Determination of the Cable Factor for Deviated Tendon Bundles

This article illustrates how the cable factor of deviated bundle tendons and accordingly the pressure between prestressing steel elements and ducts can be accurately determined. The knowledge of the maximum pressure between single tendons and the duct of a tendon bundle is important both to estimate the danger of fatigue fracture of the prestressing steel due to fretting corrosion when using corrugated steel ducts and to estimate the imprints into polyethylene (PE) ducts of unbonded tendons. PE ducts serve as corrosion protection sheathing for tendons. Especially for unbonded tendons, it is necessary to limit the wear of ducts to ensure the corrosion protection of the steel, the durability of the tendon and the tensioned structure. The remaining thickness of PE ducts after loading has to fulfill certain requirements (e.g.according to the guideline for European Technical Approval of Post-Tensioning Kits for Prestressing of Structures, ETAG 013 Ed. June 2002). In the past, graphical methods were applied as well as costly and time-consuming simulations of the arrangement of strands or wires in a duct with the help of small-scale samples. For configurations other than the ones tested or for a greater number of wires in a duct these results cannot be used. That is why two numerical approaches of how to arrange single tendons in a duct were developed. After finding a stable arrangement of the tendons it is possible to determine the cable factors and thus the maximum transverse loading by the help of a twodimensional (2D) truss calculation. Additionally, two simplified approaches for estimating the maximum cable factors are presented. They reduce the calculation effort to different extents. The first approach is based on hydrostatic analogy. The second one is a simplified method that allows for a quick estimation with the help of the relevant parameters. When using PE ducts for bonded post-tensioning fatigue fracture due to fretting occurs at the contacts between single tendons. A simplified model quantifying the maximum inner cable factor is presented for the first time. With the help of the tools presented, the curvature design of deviated tendons and the formulation of restrictions in codes can be reconsidered. In addition to this, they can contribute to a qualified assessment of the durability and efficiency of existing post-tensioning systems or to their development.