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Box-girder bridges supported by single reinforced concrete (RC) columns are expected to sustain seismic shocks with minor structural damages in seismically active regions where transportation is substantially required for rescuing and evacuating tasks. Such viaducts are vulnerable to damage when they are subjected to strong ground motions and acceleration pulse records, especially when responding in a flexural mode or having relatively low core confinement. Using a nonlinear dynamic solver that applies the fibre element method, global and local damage curves are computed based on the dissipated energy under hysteretic curves and based on constitutive curves, respectively. The RC bridge with seismic isolation bearing is used as an alternative system to control the damage, and modelled using linkage elements between the substructure and super structure. It was found that seismic isolation can be controlled to dissipate partial seismic energy so that the RC column gains the least possible minor damage. Using a MatLab program, a fibre element nonlinear model was built using a simplified iterative process and simplified constitutive relations. The number of fibres and elements under the dynamic loading was found to be affecting the final results of the analysis. Using crack growth modelling based on fracture mechanics, the combined discrete element/finite element explicit-Elfen code was applied to investigate the crack growth in 3D dynamically loaded RC columns. Despite its excessive computational cost and time, this code provides reliable information about local damage in the RC column core. Earthquake records with the pulse acceleration phenomenon have a severe damage potential on the structure. The difference in damage intensities was detected by crack growth modelling for the same problem using different loading rates. Critically stressed zones can be investigated independently by using the relative response technique, in which responses from the numerically analysed structure are re-used as applied loads onto a small-scale crack model for the critical member. Two general conclusions can be obtained; bridges with single RC columns designed by the demand/capacity criterion could suffer severe damage and possible collapse when subjected to strong ground motions. Secondly; hysteresis-based methods provide a global damage evaluation based on strength and ductility only regardless of the damage growth inside the concrete core and the buckling of bars, which could lead to progressive collapse.