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Comm. C1.] SECOND ORDER EFFECTS 187TABLE C-C1.1Amplification Factors and C mCase C m0 1.0Pu0.4 1− 04 .Pe1Pu0.4 1− 04 .Pe1Pu0.2 1− 0.2Pe1Pu0.3 1− 0.3Pe1Pu0.2 1− 0.2Pe1Galambos (1961) it was pointed out that Equation C1-3 could be used for in-planesecond order moments if the 0.4 limit was eliminated. Unfortunately, Austin (1961)was misinterpreted and a lateral-torsional buckling solution was used for anin-plane second-order analysis. This oversight has now been corrected.For beam columns with transverse loadings, the second-order moment can beapproximated by using the following equationC = + ψ P / Pm 1 u e1for simply supported memberswhereψ = π2δo EI1MoL− 2 o = maximum deflection due to transverse loading, in. (mm)M o = maximum factored design moment between supports due to transverseloading, kip-in. (N-mm)For restrained ends, some limiting cases are given in Table C-C1.1 together withtwo cases of simply supported beam-columns (Iwankiw, 1984). These values of C mare always used with the maximum moment in the member. For the restrained-end<strong>LRFD</strong> Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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 restraining<strong>LRFD</strong> Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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LOAD AND RESISTANCEFACTOR DESIGNSPE
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iiCopyright © 2000byAmerican Insti
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vTABLE OF CONTENTSSYMBOLS . . . . .
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TABLE OF CONTENTSviiSPECIFICATION (
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TABLE OF CONTENTSixSPECIFICATION (C
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TABLE OF CONTENTSxiCOMMENTARY (Cont
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SYMBOLSxviistrength (for those stee
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SYMBOLSxixS eff Effective section m
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SYMBOLSxxit s Web stiffener thickne
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xxiiiGLOSSARYAlignment chart for co
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GLOSSARYxxvEffective moment of iner
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GLOSSARYxxviiLateral bracing member
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GLOSSARYxxixPost-buckling strength.
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GLOSSARYxxxiStrain-hardening strain
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1CHAPTER AGENERAL PROVISIONSA1. SCO
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Sect. A3.] MATERIAL 3Cold-Formed We
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Sect. A3.] MATERIAL 5ASTM A449 bolt
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Sect. A6.] REFERENCED CODES AND STA
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Sect. A7.] DESIGN DOCUMENTS 9tion A
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Sect. B4.] STABILITY 11(a) When the
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Sect. B10.] PROPORTIONS OF BEAMS AN
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Sect. B10.] PROPORTIONS OF BEAMS AN
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17Chap. CCHAPTER CFRAMES AND OTHER
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Sect. C3.] STABILITY BRACING 19all
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Sect. C3.] STABILITY BRACING 214. B
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Sect. C3.] STABILITY BRACING 231.0;
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Sect. D3.] PIN-CONNECTED MEMBERS AN
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27Chap. ECHAPTER ECOLUMNS AND OTHER
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Sect. E4.] BUILT-UP MEMBERS 29(a) F
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31Chap. FCHAPTER FBEAMS AND OTHER F
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Sect. F1.] DESIGN FOR FLEXURE 33Lp=
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Sect. F2.] DESIGN FOR SHEAR 35Lpd
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37Chap. GCHAPTER GPLATE GIRDERSI-sh
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Sect. H3.] ALTERNATIVE INTERACTION
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Sect. I2.] COMPRESSION MEMBERS 41ti
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Sect. I3.] FLEXURAL MEMBERS 434. Lo
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Sect. I3.] FLEXURAL MEMBERS 45welde
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Sect. I5.] SHEAR CONNECTORS 47A c =
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49Chap. JCHAPTER JCONNECTIONS, JOIN
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Sect. J1.] GENERAL PROVISIONS 518.
