Three-dimensional frame buckling benchmark problems for direct analysis method in ANSI/AISC 360-16

Direct Analysis Method (DAM) of ANSI/AISC 360-16 prescribes the use of a rigorous second-order analysis to account for initial imperfections, the spread of inelasticity, P-?, and P-d effects accurately. The second-order analysis used in DAM should be verified against benchmark problems to ascertain whether it can accurately model all the second-order effects of a steel frame with reduced stiffness and notional loads. The benchmark problems available in the literature are primarily for frames with gravity loads acting through second-order displacements as the source of geometric nonlinearity. This paper identifies two lightly loaded structures where significant geometric nonlinearity occurs due to the behavior of individual elements and complexity in geometry. 3D frames can exhibit flexural, torsional, axial deformations and buckle through sway, non-sway, torsional and snap-through modes. For such structures, the position and direction of notional loads should be chosen accordingly to trigger the most undesirable displacements in the structure. Geometric nonlinear analyses are necessary when cable elements support the structure, even when the load is lateral. The inability of an analysis software verified against existing 1D and 2D benchmark problems in capturing the second-order effects of a cable-supported beam-column is illustrated in this study. The applicability of DAM on these structures is also discussed. Apart from software packages, a Total Lagrangian-based 3D finite element framework is also used to generate benchmark problems. These problems equip a designer to verify whether a second-order analysis software used for the DAM can accurately capture spatial behavior, flexural-torsional coupling, and different sources of nonlinearities consistently.