Keywords: steel structures, geometric nonlinearity, material nonlinearity, ultimate limit state, strength, imperfections, advanced finite element analysis, equilibrium path.

The objective of this chapter is to present state-of-the-art of finite element analysis tools for predicting the collapse load of steel structures, hence their strength. In recent years structural design codes have adopted limit state design (LSD), requiring the structure to satisfy two principal criteria: ultimate limit state (ULS) and serviceability limit state (SLS). To satisfy the ultimate limit state, the structure must not collapse when subjected to any design load combination. Thus, reliable prediction of the collapse load is a requirement for carrying out ultimate limit state checks.

The prevailing approach proposed by modern codes for carrying out such checks consists of obtaining action effects by means of linear elastic analysis of the structure subjected to design loads, and comparing them to resistances that account for both types of eventual nonlinearity, material and geometric. Thus, prediction of collapse, a highly nonlinear phenomenon, is accomplished by means of linear elastic analysis, which is simple and computationally inexpensive, can be carried out by means of widely available commercial software, and yields results that are quite reliable for ordinary structural systems.

Design codes also allow for predicting collapse by means of more elaborate, nonlinear analysis. This approach may be more suitable for members with unusual cross-sections and for uncommon structural systems, as such cases are not directly covered by buckling curves and interaction equations, and assumptions made in an effort to approximate their behavior may lead to inaccuracies. Practicing engineers applying these codes must have sufficient guidelines for setting up numerical models, selecting proper analysis methods and numerical algorithm parameters, and interpreting the results. The present work contributes in that direction.

To that end, finite element tools for understanding the behavior, predicting all possible failure mechanisms, and evaluating the ultimate strength of steel structures by means of commercially available software are critically reviewed. Failure dominated by either material yielding or instability is addressed, as well as interaction of failure modes. Steps include setting up an appropriate numerical model, obtaining critical buckling modes from linearized buckling analysis (LBA), and then using a linear combination of these modes as an imperfection pattern for geometrically and material nonlinear imperfection analyses (GMNIA). Equilibrium paths accompanied by snapshots of deformation and stress distribution at characteristic points are used for evaluating the results. Practical implementation details of the proposed strategy are discussed. The results of several case studies are used to demonstrate this methodology, including built-up members, and compression members and beams of long span roofs with varying cross-sections.

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