Design Problem Report
December 8, 2022
by Konnor Ross
Abstract:
The problem asks about the wiring needed to hold up a communications tower. We were tasked
with finding what type of steel wire to use, its diameter, and the radius at which the wires are attached to
three different supports to hold the tower up. It was found that the best radius to put the supports at was
14.43m away from the tower. The type of wire used was a 6x7 Fiber Core steel wire with a diameter of
18mm, which was able to support the load of the tower at the maximum force while minimizing the
amount of space the cables would need to extend outwards.
Introduction:
The tower in this design has a height of 25m with the supports around it all being on a horizontal
surface. The supports, as seen in Figure 1, are all equal distances away from the base of the tower and are
all equal distances away from each other. The cables had to meet the requirement of being able to hold the
tower up when there was a maximum force of 18kN at any direction horizontally. It was assumed that
there would always be one cable that is slack, meaning that if the force is oriented like in the figure
below, cables AC and AD would be supporting the tower with cable AB being slack.
Figure 1: Schematic of communications tower
It was assumed that the most severe load of the cables would happen when the force is directly in line
with one of the cables. This would cause one cable to bear the weight of the whole tower while the other
two cables are slack. Because of this, calculations were made based off of this scenario to assure every
wire can hold the weight of the tower.
Results:
To find the parameters that met the problem, the amount of force in the one cable bearing all the
force had to be found. This was done by assuming the angle that the wires come off of the top of the
tower. Three different angles were tested to see what the force in the wire would be, as can be seen in
Figure 2. The first column is the angle that the wire comes off the top of the tower, the second column is
the tension, or force, that the wire has the bear, and the third column is the radius distance of the support
based off of the angle.
Angle
20°
30°
40°
Tension
263.14 kN
180 kN
140.02 kN
Figure 2: Tensions and Radii for Different Angles (calculations seen in appendix)
Radius
9.1 m
14.43 m
20.98 m
It can be seen in Figure 2 that smaller distances of the radius results in the amount of tension in the cable
to increase exponentially. Because there is more tension in the cable at the smaller radius, a thicker wire is
needed to support the tower. As seen in Figure 3, the cost of the thicker wire is much more than that of the
other two, thinner wires. The type of wire, diameter of it, and failure tension were all found from the
ASTM Wire Rope Standards [1]. The cost of the cables were found through different hardware websites
[2][3][4]. The cost of the 22mm diameter cable was only given in the price per piece. It was assumed that
one piece was equal to one foot based on the price of other cables with similar specifications.
Radius
Tension
263.14 kN
180 kN
Failure
Tension
284 kN
190 kN
Diameter of
Cable
22 mm
18 mm
9.1 m
14.43 m
20.98 m
140.02 kN
150 kN
16 mm
Website Cost
Total Cost
$10 per foot
$10.97 per
meter
$8.68 per
meter
$2618.49
$950.11
$849.95
Figure 3: Cable Specifications and Total Cost (calculations seen in appendix)
The cable chosen for the specifications of this problem was the 6x7 Fiber Core Steel Wire with a diameter
of 18mm with supports a radius of 14.43m away from the tower. While this option is more expensive than
going with the 16mm diameter cable, it also takes up less space when the communications tower is set up.
Because these towers are going to be set up in urban and rural areas, having a large radius of unusable
space around the tower is inconvenient and/or damaging. Less unused space in an urban environment
allows for more structures to be put up around it for human use. In rural areas, a large radius around the
tower can damage more of the environment than is needed.
Summary:
By assuming the most amount of force directed on the tower will be from the force being in line
with one of the cables, the amount of tension during that moment was calculated and used to determine
the parameters needed by the cables used. The radius of the supports and the diameter of the wire were
chosen based on cost, impact on the environment around the tower, and how effective the wire performed.
The radius chosen to put the supports at was 14.43m and the cable chosen was a 6x7 Fiber Core steel wire
with a diameter of 18mm. Based on the findings from the different options, these parameters allowed for
the most effective cost of the wire while still meeting the specifications and minimizing the amount of
space that cannot be used around the tower.
Appendix:
References:
[1] ASTM Wire Rope Standards (page 8)
https://drive.google.com/file/d/1nLK5ZXEAZMq5YyxhUR4HMmZTpyGmGMrK/view
[2] Made-In-China: 6x7 Fiber Core 22mm Diameter Steel Wire Rope
https://chinazhongke.en.made-in-china.com/product/edtxObpYbRcl/China-6X7-FC-Diameter-22mmSteel-Wire-Rope-Ungalvanized-and-Galvanized-for-Belt-Conveyer-Ropeway-Drawing-and-Winch.html
[3] Engel Netze: 6x7 Fiber Core 18mm Diameter Steel Wire Rope
https://engelnetze.com/en/steel-wire-rope-trawl-warp-18-mm-diameter-construction-6x7fc-fibre-core-cutoff-length-2
[4] Engel Netze: 6x7 Fiber Core 16mm Diameter Steel Wire Rope
https://engelnetze.com/en/steel-wire-rope-trawl-warp-16-mm-diameter-construction-6x7fc-fibre-core-cutoff-length-2
Hand Calculations: