AISC LRFD 1.pdf

174 DESIGN BASIS [Comm. A5.The shaded area may be reduced and thus reliability increased in either of twoways: (1) by moving the mean of ln (R/Q) to the right, or (2) by reducing the spreadof the curve for a given position of the mean relative to the origin. A convenient wayof combining these two approaches is by defining the position of the mean using thestandard deviation of ln (R/Q) as the unit of measure. Thus, the distance from theorigin to the mean is measured as the number of standard deviations of the functionln (R/Q). As shown in Figure C-A5.2, this is stated as timesσ ln( RQ / ) , the standarddeviation of ln (R /Q). The factor therefore is called the “reliability index.”If the actual shape of the distribution of ln (R/Q) were known, and if an acceptablevalue of the probability of reaching the limit state could be agreed upon, one couldestablish a completely probability-based set of design criteria. Unfortunately, thismuch information frequently is not known. The distribution shape of each of themany variables (material, loads, etc.) has an influence on the shape of the distributionof ln (R/Q). Often only the means and the standard deviations of the many variablesinvolved in the makeup of the resistance and the load effect can be estimated.However, this information is enough to build an approximate design criterionwhich is independent of the knowledge of the distribution, by stipulating the followingdesign condition:Fig. C-A5.1. Frequency distribution of load effect Q and resistance R.Fig. C-A5.2. Definition of Reliability Index.LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION