30 Structural Stiffness Identification of Skewed Slab Bridges with Limited Information for Load Rating Purpose 245 30.2.2 Parametric Study In the parametric study, it was assumed that the bridge’s parapet has the same rectangular cross-section for the bridges with different span width and length. This is a valid assumption as the parapet’s dimensions for most slab bridges are standard. Therefore, is a function of the bridge’s spana,widthb, skew angle , and thickness t. For given parameters, the first modal frequency of the bridge can be obtained using a modal finite element analysis. Then, (a,b, ,t) is calculated as follows: .a; b; ; t/ D!.a; b; ; t/r D (30.4) The modal finite element analysis was conducted for different values of the bridge’s span a, width b, skew angle , and thickness t for obtaining (a,b, ,t). For each parameter, the following ranges were considered: a.m/ DŒ456789101112131415 (30.5) b.m/ DŒ456789101112131415 (30.6) t.m/ DŒ0:30 0:35 0:40 0:45 0:50 0:55 0:60 0:65 0:70 (30.7) ı DŒ0 5 10 15 20 25 30 35 40 45 50 (30.8) Based on these ranges for each parameter, the number of finite element models that should be run is 12 12 9 11 D14,256. To minimize the computational efforts, a finite element code was written in MATLABto model and analyze of slab bridges with all combination of each parameter automatically and continuously. Figure 30.2a shows the value of as a function of the bridge’s spanaandwidthbfor the plate’s thickness of 0.3 m and the skew angle of 0ı, whereas Fig. 30.2b illustrates the same results for the skew angle of 45ı. It can be seen that at short spans and widths the value of is larger than that for long spans and widths. This is due to the increase in the natural frequency of bridge with the decreasing the bridge’s span and width. The skew angle in a bridge causes to increase the stiffness of the Fig. 30.2 The value of as a function of the bridge’s span a and width b for the plate’s thickness of 0.3 m and: (a) the skew angle of 0ı and (b) the skew angle of 45ı
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