AND HYBRID STRUCTURAL CABLES

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims benefit of Provisional Appln. 61/940,340, filed February 14, 2014, the entire contents of which are hereby incorporated by reference as if fully set forth herein, under 35 U.S.C. § 119(e). This application also claims benefit of Provisional Appln. 62/035,188, filed August 8, 2014, the entire contents of which are hereby incorporated by reference as if fully set forth herein, under 35 U.S.C. § 119(e).

BACKGROUND

[0002] A significant problem relevant to the infrastructure of a country, including the United States, is the ability to increase strength and reduce corrosion of cables used in suspension and cable-stay bridges. For example, corrosion of main cables of suspension bridges is one of the most challenging problems that bridge owners face today. Failure of a main cable of a suspension bridge corresponds to the failure of the entire bridge. Replacement of a cable is a very costly operation, with a cost around $100 million per cable, with larger bridges often having four cables. Unfortunately, cable deterioration is happening and the technology to control and assess said corrosion is still under development. Many of these monumental bridges (usually cable suspension bridges are quite large) have already passed their expected service life and, because of the importance they have gained in our infrastructure system (such as in New York City), they must be kept fully operational.

[0003] Suspension bridge cables are made up of thousands of high strength ASTM A586 steel wires bundled in parallel wire strands. These wires are generally zinc galvanized and have a diameter of 4.98 mm, including the zinc coating. A notable exception to this specification is the Williamsburg Bridge in New York City, where "bright steel" wires with a diameter of 4.887 mm were used. These wires are arranged in hexagonal strands, which are subsequently compacted by means of hydraulic jacks to form a round cable cross section. Hydraulic compaction reduces the void ratio of a standard cable to approximately 20%; the fact that the cable is comprised of round wires limits the reduction of interstitial voids beyond 20%.

[0004] A primary hazard in the health of a suspension bridge lies in the corrosion of the main cables. Betti and Yanev (1999) have quantified the per annum cable strength loss of various bridges in the New York City tristate area at up to 0.37% per year. This rate is significant, considering that many of these bridges are approaching or have already surpassed a 100 year service life. Since the cables of a suspension bridge are the ultimate load-carrying member, great care must be taken to safeguard the condition of this system throughout the life of a bridge.

[0005] Various corrosion actuators can adversely affect a suspension bridge cable's condition: 1) residual stresses due to cold- working; 2) hydrogen embrittlement; 3) galvanic potential between zinc, steel, and other additives; and 4) intrusion of moisture into the cable cross section, potentially containing chlorides and/or sulfates from salt spray and acid rain, respectively.

[0006] Loss of cable strength is generally effected by two processes, either loss of metallic cross section (i.e. nominal area of steel carrying tensile load) or brittle cracking and fracture of individual wires. Wires in bridge cables generally fracture as a result of two distinct failure mechanisms. The first is uniform corrosion and pitting, studied by Eiselstein and Caligiuri (1988) on the Williamsburg bridge cables. They have found that wires undergo pitting corrosion when the cable is in a positive hydrogen scale corrosion potential at a pH ranging from 7 to 3. This pitting initially results in concentrated reductions of load-carrying cross section at random locations of the wire (i.e. pits), leading to local overload, yielding, and ductile failure of the wire at the location of the pitting corrosion.

[0007] The second cause for fracture of bridge wires is a result of the combination of residual stress cracking supported by hydrogen embrittlement, as outlined by Mayrbaurl and Camo (2001). Traditionally, bridge wires are drawn through dies at ambient temperature, lengthening the grains and therefore increasing the ultimate strength of the steel. During this process, the wires are given a curvature induced by the capstan, which draws the wire through the dyes. This residual but permanent radius of curvature ranges from 1.5 meters (m) to 1.8 m in traditionally manufactured wires, although it has been significantly increased with improved manufacturing techniques to 7.5 m or more. When the wires are subsequently straightened in service, they develop stresses on the inner and outer arc on the order of 200 MegaPascals (MPa, 1 MPa = 10 ⁶ pascals, Pa, 1 Pa = 1 newton/m ² ) in tension and

compression, respectively. It has been found by Hop wood and Havens (1984) that stress cracking occurs once wires have lost their protective zinc coating due to zinc oxidation and subsequently undergone significant ferrous corrosion. In such wires, pitting occurs, creating galvanic action which in turn generates free hydrogen which embrittles the steel wire. Such pits furthermore create a stress concentration within the remaining ferrous cross section, enabling the formation of a crack across the entire cross section of the wire. Such cracks have been detected in cables which have undergone significant corrosion.

[0008] In light of these hazards, various systems have been pioneered over the decades to reduce the corrosion rate in suspension bridge cables, with mixed success. The initial approach involved oiling cables with linseed oil during spinning— Brooklyn and Manhattan Bridges are an example of this— or simply covering the entire cross section of the cable with "red lead" paste, an emulsion of lead oxide mixed with linseed oil. The cross section is then wrapped circumferentially with a 9 gauge wrapping wire and painted. The red lead paste, especially, has proved to be ineffective, as it dries, cracks, and becomes friable over time. The wrapping wires have also exhibited significant corrosion, bulging, and even fracture on various bridges.

[0009] Current approaches involve neoprene wrapping of cables, as well as forced-air dehumidification of cables with mechanically desiccated air. The Akashi-Kaikio Bridge in Japan employs both of these systems, along with the use of an interlocking S-shaped wrapping wire. SUMMARY

[0010] Techniques are provided for high-strength wires for structural cable that are, in many embodiments, less subject to corrosion, and, in some embodiments, superior in strength.

[0011] In a first set of embodiments, a strand for a structural cable includes a plurality of wires and a winding. Each wire of the plurality of wires has a non-circular cross section configured to have a corresponding surface contact area with an adjacent wire of the plurality of wires. The corresponding contact area is substantively greater than a surface contact area of a circular wire having a diameter substantively identical to a largest inscribed circle for the corresponding non-circular cross section. The winding surrounding the plurality of wires is configured to hold the wires in parallel within the strand. The strand, with the plurality of wires within, has a hexagonal shape.

