Figure 12 shows both radial and tangential stresses ( σ rad and σ tang ) for the continuous flat slab with concrete shrinkage. The most interesting strain limits are marked as follows: cracking of concrete (corresponding to ε cr , see also Figure 12(a)); maximum crack opening with residual tensile strength (corres- ponding to w ctu , see Figure 12(a), calculated as w ctu = ε t,u a m , where a m is the distance between cracks; see Belletti et al. (2017)); and yielding strain of reinforcement ( ε sy ). It can be seen from Figures 12(b) –12(d), that the peak value of radial stresses σ rad corresponds to the achievement of the residual tensile strength of concrete (crack opening w ctu ) in the sagging area, which corresponds to the maximum ring effect for self- confined slabs. Depending on the intersection with the CSCT failure criterion, punchingshear failure occurs before yielding of hogging and sagging reinforcement for high reinforcement ratio ( ρ hogg = 1·5%), after yielding of hogging reinforcement for medium reinforcement ratio ( ρ hogg = 0·75%) and after yielding of hogging and sagging reinforcement for low reinforcement ratio ( ρ hogg = 0·375%). Even if not reported in the present study, it is important to observe that the sequence of events remains the same without considering shrinkage of concrete.
Much research has been dedicated to the study of the punchingshear behaviour of rein- forced concrete flat slabs due to the brittleness of the failure. The majority of this past research has been experimental, and has involved the testing of isolated slab-column connections, where the portion of the slab included in the test approximates the negative moment area around the column. Even though the existing experimental punchingshear database is extensive , , not all parameters have been sufficiently studied. For example, the punchingshear behaviour of reinforcedconcreteslabs supported on L, T, and cruciform-shaped columns has received limited attention ,  even though most current worldwide design codes include provisions for these column shapes , . The derivation and reasoning behind these code provisions are unclear.
While considering the impact load carrying capacity of reinforcedconcreteslabs, two failure mechanisms are of importance, namely bending failure of the slabs and punchingshear under impact. In many cases, however, the dynamic response of reinforcedconcreteslabs subjected to projectile impact is governed by a combination of both bending and punching failure mechanisms. Within the framework of the IMPACT III benchmark project, organized by VTT Technical Research Centre, Finland and funded by several institutions including Swiss Federal Nuclear Safety Inspectorate ENSI, several experiments were carried out focusing on a combined bending and shear response of slabs impacted by a projectile. To investigate the ultimate resistance of the slabs with different layouts of longitudinal and transverse shear reinforcements, square shaped reinforcedconcreteslabs with a lateral dimension of approximately 2.1 m and a thickness of 0.25 m were subjected to impact of missiles with a mass of 50 kg and an initial velocity of up to 168 m/s. Aim of this paper is to improve numerical predictions of a combined bending and punching response of shearreinforcedslabs subjected to impact loading and to discuss the challenges involved. In order to evaluate the influence of shear reinforcement on the improvement of the impact load capacity of the concreteslabs, some of the experiments are simulated using three-dimensional nonlinear finite element analyses by explicitly modelling the transverse shear reinforcement. The results obtained from numerical analyses and their comparison to the experimental measurements can facilitate a better understanding of shear failure due to punching under impact.
4. The collected test results show that most of the existing for- mulas gave inaccurate results with a large scatter in com- parison with the testing results, and thus, a new formula or technique should be proposed for more accurate estima- tion of punchingshearresistance of FRP-reinforcedslabs. This paper provides the designer with a reliable and accu- rate design tool for estimating the punchingshear strength of two way slabsreinforced with FRP bars or grids. Two approaches are presented; the ﬁrst is the proposed equation and the second is the Neural Networks Technique. Each of them contains two new parameters, never used before; the effects of the elastic stiffness of the FRP reinforcement and the continuity effect of slabs on punching capacity as explained previously.
3 which makes them suitable for use in the alkaline concrete surrounding (Burgoyne et al., 2007; Parnas et al., 2007; Adhikari, 2009). On the other hand, BFRP bars are characterized by their lower cost and superior chemical resistance than their GFRP counterparts (El Refai, 2013; El Refai et al., 2014b; Elgabbas et al., 2015). Furthermore, sand-coated BFRP bars showed higher bond strength and higher adhesion to concrete than ribbed GFRP bars (Altalmas et al., 2015). It is important to note that few studies have recently focused on the use of BFRP bars as internal reinforcement. Therefore, codes and standards authorities are yet to formulate equations for the design and analysis of concrete elements internally-reinforced with BFRP bars. To the author’s knowledge, no studies have been performed to investigate the structural response of continuousconcrete structures internally-reinforced with hybrid steel-BFRP bars.
