4.2 Finite Element Analysis
The numerical simulation of a concrete structure with finite
element software is a usual approach in civil engineering. At
this the structure is divided into small elements (finite elements)
and their interaction is simulated.
The photogrammetry allows the connection between finite
element simulation and a real test. The displacements of the
targets are used as displacements of the connections. In addition
the crack tracking is used to define cracked elements with
discrete or distributed basic approach functions (figure 13).
Figure 13: discrete or distributed basic approach functions
The finite element system allows calculating with material laws
stress in the concrete element. If they exceed the maximum
tension stress of the concrete at a location, the crack probability
is there increased and a new iterative program step is to run.
Knowing cracks as well as displacement, the used material laws
of the finite element software can be checked and calibrated by
controlling stresses.
S. EXAMPLES
The presented method was tested on different specimen types,
which are shown in the following chapter. Therefore different
grids of targets, camera positions and number of cameras are
used.
5.1 Tensile Test
The tensile test is basically used as a pre-test before a complex
test can be realised. The tensile strength of concrete and
reinforcement are the most important values. The following
example comes from a test series for the effect of inclined inlaid
reinforcement. The specimen was prepared with a grid of
targets (76 x 17 targets) and the photos are made by a one-
camera-system in an interval of 15 seconds. The calculation
delivers the change of distance between the targets and at the
same time directly the crack width for the horizontal cracks.
The experiment set-up, the crack pattern at the end of test, and a
schematic drawing is presented in figure 14.
d ad eH 2d =
Figure 14: a) experiment set-up with one camera b) crack
pattern at the end of test c) schematic drawing
In figure 15 the crack pattern evolution is shown. The basic
crack in the centre was generated by cuts and is dominant till
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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
failure. Neighboured are the evolutions of secondary cracks.
The width of the basic crack is more than 1 mm at the end and
the width of the secondary cracks are between 0.2 and 0.4 mm.
In addition an overturning of the specimen can be detected,
which makes it necessary to change the restraint.
During the tests it was recognized, that the plane representing
the target field is unstable in relation to the camera. The
specimen changes its distance to the fixed camera under
increasing load, so that the attitude varies marginally. Therefore
the method was extended by one or two cameras to be able to
determine three-dimensional displacements.
extracted
Ÿ
increasing load
Figure 15: Crack pattern evolution at a tensile test (display
PHIDIAS)
5.2 Shear Test
The next test presented is a 4-point loading test in form of an I-
beam with the length of 1 meter. The measurement was made at
one side to research the area of shear cracks. The grid of targets
(76 x 16 targets) was measured with two or three cameras
(Figure 16).
| DR A A
Figure 16: a) configuration of a 4-point loading test with three
cameras b) schematic drawing
Figure 17: Crack pattern evolution at a shear test (showing four
selected epochs, displayed by PHIDIAS) starting
crack width about 0.02 mm (image above right)
failure crack width about 0.20 mm (image below
right)
The testing configuration set-up of a 4-point loading test 1s
usual in civil engineering to generate bending and shear cracks.
The shear cracks are parallel to the diagonal load pressure
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