[0012] In a second set of embodiments, a strand for a structural cable includes: multiple wires. At least one wire of the multiple wires has a circular cross section; at least one portion of one wire has a non-circular cross section configured to have a corresponding surface contact area with an adjacent wire that has the non-circular cross section, and the

corresponding contact area is substantively greater than a surface contact area of a circular wire having a diameter substantively identical to a largest inscribed circle for the

corresponding non-circular cross section. The strand also includes a winding surrounding the multiple wires. The winding is configured to hold the wires in parallel within the strand. The strand with the plurality of wires within has a hexagonal shape.

[0013] In a third set of embodiments, a method includes opening a structural cable strand made up of multiple circular cross-sectional wires. The method includes electing a extant wire of the strand to be spliced; and splicing a replacement wire into a portion of the extant wire. The replacement wire has a non-circular cross section configured to have a

corresponding surface contact area with an adjacent wire of the plurality of wires. The corresponding contact area is substantively greater than a surface contact area of a circular wire having a diameter substantively identical to a largest inscribed circle for the

corresponding non-circular cross section. In some of these embodiments, the replacement wire has a hexagonal cross-sectional shape. [0014] Still other aspects, features, and advantages of the invention are readily apparent from the following detailed description, simply by illustrating a number of particular embodiments and implementations, including the best mode contemplated for carrying out the invention. The invention is also capable of other and different embodiments, and its several details can be modified in various obvious respects, all without departing from the spirit and scope of the invention. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The present invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which:

[0016] FIG. 1A is a block diagram that illustrates an example structural cable used in a suspension bridge, according to an embodiment;

[0017] FIG. IB through FIG. ID are block diagrams that illustrate an example arrangement of wires in strands in a structural cable;

[0018] FIG. 2A through FIG. 2C are block diagrams that illustrate example regular hexagonal wires for a structural cable, according to an embodiment;

[0019] FIG. 3A and FIG. 3B are block diagrams that illustrate example computed forces and deformation for circular and hexagonal wires, according to an embodiment;

[0020] FIG. 4 is a block diagram that illustrates an example strand made up of wires of a rectangular shape, according to various embodiments;

[0021] FIG. 5A through FIG. 5D are a block diagrams that illustrates example cross-sectional shapes for wires of a strand, according to various embodiments;

[0022] FIG. 6A and FIG. 6B are block diagrams that illustrate example wires of a bumpy hexagonal shape, according to various embodiments;

[0023] FIG. 7 is a block diagram that illustrates an example strand made up of wires of different sizes, with the smallest wires having a regular hexagon shape, according to various embodiments;

[0024] FIG. 8A is a block diagram that illustrates an example splice of a non-circular cross- sectional wire into a cable strand with circular cross-sectional wires, according to an embodiment;

[0025] FIG. 8B is a block diagram that illustrates an example cross section of a non-circular cross- sectional wire surrounded by circular cross-sectional wires, according to an

embodiment; [0026] FIG. 8C is a block diagram that illustrates an example cross section of a circular cross-sectional wire surrounded by non-circular cross-sectional wires, according to an embodiment;

[0027] FIG. 9 is a block diagram that illustrates example computed forces and deformation for hybrid circular and hexagonal wires, according to an embodiment;

[0028] FIG. 10A is a block diagram that illustrates example experimental setup to measure friction between wires in a strand, according to an embodiment;

[0029] FIG. 10B is a graph that illustrates example experimental results comparing friction between wires in a strand using different combinations of wire cross sections, according to an embodiment;

[0030] FIG. 11 is a flow chart that illustrates an example method for retrofitting wires in a structural cable in place on a structure, according to an embodiment;

[0031] FIG. 12A and FIG. 12B are photographs that illustrate example coiling of a bundle of wires with a non-circular cross section for a strand on a spool, according to an embodiment; and

[0032] FIG. 13 is a flow chart that illustrates an example method for constructing a structure using multiple spools, each spool holding a coiled strand of wires with non-circular cross section, according to an embodiment.

DETAILED DESCRIPTION

[0033] A strand is described for high-strength structural cables and method of using same. In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid unnecessarily obscuring the present invention.

[0034] Some embodiments of the invention are described below in the context of cables for suspension bridges, such as the George Washington Bridge connecting Manhattan, New York, with Fort Lee, New Jersey. However, the invention is not limited to this context. In other embodiments, structural cables are constructed of multiple wires and used in other structures, such as guy wires for towers and support cables for elevators, counterweights and balconies.

[0035] As used herein the following terms have the meanings given here.

Interference means either (a) the collision of the tips of the teeth of one gear-wheel with the flanks of those of the mating wheel which occurs if the teeth are not cut to a suitable profile; or (b) the amount by which the external dimension of a part exceeds the internal dimension of the part into which it has to fit.

Interference fit means a fit between two mating parts for which, within the specified

tolerances, there is always an interference between them.

To interlock means to engage with each other by partial overlapping or interpenetration of alternate projections and recesses, or to lock or clasp with each other.

Friction refers to the rubbing of one body against another and, further, in physics, the

resistance with which any body meets when in moving over another body.

Friction-tight means fitting so tightly that the desired amount of friction is obtained.

1. Overview

[0036] FIG. 1A is a block diagram that illustrates a structural cable 110 used in a suspension bridge 100, according to an embodiment. The structural cable 110 is suspended from two piers 120 and is connected to, and supports, a roadway 122 by multiple vertical cables (suspenders) 102. The cable 110 is constructed as described below, according to an embodiment.

