Equation 31.45 is reduced to the form of Equation 31.6.

The procedures to obtain the K-factor directly from the alignment charts without resorting to solve Equations 31.38 and 31.45 were also proposed by Duan and Chen (1988, 1989).

Far end F

h aL

I rh

FIGURE 31.7 Tapered rectangular girders: (a) linearly tapered girder and (b) symmetrically tapered girder.

31.5.3 Columns Restrained by Tapered Rectangular Girders

A modification factor aT was developed by King et al. (1993) for those framed columns restrained by tapered rectangular girders with different far end conditions. The following modified G-factor is introduced in connection with the use of alignment charts:

where Ig is the moment of inertia of the girder at the near end. Both closed-from and approximate solutions for modification factor aT were derived. It is found that the following two-parameter power function can describe the closed-from solutions very well:

where the parameter D is a constant depending on the far end conditions and b is a function of far end conditions and tapering factors « and r as defined in Figure 31.7. For a braced frame

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