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FIGURE 20.22 Typical moment-thrust-curvature curves: (a) reinforced concrete section and (b) steel section.

a way that fully accounts for the multiple-support input and the space-time correlation structure of the ground motion [58].

Although the random vibration approach has been adopted by the Eurocode [59] and widely used by Chinese engineers, it has not been accepted as a practical method of analysis for complex long-span structures by U.S. practicing engineers due to computation difficulties [57].

During 1990s, Lin and coworkers [60-64] have developed a new series of algorithms, that is, the pseudo-excitation method (PEM) series, on structural stationary/nonstationary random response analysis. The PEM is an accurate and extremely efficient method to solve complicated random vibration problems. The cross-correlation terms between all participating modes and between all excitations are all included in the responses. Most recently, the PEM has been used to analyze several long-span bridges in China. Cheng [65] analyzed the Hunan Yue-Yang Cable-stayed Bridge with a total length of 5700 m and a main span of 880 m, in which 2700 degrees of freedom, 15 multisupport ground motions, and 200 modes were used. Fan et al. [66] used PEM to analyze the Second Yangtze River Bridge at Nancha, a cable stay bridge with a total length of 1238 m and a main span of 628 m, in which 300 modes in the fast CQC (i.e., PEM) analysis and 12 multisupport ground motions were used. The computations showed that the "wave passage effect'' may cause the differences of some demands up to 40%.

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