[0037] FIG. IB through FIG. ID are block diagrams that illustrate an example arrangement of wires in strands in a structural cable according to some conventional approaches. For example, in a conventional suspension bridge, a cable 130 is made up of between about 7000 and 20,000 round steel wires 132, each coated with zinc metal, which often forms on its surface a layer of zinc oxide. The round wires 132 are about five (5) millimeters (mm) in

_3

diameter (1 mm = 10 meters). The wires are often pre-assembled into hexagonal strands

134, e.g., with the cross section approximating a regular hexagon of equal sides and angles. In some embodiments, the strand is contained within a winding of some sort. For example, in some embodiments the strand is coated with a sheath 136 of suitable material. In some embodiments, the strands are not themselves placed in a sheath, but they are taped with high- strength glass fiber reinforced tape 137 as a winding at several positions along the length of the cable. The strands are often assembled off-site in a manufacturing facility suitable for ordering the wires of the strand in a hexagonal grid, for keeping the wires parallel for the length of the strand, and for tightly packing the wires together within the strand. This practice and the actual strand are called Prefabricated Parallel Wire Strands (PPWS) in the industry. The regular hexagonal strands 134 are combined on site, aligned in parallel, to form the cable 130. Smaller strands with other polygonal cross sections, such as irregular hexagon strands

135, are often also added along the outer perimeter to complete the overall circular cross section of the cable 130. When completed, the cable 130 is about 18 to 44 inches in diameter. The cable 130, itself, is often coated with zinc paste, wrapped by a wrapping wire and painted or wrapped by a rubber (e.g., neoprene) sheath.

[0038] It is noted that the cables 130 so constructed have a void ratio of about 20% before compaction, and as low as about 9% after compaction. The void ratio is caused by the voids 139 between the round wires 132. Fluid with electrolytes often permeates these voids 139 and leads to corrosion of the wires 132, thus weakening the strands 134, 135, and ultimately weakening the cable 130. [0039] According to some embodiments, a strand includes a plurality of wires and a winding. Each wire of the plurality of wires has a non-circular cross section configured to have a corresponding surface contact area with an adjacent wire of the plurality of wires. The corresponding contact area is substantively greater than a surface contact area of a circular wire having a diameter substantively identical to a largest inscribed circle for the

corresponding non-circular cross section. The extra surface contact area provides friction that serves to compensate over a distance for broken wires when deployed. That is, when a wire in a deployed cable breaks, the surface contact under pressure with adjacent wires causes the wire on either side of the break to transfer the load stresses to the adjacent wires and then take up the load again on the other side of the break.

[0040] According to some embodiments, the cross section (or cross-sectional shape) is also chosen to reduce the void ratio in the strand from that of the conventional strand made up of round wires. This reduces exposure of the wires to electrolytes and reduces the rate of corrosion.

[0041] According to some embodiments, the shape is also chosen to favor self-ordering of the plurality of wires within the strand. For example, the shape is selected so that the wires are easily ordered in a grid for forming the strand, such as a hexagonal grid for forming the hexagonal stand.

[0042] According to some embodiments, the shape is also chosen to favor self -packing of the plurality of wires within the strand. For example, the shape is selected so that the wires easily fit together closely to reduce total void ratio in the strand.

[0043] According to some embodiments, the size is chosen to work with existing equipment with only minor modification. Thus, in some embodiments, the wire has a cross-sectional size and shape such that a greatest inscribed circle is about 5 mm, or the cross-sectional size and shape is inscribed within a circle of about 5 mm, or some combination.

[0044] According to some embodiments, the shape is also chosen so that the non-circular cross section of each wire has no acute angle. This adds safety, in that fast-moving wires have edges that are more likely to cut human operators if the wire cross section has one or more acute angles than if the wires have cross sections without any acute angle. Furthermore, when acute angles are avoided, fracturing of wires is less likely. Even further, avoiding acute angles reduces locations of high stress where those angles contact a flat surface that can lead to abrasion and to increased corrosion at such abrasion locations. Furthermore, avoiding acute angles reduces burnishing, the plastic deformation of a surface due to sliding contact with another object.

[0045] As in the conventional cable, the strand, with the plurality of wires within, preferably has a hexagonal shape, whether regular or irregular.

[0046] In one embodiment, hexagonal wires offer all these advantages. FIG. 2A through FIG. 2C are block diagrams that illustrate example regular hexagonal wires 200 for a structural cable, according to an embodiment. A regular hexagonal wire 200 with a zinc or zinc oxide coating 211 comprises a zinc coated regular hexagonal wire 210. As can be seen, when packed together in a group 202 of regular hexagonal wires 210, there is great surface area contact allowing for a great deal of friction. In addition, the void ratio is substantively zero (i.e., zero for most practical purposes). This configuration provides both a strand of increased strength and decreased corrosion compared to conventional strands of the same number of conventional round wires. Strand 220 is an example regular hexagonal strand made up of 37 5-mm regular hexagonal zinc-coated wires 210.

2. Relation of strength to surface contact area

[0047] Equations are presented here, which demonstrate advantages of various embodiments in causing a strand to recover from a break in an individual wire. However, embodiments are not limited by the completeness or accuracy of these equations. When considering the friction interaction between two bridge wires, both the case of round and hexagonal wires under a compaction force are considered. These serve as a basis of comparison for the friction areas, which each geometry provides. This calculation is based on classical problems in the theory of elasticity, in which a concentrated force, F, acts in a z direction (F _z ) on an elastically deformable infinite half space defined by an x-y plane. [0048] The resulting displacements the x, y and z directions, respectively, are expressed as functions of Cartesian position (x, y, z) relative to the point of application of force F _z as given by Equations la through Id.

1+v xz (l-2v)x

2πΕ r(r+z) -] Fz da)

1+v yz (l-2v)y

Uy (lb)

2πΕ r(r+z)

1+v [2 (1- v) z ² ]

u _z = (lc)

2πΕ r r ³ J

where Ύ = jx ² + y ² + Z ² (Id)

E indicates Young's modulus and vindicates Poisson's ratio (the negative ratio of transverse to axial strain, where traverse is perpendicular to the direction of force and axial is parallel to direction of force).

[0049] From these displacement functions, one can derive the Hertzian contact force of a rigid sphere and an elastic infinite half space, which can then be applied to the contact problem of two elastic bodies with curved surfaces in contact. For a detailed derivation, see Popov 2010. FIG. 3A and FIG. 3B are block diagrams that illustrate example computed forces and compaction for circular and hexagonal wires, 132 and 200, respectively, according to an embodiment.

