Structural Engineering and Mechanics

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CCQC modal combination rule using load-dependent Ritz vectors

  • Xiangxiu Li (Institute of Geophysics, China Earthquake Administration) ;
  • Huating Chen (Earthquake Engineering Research & Test Center, Guangzhou University)
  • Received : 2021.07.26
  • Accepted : 2023.05.19
  • Published : 2023.07.10
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Abstract

Response spectrum method is still an effective approach for the design of buildings with supplemental dampers. In practice, complex complete quadratic combination (CCQC) rule is always used in the response spectrum method to consider the effect of non-classical damping. The conventional CCQC rule is based on exact complex mode vectors. Sometimes the calculated complex mode vectors may be not excited by the external loading and errors in the structural responses always arise due to the mode truncation. Load-dependent Ritz (LDR) vectors are associated with the external loading and LDR vectors not excited can be automatically excluded. Also, contributions of higher modes are implicitly contained in the LDR vectors in terms of static responses. To improve the calculation efficiency and accuracy, LDR vectors are introduced in the CCQC rule in the present study. Firstly, the generation procedure of LDR vectors suitable for non-classical damping system is presented. Compared to the conventional LDR vectors, the LDR vectors herein are complex-valued and named as complex LDR (CLDR) vectors. Based on the CLDR vectors, the CCQC rule is then rederived and an improved response spectrum method is developed. Finally, the effectiveness of the proposed method in this paper is verified through three typical non-classical damping buildings. Numerical results show that the CLDR vector is superior to the complex mode with the same number in the calculation. Since the generation of CLDR vectors requires less computational cost and storage space, the method proposed in this paper offers an attractive alternative, especially for structures with a large number of degrees of freedom.

Keywords

Acknowledgement

This work was primarily supported by the National Key Research and Development Program of China (2022YFC3003505) and the National Natural Science Foundation of China (52078311).

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