They usually do a better job of defining their variables.  The key to my understanding is that it is part of the definition of the mode shape. And, we should be able to determine enough about the mode shape to come up with an answer.

Phi(z) = (h/z)^xi

If you know what your mode shape is, then you should be able to estimate your xi (mode component) value... essentially we just do a curve fit and see what value of xi most closely reproduces our known mode shape.  Make sense?


If that's too much work, I suspect that you could set this equal to the 'k' value defiend in seismic chapter (equation 12.8-12 of the 2005 version of ASCE 7). The seismic k value is trying to capture the "whipping" effect of the mode shape for the more flexible structures in comparison to a much more triangular distribution for rigid structures.  So, it is a very similar concept.   

Thanks. That explanation makes sense. Excel can be used to do the curve fit using center of mass ordinates for the primary mode shape in each building direction.