[0050] Of particular interest in this investigation is the problem of two cylinders contacting each other on the curved face; see FIG. 3A. In this case, a normal force, F, is evenly distributed along a contact length L of two cylinders with radii Ri and R ₂ , Young's moduli of Ei and E ₂ , and Poisson's ratios of vi and V2. For simplicity, only one interaction point between two round wires is considered. In reality, completely covered internal wires contact six neighboring wires at regular 60° radial intervals. This contact relationship for the number of faces and requisite friction transfer capability scales directly. The industry- standard

3

compaction force is about 2000 pounds per square inch (psi, 1 psi ~ 6.9x10 Pa).

[0051] The resulting elastic deformation of the two cylinders creates a contact area with half- width, b, defined according to Equation 2.

In the case of ASTM A586 zinc-coated parallel steel wires, 10 ¹¹ Pa, 10 ^" m; hence Equation 2 can be simplified as given by Equation 3.

As an example, with a compaction pressure of /¾·= 1.4· 10 Pa (~ 2,000 psi), assuming six contact points (n _cont ), along the circumference (C _Wire ) of a 5 mm diameter wire and a balanced concentration of said pressure on the six contact points (n _contact ), the circumferential wire distributed load (— j is given by Equation 4 and contact distributed load (— is

L ci _rc J L contact given by Equation 5:

Pff ^{■ c} wire = 1- ^■ 10 ^7■ 5π ^■ 10 ^~3 = 2.199 ^■ 10 ^{5 N} / _m (4) circ

2.199- 10 ⁵

= 3.665 - 10 ⁴ (5) contact ⁿ cont

The resulting deformed (flat) width (2b), which is in contact with its neighboring wire is given by Equation 6.

2b = 2 - 1.20 ^■ 10 ^~7 V3.665 ^■ 10 ⁴ = 4.6 ^■ 10 ^~5 m = 0.0460 mm (6)

The distribution along the contact area is semi-elliptical, with the maximum contact pressure (at the center of pressure), p _majc given by Equation 7.

2F

Vmax (7)

nbL

Continuing the numerical example, the maximum pressure for this case is given by Equation 8.

[0052] The continuum mechanics evaluation of contact face for the hexagonal wire is trivial since the regular hexagon allows for a tight packing regime with zero void ratios and complete contact on all faces without application of compaction forces. For the sake of comparison, the contact surface is enumerated for one side of a regular hexagonal wire, p

shown in FIG. 3B, with the same distributed linear load, -, along the length, L. Invoking the geometric properties of the regular hexagon, it is known that the radius (R _n ) equals the length of the vertex (V _n ). In the case of this numerical example, it follows that

Ri=R ₂ =Vi=V ₂ =2.5 - 10 ^" m. Therefore, for the hexagon, the contact surface width 2b = 2.5· 10 ^"3 m = 2.5 mm.

[0053] The maximum pressure, pmax, is rather an evenly distributed load on one face of the hexagon, Pf _ace is given by Equation 9.

Pmax = Pface = 1- ^■ 10 ⁷ Pa = 14 MPa (9)

[0054] The contact area of the hexagonal wire under 14 MPa of compaction pressure is 73 times higher than a round wire with equivalent packing cross- section. Furthermore, the contact surface area is not a function of compaction force for the hexagonal cross sections since the system is already in full geometric contact (i.e. fully packed) before application of any compaction load.

[0055] The degree of the stress concentration (stress concentration factor, SCF) at the point of contact of the round wire becomes evident when comparing the p _max of the hexagonal and round wires, as given by Equation 10.

SCF = - ^V ≡ - = = 72 (10)

Pmax 14 MPa

This magnitude of stress concentration at the points of contact can lead to fatigue cracking, surface damage due to contact friction, burnishing, etc., collectively termed burnishing. All of these consequences are highly undesirable, and should be avoided in various embodiments in order to safeguard the long-term survivability of a parallel wire bridge cable system. [0056] It has been shown experimentally that round wires with a fracture can recover 90% of load after approx. 10 cm of length, if the system is sufficiently clamped/confined. However, it has been found in subsequent experiments that the same system experiences surface burnishing, which significantly reduces the load transfer of the same system under equal clamping conditions. A reduction of load-carrying capacity from 90% to 30% has been recorded. It is offered here that the advantageous surface contact/packing of the hexagonal wires not only greatly increases the frictional load transfer and therefore decrease the recovery length by an order of magnitude, but that it also significantly reduces surface burnishing. Both the decrease in recovery length and the reduction of surface burnishing due to cyclical load fluctuations greatly increases the system's resilience to wire breaks.

3. Example Embodiments

[0057] In various example embodiments, the wire shapes with increased surface area contact include hexagons, rectangles, crosses, bumpy polygons, among other shapes of a single shape and size, or multiple sizes, or compound shapes comprising multiples of the smallest shapes, or some combination. For some compound shapes, at least one wire of the plurality of wires has a cross- sectional size and shape substantively identical to a size and shape of a plurality of other wires of the plurality of wires. As described above, in some embodiments, the wires each have a hexagonal shape and are uniform in size.

[0058] Non-hexagonal shapes can also be used to produce regular hexagonal strand with increased surface contact areas. FIG. 4 is a block diagram that illustrates an example strand 400 made up of wires 410 of a rectangular cross-sectional shape, according to various embodiments. In some embodiments, the rectangles have sides of the same length; so each of the wires has a square cross section. Again, one or more larger wires comprising a square or compound shape equivalent to a packing of several of the smallest wires 410, are used in some embodiments.

