AISC LRFD 1.pdf

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)LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION