load capacity of prismatic column sections

huangyhg

load capacity of prismatic column sections
does anyone know if a proceedure exists for finding the capacity of a column who's section varies along the height of the column?
we are assuming that the connection bewteen the two sections is fixed, and therefore stable, but what happens to the axial loads?  is the capacity based on the kl/r of the weaker portion, or is there are "effective" kl/r for the total height.  for example, a 2-inch jack rod supports an hss column.  the jack rod has a capacity for it's height (say 2-feet), and the hss has a capacity for it's height (say 20-feet).  it doesn't seem conservative to assume that the lower kl/r for the 2-foot jack rod or the 20-foot hss controls, wouldn't there be some effect based on the total length?
it'd be classified as a stepped column.  there are several engineering journal articles that may be purchased & downloaded for $10 each at aisc's website:
the analysis you propose is predicated on a continuous section.
i suspect that you introduce a pin into the column at the jack / tube.
in order to employ your predictions, you would need to carefully fully brace the joint. or provide a full moment restraint for the tube at the bearing surface of the jack.
otherwise, the system is unstable and it would take very little load before the joint wants to pop out. only with this brace can you safely reach your jack or column capacity based on a maximum kl/r for each.
i fully agree that the connection between the tube and jack must either be braced or designed as "rigid".
we are planning on designing the connection between the two to be as rigid as possible.  the intent is to design a splice between the two elements that will transfer moment.  i will agree, however, that this connection cannot be perfectly rigid, and a reasonalbe factor of saftey will be used to account for the potential flexibility in the connection.  first we are trying to see if how to find the capacity of the column section to see if it will support the intended load.  if it will support the load, then we will concetrate on the needed connections.  
the discussion was intended to be focused on what effect the individual sections will have on the total capacity (kl/r for each component vs. kl/r for the entire system).  i think the aisc journals will help guide us to a solution.
your question about the length (20' or 22'?) of the column is a good one. if you have freedom to select any reasonable size hss column, i suggest that its allowable axial load greatly exceed the applied load for either 20' or 22' length. it is quite possible that you could have an unintended eccentric axial loading condition by having a small misalignment at the jack / column interface.