where p = 1 for Gmax < 2 and p = — 1 for Gmax > 2. Gmax is the larger and Gmin is the smaller of the G-factors at the column ends.

31.6.5 Remarks

For a comparison, Table 31.6 summarizes K-factors for the frames shown in Figure 31.14a obtained from the alignment chart, the LeMessurier and Lui methods, as well as an eigenvalue analysis. The methods of both LeMessurier and Lui are based on the story-buckling concept. It is seen that errors in alignment chart results are rather significant in this case. Although the K-factors predicted by Lui's and LeMessurier's formulas are identical in most cases, the simplicity and independence of any chart in the case of Lui's formula make it more desirable for design office use (Shanmugam and Chen 1995). Essa's (1998) method overcomes some of the limitations imposed on the development of alignment chart and incorporates effects of inelastic behavior, different column stiffness parameters, and different restraining girder conditions. The Cheong-Siat-Moy (1999) method is dependent on the nondimensionalized lateral stiffness parameter of the column and can be used for partially braced frames. A comprehensive parametric study encouraged engineers to use the story-based K-factors for stability assessment (Roddis et al. 1998). Xu and Liu (2002) developed a story-based approach for both unbraced partially and fully restrained frames.

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