AISC LRFD 1.pdf

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Comm. I3.] FLEXURAL MEMBERS 219The nominal plastic moment resistance of a composite section in positive bendingis given by the following equation and Figure C-I3.1:M n = C(d 1 + d 2 ) + P y (d 3 d 2 )(C-I3-5)whereP y = tensile strength of the steel section; for a non-hybrid steel section,P y = A s F y ,kips (N)d 1 = distance from the centroid of the compression force C in concrete to the topof the steel section, in. (mm)d 2 = distance from the centroid of the compression force in the steel section to thetop of the steel section, in. (mm). For the case of no compression in the steelsection d 2 = 0.d 3 = distance from P y to the top of the steel section, in. (mm)Equation C-I3-5 is generally applicable including both non-hybrid and hybrid steelsections symmetrical about one or two axes.Approximate Elastic Properties of Partially Composite Beams. Elastic calculationsfor stress and deflection of partially composite beams should include the effects ofslip.The effective moment of inertia I eff for a partially composite beam is approximatedby( / )( )I = I + SQ C I -Ieff s n f tr s(C-I3-6)whereI s = moment of inertia for the structural steel section, in. 4 (mm 4 )I tr = moment of inertia for the fully composite uncracked transformed section,in. 4 (mm 4 )Q n = strength of shear connectors between the point of maximum positivemoment and the point of zero moment to either side, kips (N)C f = compression force in concrete slab for fully composite beam; smaller ofEquations C-I3-1 and C-I3-2, kips (N)The effective section modulus S eff , referred to the tension flange of the steel sectionfor a partially composite beam, is approximated byFig. C-I3.1. Plastic stress distribution for positive moment in composite beams.<strong>LRFD</strong> Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION
220 FLEXURAL MEMBERS [Comm. I3.( / )( )S = S + SQ C S -Seff s n f tr s(C-I3-7)whereS s = section modulus for the structural steel section, referred to the tensionflange, in. 3 (mm 3 )S tr = section modulus for the fully composite uncracked transformed section,referred to the tension flange of the steel section, in. 3 (mm 3 )Equations C-I3-6 and C-I3-7 should not be used for ratios Q n /C f less than 0.25.This restriction is to prevent excessive slip, as well as substantial loss in beam stiffness.Studies indicate that Equations C-I3-6 and C-I3-7 adequately reflect thereduction in beam stiffness and strength, respectively, when fewer connectors areused than required for full composite action (Grant, Fisher, and Slutter, 1977).It is not practical to make accurate deflection calculations of composite flexuralsections in the design office. Careful comparisons to short-term deflection testsindicate that the effective moment of inertia, I eff , is 15 to 30 percent lower than thatcalculated based on linear elastic theory. Therefore, for realistic deflection calculations,I eff should be taken as 0.80 I eff or 0.75 I eff . As an alternative, it has been shownthat one may use lower bound moment of inertia, I lb , as defined below:I = I + A ( Y - d ) + ( S Q / F )(2 d + d -Y)2 2lb x s ENA 3 n y 3 1 ENA(C-I3-8)whered 1 = distance from the centroid of the longitudinal slab reinforcement to the topof the steel section, in. (mm)d 3 = distance from P yc to the top of the steel section, in. (mm)I lb = lower bound moment of inertia, in. 3 (mm 3 )Y ENA = [A 3 d 3 + (Q n /F y ) (2d 3 + d 1 )/(A s + (Q n /F y )]Calculations for long-term deformations due to creep and shrinkage may also becarried out. Because the basic properties of the concrete are not known to thedesigner, simplified models such as those proposed by Viest, Fountain, and Singleton(1958), Branson (1964), Chien and Ritchie (1984), and Viest, Colaco, Furlong,Griffis, Leon, and Wyllie (1997) can be used.Negative Flexural Design Strength. The flexural strength in the negative momentregion is the strength of the steel beam alone or the plastic strength of the compositesection made up of the longitudinal slab reinforcement and the steel section.Plastic Stress Distribution for Negative Moment. When an adequately braced compactsteel section and adequately developed longitudinal reinforcing bars act compositelyin the negative moment region, the nominal flexural strength is determinedfrom the plastic stress distributions as shown in Figure C-I3.2. The tensile force T inthe reinforcing bars is the smaller of:T = A r F yr(C-I3-9)T =Σ Q n(C-I3-10)<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 157hf vVAwnTABLE 9
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NUMERICAL VALUES 161ht wf vVAwnTABL
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163COMMENTARYon the Load and Resist
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Comm. A2.] TYPES OF CONSTRUCTION 16
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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 =
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
Page 232 and 233: Comm. C3.] STABILITY BRACING 199The
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Page 236 and 237: 203Comm. ECHAPTER ECOLUMNS AND OTHE
Page 238 and 239: Comm. E4.] BUILT-UP MEMBERS 205TABL
Page 240 and 241: Comm. F1.] DESIGN FOR FLEXURE 207ha
Page 242 and 243: Comm. F1.] DESIGN FOR FLEXURE 2092b
Page 244 and 245: Comm. F4.] BEAMS AND GIRDERS WITH W
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Page 248 and 249: Comm. I2.] COMPRESSION MEMBERS 215d
Page 250 and 251: Comm. I3.] FLEXURAL MEMBERS 217may
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,
Page 274 and 275: Comm. J3.] BOLTS AND THREADED PARTS
Page 280 and 281: Comm. J4.] DESIGN RUPTURE STRENGTH
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Page 284 and 285: Comm. K1.] FLANGES AND WEBS WITH CO
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Page 288 and 289: Comm. K2.] PONDING 255Even on the b
Page 290 and 291: 257Comm. LCHAPTER LSERVICEABILITY D
Page 292 and 293: Comm. L5.] CORROSION 259orthotropic
Page 294 and 295: Comm. M4.] ERECTION 261It is sugges
Page 296 and 297: Comm. N4.] EVALUATION BY LOAD TESTS
Page 298 and 299: Comm. N5.] EVALUATION REPORT 265N5.
Page 300 and 301: 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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