AISC LRFD 1.pdf

206Comm. FCHAPTER FBEAMS AND OTHER FLEXURAL MEMBERSF1. DESIGN FOR FLEXURE1. YieldingThe bending strength of a laterally braced compact section is the plastic momentM p . If the shape has a large shape factor (ratio of plastic moment to the moment correspondingto the onset of yielding at the extreme fiber), significant inelastic deformationmay occur at service load if the section is permitted to reach M p at factoredload. The limit of 1.5M y at factored load will control the amount of inelastic deformationfor sections with shape factors greater than 1.5. This provision is notintended to limit the plastic moment of a hybrid section with a web yield stresslower than the flange yield stress. Yielding in the web does not result in significantinelastic deformations. In hybrid sections, M y =F yf S.Lateral-torsional buckling cannot occur if the moment of inertia about the bendingaxis is equal to or less than the moment of inertia out of plane. Thus, for shapes bentabout the minor axis and shapes with I x = I y , such as square or circular shapes, thelimit state of lateral-torsional buckling is not applicable and yielding controls if thesection is compact.2. Lateral-Torsional Buckling2a. Doubly Symmetric Shapes and Channels with L b L rThe basic relationship between nominal moment M n and unbraced length L b isshown in Figure C-F1.1 for a compact section with C b = 1.0. There are four principalzones defined on the basic curve by L pd , L p , and L r . Equation F1-4 defines themaximum unbraced length L p to reach M p with uniform moment. Elastic lateral-torsionalbuckling will occur when the unbraced length is greater than L r givenby Equation F1-6. Equation F1-2 defines the inelastic lateral-torsional buckling asa straight line between the defined limits L p and L r . Buckling strength in the elasticregion L b > L r is given by Equation F1-14 for I-shaped members.For other moment diagrams, the lateral buckling strength is obtained by multiplyingthe basic strength by C b as shown in Figure C-F1.1. The maximum M n , however,is limited to M p . Note that L p given by Equation F1-4 is merely a definition whichhas physical meaning when C b = 1.0. For C b greater than 1.0, larger unbracedlengths are permitted to reach M p as shown by the curve for C b > 1.0. For design, thislength could be calculated by setting Equation F1-2 equal to M p and solving thisequation for L b using the desired C b value.The equationCb = 175 . + 105 . ( M1 / M2) + 03 . ( M1 / M2) 2 ≤23. (C-F1-1)LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION