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31 2.5 FOSM 2.0 QL = 1.15 QD = 1.05 Resistance Factor () COVQL= 0.2 COVQD =0.1 0 QD/QL = 2.5 = 2.33 V= CO 1.5 D = 1.25, L = 1.75 0 .2 0.4 1.0 0.5 0.6 0.5 0.8 COV = 1.00 0.0 0 0.5 1 1.5 2 2.5 3 Bias () Figure 15. Calculated resistance factors as a function of the bias and COV for the chosen load distributions and DD/LL ratio of 2.5. both methods predict the same way (i.e., have the same dis- methods may have practically a similar "actual" FS (and tribution), the method, which predicts more accurately (lower hence economical viability). bias) will result in having a resistance factor lower than the underpredictive method. The judgment of the methods' eco- nomic value ("efficiency") on the basis of the resistance 2.8.3 The Design Methods' Efficiency value is therefore misleading. The same argument can be made regarding the misleading absolute values of the factor The values of the resistance factors alone (or the factors of safety disregarding the bias. The FS values in Table 1 of safety) do not provide a measure for evaluating the effi- seem to be high (and not attractive economically) for the sta- ciency of the design methods, as previously discussed. Such tic analyses compared to the dynamic prediction methods. efficiency can be evaluated through the bias factor, and its Again these values are of limited meaning if the bias of the COV, or the ratio of the resistance factor to the bias factor, method is not considered. For example, if the bias of the sta- i.e., /, as proposed by McVay et al. (2000). Figure 16 illus- tic methods (to be discussed further in Chapter 3, section trates the meaning of the efficiency factor showing that the 3.5.2) is lower than 1 (overprediction), while the bias of the ratio of / is systematically higher for methods which pre- dynamic methods is greater than one (underprediction), the dict more accurately regardless of the bias. The value of the 0.8 FOSM QL = 1.15 QD = 1.05 0.6 COVQL = 0.2 COVQD = 0.1 QD/QL = 2.5 = 2.33 Efficiency (/) D = 1.25 L = 1.75 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 COVR Figure 16. Illustration of the efficiency factor as a measure of the effectiveness of a design method when using resistance factors.

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32 efficiency factor remains constant for all bias combinations ability (COV); alternatively, design methods need to be cho- for a given COV, leading to higher values for methods with a sen based on their COV. lower COV. Using the example given in section 2.8.2, a This measure of efficiency needs to accompany prescribed method with COV = 0.4, = 1.0, and = 0.44 will result in resistance factors in order to avoid a misconception of the / = 0.44; a second method with COV = 0.4, = 1.5, and = existence of a correlation between the economy of a design 0.67 will result in the same / = 0.44. Thus, although one method and high resistance factors when compared to others. method presents a resistance factor of 0.67 and the other of Similarly, such misconceptions exist between the economic 0.44, both methods have identical efficiency and should result value of a method and the lower level of a factor of safety, in identical design; hence they have the same economic value. where a mean factor of safety (defined as FS x bias) repre- The efficiency of a given capacity prediction method can, sents the economic value of the method (the lower the bet- therefore, be improved only through a reduction in its vari- ter), as proposed by Paikowsky et al. (1994).