First and Second Order Sensitivity Analyses of the Ultimate Resistance of Steel Plane Frames to Imperfections

The article is aimed at the statistical and sensitivity analysis of the ultimate limit state of steel frames. Load–carrying capacity is calculated for steel plane frames with columns loaded in tesion or compression. The Monte Carlo based procedures are used for statistical analysis and for computing the full set of first order and second order sensitivity indices of the model. System imperfections of the frame with compressed columns are considered in the formatively identical to the first eigen mode of buckling. The geometrical nonlinear finite element solution providing numerical result per run was employed. Input random imperfections, which are most deserving of further analysis or measurements, are identified by means of the sensitivity and statistical analysis. Statistical analysis is used to study the influence of the number of columns on the change of the mean value and standard deviation of the load–carrying capacity of frames with tensed columns. Sensitivity analysis is used to identify the dominant input random variables and their higher order interaction effects. The dependence between sensitivity indices and column height is analysed in frames with compressed columns. The sensitivity index of system imperfections has a convex shape. Frame height for which the load–carrying capacity is the most sensitive to the change of system imperfections is determined.