1、附录 Study on the Propriety of Rayleighs Damping in Nonlinear Dynamic Analysis of Bridges Summary In this paper, based on the results of comparison of nonlinear dynamic analysis of 5 span bridges constructed on the I 、 、 regions by the two method (e.g. strain-energy proportional damping method & Rayle
2、ighs damping method), parametric study were made to the maximum bending curvature of the piers. As the results, it is found that the Rayleighs damping method brings a comparatively small approach to the bending curvature in many cases comparing with the strain-energy proportional damping method, and
3、 the bending curvature various in a comparatively larger areas. And also, comparatively computations were made to a complex bridge structures, e.g. 14 span bridge and a 3 span curved bridge. Suggestion was made on the practical use of the Rayleighs proportional damping method. Keyword: nonlinear, dy
4、namic analysis, the strain-energy proportional damping Rayleighs damping, bridges, the maximum bending curvature 1. Introduction After the new aseismic code of bridge design published in two years ago in Japan , the Rayleighs damping method are often used in non-linear dynamic analysis of bridges si
5、nce the assumption of damping matrix C=K+M, the time of calculating is shorter than other method . But through the computation to the many engineering problem, it shows that the results by Rayleighs damping method are various with the definition of the parameter. And also, it is found that the disco
6、ntinues of bending moment were taken place in some practical analysis. In this paper, based on the results comparison of nonlinear dynamic analysis of 5 span bridges constructed on the I 、 、 regions by strain-energy proportional damping method & Rayleighs damping method, parametric study were made t
7、o the maximum bending curvature of the piers. And also, comparatively computations were made to a complex bridge structures, e.g. 14 span bridge and a 3spancurved bridge. 2.The Study to the Common Type of Bridges 2.1 Analysis Model The 3 bridges to be analyzed were selected according to the conditio
8、ns of foundation situated in the different regions. Both of them were 5 span continues bridges with the rubber bearing. The basic conditions of the bridges were showed in Fig. 1. The standard earthquake wave from bridge code of Japan were input at the base of pier. The input earthquake directions we
9、re in the direction of longitude of bridge. The Takeda tri-linear model was used in the nonlinear dynamic analysis. At the bottom of the piers, less than 0.5m of mesh size were applied. The damping ratios of structures were shown in Table 1. The Newmark- method(=1/4)were used in the analyses and the
10、 0.002sec. If the stabilization of result is unavailable, the 0.001, 0.0005 were applied. It is very important to make selection of the 2 parameters in the Rayleighs damping method. The common method which shown in Fig. 2 use the 2 main mode of the structure. But for the bridges on foundation of regions (soft clay foundation), it lead to a the minus parameters phenomena. The method , points were selected by using the main mode and a mode which have a comparatively lager effective mass.
