## 5 Discussion  
Using fixed sensitivity factors \(\alpha_{\rm E}\) and \(\alpha_{\rm R}\) as \(-0.7\) and 0.8, respectively, according to EN1990, strongly affects the probability of exceedance of the design value and calibration process of the partial factors. In the partial factor method, the partial factors are obtained by the following expression:  
\[\gamma_{Q}=\frac{x_{d}}{x_{c}} \tag{7}\]  
where \(x_{\rm d}\) is the design value (the most probably failure points), and \(x_{\rm c}\) is the characteristic value (in general, an arbitrary value). The design value can be calculated as:  
\[x_{d}=\mu+\beta\times\alpha\times\sigma \tag{8}\]  
It is clear that the sensitivity factor is a critical input for the calculation of the partial factor. It is actually irrelevant which characteristic value one would like to choose to calibrate the load model--indeed, it can be any value--but the partial safety factor has to be calibrated accordingly. Using a safety index to calibrate the load model, and keeping the constant sensitivity factor of 0.7 gives a false impression that this choice indeed ensures a sufficient target safety index, in particular as traffic loading is not the only loading--there is a self-weight as well. Two sets of values of the sensitivity factors are suggested for concrete bridges as a result of this study in Table 3: (a) one for bridges with the longest span between 5 m and 25 m, and (b) the other for bridges with the longest span between 25 m and 80 m. The coefficient of variation for resistance \(\rm COV_{R}\) of 0.10 is chosen; for the dead load and traffic load coefficient of variation, \(\rm COV_{G}\) and \(\rm COV_{Q}\), the value of 0.10 is proposed for this purpose. For bridges with the longest span between 5 m and 25 m, \(\
u\), i.e., the ratio of dead load to total load, an equal to 0.5 has been suggested. For bridges with spans  
Figure 4: Bridge types used (ribbed section (**top left**), box girder (**top right**), slab girder (**bottom left**), precast girder (**bottom right**)). between 25 m and 80 m, v, i.e., the ratio of dead load to total load, an equal to 0.7 has been proposed. The value of sensitivity factors for traffic loads equal to approximately 0.26 for bridges with spans between 5 m and 25 m, and 0.18 for bridges with spans between 25 and 80 m, are much smaller than the values usually used as 0.7, suggested by the Eurocode and [4,5]. In order to illustrate that the Eurocode proposed values for sensitivity factors are not appropriate, the following sample situation has been discussed. The design resistance and design load has been set to 1000, with the ratio of dead load to the sum of dead load and traffic load equal to 0.7. The corresponding characteristic values of resistance, dead load and traffic load can be then calculated as 1150, 519, and 222, respectively, by applying the Eurocode partial safety factor of 1.15 for resistance, and 1.35 for loads. Assuming normal distribution for all three random variables (resistance, dead load, and traffic load), lower 5% fractile for resistance characteristic value, nominal (expected) value for dead load characteristic value, and upper 0.1% for traffic load characteristic value, distributions for each random variable can be computed (two unknown parameters from the set of two equations for each distribution). Coefficient of variations has been assumed as 0.1 for all three variables, resistance, dead load, and traffic load. Once the distributions are determined, sensitivity factors for resistance, dead load, and traffic load are calculated using Equations (2)-(4) as 0.930, 0.350, and 0.115, respectively; using Equation (1), the reliability index is computed as 4.65. The design point, i.e., the most likely failure point, can be calculated as 781.7, which differs significantly from the starting point, \(\mathrm{E_{d}}=\mathrm{R_{d}}=1000\).