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Hi All,
Until Stan, W7NI, finds his old article, and gets it up somewhere for
all to consume, I decided to spend some time comparing the two materials
for mast use and see if I could offer enough information to at least put
a fence around this discussion.
I've read several of Stan's presentations and he does a good job of
presenting enough information about how one uses the mathematics to get
from point A to point B,. So, I'll not make this a "How to" exercise.
This may be too long for some readers, far to short for others. It is
certainly NOT the answer in a thimble!
Preface:
The bulk of the discussion about the use of various mast materials has
centered around steel and aluminum. There have been many comments pro
and con for each. To date most inputs have been purely anecdotal in
content. Many have asked for more specific information with real numbers
to validate the discussion.
For the sake of this discussion, I have decided to present a commonly
available steel mast section as a benchmark and then find the steel pipe
and aluminum equivalents.
All values come from published material values and simple long-standing
mathematics.
Within certain hard physical limitations, an aluminum mast can be made
to carry the same loads as a steel mast.
The entire question revolves around whether it makes sense, in a broad
scope of considerations to do so.
I'll introduce a new value, EI into this discussion. EI is a measure of
the stiffness of a section. E is the elastic modulus of the material, I
is the section moment of inertia. The moment of inertia is a value that
represents the distribution of material around the centroid of the
section. The combination of material stiffness and its distribution
about the centroid determines a section's stiffness.
In the discussion, on the reflector last Friday, Hank Lonberg presented
a safety factor for use with this application. He suggested that the
allowable bending stress Fb should be .6 x the yield strength Fy. This
translates to a safety factor of 1/.6 = 1.67 for this application.
I totally agree with his view.
We have to be very careful to understand what we are talking about when
we talk about the wind blowing against a structure. EIA, and most other
specs talk about a fastest mile basic wind speed. This wind speed is the
average velocity for 1 mile of wind passing across the structure. During
any mile of wind the peak wind speeds can be much higher. An example
would be to say that we have a 72 mph fastest mile wind speed. During
the mile of wind we could see peak velocities of 87 mph for 3 seconds.
The wind loads at 87 mph are 1.46 times higher than at the basic speed
of 72 mph. In addition to this, there are dynamic loading factors to be
added to account for the fact that things are not stationary, but
flopping and flailing about.
So, in the comparison I used a 1.67 safety factor on static loads.
Constants:
Aluminum elastic modulus = 10,000,000 psi
Aluminum Density = .1 Lb/CuIn
6061-T6 Aluminum Fy (yield) = 35,000 psi
Steel elastic modulus = 29,000,000 psi
Steel Density = .2835 Lb/CuIn
Steel - Premium grade Fy appears below.
Steel - ASTM A53 Pipe Fy = 25000 psi
Steel - ASTM A106 Pipe Fy = 35000 psi
Note: Pick your own values, if you wish, but these are very close for
the sake of this discussion.
All comparisons are made to achieve equivalent or best available fit
(with obtainable stock) to the baseline section. The Mmax value is the
max allowable bending moment to maintain the stated safety factor.
Texas Towers 2.0" Dia x .250 wall x 20' Galvanized Mast Fy = 87000psi
Fmax = 52200 psi Mmax = 28000 In-Lb
Weight 93.5 Lbs, Safety Factor 1.67 EI = 1.56E+07
Mast projected area 3.3 SqFt
ASTM A53 pipe, 3.5" Sched 40 (4" OD)
Weight = 151.6 Lbs, Safety Factor = 1.54 EI = 8.75E+07 Area =
5.8 SqFt
ASTM A106 pipe, 2.5" Sched 80 (2 7/8" OD)
Weight = 153.3, Safety Factor = 1.67 EI = 5.58E+07 Area = 4.8 SqFt
6061-T6 Tubing, 2.5 " Dia x .500 wall
Weight = 75.4 Lb, Safety Factor = 1.67, EI = 1.67E+07 Area = 4.2 SqFt
6061-T6 Tubing, 3.0" Dia x .250 wall
Weight = 51.9 Lbs, Safety Factor =1.5, EI = 2.06E+07 Area = 5.0 SqFt
Discussion:
All of these masts will carry the same or nearly the same bending
moment. And after the aluminum mast is sized correctly for stress, it
has equivalent or greater stiffness.
If we desire a light mast we use one of the aluminum sections. What we
save in weight we lose in available antenna surface area we can put on
the mast.
Let's say that the baseline Texas Towers mast is installed in a Rohn
45AG2 tapered top section.
To use the aluminum masts we need to use the 45AG4 top section and buy a
TB4 bearing. Per the Texas towers catalogue, the additional cost will be
$110. If we want to use the smaller aluminum section we will need to
make a bushing to adapt the TB4 down to the 2 1/2" dia mast.
A potential complication can arise if we are really shopping our
aluminum for the lowest price. Extruded tube is cheaper than drawn tube,
but the tolerances for the extrusion are greater than the drawn tube.
The extruded 3" dia tube may not fit in the bearing. I recently
experienced this on an antenna project.
The texas towers mast is listed at $289.
Maybe some of the reflector gang can fill in pricing for the other
options. The toughest cost to pin down will be shipping as it can be
quite variable depending on the source and destination locations.
I hope this is useful to those interested in this discussion.
73, Kurt
--
YagiStress - The Ultimate Software for Yagi Mechanical Design
Visit http://www.freeyellow.com/members3/yagistress
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Hi All,
<P>Until Stan, W7NI, finds his old article, and gets it up somewhere for
all to consume, I decided to spend some time comparing the two materials
for mast use and see if I could offer enough information to at least put
a fence around this discussion.
