## 3 Results and Discussion
### Simulation of Seismic Response and Reliability
type is log-normal, if the probability density function (PDF) and cumulative distribution function (CDF) are plotted, one can see that the current dataset is a good representative of such type. The relationship between the arithmetic and logarithmic means can be established with the following relationships,  
\[{\sigma_{y}}^{2}=\ln\left(\frac{{\sigma_{x}}^{2}}{{\mu_{x}}^{2}}+1\right)\]  
\[\mu_{y}=\ln(\mu_{x})-\frac{1}{2}{\sigma_{y}}^{2}\]  
where \(\mu\) and \(\sigma\) corresponds to mean and standard deviation, whereas \(y\) and \(x\) subscripts correspond to the normal and lognormal distributions. Distribution obtained from the 151 analysis results is treated as log-normal distribution with the specified mean and standard deviation values, rather than following a fragility curve fitting procedure described in [46; 47]. Nevertheless, the red plots show that the log-normal distribution assumption is a good representative of the discrete data distribution obtained from time history analyses. Looking at these CDF values of a particular displacement demand, one can determine the structural reliability under that particular threshold. After the CDF is determined, the bridge performance can be evaluated according to the reference criteria. An example corresponding to an alter load case is that the US pedestrian steel bridges under live loads are limited by a maximum deflection value of L/1000 [65]. Likewise, allowable live load  
Figure 11: Peak responses indexed according to the strong motion parameters. Figure 12: Maximum displacement demands based on Northridge Earthquake records. deflection limit for the bridges in Japan ranges between L/2000 (L shorter than 10 m) and L/500 (L longer than 40 m) depending on the main span length [66]. Considering Mudd-Schapiro Bridge dimensions, L/1000 and L/2000 values correspond to approximately 0.01 and 0.005 m. Static deflection limits for the Ontario highway bridges with pedestrian sidewalks are formulated as a function of the first flexural frequency, and the allowable threshold for 10 Hz is equal to 0.002 m [67]. Although, these parameters are indirectly related to structural damage, extreme relative displacements can possess non-structural threats to the community as well. As mentioned above, Mudd-Schapiro Bridge and its glass facades lay above campus area which has pedestrian access 24 h a day. Quantifying exceedance of certain deflection values is therefore beneficial practice for occupant safety. Finally, the exceedance probabilities of exemplary reference criteria are investigated according to the CDF values. Considering 0.010, 0.005, and 0.002 m as the performance thresholds, structural reliability values of the data distribution are 0.987, 0.868, and 0.576, respectively. Likewise, log-normal distribution reliability values of the same performance thresholds are within a close range such as 0.981, 0.887, and 0.533, respectively. In general, based on similar reliability values under Northridge Earthquake example, the authorities can take action for pre-event preparation. These can include exemplary decisions such as claiming the structure's safety, service shutdown, initiating a retrofitting process, destruction if the performance thresholds are unachievable and reconstruction needed. Yet, it should be noted that for a different set of earthquake records with different frequency character, the structural performance is likely to be different. In the future, this issue can be further investigated with ground motion simulation using site-specific spectra (theory-driven), utilize location-aware smartphone seismic networks (measurement-driven), or both. Automated, remote, and computer-aided survey approaches will be more and more important for civil infrastructure systems which is in line with advances in measurement techniques and building information modeling. Basically, imagery data such as point clouds obtained from aerial or terrestrial tools can be converted into FEMs [68; 69].