Dimitry, et al:
Just a quick comment, the ultimate strength of a mast is not
as simple as the cross sectional area times the yield strength.
The ultimate strength also depends on the shape of the masts cross
section. This factor is accounted for in what is called the section
modulus. This explains why a 2" O.D. mast with a .033" wall will
be just as strong as a 1" O.D. solid rod made from the same material.
The 1" rod has about 4 times the cross sectional area of the thin wall
pipe, but its section modulus is the same. The key is that the thin wall
pipe has its mass where it counts - away from the center axis. The formulas
can be found in Leeson's "Physical Design of Yagi Antennas" or most
Static Engineering Mechanics text books.
73 de Mike, W4EF.........
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From: d.dimitry[SMTP:d.dimitry@mci2000.com]
Sent: Sunday, October 11, 1998 9:24 PM
To: K7LXC@aol.com; n4kg@juno.com; TOWERTALK@contesting.com
Cc: Hank.Longberg@harrisgrp.com
Subject: Re: [TowerTalk] Response to R for math
You wrote:
> Please enlighten me how a 118K psi yield strength chromoly mast will
fail
>before a 35K psi 6061-T6 aluminum mast? When did they change the laws of
>physics? Wall thickness has little to do with it.
>
> Have you missed the posts regarding calculations of windspeeds, antenna
>loads and bending moments?
My reply: Wall thickness has as much to do with the strength of a mast as
does the material's yield strength. Both are important factors. I will
give you the formula for it, but first a sort of analogy. Could you drive
your car at 35 mph through an 1/2" thick aluminum plate spanned across the
road and firmly secured to anchored poles on both sides? Kind of chancy,
isn't? I definately would not want to try. What if we changed the
thickness to that of common kitchen type aluminum foil? Would you take a
shot at it? Why not, your car would probably sail right through it with
little or no damage.
Now if both sheets of aluminum are made from the same type of aluminum, with
the same strengths, why could you easily pass through one and not the other?
I think
you all know the answer to that question. Thickness matters-- it increases
the strength. I don't mean to condescend, especially to an audience of
people more educated than myself, but was not your question on the
importance of thickness? (I am directing this question to K7LXC.)
The formula for calculating the cross-sectional area of tubes shows that
wall thickness is important in a mast. Of course, 'cross-sectional area'
is important in determine the load capabilities of particular structural
elements, which in this discussion are your antenna masts.
Here is a simple formula for determining cross-sectional area. Since I can
not find a
superscript on this e-mail program, I'll express it very basicly. Square
the Outer Diameter of your mast, then subract the square of the Inner
Diameter of your mast. Next, divide this difference by "4". Finally,
multiply this result by the number pi: 3.1415 That yields your
cross-sectional area. Or put in my non-conventional (e-mail) math form:
[((O.D. x O.D.) - (I.D. x I.D.)) / 4 ] x 3.14159 = Cross-sectional area of
a round tube ( or "A").
"A" would then be a factor in determining the total strength capacity of
that tube mast. "A" multiplied times the yield strength, stated in Kpsi,
would yield a result of so many thousands of pounds.
Example 1: a 2" O.D.
mast x 0.25" wall will be found to have an "A" (cross-sectional area) of
1.372 sq. inches. Multiply that "A" x 35kpsi (for 6061T6 alum.) and you
come
up with 48,020#. This is a thumb-nail result, and NOT the final amount of
pound capacity of a mast allowable load before bending (you probably want to
build in another safety factor). But these formulas encapsulate the
principles behind figuring the strength of round tubular elements (from an
initial reading, I think Hank Lonberg, P.E.'s post very accurately generated
the allowable loads on masts, although w/ a somewhat different approach).
You can see that if you had two tubes of the
exact O.D. and thickness, and that if one had a yield strength of 50kpsi and
the other had a yield strength of 100kpsi. , then one mast would actually
have twice the capacity as the other.
That's why I say that an aluminum mast will be a good value, if they
have 2 times the "A" than a chrome-moly mast, but still less than say 35%
of
its total price.
However, if you have a super heavy stainless mast of about 3/16" or thicker
(and still same O.D.), yes you will have a much stronger mast.
(BTW, alum. weighs about 38% of steel and stainless of the same Volume of
material, for those concerned about weight.)
You then asked for other information on the flexibility of masts. I'll will
respond to that question in an later e-mail. Thank you for your
forbearance.
Drake Dimitry
Heights Tower Systems
>
> What specifically are you talking about? Feel free to post the alloy,
>certification and other specifications of the aforementioned masts along
with
>the price. Broad allusions to the "best value in masts" doesn't give us any
>information.
>
>> Much more could be said. One point I want to echo is that I think
because
>> of its elasticity and flexibility, I think an aluminum mast, in terms
>> of tensile strength, may tend to bounce back and not completely fold or
>> break like steel and stainless would under similar pressure.
>>
> Please let us know what the calculations you used to reach the above
>conclusion.
>>
>> I'll try to answer one more q for you. Yes, the connections between
some
>> old style aluminum sections has been a problem after several years
>outdoors.
>> They can be very difficult to pull apart. There are precautions and
>> maintenance steps that can be done to help this problem. First, coat
the
>> section ends you are joining together with an anti-seize lubricant made
for
>> aluminum surfaces. This can be gotten at electrical, hardware and
bearing
>> stores, as well as antenna and some tower mfrs. Then take your tower
apart
>> every 3 to 5 years to check the joints. Do you need to apply more
>> lubricant? Also, on this issue, do not over-torque the nuts on
>> your leg
>> connecting bolts when assembling the tower; this can egg-shape the legs
and
>> wedge them more tightly together.
>>
> Good advice about ovalizing the legs and the use of anti-seize in
the
>leg joints. But are you serious about taking your tower apart every 3-5
years?
>
> It is my opinion that you are undermining your credibility as the
>president of a tower manufacturing company and contributer to TowerTalk
with
>the incorrect advice and conclusions that you're presented here. I'm still
>waiting for an answer to the availability of tower engineering data that
you
>mentioned previously.
>
>Cheers, Steve K7LXC
>Tower Tech
>Champion Radio Products
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