1.   Given:

Tower Height:                      h = 24 ft

Antenna Area:                     A_ant = 10 sq ft

Antenna Weight:                  A_ant = 5 lbs

Basic Wind Speed:              bws = 90 mph,

                                          Exposure C

Tower Section Length:          L_s = 8 ft

2.   Determine the wind load on the antenna.

      The wind load on the antenna is calculated by multiplying the wind pressure (deter­mined as shown in Section 5.0) by the projected surface area of the antenna (including rotator and other miscellaneous equipment). The surface area of the an­tenna is usually indicated in the antenna manufacturer's literature. If you hand-crafted your antenna, you will have to calculate the projected area.

      For simplicity, Table 6.1 lists wind pressures for antennas at various heights and wind speeds for “Exposure C” conditions and an importance factor, I_w, of 1.0. At a height of 24 feet above ground:

w_ant = 24.5 psf

      The wind load on the antenna is thus:

P_ant = A_ant w_ant

P_ant = (10.0 sq ft)(24.5 psf)

P_ant = 245 lbs

3.   Determine the size of the top section of the tower.

A.   Assume a trial section size.

Choose a tower section from the sizes listed in Table 3.0. The 11" x 100 tower section is a good place to start, and will work as the top section in most cases.

B.   Calculate the wind force on the trial section.

From Table 3.0, the wind area for the 11" x 100 section is:

A_w = 1.8 sq ft

Although the wind pressure is distributed evenly across the projected area of the tower section, for simplicity, the wind force may be lumped and applied at the mid-height of the section. With 8-foot sections, the mid-height of the top section is 20 feet above the ground. From Table 6.2, the wind pressure at this height is:

p_w1 = 50.1 psf

The wind force on the tower section is:

P₁ = A_w p_w1

P₁ = (1.8 sq ft)(50.1 psf)

P₁ = 90.2 lbs

C.   Calculate the moment and shear in the section.

The bending moment at the bottom of the tower section is:

M₁ = (245 lbs)(8 ft) + (90.2 lbs)(4 ft)

+(5 lbs + 15 lbs)(8.66 in) / 3

M₁ = 2326 lb-ft

The shear force at the bottom of the tower section is:

V₁ = P_ant + P₁

V₁ = 245 lbs + 90.2 lbs

V₁ = 335 lbs

D.   Verify that the calculated moment and shear at the bottom of the tower section is less than the allowable moment and shear listed in Table 3.0:

M_R = 4200 lb-ft     > 2326 lb-ft ® OK

V_R = 390 lb     > 335 lbs ® OK

If the allowable moment or shear is less than than the calculated values, a “heavier” section with greater strength properties must be selected.

If the allowable moment and shear are significantly greater than the calculated values, it may be possible to use a “lighter” section with lower strength properties. The most economical tower design is that where the calculated moment is equal to the allowable moment. In this condition, the tower is being fully utilized, with little “wasted” strength.

If a new section size is chosen, repeat Step 3 to ensure the new tower section is adequate.

4.   Determine the size of the next-lower section of the tower.

A.   Assume a trial section size.

Choose a tower section from the sizes listed in Table 3.0. For the middle of our three-section tower, we’ll try the 14" x 131 section.

B.   Calculate the wind force on the trial section.

From Table 3.0, the wind area for the 14" x 131 section is:

A_w = 2.3 sq ft

From Table 6.2, the wind pressure at 12 feet above ground is:

p_w2 = 47.0 psf

The wind force on the tower section is:

P₂= A_w p_w1

P₂ = (2.3 sq ft)(47.0 psf)

P₂ = 108 lbs

C.   Calculate the moment and shear in the section.

The bending moment at the bottom of the tower section is:

M₂ = 2326 lb-ft + (335 lbs)(8 ft)

+ (108 lbs)(4 ft)

+(20 lbs + 23 lbs)(11.26 in) / 3

M₂ = 5451 lb-ft

The shear force at the bottom of the tower section is:

V₁ = V₁ + P₂

V₁ = 335 lbs + 108 lbs

V₁ = 443 lbs

D.   Verify that the calculated moment at the bottom of the tower section is less than the allowable moment and listed in Table 3.0:

M_R = 8900 lb-ft     > 5451 lb-ft ® OK

V_R = 750 lb     > 443 lbs ® OK

5.   Repeat Step 4 for each remaining section in the tower.

 

Here are a few things to keep in mind when choosing tower section sizes:

1.   Aluminum tower sections are constructed such that section sizes and leg tube sizes can be changed only one size at a time. For example you can transition from an 18" section to a 22" section, but you cannot go from an 18" section directly to a 26" or larger section; similarly, you can connect a #172 leg tube to a #225 leg tube, but you cannot go from a #172 leg tube directly to a #288 leg tube.

2.   In general, when an increase in moment capacity is required, it is more economical to increase section size before increasing leg tube size. While searching for a good balance between strength and size, try this method first.

3.   For tapered towers, the usual section length is eight feet, and this is what Tables 3.0, 6.1 and 6.2 are based on. The section lengths for telescoping towers are usually multiples of eight feet, such as 16, 24, or 32 feet. Please contact Heights Tower Systems for specific information on these sections. The procedure for sizing telescoping towers is slightly different because the effects of the typical 4'-0" overlap must be included.

4.   Tables 6.1 and 6.2 are based on UBC “Exposure C” condition, which is defined as “terrain which is flat and generally open, extending one-half mile from the site in any full quadrant.” If this condition does not apply to your location, or your local building department requires otherwise, please refer to Chapter 16 of the 1997 Uniform Building Code.

5.   Towers that exceed an overall height of 200 feet or are located near airports or aeronautical flight paths require Federal Aviation Administration approval and may require aeronautical-obstruction lighting. The wind area from such lighting (considered to be “tower accessories” in the UBC) must also be included in the tower design.

6.   The effects of icing are not included in the example above. Icing conditions require special analysis to account for the added wind area and weight. Please contact Heights Tower Systems for assistance if icing must be considered.

Copyright © 2004 by Heights Tower Systems. All rights reserved.

NOTICE

To the best of our knowledge, the information presented herein is accurate and in compliance with the 1997 Uniform Building Code. However, this information is intended for general guidance only and is not meant to be all-inclusive, nor as a substitute for knowledge of engineering mechanics. Neither Heights Tower Systems, the authors, nor any of their affiliates assumes any liability for any errors, omissions, negligence or any other deficiencies that may result from the use of the information contained herein. The responsibility for determination of suitability of the information, selection of proper product, installation, placement, and adequacy of supporting structures lies solely with the purchaser.