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Sect. J2.] WELDS 53Welding ProcessT
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Sect. J2.] WELDS 55For end-loaded f
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Sect. J2.] WELDS 57Types of Weld an
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Sect. J3.] BOLTS AND THREADED PARTS
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Sect. J4.] DESIGN RUPTURE STRENGTH
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Sect. J8.] BEARING STRENGTH 69J6. F
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71Chap. KCHAPTER KCONCENTRATED FORC
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Sect. K1.] FLANGES AND WEBS WITH CO
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For P u 0.4P yR v = 0.60F y d c t
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Sect. K3.] DESIGN FOR CYCLIC LOADIN
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79Chap. LCHAPTER LSERVICEABILITY DE
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81Chap. MCHAPTER MFABRICATION, EREC
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Sect. M4.] ERECTION 83(2) Bottom su
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Sect. M5.] QUALITY CONTROL 85The fa
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Sect. N3.] EVALUATION BY STRUCTURAL
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89App. BAPPENDIX BDESIGN REQUIREMEN
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App. B5.] LOCAL BUCKLING 914kc=h/tw
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App. B5.] LOCAL BUCKLING 93é0.877
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App. E3.] DESIGN COMPRESSIVE STRENG
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App. F1.] DESIGN FOR FLEXURE 97For
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App. F1.] DESIGN FOR FLEXURE 99TABL
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App. F1.] DESIGN FOR FLEXURE 101Cri
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App. F3.] WEB-TAPERED MEMBERS 103j
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App. F3.] WEB-TAPERED MEMBERS 105Fw
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107App. GAPPENDIX GPLATE GIRDERSThi
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App. G3.] DESIGN SHEAR STRENGTH 109
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App. G5.] FLEXURE-SHEAR INTERACTION
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App. H3.] ALTERNATIVE INTERACTION E
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115App. JAPPENDIX JCONNECTIONS, JOI
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App. J3.] BOLTS AND THREADED PARTS
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App. K2.] PONDING 119æçMetric:lC
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App. K3.] DESIGN FOR CYCLIC LOADING
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Page 170 and 171: App. K3.] DESIGN FOR CYCLIC LOADING
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Page 174 and 175: NUMERICAL VALUES 141TABLE 2ItemShap
Page 176 and 177: NUMERICAL VALUES 143Klr123456789101
Page 178 and 179: NUMERICAL VALUES 145TABLE 3-50Desig
Page 180 and 181: NUMERICAL VALUES 147TABLE 4Values o
Page 182 and 183: NUMERICAL VALUES 149TABLE 5 (cont
Page 184 and 185: NUMERICAL VALUES 151TABLE 7Values o
Page 186 and 187: NUMERICAL VALUES 153f vVAwnTABLE 8-
Page 190 and 191: NUMERICAL VALUES 157hf vVAwnTABLE 9
Page 194 and 195: NUMERICAL VALUES 161ht wf vVAwnTABL
Page 196 and 197: 163COMMENTARYon the Load and Resist
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Page 200 and 201: Comm. A3.] MATERIAL 167and Chen, 19
Page 202 and 203: Comm. A3.] MATERIAL 169than the ant
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Page 206 and 207: Comm. A5.] DESIGN BASIS 173where =
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Page 210 and 211: 177Comm. BCHAPTER BDESIGN REQUIREME
Page 212 and 213: Comm. B5.] LOCAL BUCKLING 179(c) Al
Page 214 and 215: Comm. B5.] LOCAL BUCKLING 181load.
Page 216 and 217: Comm. B7.] LIMITING SLENDERNESS RAT
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Page 222 and 223: Comm. C2.] FRAME STABILITY 189Buckl
Page 224 and 225: Comm. C2.] FRAME STABILITY 191Notes
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Page 228 and 229: Comm. C3.] STABILITY BRACING 195age
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Page 240 and 241: Comm. F1.] DESIGN FOR FLEXURE 207ha
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Comm. J2.] WELDS 237due to cyclic f
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Comm. J2.] WELDS 239(b) Plane 2-2,
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Comm. J3.] BOLTS AND THREADED PARTS
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Comm. J4.] DESIGN RUPTURE STRENGTH
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249Comm. KCHAPTER KCONCENTRATED FOR
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Comm. K1.] FLANGES AND WEBS WITH CO
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Comm. K1.] FLANGES AND WEBS WITH CO
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Comm. K2.] PONDING 255Even on the b
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257Comm. LCHAPTER LSERVICEABILITY D
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Comm. L5.] CORROSION 259orthotropic
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Comm. M4.] ERECTION 261It is sugges
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Comm. N4.] EVALUATION BY LOAD TESTS
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Comm. N5.] EVALUATION REPORT 265N5.
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267Comm. A-EAPPENDIX ECOLUMNS AND O
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Comm. App. F3.] WEB-TAPERED MEMBERS
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271Comm. A-GAPPENDIX GPLATE GIRDERS
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273Comm. A-KAPPENDIX JCONNECTIONS,
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Comm. J2.] WELDS 275found to be con
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Comm. K3.] DESIGN FOR CYCLIC LOADIN
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279ReferencesAckroyd, M. H., and Ge
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REFERENCES 281Bjorhovde, R. (1972),
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REFERENCES 283Fielding, D. J., and
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REFERENCES 285Johnson, D. L. (1985)
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REFERENCES 287Ollgaard, J. G., Slut
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REFERENCES 289Zhou, S. P., and Chen
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SUPPLEMENTARY BIBLIOGRAPHY 291Kotec
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Metric Conversion Factors for Commo
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