## 5 Discussion  
### Contrasts between Observations and Structural Predictions  
Table 1 indicates that measurements of dynamic deflections of stiff bridges, including bridges of reinforced concrete, using different types of sensors (LVDT extensometers, radar interferometry, and robotic total stations (RTS) led to max values of vertical deflections of the order of a few mm. In some of these cases, combined GNSS and RTS measurements revealed that carefully collected and analyzed GNSS data are consistent with those derived using RTS (e.g., [14]), but in some cases the output of GNSS is contaminated by serious errors (Figure 4). A deflection of the order of 300 mm was recorded only for a bridge just prior to failure, in a catastrophic experiment (Table 1).  
On the other hand, GNSS measurements of dynamic deflections of various types of bridges, disproportional to the predictions of various codes, have been made in various parts of the world, and some of these results have been published in international journals. This makes the study of the Juarez bridge representative of several other cases, and worthy of discussion, especially because measurements were made with much care.  
The AASTHO [9] and other regulations predict maximum permissible dynamic deflections up to 2.0-2.5 cm for this bridge, but reported deflections were up to about one order of magnitude higher (up to 25 cm) for the three axes (Table 3). Still, no evidence of discomfort to the users, nor signs of damage (cracks, unstable foundations etc.) were reported. Computed horizontal deflections of a few cm in this bridge may be explained as secondary oscillations of the poles on which the GPS antenna and receiver units were  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline Measurement session & & 1 & 4 & 7 & 10 & 13 & 16 & 19 \\ \hline \multirow{3}{*}{Max deflection(cm)} & midspan & 4 & 9 & 21 & 5 & 9 & 8 & 5 \\ \cline{2-8}  & pier & 5 & 4 & 7 & 5 & 4 & 4 & 3 \\ \hline \multirow{3}{*}{session} & & 2 & 5 & 8 & 11 & 14 & 17 & 20 \\ \cline{2-8}  & midspan & 24 & 9 & 14 & 5 & 7 & 18 & 8 \\ \cline{2-8}  & pier & 13 & 4 & 5 & 5 & 5 & 5 & 8 \\ \hline \multirow{3}{*}{session} & & 3 & 6 & 9 & 12 & 15 & 18 & 21 \\ \cline{2-8}  & midspan & 25 & 20 & 11 & 4 & 5 & 13 & 7 \\ \cline{2-8}  & pier & 12 & 4 & 5 & 3 & 4 & 8 & 4 \\ \hline \end{tabular}
\end{table}
Table 3: Maximum vertical dynamic displacements of the Juarez bridge. Data based on Figure 9 in [30]. Measurements were collected from 6 GPS instruments during 21 sessions, which are divided in this Table in three sets of seven sessions each, with inferred quasi-similar satellite constellations. Four instruments were set above bridge piers (and are typically expected to show no deflections) and two at the midspan. Large apparent deflections were reported, up to 13 cm above piers and up to 25 cm in the midspan. This order of apparent deflections is much higher than those observed on other bridges and is expected only at bridge destruction level (cf. Table 1).  
mounted. Hence the main problem is the inferred vertical deflections, reaching 10-25 cm at the midspan and at least 10 cm above the piers of the bridge (Table 3). Under certain conditions, heavy loads may produce dynamic subsidence in piers of bridges of sub-millimeter to millimeter-scale [16]. Hence, reported vertical deflections above piers in the Juarez bridge (up to 13 cm) can only reflect bias.  
A last argument: Dynamic deflections of short-span (20-30 m long) bridges above the threshold of a few cm are visible by naked eye, can be easily video-recorded from a nearby position (for an example see [31]), produce a sense of discomfort, and occasionally of fear to pedestrians and car drivers; they can also be analyzed using a combination of photogrammetric and typical video-processing techniques [32]. In fact, in favorable conditions (good visibility and proximity to the bridge) such techniques can identify and model even micro-vibrations [33; 34; 35]. Hence a simple control to ambiguous results is possible.