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FIGURE 31.15 A frame with leaning columns: (a) a leaning column frame and (b) model for a leaning column.

31.7.1.2 Lim and McNamara Method

Based on the story-buckling concept and using the stability functions, Lim and McNamara (1972) presented the following formula to account for the leaning column effect:

where Kn is the effective length factor accounting for leaning columns; K is the effective length factor determined by the alignment chart (Figure 31.3b) not accounting for the leaning columns; ^P and Q are the loads on the restraining columns and on the leaning columns in a story, respectively; and F0 and Fn are the eigenvalue solutions for a frame without and with leaning columns, respectively. For normal column end conditions that fall somewhere between fixed and pinned, F0/Fn = 1 provides a K-factor on the conservative side by less than 2% (Geschwindner 1995). Using F0/Fn = 1, Equation 31.100 becomes

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