[0059] FIG. 5A through FIG. 5D are block diagrams that illustrate example cross-sectional shapes for wires of a strand, according to various embodiments. FIG. 5A is a block diagram that illustrates example wires 522 of a triangular cross-sectional shape, according to various embodiments. The group 520 includes 6 wires in a hexagonal pattern, but each wire 522 has a triangle shape. There is substantively complete contact along the surfaces of the wire and substantively zero void ratio. In some embodiments, the triangles are equilateral triangles with sides of the same length. Again, one or more larger wires comprising a triangle or compound shape equivalent to a packing of several of the smallest wires 522, are used in some embodiments. In some embodiments, to reduce risk of injury to those who work with the wires, the acute angle of each triangle vertex is rounded, which slightly reduces contact area and slightly increases void ratio of the group 520.

[0060] FIG. 5B is a block diagram that illustrates example wires 532 of a cam cross-sectional shape, according to various embodiments. The group 530 includes 7 wires in a hexagonal packing regime, but each wire 532 has an interlocking cam shape. There is substantively complete contact along the surfaces of the wire and substantively zero void ratio. The shape avoids acute angels and therefore reduces risk of injury to persons working with the individual wires compare to wires with acute angles in the cross-sectional shape. Again, one or more larger wires comprising a compound shape equivalent to a packing of several of the smallest wires 532, are used in some embodiments.

[0061] FIG. 5C is a block diagram that illustrates example wires 510 of a cross shape, according to various embodiments. The group 500 includes 7 wires in a hexagonal packing regime, but each wire 510 has a cross shape. There is substantively complete contact along the surfaces of the wire and substantively zero void ratio. In some embodiments, the crosses have sides of the same length. Again, one or more larger wires comprising a cross or compound shape equivalent to a packing of several of the smallest wires 510, are used in some embodiments.

[0062] FIG. 5D is a block diagram that illustrates example wires 542 of an interlocking teeth gear cross-sectional shape, according to various embodiments. The group 540 shows 25 wires in a pattern, but each wire 542 has an interlocking gear shape. There is more contact along the surfaces of the wire and smaller void ratio than in groups made up of circular wires. The shape avoids acute angles and therefore reduces risk of injury to persons working with the individual wires compared to wires with acute angles in the cross-sectional shape. Again, one or more larger wires comprising a compound shape equivalent to a packing of several of the smallest wires 542, are used in some embodiments. In some embodiments, gear teeth are added along sides of the other shapes above, e.g., rectangular cross-sections, to favor self- ordering or self -packing or both in strands made up of such wires.

[0063] FIG. 6A and FIG. 6B are block diagrams that illustrate example wires 610 of a bumpy hexagonal shape, according to various embodiments. The group 600 includes 7 wires 610 to form a hexagonal packing regime. There is substantively complete contact along the surfaces of the wire and substantively zero void ratio. The bumps help align the wires 610 for self- ordering. Again, one or more larger wires comprising a compound shape equivalent to a packing of several of the smallest wires 610 are used in some embodiments.

[0064] In some embodiments, not all wires in the strand are the same size or shape or both. Bundled cables made from differently- sized wires currently only exist in helically- spun wires. The technology described here could be extended to differently- sized wires in bundles, akin to what is shown in FIG. 7. FIG. 7 is a block diagram that illustrates an example strand made up of wires of different sizes, with the smallest wires having a regular hexagon shape, according to various embodiments. Example strand 750 is made up of three compound shaped wires 752 and 16 5-mm regular hexagonal wires 210. Each compound shape 752 is equivalent to 7 stacked 5-mm regular hexagons, which are the smallest wires in the strand. This embodiment has a void ratio of substantively zero.

4. Retrofit embodiments.

[0065] In the case of retrofit projects, it may become useful to replace individual wires in a cable with replacement wires of new virgin material due to corrosion and/or cracking of individual extant wires over the service life of the structural system. In such a case, replacement is accomplished by splicing the replacement wire into the extant wire in place in the existing structural system.

[0066] In this case, the interaction in hybrid systems containing both classical round and novel (non-round) wires are determined. In an illustrated embodiment, hexagonal wires are used as an example of a non-round novel geometry with the advantages of higher contact area and lower void ratios.

[0067] If broken wires are detected during inspection or wire samples are removed for laboratory testing, NCHRP Report 534 dictates that a new section of wire be spliced into the working cable and tensioned to the original service load of surrounding wires. New wire is spliced into extant wires in the cable by using carbon steel or stainless steel wire ferrules. Threaded ferrules involve threading the wire by either cutting or rolling and are specified to sustain 75% of the original tension capacity of the wire. Pressed-on ferrules, which are crimped onto wire by mechanical means, are specified to sustain 90% of the ultimate strength of the wire.

[0068] The structural aspects of the splicing process are depicted in FIG. 8A. FIG. 8A is a block diagram that illustrates an example splice of a non-circular cross-sectional wire into a cable strand with circular cross-sectional wires 801, according to an embodiment. The defective portion of the extant wire is removed, leaving two extant portions, extant portion

801 and extant portion 804, both with circular cross sections. The procedure involves cutting a new piece of replacement wire to the approximate length of the removed portion of the extant wire and subsequently cutting the replacement wire into two pieces, new wire portion

802 and new wire portion 803, both with non-circular cross sections. Each end of the original wire 801 and 804 is cleaned, and a pressed-on ferrule 811 and 812 is spliced onto each end, respectively. The two new wire portions 802 and 803 are then spliced into the central threaded ferrule 821 and tensioned by use of jacks to the prescribed service load. This allows wire portion 803 to be lined up to wire portion 804 and trimmed to the length that it will be under service load. The assembly is unloaded, and wire portion 803 is spliced onto wire portion 804. Care is given to properly orient the cross section of the new wire to achieve optimal packing (i.e. minimize void ratios) in the existing wire matrix. The entire new wire assembly is then tensioned by turning the opposing threads integrated into the threaded wire ferrule 821, much like a turnbuckle. Tension in each inserted wire is tested by the tension offset method using a dynamometer, as is well known in the art. [0069] As a result of such splicing, a hybrid strand is produced. A hybrid strand is any strand containing more than one type of cross-sectional geometry. For purposes of illustration, seven-wire unit cell examples consisting of six peripheral and one central wire in tight hexagonal packing are considered. FIG. 8B is a block diagram that illustrates an example cross section of a non-circular cross-sectional wire 802a surrounded by circular cross- sectional wires 801a through 80 If, according to an embodiment. FIG. 8C is a block diagram that illustrates an example cross section of a circular cross-sectional wire 80 lg surrounded by non-circular cross-sectional wires 802b through 802g, according to an embodiment.

