C-E1E1 General provisions

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, 2005b) and are essentially the same as those created for the initial AISC LRFD Specification (AISC, 1986). The resistance factor, $\phi$, was increased from 0.85 to 0.90 in the 2005 AISC Specification, recognizing substantial numbers of additional 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 categories, probabilistic analysis would have resulted in a resistance factor, $\phi=0.90$ 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 column types. This resulted in a larger data spread and a larger coefficient of variation; therefore, a resistance factor, $\phi=0.85$, was adopted for the column equations to achieve a level of reliability comparable to that of beams (AISC, 1986). Because the selected column strength curve was based on tests of actual columns, the out-of-straightness tolerances permitted in the applicable material standards were met. If those tolerances are exceeded, appropriate strength reductions must be made. 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 minimum 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).

An examination of the SSRC Column Curve Selection Table (Bjorhovde, 1988; Ziemian, 2010) shows that the SSRC 3P Column Curve Category is no longer needed. It is now possible to use only the statistical data for SSRC Column Category 2P for the probabilistic determination of the reliability of columns. The curves in Figures C-E1.1 and C-E1.2 show the variation of the reliability index, $\beta$, with the live-to-dead load ratio, $L / D$, in the range of 1 to 5 for LRFD with $\phi=0.90$ and ASD with $\Omega=1.67$, respectively, for $F_{y}=50 \mathrm{ksi}(345 \mathrm{MPa})$. The reliability index does not fall below $\beta=2.6$. This is comparable to the reliability of beams.

For this edition of the Specification, the results of the column strength curves have been changed from $F_{c r}$ to $F_{n}$. Previous editions of this Specification have not been consistent with the use of $F_{c r}$ and $F_{e}$ across Chapters E and F. Sometimes $F_{c r}$ was the result of applying a strength curve, such as what was common here in Chapter E with equations, such as Equation E3-2. Sometimes $F_{c r}$ was actually the elastic buckling stress, as is still common in Chapter F. Thus, to establish a clear designation for output from a strength curve in this chapter, $F_{c r}$ is replaced by $F_{n}$.