In this study, the testing arrangement adopted is similar to that used in tests undertaken previously at Sheffield [Li (1997) and Pilakoutas et al (1999)], using an existing rig for loading flat slabs, as shown in figure 1. The slab is supported through a column stub on a beam reacting against two reaction ring frames. Equal point loads are applied downwards symmetrically at eight locations on a circle of diameter 1.7 meters. The loading arrangement roughly corresponds to the circle of contraflexure over a column in an equivalent 4 meter uniformly distributed continuous span, or a 6 meters prototype span. Eight hydraulic jacks of 100 kN capacity are used for this purpose. The eight jacks are connected to the same pump, so that each jack applies the same load to the specimen.
This paper presents an analytical model based on the Critical Shear Crack Theory which can be applied to ﬂ at slabs subjected to impact loading. This model is particularly useful for cases such as progressive collapse analysis and ﬂat slab-column connections subjected to an impulsive axial load in the column. The novelty of the approach is that it considers (a) the dynamic punchingshear capacity and (b) the dynamic shear demand, both in terms of the slab deformation (slab rotation). The model considers in- ertial effects and material strain-rate effects although it is shown that the former has a more signiﬁcant effect. Moreover, the model allows a further physical understanding of the phenomena and it can be applied to different cases (slabs with and without transverse reinforcement) showing a good correlation with experimental data.
The accelerating admixture used in the Group 3 mix increased the early concrete compressive strength compared to that of normal concrete without accelerating admixture, and in turn, enhanced the punchingshear capacity under premature loading tests. This effect is clearly observed in Tables 2-3 and Figure 4c for Group 3 specimens. The punchingshear capacity was affected by the time of loading, even for the specimens with accelerating admixture, but the punchingshear capacity was improved compared to that of their companions without accelerating admixture at the same time of loading. Figure 4c shows the load-deformation behavior of the Group 3 specimens. It can be seen from the figure that the deflection at maximum load ranged from 6.22 mm to 7.85 mm. In addition, Specimens S3-3 had a higher deflection compared to that of its companion from the other groups because it had the lowest concrete compressive strength compared to those of the other group specimens as shown in Figure 4c. Figure 5(c) shows the load-steel strain behavior of the tested specimens. It was found also that none of the flexural steel reached the yield stress.
Abstract Punchingshear reinforcement systems such as studs and stirrups are used to improve the punchingshear strength of ﬂat slabs. A three dimensional ﬁnite element model (FEM) is developed through Ansys 10 computer software, to carry out the nonlinear analysis of 16 ﬂat-slab models with and without punchingshear reinforcement. Several important parameters are incorporated in the analysis, namely the column size, the slab thickness and the punchingshear reinforcement system in order to study their effects on the ﬂat slab behavior. A parametric study was carried out to look at the variables that can mainly affect the mechanical behaviors of the model such as the change of loading types and positions and slab with openings. Good correlation is observed between the results of the proposed model and other experimental one, resulting in its capability of capturing the fracture of ﬂat slab under punchingshear behavior to an acceptable accuracy.
A more realistic rational model was previously pro - posed by Shehta  and Shehta and Regan . It involves a more detailed analysis of the slab as a whole and of the concrete under stress concentration near the column face. This model gives a good account of both slab behaviour and the parameters affecting the punching strength, but in its present state it is considered to be too complicated to be handled by designers and adopted by current codes. Reinforcedconcrete flat slabs are widely employed in structural systems. The location of the slab - column connection is the most sensitive part of the flat slab . Although, several theoretical models are proposed in the literature to compute the punching strength of the reinforcedconcreteslabs  and only a few research projects have been conducted on the punchingshear strength of concreteslabs. Theoretical approaches proposed by few researchers [6, 8] are quite complicated. Different approaches like Truss Analogy , Fracture Analysis , Finite Element Analysis [16, 17] and the modified mechanical model  have also been proposed. Eas ier methods were proposed [19, 20] for calculating the punchingresistance of simple and high strength concreteslabs respectively.