[0070] As far as is currently known, no work has been performed in either academia or industry to study the friction interaction properties of such hybrid systems. Testing is currently underway at the Carleton Laboratory of Columbia University to quantify the interaction mechanics for one or more embodiments of such hybrid systems.

[0071] FIG. 9 is a block diagram that illustrates example computed forces and deformation for hybrid circular and hexagonal wires, 132 and 200, respectively, according to an embodiment. Equation 2 is still valid in this case, where R ₂ →∞ to quantify the flat face of the hexagonal wire, simplifying to Equation 11.

case of ASTM A586 zinc-coated parallel steel wires, as described above,

Ei=E2=E _stee i=2- 10 ¹¹ Pascals (Pa, 1 pa = 1 newton per square meter), vi=V2=v _ste ei

10 ^" m, yielding 12.

When compared to the circle-circle interface, it becomes apparent that the contact surface is Λ/2 times greater than the circular-circular interface. This is effectively a 41% improvement of the stress concentration problem inherent in the circle-circle contact problem. [0072] It is safe to say that the void ratio will decrease, but it depends on the configuration of the hybrid system. When using hexagonal wires to replace round wires, though, the void ratio will always be reduced over the original round-only configuration, when the hex wire is oriented properly.

[0073] The performance of hybrid systems resulting from such retrofitting was compared experimentally to current round wire systems. Initial pullout testing shows that the replacement of round wires by hex wires significantly increases the average maximum load required to pull out the center wire from a 7 -wire specimen (37% increase), indicating a desirable increase in the amount of load transferred to the center wire. The basic geometry of each specimen is shown in FIG. 10A. Experimental runs were performed in which a maximum load was measured that resulted in extracting the center wire from the surrounding six wires.

[0074] FIG. 10A is a block diagram that illustrates example experimental setup to measure friction between wires in a strand, according to an embodiment. A 7-wire group 1060 includes a shortened center wire. For example the group is 30 centimeters (300 mm) long, but the center wire is only half that, having a length of 15 cm (150 mm). The group 1060 is anchored to a base 1050 such as a shackle, which is about 10 cm (105 mm) in the illustrated embodiment. A removable center wire 1064 is inserted into the group 1060 in the gap left by the short but anchored center wire. The group is then compressed using clamp 1062. The maximum force (maximum load) used to remove the center wire 1064 is recorded as a measure of the frictional force applied by the group along the encompassed 150 mm of the center wire 1064. This maximum usually is the force that is required to get the center wire 1064 to move, and the force to keep the center wire 164 moving is less after the center wire 1064 begins to move. In some experiments, the maximum load was determined by mounting the setup vertically with the removable center wire 1064 extending downward, and attaching weights to the removable center wire 1064 until the removable center wire 1064 moved out of the group 1060. In various experiments, each wire of the group 1060, or the removable center wire 1064, is either a circular 5 mm wire, e.g., wire 132, or a 5 mm hexagonal wire, e.g., wire 200. [0075] As a control, a 7-wire specimen using round steel wires was constructed and pullout

3 tests were conducted on it using a calibrated MTS 220 kilopound (kip, 1 kip = 10 pounds, about 4,450 newtons) Universal Testing Machine (UTM) available from MTS Systems Corporation, Eden Prairie, Minnesota. UTM is an instrumented test frame that allows the application of either tension or compression to a specimen. Thirty experimental runs were performed and the results plotted in FIG. 10B. FIG. 10B is a graph 1070 that illustrates example experimental results comparing friction between wires in a hybrid strand using different combinations of wire cross sections, according to an embodiment. The horizontal axis 1072 indicates trial number; and, the vertical axis 1074 indicates maximum load in newtons (N). Data from control experiments using only round wires (e.g., wires 132) are given by trace 1081a. The average of these 30 runs is given by dashed horizontal line 1082a. For the control, the average maximum load was about 4450 N. The extracted wire showed significant burnishing damage. Effectively, the relatively irregular zinc coating is being burnished/scraped off the wire surface and a smooth surface results. During initial cycles, the zinc is merely being smoothed. After about 15 cycles, areas of complete zinc removal start to appear. At these points, there is undesirable steel- steel contact. It is noted here that the initial surface roughness due to the hot dip zinc coating is very rough while the final surface roughness at the points of contact is quite smooth, provided there is not an excessive number of pulling cycles.

[0076] The next geometry considered was a hybrid geometry with the removable center wire

1064 comprising a hexagonal wire in a group 1060 of round wires. Ten experimental runs were performed and the results plotted in FIG. 10B as trace 1081b. The average load was about 6100 N as indicated by dashed horizontal line 1082b. These tests showed a significant increase in the average maximum load required to pull the center wire out of the strand

(about a 37% increase). The samples still showed burnishing at the contact points, but the burnishing was less than the in the control experiment using all round wires.

[0077] The next geometry considered was an all hexagonal geometry with all six surrounding and the anchored center wire of the group 1060 and the removable center wire 1064 using hexagonal wires (e.g., wires 200). Ten experimental runs were performed and the results plotted in FIG. 10B as trace 1081c. The average load was about 5700 N as indicated by the dashed horizontal line 1082c. In this situation, a 27% increase was measured over the traditional round wire setup as represented by the control experiment, dashed line 1082a. The burnishing of the sample was significantly reduced and far more uniform than that of either the hybrid geometry or control experiments.

5. Method to retrofit structural cable with wire that has a non-circular cross section.

[0078] FIG. 11 is a flow chart that illustrates an example method for retrofitting wires in a structural cable in place on a structure, according to an embodiment. Although steps are depicted in FIG. 11, and in subsequent flowchart FIG. 13, as integral steps in a particular order for purposes of illustration, in other embodiments, one or more steps, or portions thereof, are performed in a different order, or overlapping in time, in series or in parallel, or are omitted, or one or more additional steps are added, or the method is changed in some combination of ways.

