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485 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
R. N. F. do Carmo | J. Valença | D. Dias-da-Costa
proximately 70% of the maximum load, which corresponds roughly
to serviceability conditions.
Considering the flexural stiffness value experimentally obtained,
i.e. 2679 kN.m2, and applying Equation 2 is obtained a value for
the distribution coefficient z of 0.883. This coefficient can also be
determined using the curvature computed by photogrammetry and
image processing. At this stage the bending moment is 23.5 kN.m.
Knowing the stiffness in states I and II, the curvature is: (1/r) I = 3.9
x10-3 m-1 and (1/r) II = 10.5 x10-3 m-1 . Since the average curvature,
in the analyzed region, is 9.85 x10-3 m-1 , the distribution coefficient
z is 0.902 (Figure 15). The values experimentally measured can be
compared with the EC2 [9], z = 1 - b.(Mcr /M)2. In this case, b is 1
(short-term loading) and the cracking moment Mcr is 6 kN.m, con-
sidering the concrete tensile strength and all homogenized section.
Taking into account this data, and according the EC2, the distribu-
tion coefficient value is 0.935, very close to the values obtained
experimentally.
6. Conclusions
Recently, innovative methods for monitoring structures using pho-
togrammetry and image processing have been developed. This
paper presents a practical example of these techniques, namely,
in the characterization of the structural behavior of reinforced con-
crete beams, with particular attention in plastic rotation and tension
stiffening effect.
Photogrammetry and image processing were used to monitor a
large number of points on a concrete surface until failure. Four
stages during the experimental test were analyzed, highlighting the
interest in the developed tools, which allow the computation of the
strain field on concrete surfaces and characterization of the crack-
ing pattern. Throughout the test, similar values of the vertical dis-
placements between photogrammetry and LVDTs were obtained.
The detailed information of the strain field in the concrete surface
allowed computing the curvature in specific sections and evaluating
their progress along the beam axis. This information is extremely dif-
ficult to obtain with traditional methods, since the use of mechanical
strain gauges is required. Usually, the mean curvature along regions
can only be determined with 100 or 200 mm resolution due to the
limitation of the equipment size. Photogrammetry allows obtaining
the curvature along smaller regions, in this case with 20 mm length.
The detailed evolution of the curvature along the beam axis was
used to study the plastic rotation and the tension stiffening effect.
The method allowed to experimentally verify that the plastic curva-
ture was localized in cracked sections and in a restricted length of
the beam, in this case around 350 mm. Photogrammetry was also
used to determine rotation between the cracks boundaries. These
values have also been used to compute the plastic rotation in the
pure bending zone.
In summary, the presented study aims validating and demon-
strating that photogrammetry and image processing techniques
can provide significant and relevant data relatively to traditional
methods of monitoring, both in serviceability and in ultimate states.
Furthermore, due to the amount of data recorded, is possible to
perform analyses that would otherwise be unfeasible.
7. Acknowledgments
The authors would like to express their gratitude to the Department
of Civil Engineering of the Polytechnic of Coimbra for providing the
conditions to carry out this study and the colleagues Hugo Costa,
Tiago Simões, Cátia Lourenço and Diogo Andrade, for their col-
laboration in the experimental programme.
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