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Mathematical Problems in Engineering
Volume 2014, Article ID 514872, 22 pages
Research Article

Dynamic Responses of Simply Supported Girder Bridges to Moving Vehicular Loads Based on Mathematical Methods

1School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, China
2Department of Civil and Environmental Engineering, National University of Singapore, Singapore 117576
3Zhejiang Provincial Institute of Communications Planning, Design and Research, Hangzhou 310000, China

Received 30 June 2014; Revised 18 August 2014; Accepted 19 August 2014; Published 29 September 2014

Academic Editor: Jun Cheng

Copyright © 2014 Qingfei Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For dynamic responses of highway bridges to moving vehicles, most of studies focused on single-factor analysis or multifactor analysis based on full factorial design. The defect of the former one is that it has no consideration of interaction effects, while that of the latter one is that it has large calculation. To avoid these defects, simplified theoretical derivations are presented at first; then some numerical simulations based on the proposed method of the orthogonal experimental design in batches have been done by our own program VBCVA. According to simplified theoretical derivations, three factors (κ, γ, and α) are proved as the most important factors to determine dynamic responses. Based on the modal synthesis method, the program VBCVA has been introduced in detail. Then on the basis of the orthogonal experimental design, both main effects and interaction effects are studied. The results show that, for different indices of dynamic responses, the influences of each factor are not the same. Additionally, the interaction effects have proved to be so small that they can be neglected. In the end, this method provides a good way to obtain more rational empirical formulas of the DLA and other dynamic responses, which may be adopted in the revision of codes for design and evaluation.