N2 with Cloud: A Non-Linear Dynamic Analysis Procedure for the Equivalent SDOF System

The original N2 method for reasonably regular buildings oscillating predominantly in a single mode envisioned a two-stage analysis where the first stage involved the non-linear static analysis of the MDOF system using alternative monotonically increasing lateral load patterns and the second stage involved the non-linear time-history analysis of the equivalent SDOF system. Today, the N2 method constitutes the backbone of Eurocode 8 and the Italian building Code (NTC2018) as far as it regards the seismic design and assessment of buildings. In the codebased approach, the equivalent SDOF system is defined as an elastic-perfectly-plastic model and the structural analysis is performed through the inelastic design spectrum. On the other hand, non-linear dynamic time-history analysis of the MDOF system subjected to un-scaled ground motion records, better known as the Cloud Analysis, is noteworthy due to its simplicity, relatively small number of records employed and its preservation of the original frequency content. A modified version of the Cloud Analysis can effectively consider the cases of structural collapse and/or numerical non-convergence. This modified version of the Cloud analysis proves ideal for implementation in the context of the N2 method and the code-based provisions since it can be applied as a dynamic analysis procedure directly to the code-based equivalent elasticperfectly- plastic SDOF model. This method can be applied for seismic design and assessment both for the serviceability and the ultimate limit states. The proposed non-linear dynamic analysis procedure is applied to a frame belonging to a pre-seismic code school building in Avellino (Campania), located in southern Italy. The frame is modelled by considering the interaction between the shear, axial force and flexure and the rigid-end rotation due to bar slip.