Finite-Element Reliability Analysis of Structures Subjected to Fire
Publication: Journal of Structural Engineering
Volume 141, Issue 4
Abstract
A reliability-based design methodology is urgently needed in the fire resistant design of structures to ensure adequate reliability in the face of uncertainty. This paper presents the application of the analytical reliability methods, namely the first-order reliability method (FORM) and second-order reliability method (SORM), to the design of structures subjected to fire. In particular, the FORM and SORM algorithms are implemented in a sequentially coupled thermal-structural finite-element model. A protected steel column exposed to natural fire is presented as an example. In comparison to Latin hypercube sampling (LHS), the analytical reliability method yields sufficient accuracy and provides a significant saving in computational expense. Discrepancies between the analytical methods and LHS are analyzed in depth, and it is shown that the parametric fire model produces a response surface that is highly nonlinear. Despite differences between the FORM and LHS solutions, the utilization of FORM is recommended for the rapid estimation of the reliability of structures threatened by fire.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the U.S. National Science Foundation under Grant No. CMMI-1032493. Any opinions, findings, conclusions or recommendations are those of the authors and do not necessarily reflect the views of the sponsoring agency.
References
AISC. (2011). “Steel construction manual design example v14.0.” 〈http://www.aisc.org/WorkArea/showcontent.aspx?id=29596〉.
ASCE. (2005). “Minimum design loads for buildings and other structures.”, Reston, VA.
Beck, V. R. (1985). “The prediction of probability of failure of structural steel elements under fire conditions.” Trans. Inst. Eng. Australia, 27(1), 111–118.
Breitung, K. (1984). “Asymptotic approximation for multi-normal integrals.” J. Eng. Mech., 357–366.
British Standards Institution (BSI). (2005). “Eurocode 3: Design of steel structures, part 1–2: General rules—Structural fire design.” BSI EN 1993-1-2, London.
British Standards Institution (BSI). (2007). “Eurocode 1: Actions on structures, part 1–2: General actions—Actions on structures exposed to fire.”, London.
Chan, S. L., and Chan, B. H. M. (2001). “Refined plastic hinge analysis of steel frames under fire.” Steel Compos. Struct., 1(1), 111–130.
Crisfield, M. A., Remmers, J. J., and Verhoosel, C. V. (2012). Nonlinear finite element analysis of solids and structures, Wiley, Chichester, U.K.
Culver, C. G. (1976). “Survey results for fire loads and live loads in office buildings.”, National Bureau of Standards, Washington, DC.
Der Kiureghian, A. (2005). “First- and second-order reliability methods.” Chapter 14, Engineering design reliability handbook, E. Nikolaidis, et al., eds., CRC Press, Boca Raton.
Der Kiureghian, A., and De Stefano, M. (1991). “Efficient algorithm for second-order reliability analysis.” J. Eng. Mech., 2904–2923.
D’Errico, J. R. (2006). “Understanding gridfit.” Matlab File Exchange, 〈http://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit〉 (Jan. 3, 2013).
Ellingwood, B. R. (2005). “Load combination requirements for fire-resistant structural design.” J. Fire Protect. Eng., 15(1), 43–61.
Fellinger, J. H. H., and Both, C. K. (2000). “Fire resistance: reliability vs. time analyses.” Proc., Composite Construction in Steel and Concrete IV, J. F. Hajjar, ed., ASCE, New York, 816–827.
Guo, Q., Shi, K., Jia, Z., and Jeffers, A. E. (2013). “Probabilistic evaluation of structural fire resistance.” Fire Technol., 49(3), 793–811.
Haldar, A., and Mahadevan, S. (2000). Reliability assessment using stochastic finite element analysis, Wiley, New York.
Hasofer, A. M., and Lind, N. C. (1974). “Exact and invariant second-moment code format.” J. Eng. Mech. Div., 100(1), 111–121.
Haukaas, T., and Der Kiureghian, A. (2006). “Strategies for finding the design point in nonlinear finite element reliability analysis.” Probabilist. Eng. Mech., 21(2), 133–147.
Hohenbichler, M., and Rackwitz, R. (1981). “Improvements of second-order reliability estimates by importance sampling.” J. Eng. Mech., 2195–2199.
