analysis and design of a tapered-section column

huangyhg

analysis and design of a tapered-section column
i have got a question about the analysis and design of tapered-section columns, either in a pre-engineered building, or in a steel structure.  what is the best way to approach this?  what is the theory behind it?
now, i have done some design for columns for purely axial loads, and for beam-columns for axial compressive and bending loads.  i am pretty comfortable with w-shape columns, but am not too familiar with tapered-section columns.
i remember my boss asking me to evaluate a tapered-section column, and i was kind of stumped!
i guess the reason i am not entirely sure is because the section of a tapered-section column, by its very definition, changes constantly along its entire length.  which area, and hence, which rx, ry, ix, iy, sx, sy, etc. should i use?
also, a tapered-section column is as if it were several members in one single column, and their properties varying as the column go upwards or downwards.  appreciate if someone could provide the theory behind the analysis and design of a tapered-section column, relevant formulas, a worked example, e.g. relevant references with page numbers would also be most welcome.  
thanks a lot.
how tapered are we talking here?  i am not trying to give advice because i dont have the experience but i re  
aisc/mbma will publish a new design guide for these in the next few months.  that'll be your answer for the long haul.
for the short term, you can help yourself a lot by observing that ry and rt are almost constant over almost any unbraced length.  several other props are too.  
the main difference is that rx varies significantly, which affects the strong-axis buckling load.  you can calc ix at about 2/3 the way from the small end and not be too bad off.
q should be taken as the worst along the unbraced length.
see appendix 7 for analysis requirements.  
look in the first site below under stability -> columns -> tapered : you'll be able to compare the critical load for a column with tapered section to that of a prismatic one with a section taken somewhere along the axis.
prex
agree with 271828 - there has been significant research and development put behind the new aisc/mbma design guide which has been in final draft for a while now.  this guide will also focus heavily on using the direct analysis method in conjunction with the tapered column/beam design.  
it is funny.
i think the new dg will really help a lot of folks with this subject.  i did my thesis on tapered members years ago and it was really a zoo back then.  all that "b" business that the mb guys mostly just ignore.
the subject of tapered member stability bracing still needs work, though.  i don't think they touch up on this at all in the new dg.  that junk's hard enough for prismatic   
a few references:
for design:
you must use the applicable design code such as the 1989 asd steel manual appendix f7 p.5-102 and commentary p.5-191...or maybe the 1999 lrfd steel manual appendix f3 p.103 and commentary p.268...or use staadpro with the appropriate parameters defined.  i would prefer to use staadpro so i could optimize the solution quickly.  staadpro uses the 1989 asd steel manual.  
for theory:
do some research.
i don't think the aisc asd/lfrd specs were intended to be applied to tapered metal building frames. i would get a copy of mbma for guidance.
what i see is logic is....
1)for analysis you can model the frame or whatever it is by computer and you can define the column section as tapered..
2)for buckling calculations use the properties of an intermediate section between the min and the max sections
3)for design and checking stresses use the section which suffers the max moment or/and normal forces and that's not an option (it's a necissity)
note:
if you wanna be very accurate..the tapered columns can be modelled as slightly inclined columns because the actual (structural) centerline of the column is in the cg of the section so when it's tapered from one side only the centerline is inclined  
haynewp - please tell me why you should not use aisc for a tapered column.