1. A method of estimating a load carrying capacity of a bridge, the load carrying capacity estimation method comprising: estimating, by a processor, a mode coefficient of the bridge using an acceleration signal supplied from an accelerometer that is installed in the bridge; updating, by the processor, an analysis model of the bridge using the estimated mode coefficient; applying, by the processor, a dead load to the updated analysis model, to estimate a first stress that is generated in the bridge using the dead load applied to the updated analysis model; applying, by the processor, a design live load to the updated analysis model, to estimate a second stress that is generated in the bridge using the design live load applied to the updated analysis model; estimating, by the processor, a rating factor of the bridge by a permission stress method using the first stress and the second stress; estimating, by the processor, the load carrying capacity of the bridge using the design live load and the rating factor of the bridge; doubly integrating, by the processor, the acceleration signal when a vehicle or vehicles pass the bridge to estimate displacement of the bridge during passing of the vehicle or vehicles; applying, by the processor, the dynamic displacement to a low-pass filter, to estimate static displacement of the bridge; and obtaining, by the processor, an impact coefficient from the dynamic and static displacement of the bridge in which the impact coefficient is a ratio of a difference between the dynamic displacement and the static displacement with respect to the static displacement, wherein the load carrying capacity of the bridge is estimated using the design live load, the rating factor, and the impact coefficient of the bridge.