Huang, P. T., and Delichatsios, M. A. (2010). “Quantitative risk analysis for the response of steel beams in fires.” J. Struct. Fire Eng., 1(4), 231–241.
Iqbal, S., and Harichandran, R. S. (2010). “Capacity reduction and fire load factors for design of steel members exposed to fire.” J. Struct. Eng., 1554–1562.
ISO. (2002). “Fire-resistance tests—Elements of building construction.” ISO 834, Geneva, Switzerland.
Jeffers, A. E., and Sotelino, E. D. (2009). “Fiber heat transfer element for modeling the thermal response of structures in fire.” J. Struct. Eng., 1191–1200.
Jeffers, A. E., and Sotelino, E. D. (2012). “Analysis of steel structures in fire with force-based frame elements.” J. Struct. Fire Eng., 3(4), 287–300.
Khorasani, N. E., Garlock, M. E., and Gardoni, P. (2012). “Reliability analysis of steel perimeter columns under fire.” Proc., 7th Int. Conf. on Structures in Fire, Fontana F., Frangi, A., and Knoblock, M., eds., ETH Zurich, Zurich, 541–550.
Ma, Z. C., and Makelainen, P. (2000). “Parametric temperature-time curves of medium compartment fires for structural design.” Fire Saf. J., 34(4), 361–375.
Madsen, H. O., Krenk, S., and Lind, N. C. (2006). Methods of structural safety, Dover Publications, New York.
Nowak, A. S., and Collins, K. R. (2000). Reliability of structures, McGraw-Hill, Boston.
Pebesma, E. J., and Heuvelink, G. B. M. (1999). “Latin hypercube sampling of Gaussian random fields.” Technometrics, 41(4), 203–212.
Puatatsananon, W., and Saouma, V. E. (2006). “Reliability analysis in fracture mechanics using the first-order reliability method and Monte Carlo simulation.” Fatig. Fract. Eng. Mater. Struct., 29(11), 959–975.
Rackwitz, R. (2001). “Reliability analysis—A review and some perspectives.” Struct. Saf., 23(4), 365–395.
Rackwitz, R., and Fiessler, B. (1978). “Structural reliability under combined load sequences.” Comput. Struct., 9(5), 489–494.
Ravindra, M. K., and Galambos, T. V. (1978). “Load and resistance factor design for steel.” J. Struct. Div., 104(9), 1337–1353.
Shetty, N. K., GuedesSoares, C., Thoft-Christensen, P., and Jensen, F. M. (1998). “Fire safety assessment and optimal design of passive fire protection for offshore structures.” Reliab. Eng. Syst. Saf., 61(1), 139–149.
Singh, V. P., Jain, S. K., and Tyagi, A. (2007). Risk and reliability analysis: A handbook for civil and environmental engineers, ASCE, Reston, VA.
Tan, K. H., Toh, W. S., Huang, Z. F., and Phng, G. H. (2007). “Structural responses of restrained steel columns at elevated temperatures. Part 1: Experiments.” Eng. Struct., 29(8), 1641–1652.
Vaidogas, E. R., and Juocevičius, V. (2008). “Reliability of a timber structure exposed to fire: Estimation using fragility function.” Mechanika, 73(5), 35–42.
Wainman, D. E., and Kirby, B. R. (1988). Compendium of UK standard fire test data: Unprotected structural steel, British Steel Corporation.
Wen, Y. K. (2001). “Reliability and performance-based design.” Struct. Saf., 23(4), 407–428.
Zhang, Y., and Der Kiureghian, A. (1995). “Two improved algorithms for reliability analysis in reliability and optimization of structural systems.” Proc., 6th IFIPWG 7.5 Working Conf. on Reliability and Optimization of Structural Systems and Computer Methods in Applied Mechanics and Engineering, R. Rackwitz, G. Augusti and A. Borri, eds., Assisi, Italy, 297–304.
Ziemian, R. D. (2010). Guide to stability design criteria for metal structures, Wiley, New York.
Zio, E. (2013). The Monte Carlo Simulation method for system reliability and risk analysis, Springer series in reliability engineering, Springer, London.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 141 • Issue 4 • April 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 22, 2013
Accepted: Mar 20, 2014
Published online: Jul 16, 2014
Discussion open until: Dec 16, 2014
Published in print: Apr 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.