The concept of bridging long spans with cables, flexible tension members, antecedes recorded history (Art. 15.1). Known ancient uses of metal cables include the following: A short length of copper cable discovered in the ruins of Ninevah, near Babylon, is estimated to have been made in about 685 B.C. in the Kingdom of Assyria. A piece of bronze rope was discovered in the ruins of Pompeii, which was destroyed by the eruption of Mt. Vesuvius in 79 A.D.
The Romans made cables of wires and rope; on display in the Museo Barbonico at Naples, Italy, is a 1-in-dia., 15-in-long specimen of their lang-lay bronze rope, in which the direction of lay of both wires and strands is the same.
These early specimens of rope consisted of hand-made wires. In succeeding centuries, the craftsmanship reached such a state of the art that only a very close inspection reveals that wires were hand-made. Viking craftsmanship produced such uniform wire that some authorities believe that mechanical drawing was used.
Machine-drawn wire first appeared in Europe during the fourteenth century, but there is controversy as to whether the first wire rope resembling the current uniform, high-quality product was produced by a German, A. Albert (1834), or an Englishman named Wilson (1832). The first American machine-made wire rope was placed in service in 1846. Since then, with technological improvements, such as advances in manufacturing processes and introduction of high-strength steels, the quality of strand and rope has advanced to that currently available.
In structural applications, cable is generally used in a generic sense to indicate a flexible tension member. Several types of cables are available for use in cable-supported bridges. The form or configuration of a cable depends on its makeup; it can be composed of parallel bars, parallel wires, parallel strands or ropes, or locked-coil strands (Fig. 15.30). Parallel bars are not used for suspension bridges because of the curvature requirements at the pylon saddles. Nor are they used in cable-stayed bridges where a saddle is employed at the pylon, but they have been utilized in a stay where it terminates and is anchored at the pylon.

Definition of Terms

Cable. Any flexible tension member, consisting of one or more groups of wires, strands, ropes or bars.
Wire. A single, continuous length of metal drawn from a cold rod.
Prestressing wire. A type of wire usually used in posttensioned concrete applications.
As normally used for cable stays, it consists of 0.25-in-dia. wire produced in the United States in accordance with ASTM A421 Type BA.

Structural strand (with the exception of parallel-wire strand). Wires helically coiled about a center wire to produce a symmetrical section (Fig. 15.31), produced in the United States in accordance with ASTM A586.
Lay. Pitch length of a wire helix.
Parallel-wire strand. Individual wires arranged in a parallel configuration without the helical twist (Fig. 15.31).
Locked-coil strand. An arrangement of wires resembling structural strands except that the wires in some layers are shaped to lock together when in place around the core (Fig. 15.31).
Structural rope. Several strands helically wound around a core that is composed of a strand or another rope (Fig. 15.32), produced in the United States in accordance with ASTM A603.
Prestressing strands. A 0.6-in-dia. seven-wire, low-relaxation strand generally used for prestressed concrete and produced in the United States in accordance with ASTM A416 (used for stay cables).
Bar. A solid, hot-rolled bar produced in the United States in accordance with ASTM A722 Type II (used for cable stays).

Structural Properties of Cables

A comparison of nominal ultimate and allowable tensile stress for various types of cables is presented in Table 15.3.

Structural strand has a higher modulus of elasticity, is less flexible, and is stronger than structural rope of equal size. The wires of structural strand are larger than those of structural rope of the same nominal diameter and, therefore, have a thicker zinc coating and better resistance to corrosion (Art. 15.14).
The total elongation or stretch of a structural strand is the result of several component deformations. One of these, termed constructional stretch, is caused by the lengthening of the strand lay due to subsequent adjustment of the strand wires into a denser cross section under load. Constructional stretch is permanent.
Structural strand and rope are usually prestretched by the manufacturer to approach a condition of true elasticity. Prestretching removes the constructional stretch inherent in the product as it comes from the stranding or closing machines. Prestretching also permits, under 

prescribed loads, the accurate measuring of lengths and marking of special points on the strand or rope to close tolerances. Prestretching is accomplished by the manufacturer by subjecting the strand to a predetermined load for a sufficient length of time to permit adjustment of the component parts to that load. The prestretch load does not normally exceed 55% of the nominal ultimate strength of the strand.
In bridge design, careful attention should be paid to correct determination of the cable modulus of elasticity, which varies with type of manufacture. The modulus of elasticity is determined from a gage length of at least 100 in and the gross metallic area of the strand or rope, including zinc coating, if present. The elongation readings used for computing the modulus of elasticity are taken when the strand or rope is stressed to at least 10% of the rated ultimate stress or more than 90% of the prestretching stress. The minimum modulus of elasticity of prestretched structural strand and rope are presented in Table 15.4. The values in the table are for normal prestretched, structural, helical-type strands and ropes; for parallel wire strands, the modulus of elasticity is in the range of 28,000 to 28,500 ksi.
For cable-stayed bridges, it is also necessary to use an equivalent reduced modulus of elasticity Eeq to account for the reduced stiffness of a long, taut cable due to sag under its own weight, especially during erection when there is less tension. The formula for this equivalent modulus was developed by J. H. Ernst:

The bracketed term in the denominator becomes unity when o  u , that is, when the stress is constant. The reduction in modulus of elasticity of the cable due to sag is a major factor in limiting the maximum spans of cable-stayed bridges.
The effects of creep of cables of cable-supported bridges should be taken into account in design. Creep is the elongation of cables under large, constant stress, for instance, from dead loads, over a period of time. The effects can be evaluated by modification of the cable equation in the deflection theory. As an indication of potential magnitude, an investigation of the Cologne-Mulheim Suspension Bridge indicated that, in a 100-year period, the effects of cable creep would be the equivalent of about one-fourth the temperature drop for which the bridge was designed.

