PSI - Issue 84

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

1098

• As the dimensions increase, so do the transverse pressures on the wires associated with the curvature of the cable at the points where it is deviated, namely the saddles at the tops of the towers, splay saddles, and, for aerial spinning, anchor shoes. This topic will be addressed in the next paragraph. Regarding the first aspect, it has to be noted that the overall diameter of the main cable for a suspension bridge depends on several parameters such as the span, the wire strength, the safety factor adopted in the design, the weight of the suspended deck and the amount of traffic load to be carried, i.e. all the factors that concur in determining the number of individual wires forming its cross section, while the void ratio that can be achieved in practice as a result of the compaction operation is approximately constant and in the order of 18-20%. In addition, in some cases, twin main cables are adopted at either side of the deck, having four cables in total. Table 1. – Breaking stresses σr of iron or steel for chains or wires from the beginning of the Nineteenth century till present. Note: different sources report slightly different values, rounded off ones are shown. Bridge Year Ø [mm] σ r [MPa] Span[m] Bridge Year Ø [mm] σ r [MPa] Span[m] Chains ‘800 - 200-300 - Humber 1981 4.98 1570 1410 Iron wire ‘ 800 3-7 400-800 - Storebaelt 1998 5.38 1570 1624 Brooklyn 1883 4.57 1100 486 Akashi 1998 5.23 1770 1991 Williamsburg 1903 4.88 1370 488 Yi-Sun-Sin 2012 5.35 1860 1545 Bear Mountain 1924 4.95 1500 497 Ulsan 2015 5.40 1960 1150 Benjamin Franklin 1926 4.98 1500 533 Nansha 2019 5.30 1960 1688 Ambassador 1929 4.88 1480 564 Yangsigang 2019 6.20 1960 1700 George Washington 1931 4.98 1520 1066 “1915” 2022 5.75 1960 2023 Mid-Hudson 1936 4.95 1500 457 Braila 2023 5.38 1860 1120 Triborough 1936 4.95 1600 420 Lingdingyang 2024 6.00 2060 1666 Golden Gate 1937 4.88 1520 1280 Yanji 2026 5.60 2100 1860 Verrazzano 1964 4.98 1520 1298 Shiziyang 2028 6.10 2060 2180 Bosporus 1973 5.00 1570 1074 Zhangjinggao 2028 5.65 2200 2300 Table 2 – Approximate deck and cable weight for square area in some notable bridges. Bridge Span[m] Deck type Deck weight [t/m 2 ] Cable weight [t/m 2 ] Ratio Minami Bisan Seto 1100 Truss, Road+Rail ≈ 0.71 ≈ 0.33 ≈ 0.47 Braila 1120 Box girder ≈ 0.33 ≈ 0.11 ≈ 0.33 Halogaland 1145 Box girder ≈ 0.33 ≈ 0.13 ≈ 0.40 Storebaelt 1624 Box girder ≈ 0.36 ≈ 0.24 ≈ 0.66 Nansha 1688 Box girder ≈ 0.43 ≈ 0.25 ≈ 0.59 Yangsigang 1700 Truss ≈ 0.84 ≈ 0.37 ≈ 0.44 Akashi 1991 Truss ≈ 0.65 ≈ 0.37 ≈ 0.57 1915 2023 Multibox ≈ 0.31 ≈ 0.21 ≈ 0.66 Messina 3300 Multibox, Road+Rail ≈ 0.30 ≈ 0.54 ≈ 1.77 This was done especially in historic bridges, where the dimension of the cables would have been too far from previous experience or exceeding the compaction technology available at the time, but it is still a well possible choice nowadays, as proven by the recent Yanji Yangtze Bridge in China, with a span of 1860m, which is characterized by an unfavorable sag to span ratio due to height limitations for the towers (Peng, 2022), thus requiring a substantial amount of main cable steel, which has been divided into two main cable on either side with different sags, both with a diameter of ≈ 1m each. Twin main cables are also envisaged in the detailed design of the Messina Strait Bridge, with a main span of 3300m, whose main cable would have a diameter of 1.26m each. The evolution of the diameter of suspension bridge main cables, summarized in Table 3, shows a steady growth occurring between the end of the 19 th century and the 1930s, when the maximum diameter reached approx. 900mm in both the George Washington and Golden Gate bridges, though the former has four main cables instead of two due to the provision for a heavy double deck. Diameters over 1m were achieved in 1988 by the Minami Bisan Seto and the Tsing Ma Bridges, both carrying road and railway, and the then record- breaking Akashi Bridge in 1988, while the current longest span of the “1915” Canakkale bridge has a smaller main cable due to the lighter multi-box deck and the higher wire strength of 1960 MPa. The largest diameter is currently 1.3 m in the Wufengshan Bridge in China (Wu, 2022), which carries an 8-lane highway and 4 railway tracks on a double deck, but the record will soon be held by the Shiziyang bridge in China, scheduled to be completed in 2028, with main cables of almost 1.5 m diameter (Duris, 2022) and a span of 2180m.