PSI - Issue 84

Fabio Brancaleoni et al. / Procedia Structural Integrity 84 (2026) 1095–1102

1099

Table 3 – Evolution of main cable diameter Bridge Year D [mm]

No. Cables

Span[m]

Bridge

Year

D [mm]

No. Cables

Span[m]

Brooklyn

1883 400 1903 476 1924 464

4 4 2 2 2 4 2 2 2 4

486 488 497 533 564 420 457 1066 1280 1298

Minami Bisan Seto 1988 1058

2 2 2 2 2 2 2 4 2 2

1100 1377 1991 1700 1092 2023 1666 1860 2180

Williamsburg Bear Mountain

Tsing Ma

1997 1100 1998 1122 2019 1088 2020 1300 2022 869 2024 1066 2026 1039 2028 1486 2028 1114

Akashi

Benjamin Franklin 1926 762

Yangsigang Wufengshan

Ambassador

1929 498

George Washington 1931 914

“1915”

Triborough Mid-Hudson Golden Gate Verrazzano

1936 527 1936 425 1937 910 1964 914

Lingdingyang

Yanji

Shiziyang

Zhangjinggao 2300 With respect to the void ratio, a bundle of parallel wires shall be between the theoretical square arrangement of the wires (21%) and the theoretical hexagonal arrangement (9%), while values from experience are in the order of 18 20% for the compacted main cable and 17-18% at the clamps after tensioning of the bolts (Gimsing, 2012). As the percentage of voids inside the compacted cable is approximately twice the theoretical minimum, mutual displacements between the wires might take place with the progress of erection and it is hence necessary to retighten the clamping bolts, e.g. after the erection of the deck, as a pseudo-Poisson effect tends to reduce the cable diameter when axial tension is increased. As to the transversal behaviour of main cables, the data collected during the compaction operations, as well as numerical and experimental results on tensioning of clamp bolts (Miao, 2021), show that the transverse stress/strain curve of the main cable is definitely non-linear for increasing levels of radial compression. At first the cable is easily compressed and the void ratio rapidly decreases, while in the second part a stable contact between the wires is established and the cable becomes stiffer. However, the elastic modulus in this higher stress range remains still one order of magnitude lower than the modulus of solid steel due to the concentrated nature of contact stresses between the wires. It is necessary to model this stiffness characteristic to correctly determine e.g. the circumferential slip between cable band and cable, the degree of friction mobilised and hence the pressure distribution on the cable surface, and the stress distribution in the clamp. Numerical values of the secant radial elastic modulus generally adopted for the design of cable clamps are in the range of 2000-3000 MPa up to a range of radial stress of 20-50 MPa. Instead, the tangent transversal modulus above this stress range is in the order of 10 000 to 20 000 MPa. 7. Wire stress state at saddles and anchor shoes The portions of the main cables where the stress state is more challenging and complex are located at its deviation points, i.e. the saddles and the splay saddles. At the tower saddles, the main cable experiences the highest tensile forces, as the deviation angle at these points is greater than at the splay saddles. Consequently, the maximum average transverse pressure and the most significant angular changes—induced by environmental and traffic loads—also occur at the tower saddles. Such angular change brings the cable to conform to the saddle’s geometry, imposing a curvature on the wire bundle. In this kinematic configuration, transverse pressure develops along the cable, which undergoes a “flexure” with behaviour intermediate: it does not correspond to that of a solid beam, nor to an ensemble of individual wires sliding freely against one another. The cable’s shape at the saddle is maintained by the lateral pressure, which is sufficiently high to prevent wire slippage, and by the band clamps positioned at a defined distance from the saddle. In more detail, secondary stresses are generated by the fact that the cable is restrained against deflecting as a pure axial element by the saddles, cable clamps and wrapping wire and this restraint, thus, sets up non-uniform stress distributions across the main cable section, which develop according to the erection stages of the structure. In the first place, for a freestanding main cable, besides the primary uniform axial stress, at the saddles additional bending stresses arise across the diameter of the individual wires. Such stresses are inversely proportional to the saddle curvature radius. Additional secondary stresses are then generated by all deflections that occur after the main cable erection is complete. In particular, after installation of the cable clamps, it can be assumed in practice that the cable remains straight piecewise, while concentrated rotations are applied at the ends of the clamps and at the saddles due to the changing geometry as all suspended permanent loads are applied during construction. In this condition, wire slip is prevented at saddles and clamps by transverse pressures, generating additional bending stresses across the main cable cross