Erection of Cables

Until the 1960s, parallel-wire, suspension-bridge main cables were formed with a spinning wheel carrying one wire at a time (and more recently two or four wires) over the pylons from anchorage to anchorage (Fig. 15.33). Not only were the wires spun aerially individually, but each wire had to be removed from the spinning wheel at the anchorages, looped over a circular or semicircular strand shoe, then looped again over the spinning wheel for a return trip (Art. 15.23). Furthermore, wires had to be adjusted individually, then banded into strands and readjusted (Fig. 15.34a), and finally compacted into a circular cross section (Fig. 15.34b). This process is time-consuming, costly, and hazardous.
Prefabricated parallel-wire strands are an economical alternative. Large main cables of suspension bridges may be made up of many such strands, laid parallel to each other in a selected geometric pattern. In the commonly used hexagonal, there may be 19, 37, 61, 91, or 127 large strands. In a rectangular pattern, there may be 6 or more strands in each horizontal row and 6 or more vertical rows, with suitable spacers. The strands may have up to 233 wires each, all shop-fabricated, socketed, tested, and packaged on reels. Their use can yield a tremendous saving in erection time over the older process of aerial spinning of cables on the site.
For the Newport Bridge, which was completed in 1969, shop-fabricated, parallel-wire strands form the cables. Each cable is made up of 4,636 wires, each 0.202 in diameter, shopfabricated into 76 parallel wire strands of 61 wires each. Thus, in place of thousands of spinning-wheel trips previously necessary, only 152 trips of a hauling rope were needed to form the two cables. Furthermore, thousands of sag adjustments of individual wires were eliminated from the field operation.

From a design point of view, parallel-wire cables are superior to cables made of helicalwire strands. Straight, parallel-laid wires deliver the full strength and modulus of elasticity of the steel, whereas strength and modulus of elasticity are both reduced (by about one  eighth) with helical placement. On the other hand, from the bridge-erection standpoint, standard helical-strand-type cables are superior to field-assembled parallel-wire type. Strands are readily erected and adjusted, with a minimum of equipment and manpower. Therefore, they have been used on many small- to moderate-sized suspension bridges. Prefabricated parallelwire strands, however, combine the erection advantages of strand-type cables with the superior in-place characteristics of parallel-wire cables.

For smaller cable bridges, cables with few strands may be arranged in an open form with strands separated. But for longer bridges, the strands are arranged in a closed form (Fig. 15.34a) in either a hexagonal or other geometrical pattern. They then may be compacted by machine (Fig. 15.34b) and wrapped for protection. Note that a group of helical-type strands cannot be compacted into as dense a mass as a group of parallel-wire strands.

For smaller cable bridges, cables with few strands may be arranged in an open form with strands separated. But for longer bridges, the strands are arranged in a closed form (Fig. 15.34a) in either a hexagonal or other geometrical pattern. They then may be compacted by machine (Fig. 15.34b) and wrapped for protection. Note that a group of helical-type strands cannot be compacted into as dense a mass as a group of parallel-wire strands.
Cable-stayed bridges formerly used traditional structural strands or locked-coil strands for the stays. Since then, stays composed of prestressing steels are generally used. Cable stays for cable-stayed bridges are similar to post-tensioning tendons in that they consist of the following primary elements:
Prestressing steel (parallel wires, strands, or bars)
Sheathing (duct), which encapsulates the prestressing steel and may be a steel pipe or a high-density polyethylene pipe (HDPE)
A material that fills the void between the prestressing steel and the sheathing and may be a cementitious grout, petroleum wax, or other appropriate material  Anchorages
There are two basic methods of manufacture and installation of stays: (1) assembly on site in final position and (2) prefabricated installation. Both methods have been successfully employed. Given various constraints for a specific project or site, it is generally a question of economics as to which method is employed. Prefabrication may be accomplished either at a factory remote from the construction site or, if feasible, at the project site (possibly on the bridge deck). Normally, factory-prefabricated stays are delivered to the site reeled on drums, complete with the bundle of wires or strands, the HDPE sheathing, and anchorages.
(This method cannot be used with prestressing bars or steel pipe sheathing.) Usually, one or both anchorages are fitted to the stay.
At the site, prefabricated stays usually are erected into final inclined position either by crane or by a temporary guying system that is erected between anchorage points from which the stays are suspended. The stays are brought into final position by means of a winch or other suitable hydraulic equipment.
When a guying system is used, site assembly of stays in final position begins with installation of the guying system. The sheathing, either steel or HDPE, is then positioned in the final inclined position. Next, the strand or wire-bundle stays are pulled through the sheathing by winches. When strands are used, the push-through method may be employed.
In that case, by use of specialized equipment, individual strands are pushed into the sheathing.
Parallel prestressing bars are somewhat more difficult to install inasmuch as bar couplers must also be installed at intervals along the stay length.


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