[0079] A very detailed guideline developed by Mayrbaurl and Camo (2004) sets standards for inspection protocols, field and laboratory testing, estimation of cable strength, and reporting. It is accepted as the current state of practice in the bridge engineering community.

[0080] In step 1101, a supply of wires, each with a non-circular cross section is provided. For example, single wire would be brought to the site on a standard 3' (1 m) diameter wire spool. This spool holds about 9500 m of wire and weighs about 1 ton.

[0081] In step 1103, a section of structural cable in place is opened for inspection. For example, the standard requires various levels of intensity of cable inspection, "internal inspection" being the most thorough; this level of inspection is prescribed at least every 30 years, but intervals are decreased to as little as five years if significant corrosion is detected and the bridge ages. During an internal inspection, the cable is wedged open at numerous radial positions by use of non-sparking wedges and hammers and/or hydraulic wedge jacks. Typically, each cable is inspected at a minimum of three locations: at the trough of the main span and side span and one alternately at the midpoint between the trough and peak of either the main span or the side span. (It is interesting to note that the red lead paste originally applied to the cable as a corrosion deterrent not only largely failed its purpose but now poses an environmental and occupational hazard, requiring the installation of enclosures with filtering systems and appropriate personal protective equipment (PPE) for the worker to safely remove the paste.) At each inspection point, the cable is wedged at eight locations, spaced evenly at 45° intervals. Generally, an entire panel, the distance between adjacent cable bands (about 12 m), is wedged during an inspection.

[0082] In step 1105, each exposed wire is examined for damage. For example, Hopwood and Havens (1984) proposed a visual categorization for corrosion ranging from Stage 1 to Stage 4, which is still in use today. A wire is categorized as Stage 1 when spots of white zinc corrosion are visible on the wire. A wire is considered Stage 2 when it is entirely covered by white rust (i.e. zinc corrosion), but no ferrous corrosion has yet initiated. A wire is considered Stage 3 if it exhibits spots of ferrous corrosion (red rust), not to exceed 30% of the wire area. When a wire exhibits more than 30% ferrous corrosion, it is classified as Stage 4. Beyond Stage 4 are broken wires. In some embodiments, one or more exposed Stage 4 wires are cut to use as samples for further testing.

[0083] In step 1107, it is determined whether the damage level exceeds a threshold (e.g., advanced Stage 4 or broken wires) on a portion of all or part of the exposed wire. If not, control passes back to step 1103 to open another section. If so, then, in step 1111, one or more portions of the one or more exposed wires that exceed the damage threshold are cut out of the exposed wires. The extant wires are wedged so that they bend out of the plane of the cable and are then cut with a shear cutter, a bolt cutter, or similar tool. The specific wires to be extracted for testing and/or replacement are generally dictated by a civil/structural engineer. Control then passes to step 1113 and 1115.

[0084] In step 1113, a wire with a non-circular cross section is spliced onto the remaining portions of the one or more wires that were cut. The splicing is performed to replace the damaged portion of the extant wire that was cut away. For example, if broken wires are detected during the inspection or wire samples are removed for laboratory testing, NCHRP Report 534 dictates that a new section of wire be spliced into the working cable and tensioned to the original service load of surrounding wires. As described above, new wire is spliced into the cable by using carbon steel or stainless steel wire ferrules. Threaded ferrules require the wire to be threaded by either cutting or rolling and are specified to sustain 75% of the original tension capacity of the wire. Pressed-on ferrules, which are crimped onto wire by mechanical means, are specified to sustain 90% of the ultimate strength of the wire. There are many different proprietary ferrule designs on the market, although they all function similarly. Replacement wire is provided on a spool, as described above, and the section length is cut from the spool, such that the section length matches the length of the wire removed..

[0085] As described above, the current standard procedure requires that a new piece of wire be cut to the approximate length of the removed wire and subsequently cut into two pieces (labeled wires 802 and 803 in FIG. 8A). Each end of the original wire is cleaned (labeled wires 801 and 804 in FIG. 8A), and a pressed-on ferrule 811, 812 is spliced onto each end. The two new wires 802, 803 are then spliced into the central threaded ferrule 821 and tensioned by use of jacks to the prescribed service load. This allows wire 803 to be lined up to wire 804 and trimmed to the length that it will be under service load. The assembly is unloaded, and wire 803 is spliced onto wire 8044. The entire new wire assembly is then tensioned by turning the opposing threads integrated into the threaded wire ferrule 821, much like a turnbuckle. Tension in each inserted wire is tested by the tension offset method using a dynamometer. It is noted that typical ferrules 811, 812, 821 have a significantly larger diameter than the actual wire. For example, a type of ferrule that was employed in a number of bridges in the northeastern U.S. has a diameter of 11.3 mm. This is more than twice the diameter of a standard bridge wire of 5 mm.

[0086] In step 1115, it is determined whether there is another section to inspect on the same or different structure. If so, control passes back to step 1103 to open the next section.

Otherwise the process ends.

[0087] Thus a method to retrofit a structural cable includes opening a structural cable strand comprising a plurality of circular cross-sectional wires; selecting an extant wire of the strand to be spliced; and splicing a replacement wire into a portion of the extant wire. The replacement wire has a non-circular cross section configured to have a corresponding surface contact area with an adjacent wire of the plurality of wires, and the corresponding contact area is substantively greater than a surface contact area of a circular wire having a diameter substantively identical to a largest inscribed circle for the corresponding non-circular cross section.

6. Coiled hexagonal embodiments.

[0088] In another experimental embodiment, a 61-wire sample was built out of hexagonal wires to show that pre-fabricated strands can be built and coiled for deployment onto structures using them, such as bridges. The specimen was bent with a winch attached to both ends such that individual wires were allowed to slip.

