Buckling question finding equivalent length and I

[member 392791]

Hello,

I am having trouble understanding why the equivalent length in buckling problems, as well as the moment of inertia, change depending on what plane of buckling you are looking for, and how to calculate the moment of inertia in a particular plane

 

[SteamKing]

Equivalent length in buckling problems is determined by the end conditions of the column under consideration. Most textbooks give a table showing the various combinations of end conditions, along with Le and k-factors to calculate the critical load.

Buckling also takes place about the axis which has the least moment of inertia. If an L section is used to make a column, the nature of the cross-section will cause buckling to occur about an oblique axis. For sections which are symmetrical, like an I-beam, buckling will occur about the coordinate axis which has the least moment of inertia.

The following article gives you a good background in calculating and manipulating moments of inertia:

http://ocw.nthu.edu.tw/ocw/upload/43/763/static_ch9.pdf

Buckling is discussed here:

http://www.steel-insdag.org/TeachingMaterial/Chapter6.pdf