# Load Models Representative of Brazilian Actual Traffic in Girder-Type Short-Span Highway Bridges
## 7 Target Values of the Effects Due to Real Traffic  
The steps adopted to obtain the target values of the effects due to real traffic, in the case of free flow, are the following:  
* Fit Weibull PDFs to the tail of the histogram of each static effect [2; 4; 6; 8; 9; 16; 21], for all scenarios in Figure 5, and extrapolate to the corresponding return periods, obtaining their representative values. The Weibull PDF is one of the most widespread distributions in the literature for modeling extreme value events. As well as in other PDFs adopted for traffic simulation, the parameters of these distributions were  
Figure 6: (**a**) Analytical model of the rigid three-axle vehicle (class 3C). (**b**) Axle-structure contact point displacements.  
estimated by the method of moments. The largest extrapolated value among all scenarios is considered as the characteristic static value of each effect [24].
2. Perform the dynamic analysis of the whole loading that have caused the characteristic static effect in the reference traffic scenario (Table 5), in order to obtain the DAF for this configuration. This dynamic amplification is taken conservatively as representative of the effect on the structure. The reason for that lies in the fact that, although dynamic amplifications are greater for lighter vehicles [13; 48; 49], dynamic effect always increases with static effect [50; 51].
3. Obtain the target values of each effect in each structure, to be reproduced by the load model, by multiplying the characteristic static value of the static effect by the corresponding DAF.  
To apply step (b) consistently, for each analyzed effect on each bridge, all vehicles that generated, together, the maximum static effect should be considered in the dynamic analysis. However, up to now, it has been carried out by a simplified procedure, since the analytical-numerical model for the dynamic analysis (Section 6) has been validated experimentally only for class 3C vehicles [25]. Aiming to apply this model for other vehicle configurations, the concept of an equivalent 3C vehicle was devised in which vehicles of other classes are reduced to a 3C truck [27]. Figure 7 shows examples of this reduction. Each axle of the 3C truck may represent a group of axles of the actual vehicle with equivalent properties of mass, stiffness, and damping of the original ones, so that natural frequencies of the fundamental vibration modes of both mechanical systems are similar.  
For the sake of simplification, only a single equivalent vehicle was used and standardized for each class of original vehicle, regardless of their wheelbases and GVW; for this, the values of these two quantities were averaged among all vehicles of each class that generated the greatest static effects (Table 5); the results are shown in Table 6. In the case of simultaneous presence of vehicles on the bridge when the maximum static effect occurs, only the vehicle that generated the most unfavorable effect was considered. In each structure, for each reference effect, the dynamic amplifications are obtained for 2S3-S, 2S3-L, 3S3-L, 3T4, and 3T6 trucks, each of them traveling alone, with speeds ranging from 20 km/h to 100 km/h. For each case, the DAF is taken as the highest value obtained in each analysis. Then, the maximum DAF value is retained for each pair structure-vehicle, regardless of the reference effect considered. Table 7 shows the statistical features of static effects' distribution, obtained by fitting Weibull distributions to the corresponding histograms, as well as the dynamic amplifications and the target values of the effects.  
Figure 7: Some 3C-equivalent trucks. Units: m.