I have the Eighth edition of the AISC manual and the Chapter 5 Commentary was effective 11/1/1978. Maybe they changed the paragraph number in later editions. Chapter 5 Section 1.8 of the Eighth edition is titled "Stability and Slenderness Ratios". You should look for a paragraph with that title.
Thank you for the additional information. It's clear that there is no single corresponding paragraph in the 2005 edition. The relevant Commentary chapter is now chapter C (chapters are lettered and appendices are numbered), "Stability Analysis and Design," and section C2 within that chapter discusses methods of caclulating required strengths, including "traditional" methods that use the Effective Length Factor K.
I see nothing in that chapter or elsewhere in the current manual that suggests that the WTC towers are any exception of the general rule that K values in braced frames as well as moment frames are normally greater than or equal to 1.0. (see paragraphs C1.3b, C1.3c). There is mention (in the text accompanying the C-C2.3 nomograph) that column ends "rigidly attached to a properly designed
footing" (emphasis added) can be taken to have relatively low values of G, which would lead to relatively lower values of K. However, the above-ground floors in the towers, despite being partially constructed of concrete, were in no way "footings" and in any case the column ends were not (very) rigidly attached to them.
More generally, there is nothing that suggests that the general nature of the horizontal connections between column ends, such as their total mass, their length, the materials they're made of, or whether or not they happen to be used as floors, has any bearing (no pun intended) on the effective value of K for the columns. (Naturally, the structural properties of the horizontal members would affect other aspects of any stability analysis, but they don't figure into the K of the columns.)
I think you need to do an analysis to show that any of the columns in the towers would have performed as pinned connections rather than fixed on both ends. Diagonal bracing is not the only thing that causes a frame to act as braced.
"Fixed at both ends" doesn't imply K < 1.0. Actually, according to AISC, braced-frame systems are analyzed and designed as pin-connected systems, with a K of 1.0. Moment-frame systems, which better describes the WTC towers, generally use K values greater than 1.0:
AISC Commentary C1.3b said:
Moment-frame systems rely primarily upon the flexural stiffness of the connected beams and columns, although the reduction in the stiffness due to shear deformations can be important and should be considered where column bays are short and/or members are deep. Except as noted in Section C2.2a(4), Section C2.2b and Appendix 7, the design of all columns and beam-columns must be based on an effective length, KL, greater than the actual length determined as specified in Section C2.
(emphasis added)
Lest you get the impression that Sections C2.2a(4), C2.2b, and Appendix 7 contain a statement that these rules don't apply if the columns in question happen to be connected to floors (aren't most columns in most buildings connected to floors?), the quote continues:
The Direct Analysis Method in Appendix 7. as well as the provision of Sections C2.2a(4) and C2.2b, provide the means for proportioning columns with K = 1.0.
In other words, those sections cover alternate "direct" analysis methods in which K is not used as a variable; instead the various influences of the physical parameters that figure into K are accounted for separately (generally, in a computer model).
So far, all the information from the AISC manual appears to support Newton's assessment.
Respectfully,
Myriad
ETA: Cross-posted with the last several posts by Newton, Tony, and others. It seems that learning the principles of structural engineering from reference sources can take some time. Who'd'a thought?