I would say that for many structures the general effects of shrinkage and creep is some loss of stiffness. Things that at construction time were tight and controlled become more deflected and with more liberty to deform in uncomely ways if spurious solicitations come.

Integral bridges may or not use some moment relief from the abutments. Shrinkage and creep both try to shorten the bridge and the abutments restrain such intent. Were the effects badly enough the loosening effects above described would mean concrete hanging on some wires, not far of a nightmarish version of a loose segmental constructed bridge.