## 4 Two Relevant Applications
### Fatigue Load Models for Road Bridges in EN1991-2  
As already mentioned, fatigue load models given in structural codes generally disregard vehicles' interactions. Aiming to substantiate the examples, fatigue load models for road bridges given in EN1991-2 [21] are summarized here. EN1991-2 provides five load models for fatigue verifications of road bridges. Fatigue load model no. 1 (LM1) and fatigue load model no. 2 (LM2) are intended to assess whether fatigue life is unlimited or not. These fatigue load models can be used only when a constant amplitude fatigue limit exists for the examined detail. Fatigue load model no. 3 (LM3) and fatigue load model no. 4 (LM4) are specifically devoted to damage calculations. It must be stressed that if unlimited fatigue life is assessed, fatigue damage is nil and therefore damage calculation using LM3 and LM4 is not only unnecessary, but even irrational. LM1, which can be used without restrictions also accounting very roughly for simultaneity, is extremely simple but very safe-sided, so that its use is limited to very quick preliminary checks. It directly derives from the main load model used for static verifications, where values of vertical loads are simply reduced to frequent ones, multiplying the characteristic tandem axle loads \(Q_{ik}\) by 0.7 and the characteristic weight density of the uniformly distributed loads \(q_{ik}\) by 0.3. The LM3 is a simplified model, constituted by a four-axle symmetrical equivalent fatigue vehicle. The four axles, weighing 120 kN each, are spaced 1.2, 6.0, and 1.2 m, respectively (Figure 22). If simultaneity effects are not relevant, LM3 is accurate enough for steel details and reference lengths \(L\geq 10\) m, while for \(L<10\) m it generally results unsafe-sided. LM2 (Figure 23) and LM4 (Figure 24) are fatigue load models formed by a set of five standardized vehicles, representative of the most common European lorries, characterized by \"frequent\" (LM2) or \"damage equivalent\" (LM4) values of axle loads. As anticipated, the axle typologies of the standardized vehicles are diversified as a function of the dimensions of contact surface of the wheels. Three different axle types, summarized in Figure 25, are considered: \(A\); \(B\); \(C\); depending on the lorry and on the axle position. In Figures 23 and 24, the axle types are indicated in the last column. Figure 23: Fatigue load model 2 (LM2) of EN1991-2—Set of frequentlories (adapted from [21]). Figure 24: Fatigue load model 4 (LM4) of EN1991-2—Set of equivalent lorries (adapted from [21]). Figure 22: Fatigue load model 3 (LM3) of EN1991-2 (adapted from [21]). In LM4 three different reference traffics are considered: Long distance; medium distance; local traffic, depending on the relevance of the concerned route and on the road category. Since the actual strategies governing the optimal management of the commercial lorry fleets favor the use of long and heavy vehicles on long distance traffic, increasingly devoting lighter and quicker vehicles to medium distance and local traffic, the traffic mix becomes more severe as soon as local traffic or medium or long distance traffic is considered, as indicated in Figure 24.  
Finally, fatigue load model no. 5 (LM5), which is the most general one, consists of a representative real traffic sample. LM5 can be directly derived from traffic registrations, obtained using suitable weighing in motion (WIM) devices. Clearly, since the fatigue damages induced by cars or light vehicles are insignificant, LM5 can contain only lotries. As already remarked, LM2, LM4, and even more LM5 allow very precise and refined fatigue assessments, but, when the effects produced by several vehicles traveling simultaneously the bridge cannot be disregarded, they should be duly supplemented to take into account interactions.