# Bridge Expansion Joint in Road Transition Curve: Effects Assessment on Heavy Vehicles
## 2 Heavy Vehicle-Bridge Interaction: The Expansion Joint Role  
Moving heavy vehicles apply to roads and bridges wheel (dynamic) loads, which are higher than nominal (static) loads. Static loads depend on the total weight of the vehicle and its geometric axle configuration, whereas dynamic wheel forces depend on the road pavement profile, functional characteristics of the vehicle (e.g., geometry, mass and stiffness distribution, tire and suspension type, operative speed) and structural characteristics of the bridge superstructure (i.e., span length, geometry, static scheme, natural frequencies and damping). Unevennesses due to a road BEJ can produce important dynamic load increments: this depends on the interaction between running vehicles and the bridge superstructure, as well as the interactions between structural components and vehicles [9]. Figure 2 shows the dynamic interaction (coupling) between vehicle and bridge [10]. Figure 1: Irregularity between bridge expansion joint (BEJ) and the road in a transition curve. The roughness input to the vehicle is the sum of the initial surface profile of the pavement and the dynamic deflection of the bridge. This input excites the vehicle and results in dynamic tire forces. Finally, these forces are in turn applied to the bridge and cause larger dynamic displacements of the bridge [11]. The largest bridge vibration occurs when the bridge's and vehicle's natural frequencies are similar [12]. It is not clear, however, if large bridge responses are mainly due to excitation of the vehicle caused by the initial roughness profile, or by the dynamic deflection of the bridge. There was little systematic study concerning the conditions when dynamic interaction is important and when the two systems may be regarded as essentially uncoupled. According to [PERSON] [13], bridges with a fundamental natural frequency \(f\cong 2.5\)-4 Hz (maximum span \(L\cong 25\)-40 m) are more susceptible to the dynamic actions of heavy commercial vehicles (equipped with steel leaf suspensions) than bridges with a fundamental frequency lying outside this range. This difference is because the wheel loads of such vehicles have a predominant frequency content in the same range [13]. This effect is known as \"frequency-matching\": it leads to dynamic amplification of the corresponding strong dynamic bridge response, a phenomenon also known as \"quasi-resonance\". The DIVINE (Dynamic Interaction between Vehicles and Infrastructure Experiment) research [14] correlated the dynamic bridge response under traffic to the length-span bridge:  
1. Long-span element of bridges (\(L>100\) m): The type of vehicle suspension is not very significant unless the road profile is poor. Furthermore, the fundamental frequency of bridges is less than that of heavy vehicles, and thus, these bridges tend to attenuate the dynamic components of wheel forces. 2. Medium-span bridges (\(L\cong 30\)-100 m): Frequency-matching with the truck body bounce frequencies occurs in medium-span bridges. The experimental dynamic responses were well within code recommendations for high-quality road profiles. 3. Short to medium-span bridges (\(L\cong 15\)-30 m): Bridges with natural frequencies within the range 4-8 Hz tend not to dynamically couple with vehicles at either body bounce or axle-hop frequencies, respectively characterized by frequency within the range of 1.5-4.0 and 8.0-15.0 Hz [15]. 4. Short-span bridges (\(L\cong 8\)-15 m): \"Quasi-resonance\", but with minimal amplification, occurs between short-span bridges and the axle-hop vibrations of heavy vehicles. The effects of body bounce are also transmitted to short-span bridges with minimal amplification. The dynamic response of short span bridges can be much larger than expected for dynamic effects. The DIVINE research has shown that road profile, bridge natural frequency and bridge damping are important elements to be controlled. Road profile measurement is now routine, and signal processing technologies are relatively straightforward.