This paper develops a simplified local damping approach for use in the nonlinear dynamic analysis of structures so that different energy dissipation mechanisms can be integrated. It is argued that a local damping approach allows the analyst to control the dissipative mechanisms introduced and check they are meaningful. Furthermore, a local damping approach offers the opportunity for different damping mechanisms to be integrated in the same model and independently specified, signaling a departure from the use of purely viscous damping models. An initial strategy for specifying damping within the integrated local damping framework is proposed, based on providing consistency between the response obtained using local and global viscous damping formulations, for both initial and tangent stiffness proportional damping models. Guidance on the use of such a local damping approach is provided for the characterization of a series of simple case study bridge structures and non-linear dynamic analyses are used to highlight the impact of the new approach.