<BR>I've read several of Stan's presentations and he does a good job of
presenting enough information about how one uses the mathematics to get
from point A to point B,. So, I'll not make this a "How to" exercise.
<BR>This may be too long for some readers, far to short for others. It
is certainly NOT the answer in a thimble!
<P><B><U>Preface:</U></B>
<BR>The bulk of the discussion about the use of various mast materials
has centered around steel and aluminum. There have been many comments pro
and con for each. To date most inputs have been purely anecdotal in content.
Many have asked for more specific information with real numbers to validate
the discussion.
<P>For the sake of this discussion, I have decided to present a commonly
available steel mast section as a benchmark and then find the steel pipe
and aluminum equivalents.
<BR>All values come from published material values and simple long-standing
mathematics.
<P>Within certain hard physical limitations, an aluminum mast can be made
to carry the same loads as a steel mast.
<BR>The entire question revolves around whether it makes sense, in a broad
scope of considerations to do so.
<P>I'll introduce a new value, EI into this discussion. EI is a measure
of the stiffness of a section. E is the elastic modulus of the material,
I is the section moment of inertia. The moment of inertia is a value that
represents the distribution of material around the centroid of the section.
The combination of material stiffness and its distribution about the centroid
determines a section's stiffness.
<P>In the discussion, on the reflector last Friday, Hank Lonberg presented
a safety factor for use with this application. He suggested that the allowable
bending stress Fb should be .6 x the yield strength Fy. This translates
to a safety factor of 1/.6 = 1.67 for this application.
<BR>I totally agree with his view.
<BR>We have to be very careful to understand what we are talking about
when we talk about the wind blowing against a structure. EIA, and most
other specs talk about a fastest mile basic wind speed. This wind speed
is the average velocity for 1 mile of wind passing across the structure.
During any mile of wind the peak wind speeds can be much higher. An example
would be to say that we have a 72 mph fastest mile wind speed. During the
mile of wind we could see peak velocities of 87 mph for 3 seconds. The
wind loads at 87 mph are 1.46 times higher than at the basic speed of 72
mph. In addition to this, there are dynamic loading factors to be added
to account for the fact that things are not stationary, but flopping and
flailing about.
<BR>So, in the comparison I used a 1.67 safety factor on static loads.
<BR>
<P><B><U>Constants:</U></B>
<P>Aluminum elastic modulus = 10,000,000 psi
<BR>Aluminum Density = .1 Lb/CuIn
<BR>6061-T6 Aluminum Fy (yield) = 35,000 psi
<P>Steel elastic modulus = 29,000,000 psi
<BR>Steel Density = .2835 Lb/CuIn
<BR>Steel - Premium grade Fy
appears below.
<BR>Steel - ASTM A53 Pipe Fy
= 25000 psi
<BR>Steel - ASTM A106 Pipe Fy = 35000 psi
<P>Note: Pick your own values, if you wish, but these are very close for
the sake of this discussion.
<P>All comparisons are made to achieve equivalent or best available fit
(with obtainable stock) to the baseline section. The Mmax value is the
max allowable bending moment to maintain the stated safety factor.
<BR>
<P><B><U>Texas Towers 2.0" Dia x .250 wall x 20' Galvanized Mast</U></B>
<B><U>Fy = 87000psi</U></B>
<BR>Fmax = 52200 psi Mmax = 28000 In-Lb
<BR>Weight 93.5 Lbs, Safety Factor 1.67 EI = 1.56E+07
<BR>Mast projected area 3.3 SqFt
<P>ASTM A53 pipe, 3.5" Sched 40 (4" OD)
<BR>Weight = 151.6 Lbs, Safety Factor = 1.54 EI
= 8.75E+07 Area = 5.8 SqFt
<P>ASTM A106 pipe, 2.5" Sched 80 (2 7/8" OD)
<BR>Weight = 153.3, Safety Factor = 1.67 EI =
5.58E+07
Area = 4.8 SqFt
<P>6061-T6 Tubing, 2.5 " Dia x .500 wall
<BR>Weight = 75.4 Lb, Safety Factor = 1.67, EI = 1.67E+07
Area = 4.2 SqFt
<P>6061-T6 Tubing, 3.0" Dia x .250 wall
<BR>Weight = 51.9 Lbs, Safety Factor =1.5, EI = 2.06E+07
Area = 5.0 SqFt
<BR>
<P><B><U>Discussion:</U></B>
<P>All of these masts will carry the same or nearly the same bending moment.
And after the aluminum mast is sized correctly for stress, it has equivalent
or greater stiffness.
<P>If we desire a light mast we use one of the aluminum sections. What
we save in weight we lose in available antenna surface area we can put
on the mast.
<P>Let's say that the baseline Texas Towers mast is installed in a Rohn
45AG2 tapered top section.
<BR>To use the aluminum masts we need to use the 45AG4 top section and
buy a TB4 bearing. Per the Texas towers catalogue, the additional cost
will be $110. If we want to use the smaller aluminum section we will need
to make a bushing to adapt the TB4 down to the 2 1/2" dia mast.
<P>A potential complication can arise if we are really shopping our aluminum
for the lowest price. Extruded tube is cheaper than drawn tube, but the
tolerances for the extrusion are greater than the drawn tube. The extruded
3" dia tube may not fit in the bearing. I recently experienced this on
an antenna project.
<P>The texas towers mast is listed at $289.
<BR>Maybe some of the reflector gang can fill in pricing for the other
options. The toughest cost to pin down will be shipping as it can be quite
variable depending on the source and destination locations.
<P>I hope this is useful to those interested in this discussion.
<P>73, Kurt
<BR>
<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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