GEOMETRICALLY NON-LINEAR FINITE ELEMENT RELIABILITY ANALYSIS OF STEEL PLANE FRAMES WITH INITIAL IMPERFECTIONS

The random load carrying capacity of steel plane frames with bracing stiffness is studied. The load carrying capacity is evaluated using the geometrically non-linear FEM analysis. The incremental stiffness matrix of a slightly curved element utilized in the non-linear incremental analysis is listed. Initial imperfections are considered as random variables. Statistical analysis and Sobol sensitivity analysis are performed using the Latin Hypercube Sampling method. The effect of initial random imperfections on the load carrying capacity is studied, whilst assuming constant slenderness of the columns. The evaluation parameters are the pair of non-random values of elastic bracing stiffness, and system length of the columns. The paper illustrates that the load carrying capacity is very sensitive to initial crookedness of the columns in the event that the non-sway (symmetric) and sway (anti-symmetric) buckling modes coincide. In this case, the design load carrying capacity obtained from statistical analysis according to the EN 1990 (2002) standard is relatively very small (of low safety). Results show that the reliability of design of a steel frame according to EUROCODE 3 (1993) is significantly misaligned. The significance of the first and the second buckling forces as indicators of sensitivity of the load carrying capacity to the imperfections is discussed.