Probabilistic Models for Fatigue Resistance of Seven-Wire Prestressing Strands and Stay Cables Azam Nabizadeh 1 ; Mohammad O. Al-Barqawi 2 ; and Habib Tabatabai, M.ASCE 3 Abstract: Parallel seven-wire steel prestressing strands are the dominant form of the main tension elements (MTE) used in stay cables. In this paper, probabilistic models for fatigue resistance of seven-wire prestressing strands that are not embedded in concrete and are subjected to axial stresses are developed. Available test data from seven-wire strand fatigue tests were collected and analyzed to develop probabilistic models and nonlinear S–N curves using survival analysis techniques. Results indicate that the fatigue resistance of classic stress-relieved strands produced before early 1980s is higher than the modern low-relaxation strands that have been manufactured since then. Neither the conventional classic nor the modern strands have a good chance of passing the fatigue qualification tests required by the latest design standards for use in stay cables. Only the cable-quality (CQ) strands can pass the latest fatigue qualification tests with a less than 2.5% prob- ability of failure. Nonlinear S–N equations for all three strand types and stay cables made with CQ strands are proposed using a log-logistic parametric survival model. DOI: 10.1061/(ASCE)BE.1943-5592.0001768. © 2021 American Society of Civil Engineers. Author keywords: Prestressing strand; Fatigue; Stay cables; Cable-stayed bridges; Probabilistic models; S–N curves. Introduction Parallel seven-wire steel prestressing strands meeting the ASTM A416/A416M-18 (ASTM 2018a) requirements are the dominant form of the main tension elements (MTEs) used in stay cables in the United States. Stay cables serve as crucial structural resisting elements in cable-stayed bridges. These elegant bridge structures have grown rapidly in recent years, in both number and span length, throughout the world (Tabatabai 2005). Prior to the early 1990s, stay cables in the United States were typically assembled as a bundle of uncoated seven-wire strands that were encased in high-density polyethylene (HDPE) pipes, or less commonly steel pipes, and then grouted (as a corrosion protection measure) (Tabatabai 2005). Other less commonly used stay cable systems in the United States were parallel bar (ASTM A722/A722M-18, ASTM 2018b) and parallel wire (ASTM A421/A421M-15, ASTM 2015) systems. In that same time frame, parallel wire and locked coil stay cables were predominant elsewhere in Europe and Asia. However, stay cable qualification fatigue tests performed in the United States in the early 1990s revealed potential durability concerns with the grouted stay cable approach (Tabatabai et al. 1995). Early stay cable designs were subject to frequent design changes (from project to project) as cable suppliers learned and ap- plied their experiences to improve their systems. In the last 30 years, however, a consensus has emerged worldwide on a stay cable design in which parallel individually sheathed seven-wire strands with corrosion-inhibiting coating (also known as greased-and-sheathed or waxed and sheathed strands) are encased in an external HDPE pipe providing two nested protective barriers for the steel strands. The strands splay out near the anchorages and terminate in an anchorage plate with specially designed wedges. An important factor that clearly distinguishes stay cables from post-tensioning (PT) tendons is their higher potential susceptibility to fatigue. Stay cable design must address the potential for fatigue due to live and wind loads, which can impose repetitive axial and bending stresses in the cable. In this paper, probabilistic models for fatigue resistance of seven-wire prestressing strands subjected to axial stresses in air (i.e., not embedded in concrete) are first developed and presented. Test data from seven-wire strand fatigue tests performed during the last 60 years were collected and analyzed to develop probabilistic S–N curves using survival analysis techniques. The influence of the type of strand (stress relieved or low relaxation) and the manu- facturing process (with or without the use of lead patenting) on fa- tigue resistance is considered. Early fatigue test data (obtained prior to the early 1980s) were mostly developed using stress-relieved strands (before the widespread production of low-relaxation strands). As described later, the wire manufacturing process also underwent a major change within the same general time frame. The change involved discontinuation of lead patenting (an isother- mal phase transformation process) in favor of other nonlead pro- cesses due to environmental concerns with the use of lead. Therefore, separate probabilistic models are developed in this paper for classic and modern strands. For the purpose of this paper, classic strands are defined as stress-relieved strands made prior to the early 1980s using lead patenting. Modern strands are defined as low-relaxation strands made after the early to mid-1980s using nonlead-based processes. During data analyses, it became clear that another category of strands has substantially different fatigue performance when com- pared with the classic and modern strands. As described later, the strict quality control fatigue test requirements for stay cable MTE as specified by the Post-Tensioning Institute (PTI) committee on cable-stayed bridges (PTI DC-45 committee) resulted in the devel- opment of a cable-quality (CQ) strand category and thus required its own separate probabilistic fatigue model. Despite its superior 1 Ph.D. Graduate, Dept. of Civil and Environmental Engineering, Univ. of Wisconsin, Milwaukee, WI 53211. Email: azam@uwm.edu 2 Ph.D. Student, Dept. of Civil and Environmental Engineering, Univ. of Wisconsin, Milwaukee, WI 53211. Email: albarqa2@uwm.edu 3 Professor, Dept. of Civil and Environmental Engineering, Univ. of Wisconsin, Milwaukee, WI 53211 (corresponding author). ORCID: https://orcid.org/0000-0001-7542-2425. Email: ht@uwm.edu Note. This manuscript was submitted on March 7, 2021; approved on May 27, 2021; published online on July 22, 2021. Discussion period open until December 22, 2021; separate discussions must be submitted for individual papers. This paper is part of the Journal of Bridge Engineer- ing, © ASCE, ISSN 1084-0702. © ASCE 04021070-1 J. Bridge Eng. J. Bridge Eng., 2021, 26(10): 04021070 Downloaded from ascelibrary.org by Habib Tabatabai on 07/25/21. Copyright ASCE. For personal use only; all rights reserved.