Effective area for tower section.

[sawyers]

Here good question and my answer to it with regard to the Central States 
VHF/UHF Conference paper I have mentioned here previously. Hope this forum 
finds it interesting.

de n0yvy steve


______________________________ Forward Header __________________________________
Subject: Re: Effective area for tower section.
Author:  sawyers at po5
Date:    8/27/96 9:45 AM


I just followed the EIA-222 standard. It is not an obvious way of doing it, 
but it is the way they specify. I will try to walk you through this.

You take one face of the tower (I use a single tower section) and total up 
the projected area of the round members and the projected area of flat 
members in that one face. In the example I also threw in one 3/4" hard line 
in the middle of each face. This is the easy part.

The equation for determining total effective area per EIA-222 is:
(please note that I have rearranged this slightly from the standard for the 
purposes of the paper. Also I hope you follow the notation. I am ssomewhat 
limited with straight ASCII text.)

Total effective Area = Csub_f * Asub_e

where

Csub_f is defined below and

Asub_e = (Dsub_f * Asub_f) + (Dsub_r * Asub_r * Rsub_r)

where

Dsub_f = wind directional factor for flat plate members ( see table below)

Dsub_r = wind directional factor for round members members ( see table 
below)

Asub_f = area of the flat plate members in one face that we totaled above.

Asub_r = area of the round members in one face that we totaled above.

Rsub_r = (0.51 * e^2) + .57   where Rsub_r is less than or equal to 1.0

where e^2 is e squared and e is the density of the face i.e the area of the 
round members and flat members added together and divided by the toal area of 
the face i.e. the total width times the total length of the section.

This last is obviously a curve fit to some empirical data which is not presented
in the standard.

Csub_f = (4.0 * e^2) - (5.9 * e) + 4.0 for Square Cross Sections (4 leggged)

and    = (3.4 * e^2) - (4.7 * e) + 3.4 for Trianglular Cross Sections (3 legged)

Again this is obviously a curve fit to some data.

Now for those Dsub_?:

(make sure this is in a mono spaced font and line up the vertical bars | at one 
per line)

Tower Cross Section ->     Square          |         Round
                                           |
Wind Direction     Normal     +-45 degrees |  Normal  60 degrees  +-90 degrees
                                           |
Dsub_f              1.0        1 + 0.75*e  |  1.0        0.80       .85
                                           |
Dsub_r              1.0        1 + 0.75*e  |  1.0        1.0         1.0


Note that the 1 + 0.75*e has 1.2 max value.

As you can see the triangular tower with all round members is easy to handle, 
according to the formulas, it looks the same in all directions. That is why Rohn
sections are used my example.

For anything with flat members, you have to consider the wind direction. The 
Normal wind direction is blowing straight into a given face, and the other wind 
directions are measured from this starting point.  

When I did the ice loading area, I added a 1/2" of radial ice per the standard 
to all members. This means that a 5/16 latice is 1-5/16" wide. Also once you add
the ice, everything is considered round, and you run back through the 
calculations.

Hope this explains a rather unique method that the the standard uses. Hope it a 
little clearer than a wall of mud.

I have been trying to get some time to set this much up in spread sheet, as I 
get tired of punching the numbers myself. Maybe I will get to it this winter.

de n0yvy steve

Steven H. Sawyers PE - ARRL Volunteer Consulting Engineer.


Disclaimer: My Company and I agree on at least one thing: My Opinions Are My 
Own.



______________________________ Reply Separator _________________________________
Subject: Effective area for tower section.
Author:  Gene Smith <Gene.Smith@mailhost.bellhow.com> at ccmgw1 
Date:    8/26/96 1:24 PM




Steven:

In your article "Preliminary Tower Analysis Techniques" you 
presented the effective area per section of Rohn 25 and 55 
although it is not clear how you arived at these numbers.

Can you give me some insight or details as to how these 
were calculated because I'm considering using a different 
brand of tower and I will need to calculate the effective 
area of it.

Thank you very much!!!

Gene
WD8OZL