Keywords: deteriorating members, lateral torsional buckling, survival probability, reliability index.

Time-dependent survival probabilities of deteriorating and non-deteriorating steel beams under lateral torsional buckling are modelled. Computational probabilistic design of steel beams considering time-dependent stability is based on the generalized reliability index concept. The object of this paper is to assess the difference in reliability indices of non-deteriorating and deteriorating rolled and welded flanged beams under lateral torsional buckling and to encourage designers having minimum appropriate skills and experience to use probability-based methods in their design practice.

Steel structures are required to satisfy torsional flexural buckling resistance requirements for rolled and welded sections [1]. The presented probabilistic analysis of buckling members subjected to sustained and intermittent recurrent variable loads is presented.

The time-dependent mean values of buckling resisting moments of deteriorating rolled and welded steel beams depend on their statistically independent components (reduction factor, section modulus and yield strength). However, all statistical moments of beams depend on the additional random variables representing uncertainties of a resisting moment model. According to probability-based approaches and assumptions, the time-dependent resistance safety margin of deteriorating particular members exposed to permanent and variable service loads may be defined as their hierarchical random performance process characterized by the vectors of additional and basic random variables [2]. The probability distributions of a resisting moment of rolled and welded flanged beams and permanent loads may be described by the lognormal and Gaussian distribution laws, respectively. Gaussian or lognormal and Gumbel distributions may be assumed for sustained and extreme variable actions [2,3].

The prediction of time-dependent survival probabilities of particular members may be based on the analysis of a decreasing sequences of random safety margins. However, it is more reasonable to use the unsophisticated analytical method of transformed conditional probabilities [4]. The computer program TCPM was written in the Matlab environment and adapted for prediction of time-dependent survival probabilities of particular members.

Steel sections and other particular members of load-carrying structures may be designated in the same reliability class as for the entire structure. Comparisons of the buckling responses of non-deteriorating and deteriorating rolled and welded steel beams show that due to strength welds the resisting moment of an equivalent welded flanged beam decreases significantly.

Instead of an analysis of design values of buckling resisting and failure bending moments of rolled and welded steel beams it is expedient to determine their reliability indices and compare them with specified target values and select an objective relevant structural decision in a fairly simple and reliable manner.

1

EN 1993-1-1, Eurocode 3, "Design of steel structures: Part 1-1. General rules and rules for buildings", Brussels, CEN, 2004.

2

JCSS, "Probabilistic model code: Part 1- Basis of design", Joint Committee on Structural Safety, 2000.

3

EN 1990, "Eurocode-Basic of structural design", Brussels, CEN, 2002.

4

A. Kudzys, "Transformed conditional probabilities in analysis of stochastic sequences", Summer Safety and Reliability Seminars, SSARS 2007, Gdansk-Sopot, Poland, 243-250, 2007.

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