buckling of tapered section

huangyhg

buckling of tapered section
hey,
does anyone have any good reference about how to calculate the critical buckling load of a tapered section?
the section that i am investigating is an underwater spar.  its essentailly a trusss that is diamond shaped (in 3 dimensions) with one central member connecting to 4 adjacent members (cross section).
my description is not very good, but hopefully it makes some sense!
when calcultaing the moment of inertia of the section, where should the cross section be taken?
if anyone has any reference for this please let me know.
thanks!
you could model it in an analysis program such as etabs or sap. some programs provide output using mode shape calculations to calculate the effective length factor for use in design.
the attached shows a numerical method for calculating the buckling load of a column with varying ei.  it is a bit yellowed with age, but so am i.
ba
i don't know what you're doing from your description.
in general, for tapered i-shapes:
the weak-axis radius of gyration won't change appreciably, so just pretend like it's prismatic for weak-axis flexural buckling (column buckling).
the strong-axis is more difficult.  a reasonably well accepted procedure is in the following reference, if you can get it:
lee, g.c., morrell, m.l., and ketter, r.l. (1972) "design of tapered members." welding research council bulletin #173, june 1972.
a newer method is shown in the aisc/mbma tapered member design guide, but i don't know if it's out yet.  it's on page 21 of the draft copy.  assuming pinned ends, the elastic buckling load is computed as
pe = pi^2*ei'/l^2
i' is the moment of inertia of the segment calculated at 0.5l*(ismall/ilarge)^0.0732 from the small end.  don't try to use this if there is end restraint.
now that you have pe, you can calculate the elastic buckling stress and be on your merry way.
indepth's idea will work if you have the advanced version of sap2000--sorry, but etabs won't do this unless i'm mistaken.  
another idea is to use the new direct analysis method in app. 7.  it's ideally suited for problems like this.