3/yagistress</A>
<BR> </HTML>
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