The effects of period and nonlinearity on energy demands of MDOF and E-SDOF systems under pulse-type near-fault earthquake records

The use of an earthquake input energy concept and types of internal energy in structures has been less considered for near-fault pulse-like earthquakes. This paper calculates the applied ratios of energy types in the E-SDOF and MDOF systems and identifies the relationship between them. For this purpose, five steel frames (4, 10, 15, 20, and 30 story steel MRFs with 3-span) were designed, and the E-SDOF structure was obtained equivalent to the first mode, using the Modal Pushover Analysis (MPA) method. All models were analyzed under 10 near-fault pulse-like earthquake records using nonlinear time history analysis. The results show that the Total Dissipated Energy (TDE) of the structure depends on its nonlinear degree and period. The TDE of the MDOF and ESDOF systems is equal for long periods, and its size is independent of the design resistance (R) and the degree of nonlinearity. However, during short periods, this ratio is close to the effective modal mass coefficient corresponding to the first mode. The story normalized hysteretic energy ratio is also a function of the height, nonlinear degree; and period of the structure. In addition, the effect of higher modes affects the distribution of this ratio in tall structures.