AISC LRFD 1.pdf

Comm. C2.] FRAME STABILITY 193Where the actual conditions differ from the assumptions above, unrealistic K factorsmay result. There are modifications available that may be used with FigureC-C2.2b or Equation C-C2-1 to give buckling loads that better reflect the conditionsin real structures (ASCE Task Committee on Effective Length, 1997 and Chenand Lui, 1987). Some of the modifications are summarized below.Columns loaded into the inelastic range of column behavior can be viewed as havinga tangent modulus E T that is smaller than E. For such columns, E c /E g = E T /E inEquation C-C2-2, which gives smaller G values, and therefore, smaller K factorsthan those based on elastic behavior (assumption 1). It is conservative to base thecolumn design on elastic K factors. For less conservative solutions, inelastic K factorscan be determined by using E for E c in Equation C-C2-2 where = E T /E is astiffness reduction factor (SRF). Yura (1971) and Disque (1973) showed that theSRF could be determined from the ratio of the inelastic column design strength tothe elastic column design strength. Using the column design strengths P n fromEquation E2-2 (inelastic) and E2-3 (elastic) gives(a) For ( Pu / Py)≤ 1 (elastic); = 1.03(b) For ( P / P )u y > 1 3 (inelastic) æ( Pu/ Py)öt=-7.38( Pu/ Py) logç (C-C2-3)è 0.85 ÷øwhere P y is the column squash load, (F y A g ), and P u is the required column strength.P u must not exceed c P y .When a beam connection at the column under consideration is a shear connection(no moment), then that beam cannot be considered in the (EI/L) g term of EquationC-C2-2. Only FR connections can be used directly in the determination of G(assumption 3). PR connections with a documented moment-rotation responsecan be utilized, but the (EI/L) g of each beam must be adjusted to account for the connectionflexibility. ASCE Task Committee on Effective Length (1997) provides adetailed discussion of frame stability with PR connections. PR connections cannotbe considered as rigid (FR) connections when assessing frame stability. Section A2contains additional information on PR connections.A beam stiffness of 6EI/L was used in the development of Equation C-C2-1(assumption 5). For other values of beam stiffness, use m(EI/L) g in determining Gwhere m = (actual girder stiffness coefficient)/6. When the far end of a girder has ashear connection instead of a FR connection, m = 0.5. A general expression for mwhen the inflection point from a lateral load analysis is located anywhere along thegirder span is available (ASCE Task Committee on Effective Length, 1997).Compressive axial load in a girder reduces its stiffness, which will have an adverseeffect on K of the column (see assumption 9). To account for any compressive axialload in a girder, the girder stiffness parameter (EI/L) g in Equation C-C2-2 should bemodified by the factor⎡ Q⎢1−⎣ Q cr⎤⎥⎦LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION(C-C2-4)