If a bridge is subjected to a blast load when there is vehicle traffic, not only its own safety is threatened, but it can also lead to damage to vehicles. In addition, the coupling of a vehicle load and an explosion load may further aggravate the impact of an explosion. To understand the coupling relationship between the two kinds of loads on a bridge, a static load was applied on the bridge using the impact coefficient while a blast load was applied on the outside of the bridge. A numerical simulation was also used to further study the coupling effect of the vehicle load and the explosion load. The results showed that the vehicle load could effectively limit the vertical deformation. The numerical model was accurate in predicting the response process of the stiffened beam. With the coupling of the vehicle load, the equivalent plastic strain of the box multistage stiffened beam was mainly concentrated at the hinge and decreased when the blast loading remained constant. The transverse anti-blast performance of the stiffened beam was mainly provided by the bridge web and the diaphragm under the coupling effect of the vehicle load and the blasting load, but the function of the diaphragm was weakened. Additionally, the hinge used as a connector was able to directly affect the bearing capacity of the bridge. Even if the hinge was only slightly damaged, it could cause the bridge to enter the failure stage, meaning that the strength of the hinge must be greater than that of the bridge.