## 4 Reported Large Deflections of Stiff, Structurally Healthy Bridges  
Although structural constraints predict small deflections in stiff bridges (Table 1), there exist certain reports of abnormally large GNSS-derived deflections. Structural damage has usually been claimed as an explanation, but no signs of such damage were found (cracks in concrete, etc.), nor any sense of dysfunction by users of the bridges has been reported.  
An example is the results of GPS monitoring of the Juarez Bridge, in Culiacan, Mexico [30]. This is a typical reinforced concrete road bridge, with openings of 20 m supported by beams on piers and two lanes per direction. Measurements were made in seven consecutive days, during specific time intervals, at traffic rush hours in order to identify the response of the bridge to the traffic load. Six GPS compact antenna/receivers were mounted on poles about 2.0 m high clamped on stiff metal railings at the two sides of the bridge, including its midspan. Measurements were collected with a sampling rate of 1 Hz and were probably limited to GPS satellites only, while a low cut-off (mask) angle of 10\({}^{\circ}\) was adopted (i.e., accepting satellites at zenithal angles of 0-80\({}^{\circ}\) around each antenna). As a consequence, certain stationary or moving reflecting surfaces (passing vehicles) at an  
Figure 5: Noise in GPS monitoring of bridges imposed by passing vehicles. **(a)**: the GNSS antenna is in an optimal position, and the signal from the satellites (green lines) is not influenced by passing vehicles. **(b)**: The GNSS antenna is at a low-level, so that certain passing vehicles produce two effects; first, some satellites are instantaneously shadowed (those shown with dashed red lines); this imposes changes on the observations system and on computed instantaneous coordinates and deflections; second, the signal of some satellites arrives at the GNSS antenna from two paths, directly (continuous green line) and after reflection on the passing vehicle (dashed green line), so that the instantaneous distance between antenna and satellite is modified and spurious instantaneous coordinates are computed. This gives the impression of a much higher or lower deflection, correlating with the passing vehicle. See [28] for details. If the GNSS antenna is located on a stiff, high pole, this double source of noise is avoided (see [29]).  
elevation slightly above the antennas were influencing calculations. The analysis was made in reference to stations in stable ground, using high precision software. The output was instantaneous (1 Hz) changing coordinates in three axes, forming an angle of approximately 40\({}^{\circ}\) with the road axis. These results indicate apparent displacements up to tens of cm in the horizontal and vertical axis. After removing the long-period component of satellite signal, the authors argued that they recorded dynamic deflections of several cm in both the horizontal and vertical axes. In some cases, vertical apparent deflections up to 25 cm in the midspan were recorded. Deflections were not confined to the mid-span, but they were also observed at stations above piers of the bridge (Table 3). The authors were surprised with these results, noticed that the deflections were exceeding the serviceability limits of this bridge, and although they found no signs of damage, they explained them as results of a possible unnoticed structural damage.