Reliability-based design for buckling strength of stiffened steel plates : ultimate and serviceability limit states

The strengths of longitudinally continuous stiffened steel plates under uniaxial compression were investigated by employing a combination of numerical and probabilistic approaches. The probabilistic compressive strengths were obtained for two different limit states, i.e. the Ultimate Limit State (ULS) and the Serviceability Limit State (SLS). For slender stiffened plates, the SLS is particularly important because large out-of-plane deflection occurs due to elastic buckling, before reaching the ultimate strength. Due to lack of specific criteria to determine the compressive strength at SLS, a rational criterion has been proposed based on elastic buckling strength and fabrication tolerance. Three different stiffened plate models with three, two, and one flat plate longitudinal stiffeners, corresponding to Model-1, Model-2, and Model-3 were considered for the study, where Model-1 and Model-2 shows column-like behavior (small post-buckling strength) and Model-3 exhibits plate-like behavior (significant post-buckling strength reserve). The plates of both normal and high-performance steel (SBHS) were taken into account, and their thickness was varied from 10 to 90 mm. The compressive strengths at ULS and SLS were determined from nonlinear elasto-plastic finite element analysis (FEA), where both material and geometric nonlinearity were taken into account. As a source of variability of the compressive strengths, variation of the initial out-of-plane deflection and residual stress were considered simultaneously in the FEA. The probabilistic distribution of the compressive strengths for Model-1 and Model-2 were obtained through Monte Carlo simulations in association with the response surface method. The response surface function is a second order polynomial of the independent random variables, i.e. the initial out-of-plane deflections and the residual stresses. For Model-3, an approximate estimation procedure was followed to obtain the first-order mean values. The first order variances were also estimated approximately, employing the Taylor series finite difference (TSFD) method. Based on the obtained probabilistic information, partial safety factors were proposed, considering the mean value strengths as the nominal strengths, as an example. The study results were compared with different design codes e.g. JSHB, AASHTO, Eurocode, and Canadian Code. Comparing to the ULS strengths for Model-1 and Model-2 with a 5% non-exceedance probability indicate that the JSHB, AASHTO, and Canadian Code provides significantly conservative design, specifically for stiffened plates with high reduced slenderness parameters. However, in the middle range of reduced slenderness parameters, AASHTO and Canadian Code predicts overestimated strengths for Model-3. All of the three Models showed better agreement with the Eurocode than other design specifications. Nevertheless, a scope for improvement of the Eurocode was addressed by considering continuous stiffened panels (in the longitudinal direction) rather than an isolated panel. The uniqueness of this research is that the effect of thick plates and SBHS steels were included. Furthermore, rather than deterministic strengths, probabilistic strengths are provided for column-like behavior and plate-like behavior, which can be used as an important reference for developing a reliability-based design strength curve.

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