Civil Engineering March 2022 | Vol 30 No 2

Civil Engineering March 2022 33 It is reasonable to assume that the effect of road surface defects on dynamic amplification will be limited because se- vere defects will cause a road to be closed and maintenance to be performed. 2. Span length and Eigen frequencies Generally, dynamic amplification is larger for shorter spans. An exception to this is when there is frequency matching between the applied load and the first Eigen frequency of the bridge. This may occur at any span length and lead to increased dy- namic amplification, even for longer spans. 3. Bridge type Most studies have focused on I-girder bridges for short to medium span struc- tures. The main parameter influence by bridge type is the ratio of the mass of the bridge to the mass of the crossing vehicles. Heavier decks have more inertia and ex- perience less dynamic amplification than lighter bridges carrying the same traffic. 4. Bridge material and damping Dynamic amplification decreases with an increase in damping. As different mate- rials have different damping properties, it is logical to assume that the dynamic amplification will also be different. As an example, timber bridges have been found to have more damping than steel bridges and hence lower dynamic amplification. This trend is, however, not the case with newer materials like fibre-reinforced polymers, and more research is needed in this area. 5. Vehicle velocity The influence of speed on dynamic amplification is controversial, as results from studies are contradictory. Increased dynamic amplification can occur when the speed of the vehicle is such that the loading frequency matches the first natural frequency of the bridge. Investigations on simply supported and continuous beams have found that the dynamic amplification is proportional to vehicle speed at mid span. There is strong evidence that dynamic amplification changes with acceleration and deceleration. Specifically, deceleration has been shown to increase dynamic amplification due to the change in load distribution between the front and back wheels of a vehicle which could increase vibrations. It is clear that, although speed has an influence on dynamic amplification, it is difficult to predict this relationship due to the large number of variables involved. 6. Vehicle weight It has widely been shown that dynamic amplification reduces with an increase in static vehicle weight. Light vehicles cause the highest dynamic amplification, but this is insignificant as they also cause the smallest static load effects. 7. Number of axles Although some design codes specify dynamic amplification as a function of the number of axles, little evidence exists to support this correlation. Studies found that there is nearly no statistical relationship between number of axles and dynamic amplification. The correlation between number of axles and vehicle weight is poor as vehicles with the same number of axles can vary greatly in weight. The fact that dynamic amplification reduces with an in- crease in vehicle weight therefore does not imply a reduction in dynamic amplification with an increase in the number of axles. 8. Number of vehicles As noted previously, the dynamic amplifi- cation reduces as the static vehicle weight increases. It is thus reasonable to assume that the dynamic amplification for multi- vehicle events will be lower than for single vehicle events. Vehicles travelling next to each other exert much higher dynamic amplification than vehicles that are fol- lowing or staggered. 9. Vehicle suspension type Vehicle suspension can be characterised by axles consisting of springs with certain stiffnesses and dampers with a certain damping coefficient. It has been found that lower suspension stiffness results in lower dynamic amplification and that changes in the damping coefficients have a very small impact. Studies confirm these findings by showing in field tests that high suspension stiffnesses cause high dynamic amplification. 10. Vehicle loading position Due to lateral load distribution in bridge decks, the transverse position of a vehicle induces static load effects in all other girders under positive influence, also inducing dynamic amplification in these girders. It has been found that the dynamic amplification in these girders reduces with an increase in static load. DYNAMIC AMPLIFICATION AT ULTIMATE LIMIT STATE Analytical and experimental studies of dynamic amplification assume that the structures behave elastically. This is the case for serviceability limit states (SLS) and fatigue limit states, but not for ulti- mate limit states (ULS). At ultimate limit state a bridge behaves plastically, and dynamic amplification fac- tors based on elastic theory are no longer valid. Ductile deformations in bending at ultimate limit state act as highly effective dampers and vehicle bridge interaction is therefore completely different at ultimate limit state compared to serviceability limit state. Plastic hinges act as effective energy dissipating mechanisms, and it has been shown that the energy dissipation capacity of the non-linear domain is sufficient to dissipate all the energy associated with dynamic effects. Further to this, increased At ultimate limit state a bridge behaves plastically, and dynamic amplification factors based on elastic theory are no longer valid. Ductile deformations in bending at ultimate limit state act as highly effective dampers and vehicle bridge interaction is therefore completely different at ultimate limit state compared to serviceability limit state. There is strong evidence that dynamic amplification changes with acceleration and deceleration. Specifically, deceleration has been shown to increase dynamic amplification due to the change in load distribution between the front and back wheels of a vehicle which could increase vibrations.