ABSTRACT - A parametric study using Non-Linear Finite Element Analysis (NLFEA) was carried out to investigate the response of slabs on grade to industrial trucks with single wheel axles loading. The studied parameters were the load position in relation to slab edges, slab proportions, the reinforcement content, method of reinforcement arrangement, and the modulus of subgrade reaction. The subgrade is represented in the analysis by boundary-spring elements of a non- tension model to simulate the soil-resistance characteristics. The study showed that the load-carrying capacity of slab panels is substantially influenced by panel thickness and, to a lesser extent, the modulus of subgrade reaction. It was found that adequate and practical results can be obtained in case the safety factor of bearing capacity was assigned a value close to 7. In addition, increasing the modulus of the subgrade reaction enhanced the slab strength to some extent. The enhancement diminished with increasing the subgrade modulus beyond 2E-2 N/mm 3 . Moreover, the reinforcement
shear use variety of test configurations, a review of selected experimental setups is presented. Isolated specimens subjected to gravity loading at the center of the slab were tested among others by Elstner and Hognestad (1956), Kinnunnen and Nylander (1960) and Moe (1961). Elstner and Hognestad (1956), Hanson and Hanson (1968) and Corley and Hawkins (1968) tested specimens with distributed uniform load. Most of the slabs, tested under gravity load, were supported at the edges (Elstner and Hognestad (1956), Moe (1961), Sieble et al. (1980), Swamy and Alo (1982), Harajli et al. (1995), Adetifa and Polak (2005), Naaman et al. (2007)). However, Broms (2007) and Brikle and Dilger (2008) tested specimens supported at discrete points and not around the edges in order to simulate the points of contra-flexure. Specimens subjected to gravity load and unbalanced moments were tested by Hawkins et al. (1974), Robertson et al. (2002), Pan and Moehle (1989), Elgabry and Ghali (1987) and El-Salakawy and Polak (1999). Pan and Moehle (1989) tested slab-column connections subjected to lateral displacement cycles and gravity load. They found that the lateral drift capacity of the connections is dependent on the gravity to shear ratio. An increase in the gravity shear ratio with the lateral cyclic loading led to a reduction of strength, stiffness and displacement. It was recommended that the 0.4 gravity to shear ratio as the upper limit in order to have a drift capacity in the range of 1.5%. Many important contributions regarding the lateral cyclic loading applied to the slab-column connections have been offered also by Robertson and Durrani (1992), Megally and Ghali (2000) and Bu and Polak (2009).
Sharaf et al.  studied the effect of strengthening by externally CFRP strips on full-scale slab-columns failed in punchingshear. The variables of this experimental work were the amount and configuration of CFRP sheets. The results indicated that the strengthening by CFRP delay in the initiation of flexural cracks of the slabs. The increase in punchingshearresistance of the modified slabs was better than that for unmodified slabs by 16%. Thus, in the previous several years, many studies have considered the shear failure mechanism of self- compacting concrete (Lin et al. ). Punchingshear is brittle. The mode of failure which occurs without warning. An increase in fine aggregate content of SCC members may be a cause for concern, as it is believed to lead to a decrease in the shear strength of a structural member. Lin et al.  found that the increase in fine content may cause a reduction in aggregate interlock, which is considered as the main resisting factor for shear stresses in beams. The most recent construction technique alleviates this problem is by using high strength self- compacting concrete rather than using traditional shear reinforcement to enhance the capacity of the flat slab. In the case of flat floor systems, there is usually a need to create new elements that need openings near the columns. These openings are required for many reasons, such as ventilation, heating, sanitary, electrical ducting, and air conditioning. The presence of openings could reduce the quantity of concrete liable for resisting shear strength and unbalanced torque, which in sequence reduces the shearing ability to punch in the slab-column bonding area. Hence, the bonding area is more susceptible to brittle and punchingshear failure. Guan  and Moe  investigated the case of failure in footing and reinforcedconcreteslabs in shear. A wide range of tests was conducted on a diversity of slabs with openings close to the columns.
