EXPERIMENTAL VERIFICATION OF PUNCHING SHEAR RESISTANCE OF FLAT SLAB FRAGMENTS

The paper deals with the loading test results of an experimental reinforced concrete flat slab fragments, which were supported by an elongated rectangular column. The slab specimens were 200 mm thick and were designed without any shear reinforcement. During the experimental test, in addition to the shear resistance of the flat slab, deformation state during the whole loading was also examined. Deformations were measured in two ways, using LVDT sensors placed under the slab specimen and by photogrammetric measurement based on measuring the deformations of the code marks glued on the top surface of the specimen. Based on the photogrammetry, it was also possible to determine the concrete strains on the specimen upper surface. The concrete strains on the bottom surface were measured around the column using the strain gauges. By experimentally obtained punching shear resistance, the accuracy of the standard design models for prediction punching resistance was compared. The results of the experiments were also compared with the results of a numerical non-linear analysis performed in the Atena program.


INTRODUCTION
Punching shear resistance of locally supported slabs is still a current and discussed topic in the field of assessment of load-bearing structures of buildings. Punching shear of slabs supported on a rectangular column, where we assume an uneven distribution of shear load, has been investigated in many scientific research teams in the Slovak Republic and abroad.
The punching shear resistance of slabs supported by a rectangular column is lower than the shear resistance of slabs supported by a square column with approximately the same length of control perimeter. This phenomenon is due to the fact that the formulas for the evaluation of the punching shear resistance of the slabs include empirical factors that take into account only the geometry of the column, but do not take into account the deformed shape of the slab [1]. In addition to the influence of the column geometry, the influence of various other aspects was investigated, such as the influence of loading conditions or new types of shear reinforcement [2,3].
This research follows an analysis from 2019 [4], when, based on a nonlinear analysis in the Atena program, it was preliminarily concluded that in the case of uniform loading around the entire specimen, the length of the control perimeter is not reduced. In order to confront this statement, the specimen was further analyzed with a 0.15 m x 0.95 m column, which was subjected to a load test as well as a 3D nonlinear analysis in the Atena program.

Eurocode 2
The shear resistance in flat slabs without shear reinforcement is ensured by several aspects. It mainly depends on the aggregate interlock in shear crack, compressed concrete area under neutral axis and longitudinal reinforcement. These facts are considered in the empiric formula which determines the punching shear resistance of a slab according to EC2.

Model Code 2010
Model Code 2010 is based on the Critical shear crack theory (Ruiz, Muttoni 2014). The shear resistance which depends on the crack widths is proportional to the slab rotation ψ. However, the load rotation is significantly non-linear. This fact was investigated with the result of a quadrilinear moment-curvature diagram which has been simplified for the design application. There are four levels of approximation of rotation calculation around the supported area. For this analysis the Level III of Approximation was used. The values of rs and mEd were calculated from a linear elastic model.

The non-linear analysis
The non-linear analysis was performed in Atena -program based on finite element method [5]. Several research teams dealt with non-linear analysis in Atena, including [6], who focused on the strengthening of flat slabs. According to the linear analysis, there is a partial decrease in shear forces at a distance of 1.5d from the support corners [4]. Figure 1 shows the decrease in shear forces of a specimen supported by a column with cross-sectional dimensions of 950 x 150 mm using different loading conditions. However, in the non-linear analysis, the reduction of the control perimeter length was not demonstrated despite the fact that the ratio of the longer column cross-sectional dimension to the effective depth was cmax / d > 3. This phenomenon is caused by several aspects including redistribution of stresses around the support. Model calibration was implemented on the basis of previous experiments [7].
Because 3D non-linear evaluations are time consuming, symmetry conditions were used and only a quarter of the whole specimen was modeled ( Figure 2

Experimental set-up
The experimental set-up consists of four hydraulic jacks placed around the specimen perimeter, which are spread by a system of beams. These beams are made of two UPE profiles which are fixed to steel bars ( Ø = 42 mm) placed among them and anchored to the laboratory floor. Concentrated forces are transferred from the hydraulic jacks to the bottom distribution pair of beams, which are supported with calottes to ensure joint connection of the frame and specimen.

Loading conditions
The first loading step of approximately 20 kN was performed to activate the experimental setup. Gradually even loading of the specimen was performed in individual loading steps of 50 kN and 100 kN, i.e. 12.5 kN (or 25 kN) per one hydraulic jack. Just before the expected failure, the loading step was reduced to 25 kN. Short pauses were taken between the individual steps to stabilize the specimen deformations, to record photos for the photogrammetry measurement and to draw newly occurred cracks.

Measuring devices
The concentrated load in the form of eight forces distributed around the specimen perimeter was measured by four load cells connected to one hydraulic system. The loading force from one hydraulic jack was applied to the specimen at two points with a mutual distance of approximately 1 m (distance of steel calottes).
Several measuring devices were also installed on the specimen, recording its deformation behavior during the entire process of loading until its failure. Strain gauges were glued to the bottom force cell hydraulic jack system of beams callotes steel support surface around the support according to the scheme in Figure 5a. Using the strain gauges, it was possible to determine the concrete strains both in the radial and tangential direction. Specimen deformations were measured in two directions using LVDT sensors located in the slab axis lines (Figure 4b). The full stroke range of used LVDT sensors varies from 50 mm located close to column to 300 mm located between to steel rods. The deflection measured in millimeters could be determined up to an accuracy of five decimal places.

Fig. 5 -The sensor layout scheme: a) strain gauges b) LVDT sensors c) code marks on the top surface of the specimen used for convergent photogrammetry measurement
In cooperation with the Department of Geodesy in Faculty of civil engineering of Slovak university of technology in Bratislava, a method of measurement using convergent photogrammetry was implemented in this experimental test. Multi-image convergent photogrammetry was performed to achieve 3D coordinates of observed points [8]. The Nikon D800E DSLR camera (full frame 36 Mpixel sensor) equipped with a Nikkor 35mm AF-S ED 1:1.8G lens was used to take photos around the specimen in each loading step ( Figure 6). To eliminate the blur motion caused by poor illumination conditions, an external flash was used. An exposure time of 1/250 s was achieved at the following camera settings: aperture priority -F/8, ISO 200, autofocus.

Fig. 6 -Image configurationaxo view (left) and top view (right)
131 observed points were signalized by RAD (Ringed Automatically Detected) coded targets, which enable automatic detection and measurement with subpixel precision. Images were processed by Photomodeler Software [9] on the principles of bundle block adjustment. The project scale was determined using two scale bars attached to the specimen surfacethe length of the scale bars was derived from the calibration plate of the Comet L3D scanner with an accuracy of 0.01 mm. The results of photogrammetric processing are shown below.

TEST RESULTS
The failure was fragile in both experimental tests, indicating that the collapse of the specimen was due to the achievement of shear resistance. The experimentally obtained values of shear resistance were compared to selected design models, which verified their reliability ( Table 2). The Vtest given in Table 2 is the sum of the maximum forces measured in the load cells and the body force of the specimen with a value of 31 kN. Based on the shear strength obtained from the experiment and non-linear analysis, the length of the control perimeter was derived using the shear resistance evaluation formula according to EC2 [10].

Tab. 2: Results obtained from experimental test and Atena compared to design models
The concentration of shear forces around the corners of the support can be confirmed by the formation of the first appeared shear cracks in this area. First, radial cracks formed and with increasing load were joined by newly formed tangential cracks. However, by comparing the experimentally obtained shear resistance with the values according to the design models, the necessity to reduce the length of the control perimeter was demonstrated for both specimens compared to selected design models, as their reliability reaches 0.87 to 1.12 considering the full length of control perimeter. Figure 7 shows specimen deformations in the lines of the main axes. According to design model EC2, a slab supported by a square column would have the same shear resistance as a slab supported by a column with a rectangular cross-section with the same length of control perimeter. The EC2 design model therefore only takes into account the length of the control perimeter, not the geometry of the support. However, by comparing the deformation courses of the slab, the influence of the column geometry on its shear resistance can be confirmed. Significantly larger deflection of the specimen was measured in the direction perpendicular to the longer side of the column cmax. In the case of specimen D00, the deflection in the direction perpendicular to the longer side of the column reached significantly higher values. This phenomenon is caused by the fact that the drawn deflection is already captured on the specimen with developed cracks, which arose as a result of previous loading, which had to be suspended and the specimen was unloaded again.

Strains
The concrete strains on the top surface of the specimen were evaluated on the basis of the results of photogrammetric measurements. The maximum strains reached a value of up to 4.1 ‰. Figure 8 shows the course of the concrete strains in the individual loading steps. On the top surface of the slab, no significant differences were observed in the concrete strains in the section through the center of the longer side of the column compared to the area of its corners. The concrete strains were measured on the bottom surface of the specimen in the area around the support using strain gauges glued in both the radial and tangential directions according to the diagram in Figure 5a. The largest concrete strains were measured in the tangential around the corners of the support (strain gauges no. 3 and 7), on the contrary, the contrary, the concrete strains in the radial direction reached the lowest values at these points ( Figure 10).