Reliability-Based Design Rules for Thin-Walled Structural Steel Beam-Column Elements

Abstract

The problem considered in this study is to deterministically and probabilistically evaluate the adequacy of the design methods of cold-formed structural steel beam-columns having doubly-symmetric cross-sections in accordance with the AISI Specification of 1968 and ECCS Recommendation of 1987 with a view to proposing equivalent optimal criteria. The validity of the design formulae are verified using test results drawn from literature and those observed at the Heavy Structural Laboratory at the University of Dortmund, Dortmund, West Germany. Depending on the ratio of width to thickness of wall members, varying degrees of incongruities exist between the predictions given by the design formulae and test results. Both cases of good and over-estimation of member strength are noted and generally the predictions of ECCS (1987) show more conservatism than AISI (1968). Due to scatter in test results, the influence of the statistics of the design variables on the predicted strength is analyzed. The sensitivity is compared giving recognition to the parameter, Qw, which represents the local buckling phenomenon. The design formulae are found sensitive to this parameter. Safety factors are applied either to loading or strength parameters in the two design equations studied. The vii dependability of such factors is measured by computing the reliability levels implicit in the design equations under uncertain dead and maximum life-time live loads. Within the range of practical data points considered, significant inconsistency is noted. Although the reliability levels computed assume random values, their distributions show that a target level is in focus. Thus, employing a socio-economic criterion, a target reliability level, 82, of 4.265 is obtained for each design equation. This value is equivalent to a failure probability level of 1 x 10-5. Since an ultra safe design method can be unduly expensive and that it is not economically feasible to design a structure that cannot fail, resistance and load factored Limit State Design Formats which trade-off safety and economy are derived as alternatives to the corresponding formulae in AISI (1968) and ECCS (1987). These formats are optimal having a minimum total cost implication as far as the design of thin-walled structural steel beam-column members of doubly-symmetric shapes or shapes not subject to torsional or torsional-flexural buckling is concerned. In addition, they supercede the current formats by providing uniform reliability level at minimum cost. This objective became realistic as a consequence of rigorous combination of the Advanced First-Order Reliability Method (FORM) and a Nonlinear Quadratic Programming Technique.