Simply supported bridges occupy the majority of bridges. Compared with the flexible large span bridges, Dynamic Amplification Factor (DAF) of them is relatively large and attracts lots of studies. However, most of these studies are focused on the simplified condition that a single vehicle passes through a single span bridge. In general, the bridge bears complex traffic flow rather than a single vehicle. The vehicle type and dynamic loads on the bridge are thus dispersed. It is necessary to explore the multi-vehicle effects on the DAF caused by the complex traffic flow. Also, adjacent spans of a multi-span simply supported beam bridge may have continuous dynamic effects on the vehicles. In this regard, the DAF of a simply supported bridge considering the multi-vehicle and multi-span effects are explored numerically based on the coupling dynamic analysis of traffic flow and bridge, which can also consider the acceleration and deceleration of the vehicles. Cellular Automata (CA) method is used to simulate the traffic flow. It is found that the worse the driving condition of the road roughness, the greater the DAF. When road roughness is Class C, the DAF exceeds the values of American and Chinese codes. Under the action of traffic flow, DAF of the first span of the multi-span simply supported beam is larger than that of the span under the single vehicle. Only considering the effect of a single vehicle may underestimate the dynamic impact on the bridge. Sparse traffic flow has a larger DAF than moderate traffic flow and dense traffic flow in the statistic meaning of the multi-span, because the driving speed of sparse traffic flow is closer to the resonant speed of the bridge and the vibration disharmony of multi-vehicles is smaller. The greater the deceleration of the traffic, the greater the dynamic impact on the bridge.

Among large-span bridges, arch bridges have relatively high stiffness, which may lead to large dynamic amplification factors (DAFs). The DAFs suggested by current codes mostly originate from common simply supported beam bridges. Previous DAF studies on dynamic vehicle–bridge solutions for arch bridges have mainly focused on one or two side-by-side vehicles. However, complex traffic flows with randomness rather than one or two vehicles act on bridges. DAFs that consider the effects of random traffic flows have not previously been reported. In this study, a random traffic–bridge vibration solution was established to explore the DAFs of arch bridge components. The randomness of the traffic parameters and road roughness was explored. The randomness of the external excitation, including traffic flow and road roughness, resulted in random dynamic responses and DAFs of the arch bridge components. Normal distributions could be used to fit the DAF distributions of each arch bridge component under random vehicle spacing, weight, speed, and road roughness. Under random traffic parameters, the coefficients of variation of the DAFs exceeded the 5% accepted level. The shortest suspenders were more sensitive to the randomness of the traffic flow parameters. Both the mean and coefficient of variation of the DAFs increased with worsening of the road conditions. The influence of the randomness of the road roughness on the DAFs of arch bridges must be considered, particularly for the shortest suspender. The 95% upper confidence limits of the DAFs for all components may be greater than the suggested values in the code.