Two comments on your question:
1) Fundamentally, bridge design follows the weak column/strong beam concept (basically opposite of buildings.) Because of this, the superstructure (bridge deck) is a capacity protected element and must be able to behave elastically under plastic hinging of the column. The AASHTO I-A seismic code describes the design specifics for both steel and concrete superstructures.
2) Depending on your specific location, several codes in high seismic areas have included a vertical component to the seismic design forces (typically 2/3 the horizontal spectra, but this is very general.) Again, the superstructure needs to remain elastic under this event.
Your question was fairly broad, but I hope this helps, or starts further discussion.
