Damping support for bridge and bridge

The embodiment of the utility model provides a damping support for a bridge and the bridge, and relates to the technical field of bridge engineering. The support comprises a bottom plate, a guide rod, a support main body and a flexible damping piece, the flexible damping piece is connected with the bottom plate and movably connected with the support main body, in the first state, the support main body does not drive the flexible damping piece to deform when moving, and the flexible damping piece is kept in a static state; and in the second state, the support main body can drive the flexible damping piece to deform, so that the motion energy of the bridge structure is consumed and reduced. Graded energy dissipation and shock absorption are achieved through different movement conditions of the flexible damping piece in the two states, meanwhile, the flexible damping piece only plays a role in the second state, the use frequency of the flexible damping piece is effectively reduced, the use duration of the flexib