Safety & Reliability Assessment of Composite Columns in Steel and Concrete Using Nonlinear Stochastic Finite Element Analysis

The focus of this study is the safety and reliability assessment for the design of composite columns in accordance with the general method with the overall safety factor 𝛾0 based on the strain-limited N-M interaction diagram, as this method is not yet explicitly included in the EN 1994-1-1 but it is in discussion to be considered in the second generation of Eurocode 4. This dissertation employs the Stochastic Finite Element Method (SFEM), which combines the standard Finite Element Method (FEM) procedure with the probability theory to solve stochastic problems and evaluate the reliability and safety. The semi-probabilistic approach, which is also known as the Level II method or First Order Reliability Method (FORM) in Eurocode 0 EN 1990, is used to further develop Eurocodes, while in this study, is implemented to validate the safety and reliability of the general method with the overall safety factor 𝛾0 determined by the strain-limited N-M interaction diagram for composite columns. To conduct nonlinear Stochastic Finite Element Analysis (FEA), Monte Carlo Simulation (MCS) or sampling technique such as Latin Hypercube Sampling (LHS) should be used. In this study, Latin Hypercube Sampling (LHS) is used to generate random variables resulting from statistical distribution of the geometry and material parameters of the composite columns in steel and concrete. The concept of safety and the approved safety levels in Eurocode 0 and Eurocode 4 have been thoroughly discussed.
The parametric nonlinear SFEM analysis results demonstrate that, the overall safety factor 𝛾0 based on the strain-limited N-M interaction diagram within the general method attain the safety level as required by Eurocode 0 (reliability index β=3.04), which corresponds to a probability of failure of 0.1% quantile for a normal building at the ultimate limit state with a reference period of 50 years.
Additionally, sensitivity analyses are carried out implementing the Sobol’s indices method in order to determine the extent to which each random variable affects the resistance of the composite columns in steel and concrete under compression load.