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Compression Members and ANSI/AISC 360-05

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I've started working with this spec for this new project because I knew I would run into members that would have slender elements.  And with the increased cost of steel, I figured it would be worth the effort to entertain the idea of slender element analysis in hopes of saving money in steel, as I know I will have members in both bending and compression and I would likely run into an issue of slender element analysis.
 
That being said, I am looking at equation E4-4 in this new spec on page 34, and I ran across something that got me interested.  The term L, in calculating Fe is with respect to torsional buckling along with Kz.  I've read the commentary on Kz, so there is no problem with that.  However, the L term I'm not entirely sure about.  The commentary also states that, at points of bracing, lateral and/or torsional bracing shall be provided.  Does that lateral bracing, in order to act as torsional bracing, have to be in both directions (strong and weak axial directions) in order to act as torsional bracing, or is it just in one direction (x or y)?  It certainly makes a difference when calculating that Fe number.
 
Any clarification would be great for this.  Thanks.
 
Sincerely,
David Maynard, PE
Gillette, Wyoming