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480 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
Plastic rotation and tension stiffening effect analysis in beams using photogrammetry
(Figure 4). The main load was applied by a 300 kN capacity hydraulic
servo-actuator, attached to the metallic support frame. The test was
performed using displacement control at a constant rate of 0.01 mm/s.
Several parameters were measured during the test to characterize the
beam behavior, namely, support reactions and displacements at se-
lected critical sections. The test was also monitored using the image
processing methods described in Section 3 and traditional instrumenta-
tion, in particular, load cells under the supports and displacement trans-
ducers (LVDTs) placed in the pure bending region. Three LVDTs were
used to measure vertical displacements, two placed at 1.0 m from each
support (sections where loading was applied) and the third was placed
exactly at mid-span. Two LVDTs were also placed to measure the hori-
zontal stretching of the beam at the pure bending region (Figure 5).
4.2 Preparation and image acquisition
Previously works using photogrammetry and image processing in
structural monitoring have shown that the precision obtained in the
displacement field is typically better than 0.050 mm. Thus, in order
to measure a uniform strain field with 0.5% precision (value suit-
able for characterizing the crack formation) a minimum distance
between targets of 20 mm is required (Dias-da-Costa et al. [3]).
Therefore, the circular targets were painted in the surface of the
specimen composing a square grid with sides of 20 mm length, op-
positely to the surface used for placing the traditional instruments.
All images were captured by a digital camera installed in front of
the beam, at a distance of 1.75 m. A tripod and a remote shutter
were used to trigger the camera without compromising the stability.
The images were acquired at full resolution of 4608×3072 pixel.
Before start loading, ten images were sequentially acquired and
later on used for scaling and orientating all images used to moni-
toring the experimental test and also for estimate the error in the
results. Four stages of the test are herein analyzed (Figure 6).
4.3 Error analysis
As previously mentioned the ten images acquired before start
loading were used to estimate the error of the results, namely: i)
the error of the homography; and ii) the precision of the coordi-
nates at each target. In the first case, the error was 0.236 mm and
Figure 6 – Force vs. testing time duration
0
20
40
60
80
0:00 0:28 0:57 1:26 1:55 2:24
Force P (kN)
photogrammetry
Figure 7 – Error map of target detection in the monitored surface
Table 1 – Vertical displacements in mm using LVDTs and photogrammetry (units in mm)
Section 1.0 m at the left support Section at mid-span Section 1.0 m at the right support
Photog. Photog. Photog. LVDT-1 LVDT-2 LVDT-3
Stage 1
Stage 2
Stage 3
Stage 4
9.60
17.14
33.55
60.49
10.62
19.65
40.09
78.77
8.98
17.12
34.89
74.18
8.68
15.97
32.57
67.27
9.69
18.31
39.21
83.13
9.62
18.05
35.81
72.10