AISC LRFD 1.pdf

188 SECOND ORDER EFFECTS [Comm. C1.cases, the values of B 1 will be most accurate if values of K < 1.0 corresponding tothe end boundary conditions are used in calculating P e1 . In lieu of using the equationsabove, C m = 1.0 can be used conservatively for transversely loaded memberswith unrestrained ends and 0.85 for restrained ends.If, as in the case of a derrick boom, a beam-column is subject to transverse (gravity)load and a calculable amount of end moment, the value 0 should include the deflectionbetween supports produced by this moment.Stiffness reduction adjustment due to column inelasticity is permitted.C2. FRAME STABILITYThe stability of structures must be considered from the standpoint of the structure asa whole, including not only the compression members, but also the beams, bracingsystem, and connections. The stability of individual elements must also be provided.Considerable attention has been given in the technical literature to this subject,and various methods of analysis are available to assure stability. The Guide toStability Design Criteria for Metal Structures (Galambos, 1998) considers the stabilityof individual elements, and the effects of individual elements on the stabilityof the structure as a whole.The effective length concept is one method of estimating the interaction effects ofthe total frame on a compression element being considered. This concept uses Kfactors to equate the strength of a framed compression element of length L to anequivalent pin-ended member of length KL subject to axial load only. Other rationalmethods are available for evaluating the stability of frames subject to gravity andside loading and individual compression members subject to axial load andmoments. Although the concept is completely valid for ideal structures, its practicalimplementation involves several assumptions of idealized conditions whichwill be mentioned later.Two conditions, opposite in their effect upon column strength under axial loading,must be considered. If enough axial load is applied to the columns in an unbracedframe dependent entirely on their own bending stiffness for resistance to lateraldeflection of the tops of the columns with respect to their bases (see Figure C-C2.1),the effective length of these columns will exceed the actual length. On the otherhand, if the same frame were braced to resist such lateral movement, the effectivelength would be less than the actual length, due to the restraint (resistance to jointtranslation) provided by the bracing or other lateral support. The ratio K, effectivecolumn length to actual unbraced length, may be greater or less than 1.0.The theoretical K values for six idealized conditions in which joint rotation andtranslation are either fully realized or nonexistent are tabulated in Table C-C2.1.Also shown are suggested design values recommended by the Structural StabilityResearch Council (SSRC) for use when these conditions are approximated in actualdesign. In general, these suggested values are slightly higher than their theoreticalequivalents, since joint fixity is seldom fully realized.If the column base in Case (f) of Table C-C2.1 were truly pinned, K would actuallyexceed 2.0 for a frame such as that pictured in Figure C-C2.1, because the flexibilityof the horizontal member would prevent realization of full fixity at the top of thecolumn. On the other hand, it has been shown (Galambos, 1960) that the restrainingLRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION