International Symposium (NDT-CE 2003)Non-Destructive Testing in Civil Engineering 2003
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Analysis of the crack characteristics under shear load of reinforced concrete structures by using photogrammetryJosef Hegger, Institute of Structural Concrete (IMB), University of Technology, Aachen, Germany
Stephan Görtz, Zerna, Köpper & Partner Ingenieurgesellschaft für Bautechnik, Bochum, Germany
Frank Häusler, Institute of Structural Concrete (IMB), University of Technology, Aachen, Germany
An economic design of structural components requires the quantification of the different mechanisms of shear resistance. Latest design models consider the aggregate interlock of shear cracks and their influence on the load bearing capacity. It is important to investigate if there is a parallel shift of the shear cracks which creates a concrete contribution by aggregate interlock, or if the existing cracks just widen vertically. In order to determine the displacement of the crack edges the measurement technique of digital photogrammetry was used. The displacement of the shear field was recorded by the digital analysis system PHIDIAS-MS . Subsequently the cracks were localized using a computer program developed at the Institute for Structural Concrete (IMB). Thereby the crack widths and the parallel shift of the edges could be determined. By comparing different load levels it was possible to derive the friction forces within the cracks.
The crack behaviour has a significant influence on the ultimate load bearing capacity in the latest design models. Cracks do not only open vertically but there is also a parallel shift of the cracked edges, which is blocked by the mutual interlock caused by the contact of the coarse edges (Fig.1). In this way the ultimate load bearing capacity can be increased, which can result from the more favourable inclined cracks or also by the force transferred between the cracks.
By using planar measuring methods the deformations after the crack-formation were analysed accurately. Thereby the structure is investigated at different load levels. The deformation and damage are analysed on the basis of deviations. Besides the course and the opening of the cracks the parallel shift of the edges can be stated by editing the results of the measurements.
2. Analyses of the development of cracks
2.1 Method of photogrammetry
In the region of the expected shear cracks the deformations of the I-beams were registered area-wide. Therefore black measuring tags with a white frame were attached to the web on an area of approximately 27,5 x 100 cm spaced 2,5 cm (Fig. 2, left). The maximum distance of the measuring tags results from the crack which is created between two tags in order to determine the widening of the crack precisely. An exact equidistance of the tee meshwas not necessary since relative movements of points were analysed. Due to the high-contrast transition the tags could be localised by picture-processing-algorithms. Therefore the coordinates of the tag's center could be determined. The core diameter requires a minimum of 6-8 pixels per picture in order to show accurate images. Thus the diameter of the measuring tag had to be at least 5mm. In order to transform the coordinates of the displacement into the object area, calibration sticks, each with three fix aiming-points, have been attached under and above the experimental beam without being coupled to it. The distances of these fixed points were surveyed closely before and after the tests since they served for scaling the area for the measuring points. For selected load levels nine pictures at different positions of the measuring field were made using a digital camera (1500 x 1000 Pixels) (Fig. 2, right). Each picture contains all measuring tags and the calibration sticks.
2.2 Processing of the measurement
After the three-dimensional coordinates of the measuring tag were located, the deformed structure could be represented (Fig. 4) and a first evaluation could be made. The typical deformation and the failure crack of a slightly shear reinforced beam is clearly recognizable. In fig.4 each corner of a rectangle represents a measuring tag.
To derive the widening of the crack an algorithm was developed at the IMB which calculates the crack-opening vectors from the 3-D coordinates. Thus the crack width w and the parallel shift of the crack edges v can be determined.
The method of analysis can be divided into 4 steps.
The shear field is divided into rectangles in which the corners are the measuring tags. Based on the measured corner point displacements and by using bilinear shape functions , the principle tensile strains e1 are determined. By comparing the calculated strains with the tensile strain limit et of the concrete, the cracked elements could be differentiated from the uncracked elements.
The strains along the edges of the cracked elements were calculated. The crack will pass through the two edges with the highest tensile strains.
A crack separates the element into two parts. Based on the assumption that the deformation of the element is governed by the crack opening, it is possible to determine a crack opening vector with its corresponding crack opening angle q.
The crack opening vector is divided into components parallel and perpendicular to the crack angle b as shown in fig. 5d. These components are the required relative displacement of the crack width w and the parallel shift of the crack edges v.
The average vertical strains of the shear field, which have been recorded at several tests by using the method of photogrammetry, indicates a clearly dependence from the shear reinforcement ratio. For beams with low shear reinforcement ratios, the stirrups exhibit large strains immediately at first cracking. For higher shear reinforcement ratios the cracks were restrained by the low strains in the stirrups up to higher load levels. The lateral strains of the shear field do not depend on the shear reinforcement ratio, but as a result of the approximately same longitudinal reinforcement ratio, only on the external load.
Nearly the same dependences as shown for the shear field strains are detectable for the measured crack openings as well. Therefore the ratio between the vertical (Dz) and the lateral proportion (Dx) of the whole crack opening increases obviously with declining shear reinforcement ratio. According to the generally flater crack angle at low shear reinforcement ratios , the crack width predominates the parallel shift of the crack edges at the segmentation of the vertical proportion Dz. It can be assumed that there is no shear transfer possible by aggregate interlock for low shear reinforcement ratios, independent of the roughness of the crack borders, even for lower load levels. Fig. 6 shows this exemplary for the slightly stirrup reinforced test LC 1L.
For high shear reinforcement ratios the crack width at failure was limited to less than 0,5mm by the low strains in the stirrups. An exact analysis of the cracks showed that the crack edges were not completely separated and a slight transfer of forces across the edges was still possible. The results of the measurement show that the crack width and the parallel shift of the crack edges are of approximately the same order of magnitude. Using the empirical equations according to  it is detectable that shear transfer occurs due to aggregate interlock, but the proportion of the ultimate load bearing capacity is quite low.
For the investigation of the crack development and the crack behaviour it was necessary to measure the displacements of the shear field and the parallel shift of the crack edges for selected load levels. Using a digital analysis system the displacements of the measuring tags were determined. By dint of an added computation algorithm the cracks were located and the crack opening was calculated. From the calculated crack widths and parallel shifts of the crack edges the transferable forces by aggregate interlock were determined.