FIGURE 31.25 Effective length factor for tapered columns in unbraced frames (Galambos 1988).

FIGURE 31.26 A tapered portal frame.

Fraser 1989, 1990; AISE 1991; Bendapudi 1994). Those procedures have limitation in terms of column geometry, loading, and boundary conditions. Most importantly, most of these studies ignored the interaction effect between the left and right columns of frames and were based on isolated member analyses (Lui and Sun 1995). Recently, a simple, yet reasonably accurate, procedure for calculating the K-factors for crane columns with any value of relative shaft length, moment of inertia, loading, and

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