Issue 29

W. Guodong, Frattura ed Integrità Strutturale, 29 (2014) 376-384; DOI: 10.3221/IGF-ESIS.29.33 382 (ii) When comparing absolute displacement method with random vibration method, the error of acceleration response power spectral density is the smallest, the biggest error of main span is only 1.15%, the biggest error of back span is only 1.37%. The main reasons resulting into such phenomenon is that the inputted stimulus is the acceleration power spectrum density during the early analysis stage of model, thus after a series of calculation, its corresponding acceleration response power spectral density is closest to actual situation, while displacement and velocity response power spectral density have experienced more calculation steps than acceleration response power spectral density, then results into error accumulation, thus the maximum error of displacement power spectral density in main span reaches 11.1%, the maximum error of displacement power spectral density in back span reaches 9.14 %. Displacement power spectral density (main span ) Velocity power spectral density (main span ) Acceleration power spectral density (main span ) Displacement power spectral density (back span ) Velocity power spectral density (back span ) Acceleration power spectral density (back span ) The minimum error/% 6.14 2.58 0.50 3.11 5.50 0.43 The maximum error/% 9.99 7.50 1.04 8.23 8.77 1.23 Table 1: T he error comparison for two methods. The Comparison for Absolute Displacement Method, Time History Method and Spectra Analysis In current vibration resistance analysis, in addition to above mentioned random vibration method and harmony response analysis, spectrum analysis and time history method are also very important research method, the essence of dynamic time history analysis method is transient analysis Full method, various nonlinear factors could be considered, thus for the algorithm cases studied in this paper, the linearization process could be skipped to perform dynamic time history analysis directly. Vibration isolation bearing is considered during calculation, the structure is non-orthogonal damping system, the inputted artificial wave is generated according to the above adopted condition, and seismic action adopts both horizontal and consistent earthquake excitation. According to seismic code, earthquake acceleration at the second-rate direction is multiplied by the coefficient of 0.85. In order to compare above analyzed nonlinear and linear results, the method in last section is equally applied. As it is shown in Fig. 4, the straight line in (a) and (b) represents spectra analysis, point and line interval represents time history method, dotted line represents absolute displacement method; (c),(d) square lines represent spectra analysis, dot line represents time history method, triangle line represents absolute displacement method. Through comparing the displacement time history diagram of nodes across main span and back span in Fig. 4(a) and (b), we could find out following rules: (i) as spectral analysis is to study the displacement response of cable-stayed bridge within linear elastic range, thus all the displacement response value of absolute displacement method are too small when compared with dynamic time history method and the absolute displacement method after linear processing, and the maximum deviation reaches more than 50% when compared with dynamic time history method which has the largest displacement response, it demonstrates that when studying the anti-seismic property of structure, the structural nonlinearity must be considered, otherwise more error will occur and the calculation results will be made deviate from true value. (ii)The calculation results of absolute displacement method and dynamic time history after taking account nonlinearity are very close, the maximum displacement error at main span X direction is only 7.8%, for back span Y direction ,its maximum error is 7.3%.And through research ,we find that there is similar regularity among the displacement response of main girder, main tower and stay-cables node, it demonstrates that the absolute displacement method could sufficiently consider structural nonlinearity after linearization, thus it could be taken as an effective method for aseismic design. Through observing axial force response mean contrast figure at Z direction of typical unit under the action of consistent earthquake for three calculation method in figure 3.4, we could see that the unit axial force response value obtained through absolute displacement method after linearization is the biggest, and it is basically the same with unit axial force value obtained through calculating with dynamic time history method, its maximum error is only 0.23% (the units near the middle section of main span), for spectral analysis, all its axial force response values at Z direction are too small, when compared with dynamic time history method, the maximum error reaches 8%, thus it demonstrates that nonlinearity has certain effect on structural anti-seismic property, which should be considered in anti-earthquake analysis of bridge structure.