The column equations in Section E3

The column equations in Section E3 are based on a conversion of research data into strength equations (Ziemian, 2010; Tide, 1985, 2001). These equations are the same as those that have been used since the 2005 AISC Specification for Structural Steel Buildings (AISC, 2005) and are essentially the same as those created for the initial LRFD Specification (AISC, 1986). The resistance factor, , was increased from 0.85 to 0.90 in the 2005 AISC Specification, recognizing substantial numbers of addi- tional column strength analyses and test results, combined with the changes in industry practice that had taken place since the original calibrations were performed in the 1970s and 1980s.In the original research on the probability-based strength of steel columns (Bjorhovde, 1972, 1978, 1988), three column curves were recommended. The three column curves were the approximate means of bands of strength curves for columns of similar manufacture, based on extensive analyses and confirmed by full-scale tests (Bjorhovde, 1972). For example, hot-formed and cold-formed heat treated HSS columns fell into the data band of highest strength [SSRC Column Category 1P (Bjorhovde, 1972, 1988; Bjorhovde and Birkemoe, 1979; Ziemian, 2010)], while welded built-up wide-flange columns made from universal mill plates were included in the data band of lowest strength (SSRC Column Category 3P). The largest group of data clustered around SSRC Column Category 2P. Had the original LRFD Specification opted for using all three column curves for the respective column cate- gories, probabilistic analysis would have resulted in a resistance factor   0.90 or even slightly higher (Galambos, 1983; Bjorhovde, 1988; Ziemian, 2010). However, it was decided to use only one column curve, SSRC Column Category 2P, for all col- umn types. This resulted in a larger data spread and thus a larger coefficient of variation, and so a resistance factor   0.85 was adopted for the column equations to achieve a level of reliability comparable to that of beams (AISC, 1986).Since then, a number of changes in industry practice have taken place: (a) welded built-up shapes are no longer manufactured from universal mill plates; (b) the most commonly used structural steel is now ASTM A992/A992M, with a specified mini- mum yield stress of 50 ksi (345 MPa); and (c) changes in steelmaking practice have resulted in materials of higher quality and much better defined properties. The level and variability of the yield stress thus have led to a reduced coefficient of variation for the relevant material properties (Bartlett et al., 2003)