tables and the examples to explain the use of the tables for analysis of slab are presented. Kwan (2004) developed a new yield line method that can be applied to any convex polygonal-shaped slab. In this method, the deflections of the slab regions divided by yield lines are measured in terms of the dip and strike angles of the slab surfaces which can define the geometry of all kinematically admissible collapse mechanisms or yield line patterns. The external work done and the internal energy dissipation at yield lines are evaluated as functions of the dip and strike angles and the principle of virtual work is used to determine the corresponding load factor. The final solution is obtained by minimizing the load factor with respect to the dip and strike angles. A computer program to implement this method was also presented. Oliveira et al. (2004) reported the punchingshearresistance of high strength concreteslabs with rectangular supports and three different load patterns. Prabhat Kumar and Rajesh Deoliya (2004) found that the finite difference method is ver y for slabs to simultaneously satisfy the condition of bending and the serviceability is presented. Design charts are provided allowing practical application of this method to enable the design engineer to adjust the steel reinforcement and depth. Design charts are also provided to find out effective depth when the area of steel to resist the bending is just adequate for deflection criteria. Susanto Teng et al. (2004) summarize the research program on flat plate structures conducted jointly by the Nanyang Technological University (NTU) and the Building and Construction Authority (BCA) Singapore. The paper focuses on the punchingshear strength
Ospina et al. (2003)  reported that the behavior of an FRP-RC slab-column connection is affected by the elastic stiffness of the reinforcing material as well as the quality of its bond characteristics with the concrete. However, the FRP grids may not provide the same punching-shear capacity as the FRP bars owing to the difference in bond behaviour and concentration of stresses in the grids. Nguyen- Minh and Rovnak  concluded that both the size factor and the effect of the span-to-effective-depth ratio (L=d) should be taken into account in computing the punching-shearresistance of the FRP-RC slab-column connections. Zhang et al.  reported that the reinforcement type significantly influenced the punching strength of slabs and the concrete strength significantly affeced the load carrying capacity and the post-punching capacity of slabs. However, it was found to be a little influence on the stiffness of the cracked slabs.
strength of concreteslabs: 1- increasing the slab thickness in the vicinity of the column by providing a drop panel or a column head; 2- Providing shear reinforcement. Sometimes, after the construction of some building, the increase of punchingshearresistance for reinforcedconcrete slab-column connection may be needed. The strengthening of slab-column connection against punchingshearresistance by using traditional methods (steel plates, steel stirrups, steel studs, or increasing concrete dimensions) was studied [3-5]. Few studies concerned with using the FRP strengthening systems for flat slabs . The present study aims to evaluate the using of FRP materials to increase the punchingshearresistance of concrete slab-column. The values of punchingshear strength were predicted taking into account the contribution of the applied strengthening systems. The calculated values were compared with the corresponding experimental results in order to evaluate the used equations.
was reached on average (Faria et al. 2012). A similar solution for improving punchingshearresistance was presented in Section 3.1. In this case, four non-laminated prestressed CFRP straps (Meier and Winistörfer 1998; Lees and Win- istörfer 2011) were installed crosswise around the column (Keller 2010); see Figure 3.18(a)–(b). The thin, flexible straps allowed small radii of curvature and thus an optimum strap inclination of between 30° and 60° (perpendicular to the shear crack), avoiding a glancing intersection between the borehole (diameter 55 mm) and the upper concrete surface. Furthermore, the straps were anchored below the slab using steel anchors adhesively bonded to the concrete surface. Laboratory experiments on eight full-scale flat slabs showed that, although CFRP is a brittle material, a strap prestressing of at least 15% assured a ductile system behavior with a first peak load, a subsequent plateau with redistribution of forces from the concrete to the strap system and a second peak load at 89 to 103% of the first peak load. A punchingshearresistance increase of up to 114% was observed in the ductile case.
A series of the elements tested by Swamy and Ali  were selected to gain a better understanding of the predicted effect of the steel ﬁbre volume on the punchingshear strength of slab– column connections. The selected test elements had identical geometrical dimensions and ﬁbre type and the concrete compres- sive strength was similar for all batches. The failure criteria and the estimated load rotation relationships for the elements selected are presented in Fig. 9 a. As is shown in Fig. 9 b, the proposed model predicts well the increase of the punchingshear strength with the increase of the ﬁbre volume. Furthermore, an increase in the quantity of similar ﬁbres provides for an increase in the deforma- tional capacity. As the concrete contribution to the punching strength decreases with the increase of the slab rotation, the weight of the ﬁbre contribution becomes more relevant to the resistance mechanism. The predicted concrete and ﬁbres contribu- tions to the punchingshear strength for elements tested by Swamy and Ali (  are shown in Fig. 9 b, with an excellent correlation ob- served between the model predictions and the test results. 5. Code-like formulation
After the war in Kosovo buildings are often constructed using reinforcedconcrete flat slabs with no beams and no enlarged column heads combined with punctual supports such as columns of varying cross section and slenderness. The advantages of flat slabs are easy solution of architecture design that enables flexibility in the movement of non-structural walls in the desired position, easy placement of equipment, and installation underneath the slab. But these slabs are subjected to punchingshear failure of slab-column connections. Load concentration around the column head generally leads to increased stresses which cannot be absorbed solely in thin slab thicknesses.