Short column buckling theory

[charliealphabravo]

My Canadian colleague is taking me to task for not being familiar with Johnston column buckling theory. After some poking around it looks like Johnston developed a tangent modulus theory to describe the inelastic buckling of columns. I also see a single reference to his name in my 1000 page university text. It's not something that I see very often but I think AISC uses a less conservative method of reduced modulus. Does anyone know any background on this and why one is used over the other when you are outside the elastic/Euler range?

Also just as a refresher, what are some design scenarios where inelastic column buckling modes are common?

TIA

 

[Hokie93]

Is your colleague speaking of Bruce G. Johnston? He helped to form the Column Research Council (CRC), the precursor to today's Structural Stability Research Council (SSRC). In that capacity, his fingerprints were all over AISC column equations from the 1940's to 1960's. I don't believe there is a particular equation attributed to Johnston (e.g., the "Johnston equation/theory") but, again, he played a significant role in the development of the CRC column curves that formed the basis for the AISC allowable stress column design requirements. Mr. Johnston also served as editor of "Design Criteria for Metal Compression Members", the predecessor to the current "Guide to Stability Design Criteria for Metal Structures", published by SSRC and now in its sixth edition.

 

[BAretired]

Short columns don't buckle, so the thread title is misleading. Long columns buckle elastically using the Euler theory. Short columns fail be crushing of the material. Intermediate columns fail by inelastic buckling. If you are using the Canadian code, this is taken into account by the formulas given in CSA S16-01.

This article sheds some light on the subject:

http://www.efunda.com/formulae/solid_mechanics/columns/inelastic.cfm

BA

 

[KootK]

Also just as a refresher, what are some design scenarios where inelastic column buckling modes are common?

Almost all design scenarios actually. Using BA's definitions, which are the right ones, it's pretty rare to have either long or short columns. A short column suggests inefficiency; a long column suggests a high slenderness ratio and perhaps madness.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[BAretired]

In the Canadian code, Unit Factored Compressive Resistances Cr/A have been calculated and listed for KL/r values from 1 to 200 which includes the entire gamut of short, intermediate and slender columns, all of which are permitted under CSA S16-01. I agree that columns near both ends of the scale are not common, but they do occasionally occur.

BA

 

[JoshPlumSE]

Well, I understood what he meant by short column buckling. Columns that are too short to buckle via euler buckling and which instead buckle via inelastic buckling.

Inelastic buckling is probably the most common scenario for steel buildings. If you look at AISC 14th edition, equation E3-3 is based on Euler buckling. But, equation E3-2 is based on inelastic buckling.