[0089] FIG. 12A and FIG. 12B are photographs that illustrate example coiling of a bundle 1210 of wires 1212 with a non-circular cross section for a strand on a spool, according to an embodiment. In the illustrated embodiment, the sample bundle 1210 was built out of hexagonal wires 1212 to show that pre-fabricated strands can be built and coiled for deployment onto bridges. The specimen was bent with a winch attached to both ends and allowed to slip. FIG. 12A depicts the bundle 1210 of hexagonal wires, which includes a series of bands 1214 (such as tape) to hold the bundle 1210 together. The group 1210 has been bent into a portion of a coil by winch 1290 that applied torque to the ends of the bundle 1210 through straps 292. For scale, a meter stick 1298 is also depicted in FIG. 12A. FIG. 12A shows that the diameter of a coil of a bundle of hexagonal wires can be reduced to a meter without breakage occurring in the wires.

[0090]There is slippage among wires in the bundle as evident at the ends, as can be seen in FIG. 12B, a photo of the end of the wire. In FIG. 12B individual hexagonal wires 121 of bundle 1210 are shown along with winch 1290 and strap 1292. The ends of the same length wires 1212 are no longer aligned, indicating slippage during bending into the partial coil. Under tension of even just the self-weight of the cable, such as what would be present in an installed bridge, the recovery is expected to happen easily. These experiments showed that large-scale samples of strands of hexagonal wires can be successfully coiled and deployed. 7. Method to install structural cables with wire that has a non-circular cross section.

[0091] FIG. 13 is a flow chart that illustrates an example method 1300 for constructing a structure using multiple spools, each spool holding a coiled strand of wires, each wire with non-circular cross section, according to an embodiment. In step 1301 a supply of multiple spools is provided at the construction site, e.g., on one or more barges at a bridge site, where each barge is configured with multiple spindles for holding multiple such spools so that strands coiled on the spools can be uncoiled in parallel without removing the spools from the barge. In various embodiments, each spool has an inner diameter from about 1 meter to about 4 meters. The Prefabricated Parallel Wire Strand would be shipped on a spool, on the order of 12' (4 m). These are generally extra-size loads. Each spool holds at least one strand of length sufficient to span a cable distance for the structure, e.g., a 3 km cable length for a cable to be strung from towers to support a roadway for bridge with a 2 km roadway.

Historically, bridge cables were spun wire-by- wire. In the recent past, though, this method has been largely abandoned. Today, the PPWS method is preferred by most builders since it allows for faster construction of the main cable than single wire spinning.

[0092] In some embodiments, the compacted strands are almost identical to those using round wires. For some hexagonal wire embodiments, the only difference is that the edges are a bit sharper (due to the single hexagons) than with the round wires. The same winches, barges, etc. can be used as with the current system. Even today, contractors are able to tackle different-sized strands (61, 91, 127 wire, etc.) wider than the range of differences expected by using different shaped wires in each strand. Thus, in some embodiments, it is

advantageous to make strands of non-circular wires that are compatible with existing construction systems. In some embodiments, strands of different shapes and dimensions are formed. For example, for some strands made of non-circular and non-hexagonal cross- sectional geometries, it may be advantageous to have considerably different dimensions and cross-sectionally shaped strands. In some such embodiments, winches and guides are modified to accept the considerably differently dimensioned and shaped strands. [0093] In step 1303, a strand is uncoiled from two or more spools that contribute to an individual structural cable. In step 1305, strands from multiple spools for an individual structural cable are aligned.

[0094] In step 1307, the strands are compressed to form an individual structural cable. For example, strands are compacted by means of hydraulic jacks to form a cable with a round cable cross section. The cable's packing efficiency will be much less dependent on jacking since the various embodiments will not have 20% void ratio before compaction. Except for some minor interstitial spaces between the strands (not wires), packing efficiency is almost 100% before the cable is compacted. Compaction is still useful, but the volume change between the uncompacted and compacted sections will be much lower. For the illustrated hexagonal 5 mm wires of some embodiments, the cable will be about 9% smaller since there will be essentially no remnant voids in the cable after all of the strands are arranged and compacted. This difference should be apparent on a construction site, and would indicate the use of wires of non-circular cross section.

[0095] In step 1311, a leading end of the individual structural cable is attached to the structure, e.g., at a terminal anchor called a cable anchorage. Each strand, or the cable itself, or some combination, is potted using either zinc (traditional) or proprietary socketing resin (current state of the art). The cable is then attached to the anchorage or tower/deck connection point of the bridge for suspension and cable-stayed bridges, respectively. Each strand or cable is terminated in a steel socket with a conical bore. Sockets are available in a large range of sizes suitable for most cables expected using any of the geometries depicted herein. In step 1313 the structural cable is attached to the structure at one or more additional locations, such as at the tops of one or more suspension piers 120 or towers, or a second terminal anchor, or some combination. In step 1315, the structural cable is cut or otherwise terminated, including, in some embodiments, sealing the open faces of the ends of the strands or wires, or some combination, and encasing the terminal end in another steel socket..

[0096] In step 1317, it is determined whether another cable is to be added to the structure to support a particular structural element, such as a roadway platform. If so, control passes back to repeat step 1303 and following steps for the new cable. If not, then in step 321, the structural element, such as a suspension bridge roadway platform, to be supported by the structural cable is attached to the structural cable, e.g., by one or more vertical cables (suspenders) 102. The process then ends or is repeated for another structural element or structure.

8. Extensions, modifications and alternatives.

[0097] In the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. Throughout this specification and the claims, unless the context requires otherwise, the word "comprise" and its variations, such as "comprises" and "comprising," will be understood to imply the inclusion of a stated item, element or step or group of items, elements or steps but not the exclusion of any other item, element or step or group of items, elements or steps. Furthermore, the indefinite article "a" or "an" is meant to indicate one or more of the item, element or step modified by the article. As used herein, unless otherwise clear from the context, a value is "about" another value if it is within a factor of two (twice or half) of the other value. While example ranges are given, unless otherwise clear from the context, any contained ranges are also intended in various embodiments. Thus, a range from 0 to 10 includes the range 1 to 4 in some embodiments.

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