BENCHMARK PROBLEMS WITH FLEXURAL-TORSIONAL COUPLING FOR DIRECT ANALYSIS METHOD IN ANSI/AISC 360-16

The Direct Analysis Method (DAM) of ANSI/AISC 360-16 enables the prediction of design strength in columns without the use of effective length factors. While adopting DAM, a designer must ensure that the software used to calculate the design demands, can capture the second-order effects accurately. For two-dimensional (2D) second-order analysis of steel framed structures, there are several benchmark problems published in the literature, and in contrast very few for 3D frames. This paper presents 3D benchmark problems that accurately capture coupled flexural, and torsional behavior. A geometrically exact total Lagrangian formulation is used where Euler angles define the rigid body dynamics of the system in space. The governing equations in space coordinates are formed using fully nonlinear, objective Jaumann strains and stresses before using principle of virtual work to obtain a 16-degree-of-freedom space beam element. Two benchmark problems are presented - (i) a right angle bent which has no restraint to out-of-plane displacements, and (ii) the bent frame with adequate restraints against out-of-plane displacements at the joints. In the former, the lateral-torsional deformations of the beam cause significant biaxial bending moments in the column. In the second benchmark problem, the behavior of the frame with adequate lateral restraint is brought out. The notional loads have been applied to cause a coupled biaxial bending and twist deformations. It was shown that the exclusion of twist from the deformation response of the frame leads to the underestimation of design demands which is evident from the interactive surface. The paper also suggests a few combinations of notional loads to bring out the true buckling behavior of the frame.

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