Mode selection and combination rules of energy-based multimodal pushover method for simply supported beam bridges

Abstract

The energy-based method (EBM) has been improved as Energy-based Multimodal Pushover Method (EMPM), and is introduced and verified to be effective and convenient for evaluate the seismic performance of the simply supported beam bridges. This paper mainly focuses on the research of vibration mode selection and combination rules of EMPM. Firstly, the longitudinal vibration modes of simply supported beam bridge are categorized into five cases based on mode shapes, and the case definition is emphasized. Then, corresponding to each case, the Pushover loading force are established, and the modal energy, modal displacement, and modal energy capability curve are proposed. After that, the energy-based demand curve and the corresponding energy coefficient for each case is recommended. Finally, only the mode with maximum mode participation factor (MPF) of each case is suggested to take part in the calculation of the seismic response with the proposed mode participation factor combination rule. Case studies of a practice bridge under Chi-Chi and El Centro earthquake waves are used to illustrate the effectiveness and accuracy of the proposed mode selection and combination rules. The study found that the EMPM with the proposed rules could effectively and rapidly assessing the seismic performance of the simply supported beam bridge, resulting in a 70 % decrease in time consumption compared with the Nonlinear Time History Analysis Method (NTHAM). Compared with the CQC and SRSS combination results, the proposed Mode Participation Factor (MPF) combination rule reduced the maximum relative deviation from 39.4 % to 21.09 % between EMPM and NTHAM for peak displacement. Further research showed that the proposed mode selection approach only uses modes with the highest MPF in each case, decreased the number of modes involved more than 50 % and the result accuracy remained almost identical.