Page 136 - Riem-Vol6_nº3

481 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
R. N. F. do Carmo | J. Valença | D. Dias-da-Costa
0.315 mm in average and at a 95% confidence level, respectively.
The precision in target detection was 0.031 mm and 0.046 mm in
average and at a 95% confidence level, respectively (Figure 7).
It is important to highlight that the error of the homography is a
systematic error, i.e, the error on the displacement is assumed to
correspond to the error in the target detection. Finally, the error in
the strain field was circa 0.3% for the defined grid spacing.
5. Results analysis
5.1 Preliminary results
The vertical displacements obtained using photogrammetry were
compared with those obtained by traditional monitoring. The ob-
tained differences were relatively small, 6% on average (Table 1).
From the displacements measured at each target it is possible to com-
pute the strain field (see Section 3.1). In Figure 8, the first principal
strain field at stage 3 is shown (see Section 3.2). It is highlighted that it
is consistent with the existing cracking pattern. Additionally, image pro-
cessing can be used to measure the crack width at each test stage.
This information is later used to determine the rotation in Section 5.3.
5.2 Curvature
The mean curvature at the pure bending region can be defined us-
ing the parabolic equation that best fits the vertical displacements.
The curvature is the directly computed by the 2nd derivative of the
equation. For this purpose, photogrammetry presents a significant
advantage because it allows recording the displacement at a large
number of cross sections which can be used to obtain a reliable
approximation of the parabolic equation.
The average curvature can also be assessed by measuring the hori-
zontal stretching at the pure bending region. As mentioned above, two
horizontal LVDTs were used to measure these deformations. Knowing
the vertical distance between the LVDTs axis and the horizontal dis-
tance between reading points, the average strains and corresponding
curvature, can be computed. In Figure 9, the moment versus curva-
ture relation for the pure bending region (800 mm) is shown, identify-
ing the onset of reinforcement yielding, stage 3 and stage 4.
The curvature for a specific section and at a particular stage is deter-
mined based on strains measured along the section height. Initially, it
is necessary to define the best fit straight line to the strains. Figure 10
presents the strain evolution and the corresponding curvature comput-
Figure 8 – Cracks pattern and strain map (stage 3)
Cracks pattern First principal strain map A B
Figure 9 – Bending moment vs. average curvature measured using horizontal LVDTs
0
8
16
24
32
40
0 32 64 96 128 160
M (kN.m)
1/rm (×10-3 m-1)
(1/r)3 - (1/r)y
(1/r) 4 - (1/r)y
800 mm
Start of steel
yielding
Stage 3 Stage 4