|Steel cables on a pulley|
Cables are constructed from a large number of wires wound in some particular manner. While many arrangements are available depending upon how the cable will be used, a common type of cable, is formed by six strands wound helically around a central strand. Each strand is in turn constructed of many wires, also wound helically. For this reason, cables are often referred to as wire rope.
The cross-sectional area of a cable is equal to the total crosssectional area of the individual wires, called the effective area or metallic area. This area is less than the area of a circle having the same diameter as the cable because there are spaces between the individual wires. For example, the actual cross-sectional area (effective area) of a particular 25 mm diameter cable is only 300 mm2, whereas the area of a 25 mm diameter circle is 491 mm2.
Under the same tensile load, the elongation of a cable is greater than the elongation of a solid bar of the same material and same metallic cross-sectional area, because the wires in a cable “tighten up” in the same manner as the fibers in a rope. Thus, the modulus of elasticity (called the effective modulus) of a cable is less than the modulus of the material of which it is made. The effective modulus of steel cables is about 20,000 ksi (140 GPa), whereas the steel itself has a modulus of about 30,000 ksi
When determining the elongation of a cable from equation,
δ = PL/EA
the effective modulus should be used for E and the effective area should be used for A. In practice, the cross-sectional dimensions and other properties of cables are obtained from the manufacturers. Note that the last column contains the ultimate load, which is the load that would cause the cable to break. The allowable load is obtained from the ultimate load by applying a safety factor that may range from 3 to 10, depending upon how the cable is to be used. The individual wires in a cable are usually made of high-strength steel, and the calculated tensile stress at the breaking load can be as high as 1400 MPa.