Reliability analysis of prestressed concrete beams exposed to fire Christopher D. Eamon a,⇑ , Elin Jensen b a Civil and Environmental Engineering, Wayne State University, Detroit, MI 48202, United States b Graduate Studies and Research, Lawrence Technological University, Southfield, MI 48075, United States article info Article history: Received 12 April 2012 Revised 17 May 2012 Accepted 18 May 2012 Available online 18 June 2012 Keywords: Reliability Fire Prestressed concrete abstract A procedure for conducting reliability analysis of prestressed concrete beams subjected to a fire load is presented. This involves identifying relevant load combinations, specifying critical load and resistance random variables, and establishing a high-temperature performance model for beam capacity. Based on the procedure, an initial reliability analysis is conducted using currently available data. Significant load random variables are taken to be dead load, sustained live load, and fire temperature. Resistance is in terms of moment capacity, with random variables taken as prestressing steel ultimate strength, con- crete compressive strength, placement depth of strands, beam width, and thermal diffusivity. A semi- empirical model is used to estimate beam moment capacity as a function of fire exposure time, which is calibrated to experimental data available in the literature. The effect of various beam parameters were considered, including cover, aggregate type, concrete compressive strength, dead to live load ratio, rein- forcement ratio, end restraints, fire exposure, and proportion of end strands to total strands. Using the suggested procedure, reliability was estimated from zero to four hours of fire exposure using Monte Carlo simulation. It was found that reliability decreased nonlinearly as a function of time, while the most significant parameters were concrete cover, load ratio, fire type, end restraints, and proportion of end strands to total strands. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Building fires cause significant loss of human life and tremen- dous damage to property. In 2005 alone, fires caused 3762 deaths, 17,925 civilian injuries, and $10.7 billion in property damage in the United States [1]. In addition to fire prevention techniques, various means of fire damage mitigation are used. Some of these include providing the proper architectural planning of exits and escape routes; the use of active fire protection techniques such as sprin- klers to reduce the number of severe fires; and providing structural fire protection to achieve a minimum fire resistance rating, with the intent to allow structural members to maintain their integrity throughout the escape and firefighting phases. A fire rating is frequently expressed in terms of time; i.e. the time which a mem- ber is expected to maintain its structural integrity when subjected to a standard test fire. Traditionally, a structural member’s fire resistance rating is determined by conducting a fire endurance test such as specified in ASTM E119 [2], or by calculation. Calculation methods are read- ily available which can be used for limited cases when previous fire endurance test results exist for similar structures (ACI 1989 [3]; 2007 [4]; ASCE 2006 [5]). More sophisticated techniques are also available and allow for potentially greater accuracy, including empirical and semi-empirical [6–8], as well as finite element or finite difference approaches [9–11]. For prestressed concrete (PC) slabs and beams, the Prestress Concrete Institute provides a fire rating procedure in MNL-124-89 [12]. A fire rating, however, pro- vides no quantitative measure of safety in terms of failure proba- bility, and the reliability of PC structures exposed to fire loads is largely unknown. This is not consistent with prevalent Load and Resistance Factor Design (LRFD) philosophy, where load and resis- tance factors in various load combinations were specifically devel- oped using probabilistic principles to insure a consistent and adequate level of safety for structural members of the same impor- tance level. In the case of fire resistance, there is no guarantee that members have a consistent level of safety, and in fact it is well- known that significant performance variation results in traditional prescriptive fire load design methods [8,13–16]. Furthermore, significant differences in treatment of other loads when structural members are exposed to fire exist among other- wise usually consistent structural load standards. For example, in ASCE 7, Minimum Design Loads for Buildings and Other Structures [17], the recommended loads that a structural member should carry during a fire for its given fire rating are taken as 120% of the service dead load and 50% of the service live load. However, ACI 216.1-07, Code Requirements for Determining Fire Resistance of Concrete and Masonry Construction Assemblies [4], recommends 0141-0296/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2012.05.016 ⇑ Corresponding author. Tel.: +1 313 577 3766; fax: +1 3131 577 3881. E-mail address: eamon@eng.wayne.edu (C.D. Eamon). Engineering Structures 43 (2012) 69–77 Contents lists available at SciVerse ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct