Investigations on System Stability of Three-Dimensional Frames

With the usage of high-strength steel structures, system instability has become an essential aspect of stability design. In this context, the published research work gravitates toward the nonlinear stability analysis of 3D steel frames. The advanced analysis-based design procedures, as per ANSI/AISC-360, allow the designers to utilize the system's total capacity by directly modeling the effect of imperfections and the spread of inelasticity within the context of a second-order analysis. Hence, a 3D second-order frame analysis must be accurate enough to capture the overall system behavior without excluding any impending failure modes. The present paper develops a novel Total Lagrangian three-dimensional beam element formulation based on the N1-N2 formalism of Mallet & Marcal. Kirchhoff's constraints are enforced in the variational formulation after generating the fundamental kinematic relations of the three-dimensional beam element. The nonvectorial rotations are parameterized using Bryant angles, and the holonomic constraints on beam configuration are enforced. The resulting equations are cast into finite element formulations to develop a novel three-dimensional beam element. Using the developed formulation, a detailed parametric study has been carried out on the stability design provisions of the ANSI/AISC-360 code, and a comparison is made over the conventional stability design using effective length. Two three-dimensional steel frame benchmark problems are chosen to investigate the system stability. The first example is a three-dimensional two-bay-two-story frame in which, depending on the direction of notional loads, the bending moment demand of columns gets resolved into major and minor axes’ demands. Usually, notional loads are applied in the direction that provides the greatest destabilizing effect. It is shown that the possible chance of a minor axis demand could become potentially troublesome in the design. Since the problem is a regular frame, the designer may tend to apply notional loads in the direction of applied lateral loads alone, but an additional minor axis demand resulting from the twist might not be captured in the analysis. The second benchmark problem is a one-bay, two-story frame subjected to gravity and lateral loads in two orthogonal directions. It could be shown that instead of doing two separate DAM analyses for each orthogonal direction, a single DAM analysis would suffice in which the notional loads are applied in the direction of the resultant lateral loads at each level. This is in accordance with the guidelines mentioned in ANSI/AISC 360-16. From both the frame problems, it could be concluded that DAM gives accurate results and a realistic picture of force distribution with considerably less effort for the stability design of steel frames.