PSI - Issue 84

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

1101

the results obtained with the new approach cannot be considered conclusive nor be immediately transferred into design practice, the trend is clear and shows stresses significantly lesser than those obtained from standard conservative approaches. Some recent papers treat the matter with different approaches (Wang, 2019; Wang, 2020; Zhang 2016; Zhang, 2018), showing this s to be an interesting research field, where modern supercomputers could be effectively used for large scale numerical models tuned on experimental data, achieving a better understanding of such complex phenomena: the authors hope this paper to be a stimulus for young researchers to enter this challenging field, more and more significant with the increase of size of the super-long spans that are to come. 8. Fatigue and fretting fatigue Finally, brief attention is given to fatigue aspects, typically not of primary relevance for large suspension bridges due to the small stress fluctuations in a structure where permanent loads are dominant. For most of the cable length stress variations are negligible, while at the saddles, even considering with conservative approaches the local effects discussed herein, they become larger but still moderate with respect to the limits of high strength wires. E.g., for the proposed road and rail bridge on the Messina Strait, 3300 m span, the stress variation due to fatigue loads is about 3% of the permanent cable force when considering pure axial tension, while becomes approximately 15% when considering primary and secondary stresses combined. As to fretting fatigue, to the authors knowledge such phenomena have never been observed in parallel wire cables for suspension bridges. Basic reason is indeed the moderate stress fluctuation discussed, but other aspects concur. For fretting to take place, a relative displacement field must occur between adjacent wires, resulting in shear stresses at the contact surface and possible strain and microslip. For parallel wires the contact area is linear and of long extension, reducing strongly such shear stresses along the contact area, much larger than for spiral strands (ropes) where the wires feature a “trellis” contact, with by far smaller contact area and higher strain concentration. Furthermore, relative displacements in parallel wire cable occur only due their curvature at the saddles and not for pure extension of the bundle, while spiral strands show the relative displacement both for curvature and elongation. Such excellent experience explains why specific fretting tests for the wire arrangement in parallel wire cables are absent in the published literature to the authors knowledge, while are numerous for spiral ropes. For this reason, fatigue and fretting fatigue are design issues for stay cables passing over saddles, not for the main cables of suspension bridges.

Fig. 2 – Plaxis 2D Model of tower saddle Table 4 – Stresses in the bottom wire layer according to different approaches. Vertical Average Stress Vertical Contact Stress

Horizontal Average

Horizontal Contact Stress

Hydrostatic Silos Theory

35

≈ 2 900 ≈ 2 700 ≈ 1 600

35

≈ 2 900 ≈ 1 150

33.6 19.5

14.0

Present Approach

2.3

≈ 570

9. Conclusion After presenting an overview of two centuries of development in technologies and materials for the construction of suspension bridge cables, attention is given to their complex behaviour at the saddles, with a number of considerations on present and possible future approaches: if not an open issue, as the current practice is well established and conservative, a possible interesting research field, in view of the possible future super-long spans.