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Comm. F1.] DESIGN FOR FLEXURE 207has been used since 1961 to adjust the flexural-torsional buckling equation for variationsin the moment diagram within the unbraced length. This equation is applicableonly to moment diagrams that are straight lines between braced points. Theequation provides a lower bound fit to the solutions developed by Salvadori (1956)which are shown in Figure C-F1.2. Another equationCb =1M06 . − 04 .M12≤ 25 . (C-F1-2)fits the average value theoretical solutions when the beams are bent in reverse curvatureand also provides a reasonable fit to the theory. If the maximum momentFig. C-F1.1. Nominal moment as a function of unbraced length and moment gradient.Fig. C-F1.2. Moment modifier C b for beams.<strong>LRFD</strong> Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION
208 DESIGN FOR FLEXURE [Comm. F1.within the unbraced segment is equal to or larger than the end moment, C b = 1.0 isused.The equations above can be easily misinterpreted and misapplied to moment diagramsthat are not straight within the unbraced segment. Kirby and Nethercot(1979) presented an equation which applies to various shapes of moment diagramswithin the unbraced segment. Their equation has been adjusted slightly to the following12.5MmaxCb=(C-F1-3)2.5Mmax+ 3MA + 4MB + 3MCThis equation gives more accurate solutions for fixed-end beams, and the adjustedequation reduces exactly to Equation C-F1-2 for a straight line moment diagram insingle curvature. The C b equation used in the specification is shown in FigureC-F1.3 for straight line moment diagrams. Other moment diagrams along withexact theoretical solutions in the SSRC Guide (Galambos, 1998) show good comparisonwith the new equation. The absolute value of the three interior quarter-pointmoments plus the maximum moment, regardless of its location are used in the equation.The maximum moment in the unbraced segment is always used for comparisonwith the resistance. The length between braces, not the distance to inflectionpoints, and C b are used in the resistance equation.It is still satisfactory to use the former C b factor, Equation C-F1-1, for straight linemoment diagrams within the unbraced length.The elastic strength of hybrid beams is identical to homogeneous beams. Thestrength advantage of hybrid sections becomes evident only in the inelastic andplastic slenderness ranges.C-F1.3. C b for a straight line moment diagram–prismatic beam.<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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NUMERICAL VALUES 141TABLE 2ItemShap
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NUMERICAL VALUES 143Klr123456789101
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NUMERICAL VALUES 145TABLE 3-50Desig
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NUMERICAL VALUES 147TABLE 4Values o
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NUMERICAL VALUES 149TABLE 5 (cont
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NUMERICAL VALUES 151TABLE 7Values o
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NUMERICAL VALUES 153f vVAwnTABLE 8-
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NUMERICAL VALUES 155f vVAwnTABLE 8-
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Page 194 and 195: NUMERICAL VALUES 161ht wf vVAwnTABL
Page 196 and 197: 163COMMENTARYon the Load and Resist
Page 198 and 199: Comm. A2.] TYPES OF CONSTRUCTION 16
Page 200 and 201: Comm. A3.] MATERIAL 167and Chen, 19
Page 202 and 203: Comm. A3.] MATERIAL 169than the ant
Page 204 and 205: Comm. A4.] LOADS AND LOAD COMBINATI
Page 206 and 207: Comm. A5.] DESIGN BASIS 173where =
Page 208 and 209: Comm. A5.] DESIGN BASIS 175( )bsln(
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
Page 218 and 219: Comm. C1.] SECOND ORDER EFFECTS 185
Page 220 and 221: Comm. C1.] SECOND ORDER EFFECTS 187
Page 222 and 223: Comm. C2.] FRAME STABILITY 189Buckl
Page 224 and 225: Comm. C2.] FRAME STABILITY 191Notes
Page 226 and 227: Comm. C2.] FRAME STABILITY 193Where
Page 228 and 229: Comm. C3.] STABILITY BRACING 195age
Page 230 and 231: Comm. C3.] STABILITY BRACING 197pla
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Page 238 and 239: Comm. E4.] BUILT-UP MEMBERS 205TABL
Page 242 and 243: Comm. F1.] DESIGN FOR FLEXURE 2092b
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Page 248 and 249: Comm. I2.] COMPRESSION MEMBERS 215d
Page 250 and 251: Comm. I3.] FLEXURAL MEMBERS 217may
Page 252 and 253: Comm. I3.] FLEXURAL MEMBERS 219The
Page 254 and 255: Comm. I3.] FLEXURAL MEMBERS 221wher
Page 256 and 257: Comm. I3.] FLEXURAL MEMBERS 223proc
Page 258 and 259: Comm. I4.] COMBINED COMPRESSION AND
Page 260 and 261: Comm. I5.] SHEAR CONNECTORS 227tal
Page 262 and 263: 229Comm. JCHAPTER JCONNECTIONS, JOI
Page 264 and 265: Comm. J1.] GENERAL PROVISIONS 231 P
Page 266 and 267: Comm. J2.] WELDS 2332b. Limitations
Page 268 and 269: Comm. J2.] WELDS 235When longitudin
Page 270 and 271: Comm. J2.] WELDS 237due to cyclic f
Page 272 and 273: Comm. J2.] WELDS 239(b) Plane 2-2,
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Page 288 and 289: 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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