Sky-N-Sun - Bridge Design

Suspension Bridge Design Considerations and Math
Cables

Wire Rope, or Cables, are the support for the bridge. While they are probably the most important single part of the bridge from a structural point of view, there are only a few considerations in selecting cable.

Today there are many categories of wire rope. They differ mostly in flexibility and deformation resistance. For example, the cable used in cranes is very flexible so that it can run through the pulleys and wrap smoothly on the drum. A lot of flexibility is not necessary for building a bridge on our scale, so the less expensive versions are quite suitable.

What does matter most to this project is the strength of the cable. Cables have two ratings, Breaking Strength and Working Load. Breaking Strength is just that, while Working Load is considered a safe continuous or repeated strain. For safety, we will select a cable size with a Working Load rating greater than anything we expect to subject our bridge to.

The other property of the cable we will need is it's weight in order to calculate the total weight of the bridge. The total weight of the bridge is used to calculate the strain on the cables.

Tables with values for various cable sizes and types are easy to find on the web or in the "Engineer's Handbook". I prefer a formula to a table look up in a computer program so I derived some formulas (using pounds and inches) from the most conservative tables. The formulas I used are:

Breaking Strength = Diameter * Diameter * 72800.0

Working Load = Diameter * Diameter * 10000.0

Weight = Diameter * Diameter * Length * 0.14

You can safely use these or modify the numbers in the formulas for the cable you have chosen to use. Look up the values for a one inch cable of the type you have chosen and if necessary convert to pounds and inches. Length is usually given in feet, so divide by 12 to get inches. If strength is given in tons, multiply by 2000 to get pounds. If your table doesn't list a Working Load value, the generally accepted "Rule of Thumb" is Working Load = 20% of Breaking Strength (Working Load = Breaking Strength / 5) and round down. As you can see from my formulas, the most conservative table I have seen uses 14% (Working Load = Breaking Strength / 7) and round down.

Note: I use pounds and inches as the units because I'm in the United States. The units you use are not important as long as you are consistent. It will be simplest if your unit of length matches the unit used to specify the cable diameter so you can look up a one unit cable on your table to get the values to put into the formulas.