PSI - Issue 84

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

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section. Inter-wire slip is instead free to occur away from clamps. After deck erection is complete, the main cable wires are generally lined with a pre-stressed wire wrapping, which has the side effect of applying some degree of radial compression, thus generating inter-wire friction and preventing full-slip between wires. The main cable is therefore able to resist a limited but varying amount of flexure within the length between cable clamps, generating further secondary stresses due to the rotations occurring in the service stage due to e.g. live loads. It has to be noted that the final section of main cable closest to the tower is generally left unwrapped, though protected by a sleeve connected to the tower saddle shelter (dehumidified in recent applications), reducing locally the restraint to slip and the amount of secondary stresses. Moreover, secondary stresses can be reduced significantly if the end clamps, which force the cable wires to assume a circular shape instead of the hexagonal arrangement adopted on the saddle trough, are installed only after the deck is erected, immediately before cable wrapping, or by tensioning their bolts to the full clamping force only at this stage. From a design perspective, the problem of secondary stresses is still usually analysed via the classic approach (Wyatt,1960), which provides approximate analytical solutions, though this topic has been the subject of more recent analytical and experimental research (Lee, 2016), highlighting how for the case of the Yi Sun-Sin bridge in Korea secondary stresses can reach the order of 10% of the wire tensile strength. In this regard, it has to be noted that, though the sizing of suspension bridge cables is generally based on pure axial stress, the application of significant safety factors on service stresses, generally in the order of 2.10-2.20, covers the effects of secondary stresses and ensures an appropriate degree of safety against yielding. The distribution of transversal stresses at the saddles is also a complex problem: too conservative the assumption of the pressure to be “hydrostatic”, i.e. to develop as the cable bundle was a high-density fluid, it is often adopted in design practice the maximum horizontal pressure to be one third of the vertical, result that can be obtained assuming a perfect hexagonal arrangement and neglecting the beneficial effect of friction (Jones, 2008). Experimental behaviour shows that the friction between the wires has a significant effect and the mass of wires behaves instead in a manner analogous to a granular material, phenomenon that is well known and studied for the actions of granular materials in storage silos see a review in (Horabik, 2014). The feasibility of a similar approach for the wire mass behaviour in saddles was studied in (Felici, 2016), where a plane F.E. model of the wire contact was adopted to determine the properties of a homogeneous material equivalent to the wire mass, Fig. 1. The study case considered was the saddle of the Fatih Sultan Mehmet Bridge (Second Bosphorus Bridge), the interaction between wires was treated via the Hertzian theory for linear contact between parallel cylinders considering two different arrangements of the wires, a perfect hexagonal array and a quadrangular one, the latter as the limit case of a non-perfect compaction of the cable. The two cases showed equivalent elastic moduli between ≈ 12 500 and ≈ 16 000 MPa, well coherent with the experimental results described in the previous paragraphs for higher level of transverse stresses, with an equivalent Poisson modulus of 0.1.

Fig. 1 – Typical tower saddle, Braila suspension bridge (left), typical strand (centre), typical f.e. mesh (right, from Felici, 2016) The above results were introduced in a F.E. model for geotechnical analyses, software Plaxis 2D, Fig. 2, where the forces generated by the cable curvature were simulated via an equivalent density of the equivalent homogeneous material, whose properties were defined as elastic modulus 14 000 MPa and Poisson modulus of 0.1. The friction between the homogeneous material and the steel of the vertical walls of the saddle was simulated introducing a thin layer of frictional material with the same properties plus an angle of friction 26.5°. The latter was determined from a friction coefficient of 0.5, in agreement with literature results (Takena, 1992). Sensitivity analyses showed a good stability of the results for the variation of the elastic modulus, instead with a moderate sensitivity for the variation of the Poisson coefficient. The following Table 4 shows maximum stress values for the lower wire layer, calculated as a) hydrostatic; b) with the silos approach as per the Eurocodes; c) according to the approach presented herein. While