Probabilistic models for mechanical properties of prestressing strands Luciano Jacinto a,⇑ , Manuel Pipa b , Luís A.C. Neves c , Luís Oliveira Santos b a Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisbon, Portugal b Laboratório Nacional de Engenharia Civil, Avenida do Brasil 101, 1700-066 Lisbon, Portugal c UNIC, Faculdade de Ciências e Tecnologia da UNL, 2829-516 Caparica, Portugal highlights " The study shows the low variability of the mechanical properties of strands. " During the period analysed (2001–2009) the properties did not show any trend. " Generally, the results obtained agree with the results reported in PMC. " However, some of the proposed models in the PMC should be updated. article info Article history: Received 15 January 2012 Received in revised form 16 April 2012 Accepted 29 April 2012 Available online 15 June 2012 Keywords: Prestressing strands Probabilistic models Tensile strength 0.1% proof stress Modulus of elasticity Bayesian statistics abstract This study focus on the probabilistic modelling of mechanical properties of prestressing strands based on data collected from tensile tests carried out in Laboratório Nacional de Engenharia Civil (LNEC), Portugal, for certification purposes, and covers a period of about 9 years of production. The strands studied were produced by six manufacturers from four countries, namely Portugal, Spain, Italy and Thailand. Variabil- ity of the most important mechanical properties is examined and the results are compared with the rec- ommendations of the Probabilistic Model Code, as well as the Eurocodes and earlier studies. The obtained results show a very low variability which, of course, benefits structural safety. Based on those results, probabilistic models for the most important mechanical properties of prestressing strands are proposed. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The properties of prestressing strands have a considerable influ- ence on the safety of prestressed structures, in particular bridges, as well as on the total construction cost. For this reason, it is funda- mental to define adequately the mechanical properties of these ele- ments. In this study, a statistical analysis of three families of strands with nominal diameters of 13.0, 15.2 and 15.7 mm (cross-section areas of 100, 140 and 150 mm 2 , respectively) is presented. All strands have nominal tensile strength of 1860 MPa (Y1860 grade) and are all composed by seven wires. The analysed strands corre- spond to the most widely used world wide in the last decades. Samples were collected from tensile tests performed between 2001 and 2009 in Laboratório Nacional de Engenharia Civil (LNEC), Portugal. During this period, over 500 tensile tests were carried out for the three families mentioned above. However, several of these tests refer to strands produced from the same heat (same casting). As it is known, the variability within a single heat is lower than the variability between different heats. Thus, for the purpose of statistical analysis, only one test from each heat was selected (at random), which reduced the sample to 131 tests. Differently to what was done in a previous study [1], where stresses were computed dividing the forces measured in those tests by the actual strands cross-section areas, in the present study all the stresses were computed using nominal cross-section areas. This is common practice [2,4]. For each of the three families of strands, the studied properties were: tensile strength or maximum stress (f p ), 0.1% proof stress (f p0.1 ), total elongation at maximum force (e u ) and modulus of elas- ticity (E p ). It was found out that the difference in the mean of those properties between families was of the same order of magnitude as the standard deviations, which allowed us to consider the three families of strands as belonging to the same population. The three families were thus merged into a single sample. The tested strands came from six manufacturers of different countries, including Portugal, Spain, Italy and Thailand. However, 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.04.121 ⇑ Corresponding author. Tel.: +351 969401576; fax: +351 21 831 70 21. E-mail address: ljacinto@dec.isel.ipl.pt (L. Jacinto). Construction and Building Materials 36 (2012) 84–89 Contents lists available at SciVerse ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat