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

Direct Analysis Method (DAM) in ANSI/AISC 360-16 is used when a designer wants to avoid using effective length factors in column design strength checks. However, DAM prescribes the use of rigorous second-order analysis software to obtain the amplified moments due to P-D and P-d effects. This second-order analysis software must be validated against certain benchmark problems to ascertain whether it can accurately model all the second-order effects of a 3D frame with a reduced nominal elastic stiffness with notional loads. ANSI/AISC 360-16 has prescribed two such benchmark problems (1D), but many benchmark problems are available in the literature for 2D frames. Structures with complex geometries require three-dimensional frame buckling benchmark problems that would incorporate flexural, twist, and axial deformations, and the effect of rotational restraints.

This paper presents several 3D frames buckling benchmark problems so that designers may verify whether a second-order analysis software used for DAM can capture the spatial behavior, flexural-torsional coupling, and P-D and P-d effects accurately. Examples are provided in this paper to illustrate the applicability of DAM on 3D frames. This paper uses a total Lagrangian computational framework to generate the benchmark problems.

The research work presented in this paper addresses one of Task Group 3 of SSRC themes for future research.

Learning Objectives:
The coupling of flexural, stretching, and twisting deformations is important in a 3D frame, and DAM is applicable only if the analysis software used can capture these effects accurately.

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