AISC LRFD 1.pdf

Comm. App. F3.] WEB-TAPERED MEMBERS 269matic members, and r ox and r oy are the radii of gyration about the x and the y axes,respectively, taken at the smaller end of the tapered member.For stepped columns or columns with other than a single web taper, the elastic criticalstress is determined by analysis or from data in reference texts or researchreports (Chapters 11 and 13 in Timoshenko and Gere (1961), Bleich (1952), andKitipornchai and Trahair (1980)), and then the same procedure of using eff is utilizedin calculating the factored resistance.This same approach is recommended for open section built-up columns (columnswith perforated cover plates, lacing, and battens) where the elastic critical bucklingstress determination must include a reduction for the effect of shear. Methods forcalculating the elastic buckling strength of such columns are given in Chapter 12 ofthe SSRC Guide (Galambos, 1998) and in Timoshenko and Gere (1961) and Bleich(1952).3. Design Compressive StrengthThe approach in formulating F a of tapered columns is based on the concept that thecritical stress for an axially loaded tapered column is equal to that of a prismatic columnof different length, but of the same cross section as the smaller end of thetapered column. This has resulted in an equivalent effective length factor K for atapered member subjected to axial compression (Lee, Morrell, and Ketter, 1972).This factor, which is used to determine the value of S in Equations A-F3-2 and c inEquation E2-3, can be determined accurately for a symmetrical rectangular rigidframe comprised of prismatic beams and tapered columns.With modifying assumptions, such a frame can be used as a mathematical model todetermine with sufficient accuracy the influence of the stiffness (I/b) g of beamsand rafters which afford restraint at the ends of a tapered column in other cases suchas those shown in Figure C-A-F3.3. From Equations A-F3-2 and E2-3, the criticalload P cr can be expressed as 2 EI o /(K l) 2 . The value of K can be obtained by interpolation,using the appropriate chart from Lee et al. (1972) and restraint modifiers G Tand G B . In each of these modifiers the tapered column, treated as a prismatic memberhaving a moment of inertia I o , computed at the smaller end, and its actual lengthFig. C-A-F3.3. Restraint modifiers for tapered columns.LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION