Non-deterministic Approach for Reliability Evaluation of Steel Portal Frame

Hawraa Qasim Jebur, Salah Rohaima Al-Zaidee


In recent years, more researches on structural reliability theory and methods have been carried out. In this study, a portal steel frame is considered. The reliability analysis for the frame is represented by the probability of failure, P_f, and the reliability index, β, that can be predicted based on the failure of the girders and columns. The probability of failure can be estimated dependent on the probability density function of two random variables, namely Capacity R, and Demand Q. The Monte Carlo simulation approach has been employed to consider the uncertainty the parameters of R, and Q. Matlab functions have been adopted to generate pseudo-random number for considered parameters. Although the Monte Carlo method is active and is widely used in reliability research, it has a disadvantage which represented by the requirement of large sample sizes to estimate the small probabilities of failure. This is leading to computational cost and time. Therefore, an Approximated Monte Carlo simulation method has been adopted for this issue. In this study, four performances have been considered include the serviceability deflection limit state, ultimate limit state for girder, ultimate limit state for the columns, and elastic stability. As the portal frame is a statically indeterminate structure, therefore bending moments, and axial forces cannot be determined based on static alone. A finite element parametric model has been prepared using Abaqus to deal with this aspect. The statistical analysis for the results samples show that all response data have lognormal distribution except of elastic critical buckling load which has a normal distribution.


Reliability Analysis; Monte Carlo Method; Matlab; Abaqus.


Morio, J., and M. Balesdent. “Introduction to Rare Event Probability Estimation.” Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems (2016): 1–2. doi:10.1016/b978-0-08-100091-5.00001-0.

Ebenuwa, Andrew Utomi, and Kong Fah Tee. “Fuzzy-Based Optimised Subset Simulation for Reliability Analysis of Engineering Structures.” Structure and Infrastructure Engineering 15, no. 3 (January 31, 2019): 413–425. doi:10.1080/15732479.2018.1552977.

R. Melchers and A. Beck, Structural Reliability Analysis and Prediction. John Wiley & Sons; 2017.

I. Elishakoff, Probabilistic Methods in the Theory of Structures, United State of American: World Scientific Publishing Co. Pte. Ltd., 2017.

Gordini, M., M.R. Habibi, M.H. Tavana, M. TahamouliRoudsari, and M. Amiri. “Reliability Analysis of Space Structures Using Monte-Carlo Simulation Method.” Structures 14 (June 2018): 209–219. doi:10.1016/j.istruc.2018.03.011.

Cardoso, João B., João R. de Almeida, José M. Dias, and Pedro G. Coelho. “Structural Reliability Analysis Using Monte Carlo Simulation and Neural Networks.” Advances in Engineering Software 39, no. 6 (June 2008): 505–513. doi:10.1016/j.advengsoft.2007.03.015.

Zhang, S., and W. Zhou. "System reliability assessment of 3D steel frames designed per AISC LRFD specifications." Adv. Steel Constr. 9, no. 1 (2013): 77-89.

Kirk, Beatriz Gonçalves, and Lara Alves da Silva. "Reliability Analysis of a Steel Beam Using the Monte Carlo Method." Revista Interdisciplinar De Pesquisa Em Engenharia 2, no. 2 (2017): 15-25.

V. Sagar J. and M. GS., "Probability of Failure of Column and Beam in Steel Structure Due to Plan Irregularities," 2017.

Zhang, Hao, Haoyu Liu, Bruce R. Ellingwood, and Kim J. R. Rasmussen. “System Reliabilities of Planar Gravity Steel Frames Designed by the Inelastic Method in AISC 360-10.” Journal of Structural Engineering 144, no. 3 (March 2018): 04018011. doi:10.1061/(asce)st.1943-541x.0001991.

Liu, Wenyu, Hao Zhang, Kim J.R. Rasmussen, and Shen Yan. “System-Based Limit State Design Criterion for 3D Steel Frames Under Wind Loads.” Journal of Constructional Steel Research 157 (June 2019): 440–449. doi:10.1016/j.jcsr.2019.02.015.

A. Ghali, A. Neville and T. G. Brown, Structural Analysis, 6th ed., Canada: Taylor & Francis Group, 2009.

Mohammad Masoud and Medi Moudi, "Analysis of Beam Failure Based on Reliability System Theory Using Monte Carlo Simulation Method," 2012.

A. S. Nowak and K. R. Collins, Reliability of Structures, New York: McGraw-Hill, 2000.

Ayyub, Bilal M., and Richard H. McCuen. Probability, statistics, and reliability for engineers and scientists. CRC press, 2016.

Chen, Ding-Geng, and John Dean Chen, eds. “Monte-Carlo Simulation-Based Statistical Modeling.” ICSA Book Series in Statistics (2017). doi:10.1007/978-981-10-3307-0.

Thomopoulos, Nick T. Essentials of Monte Carlo simulation: Statistical methods for building simulation models. Springer Science & Business Media, 2012.

Li, Zhongwei, and Mayuresh Patil. "Reliability Analysis of Ultimate Strength for Beam-Columns." In SNAME Maritime Convention. The Society of Naval Architects and Marine Engineers, 2017.

Grooteman, Frank. “An Adaptive Directional Importance Sampling Method for Structural Reliability.” Probabilistic Engineering Mechanics 26, no. 2 (April 2011): 134–141. doi:10.1016/j.probengmech.2010.11.002.

Shadab Far, Mahdi, and Yuan Wang. “Approximation of the Monte Carlo Sampling Method for Reliability Analysis of Structures.” Mathematical Problems in Engineering 2016 (2016): 1–9. doi:10.1155/2016/5726565.

Jirgl, M., Z. Bradac, K. Stibor, and M. Havlikova. “Reliability Analysis of Systems with a Complex Structure Using Monte Carlo Approach.” IFAC Proceedings Volumes 46, no. 28 (2013): 461–466. doi:10.3182/20130925-3-cz-3023.00031.

Kala, Zdeněk, Jindřich Melcher, and Libor Puklický. “Material and Geometrical Characteristics of Structural Steels Based On Statistical Analysis of Metallurgical Products.” Journal of Civil Engineering and Management 15, no. 3 (June 30, 2009): 299–307. doi:10.3846/1392-3730.2009.15.299-307.

Singh, Raminder. "Reliability Analysis of Statically Determinate and Indeterminate Beams Designed with Moment Redistribution." PhD diss., The George Washington University, 2016.

Darmawan, M. Sigit, A.N. Refani, M. Irmawan, R. Bayuaji, and R.B. Anugraha. “Time Dependent Reliability Analysis of Steel I Bridge Girder Designed Based on SNI T-02-2005 and SNI T-3-2005 Subjected to Corrosion.” Procedia Engineering 54 (2013): 270–285. doi:10.1016/j.proeng.2013.03.025.

Buonopane, S. G., and B. W. Schafer. "Reliability of steel frames designed with advanced analysis." Journal of Structural Engineering 132, no. 2 (2006): 267-276. doi: 10.1061/(ASCE)0733-9445(2006)132:2(267).

Karmazínová, M. A. R. C. E. L. A., and J. I. N. D. R. I. C. H. Melcher. "Influence of steel yield strength value on structural reliability." Recent Researches in Environmental and Geological Sciences (2012): 441-446.

ANSI, B. "AISC 360-10-Specification for Structural Steel Buildings [J]." Chicago AISC (2010).

Naess, A., B.J. Leira, and O. Batsevych. “System Reliability Analysis by Enhanced Monte Carlo Simulation.” Structural Safety 31, no. 5 (September 2009): 349–355. doi:10.1016/j.strusafe.2009.02.004.

E. P. Popov, Engineering Mechanics of Solids, California: John Wiley & Sons, 1990.

Kala, J., and Z. Kala. "Influence of yield strength variability over cross-section to steel beam load-carrying capacity." Nonlinear Anal Model Control 10, no. 2 (2005): 151-160.

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DOI: 10.28991/cej-2019-03091363


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