initial displacementvs. This displacement, combined with the DL weight of the superstructure, can be used todetermine the resultant loading.The first step is to calculate the initial displacement of our generalized model. Figure 2.2shows the longitudinal loading of the structure. The initial displacement vs is illustrated atthe piers and at the end of the last span. This value varies depending on the type of piersin place. The displacement is calculated assuming an arbitrary unit load of po = 1.The next step is to calculate the DL value w(x). This represents the DL of thesuperstructure and contributing substructure elements. It is even possible to include liveload values for structure in high traffic urban area where large numbers of vehicles may bepresent on the structure during an earthquake.Once the values of vs and w(x) are known the following three factors can be calculated: ( = ( vs (x)dxEq. 1( = ( w(x) vs (x)dxEq. 2( = ( w(x) vs (x)2dxEq. 3where L = length of bridgeWith these factors known, the fundamental period of the bridge can be computedwith the following:T = 2((((/( pog())Eq. 4Where po = 1g = acceleration to gravityNow it is almost time to compute the resultant horizontal earthquake loading onthe structure. This loading can be described as a function of* The acceleration coefficient* The soil type* The fundamental periodAASHTO provides an elastic seismic response coefficient which quantifies theseparameters into dimensionless value. This single coefficient greatly simplifies the analysissince it does not require the designer to calculate an overall site period. The coefficient isdescribed byCs = (1.2AS)/(T2/3)Eq. 5Where A = Acceleration Coefficient (see figure 2.3) S = Site Coefficient (see table 1.2)With the values from these equations in place, the intensity of the earthquakeloading can be computed. This loading is an approximation of the inertial effects resultingfrom the dynamic deflection of the ...
