# Impact of Road Traffic Tendency in Europe on Fatigue Assessment of Bridges
## 4 Case Studies
### Outcomes of the Analysis and Discussion
* Fatigue load models are particularly on the safe side when \(L\) is around 100 m. In that area, the fatigue assessment is certainly governed by the set of \"equivalent\" lorries given in LM4, but also interactions between consecutive vehicles traveling simultaneously the lane can be significant. The hypothesis that two consecutive lorries are both belonging to the standardized set of LM4 is thus evidently on the safe side, because the probability that the weights of consecutive lorries are regularly close to the equivalent values, which are in some cases outside the legal limits, is small. Figure 11: Equivalence factor \(k_{eq}-L\) for bending moment at midspan of simply supported beams (case study no. 1—total lorry flow: \(5\times 10^{6}\) lorries): (**a**) subcase 1—\(S-N\) curves as per Figure 7a,b; (**b**) subcase 2—\(S-N\) curves as per Figure 7c,d. * In any case, fatigue load models LM2 and LM4 of EN1991-2 generally reproduce very satisfactorily the fatigue effects induced by Auxerre traffic, so confirming the validity of pre-normative studies and the substantially accuracy of Eurocode fatigue models. * As the total lorry flow decreases, \(k_{eq}\) increases and fatigue load models EN1991-2 tend to be constantly on the safe side (Figure 11). * The \(k_{eq}-L\) curves associated with \(S-N\) curves as per subcase 1 are generally below \(k_{eq}-L\) curves associated with \(S-N\) curves as per subcase 2, but the differences become practically insignificant when \(L\) is high, since for large value of \(L\) the fatigue assessments depend on fatigue damage. * Referring to Moerdijk and Igualada traffics and high global flow, the \(k_{eq}-L\) curves associated with subcase 1 are over the \(k_{eq}-L\) curves associated with subcase 2. In fact, contrary to what happens considering Auxerre traffic, in that field the minimum detail categories \(\Delta\sigma_{C,\min}\) (Equation (8)) required by Moerdijk and Igualada traffics basically depend on the equivalent stress ranges \(\Delta\sigma_{C,\alpha\eta}\), rather than on \(\Delta\sigma_{C,D}\). * In comparison with Igualada fatigue effects, those evaluated using EN1991-2 fatigue load models are always sensibly on the safe side. * Moerdijk traffic is constantly less demanding than the Auxerre traffic, except for high global traffic flow in case study 2, subcase 1 (Figure 9a) when \(L\approx 15\) m, when it results in \(k_{eq}\approx 1.03\); Nonetheless, for \(L\geq 75\) m, \(k_{eq}\) factors associated to Moerdijk traffic substantially results \(k_{eq}<0.85\); moreover \(k_{eq}\) tends to slightly reduce as the total flow decreases. * Considering high flow rate and \(S-N\) curves as per subcase 1: \[\begin{array}{ll}\odot&\text{in case study 1 (Figure 8a) Moerdijk traffic is more demanding than Igualada traffic if $L>15$m};\\ \odot&\text{in case study 2 (Figure 9a), Moerdijk traffic is more demanding than Igualada traffic in the interval \(15\) m \(<L<50\) m; \(\odot\) in case study 3, (Figure 10a) Moerdijk traffic is more demanding than Igualada traffic. * Considering high global traffic flow and \(S-N\) curves as per subcase 2, Moerdijk traffic curves are substantially below the Igualada traffic curve: in the whole considered range in case study 2 (Figure 9b), and when \(L<60\) m in case studies 1 (Figures 8b and 10b). * Considering low global flow, if \(L<100\) m, Moerdijk traffic composition is always less damaging than the Igualada traffic composition (Figure 11a,b). * It can be remarked that, for a high value of \(L\), Moerdijk traffic looks generally more demanding than Igualada traffic in all examined cases. * The differences between Moerdijk and Igualada traffics just pointed out can be rationally explained recalling the previous discussion about axle loads and total lorry weight distributions (see Section 2.4).