A Relationship between the Energy Demands of MDOF and Equivalent SDOF Systems under Pulse-Type Near-Fault Earthquakes

The purpose of paper is qualitative and quantitative study of the relationship between the energy demand of multi-degree-of-freedom systems, MDOF, and equivalent-single-degree-of-freedom systems to calculate the total energy demand of the MDOF system using the ESDOF energy demand. For this purpose, multi-story special steel moment frames designed and analyzed under 10 near-fault earthquake with forward-directivity effects. Moreover, the process done for the ESDOF system considering specified values of R (degree of nonlinearity). Accordingly, linear and nonlinear total dissipated energy (TDE), hysteretic energy (HE), and damping energy (DE) ratios were introduced to estimate the relationship of the ESDOF and MDOF energy. Results shows that ratio of nonlinear to linear TDE and HE/TDE is affected by period and R in ESDOF system. However, as the period and R increase, the ratio converges to one. The same result was observed between the nonlinear TDE of the MDOF system and the linear TDE of the ESDOF system. In other words, ESDOF linear TDE can be used instead of MDOF for long periods. In addition, the nonlinear TDE of the MDOF system to the nonlinear TDE of the ESDOF system ratio is affected by higher modes and period, by increasing the period the ratio is generally greater than one for the constant R. Also the effect of higher modes on the ratio of total story dissipated energy to total structure dissipated energy was significant for low R values. With increasing R, the structure tends to damp all the dissipated energy in the first mode.