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, **punching** **shear** 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**.

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Much research has been dedicated to the study of the **punching** **shear** 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 **punching** **shear** database is extensive [1], [2], not all parameters have been sufficiently studied. For example, the **punching** **shear** behaviour of **reinforced** **concrete** **slabs** supported on L, T, and cruciform-shaped columns has received limited attention [3], [4] even though most current worldwide design codes include provisions for these column shapes [5], [6]. The derivation and reasoning behind these code provisions are unclear.

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While considering the impact load carrying capacity of **reinforced** **concrete** **slabs**, two failure mechanisms are of importance, namely bending failure of the **slabs** and **punching** **shear** under impact. In many cases, however, the dynamic response of **reinforced** **concrete** **slabs** 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 **reinforced** **concrete** **slabs** 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 **shear** **reinforced** **slabs** 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 **concrete** **slabs**, 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.

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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 **punching** **shear** **resistance** of FRP-**reinforced** **slabs**. This paper provides the designer with a reliable and accu- rate design tool for estimating the **punching** **shear** strength of two way **slabs** **reinforced** 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.

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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 **continuous** **concrete** structures internally-**reinforced** with hybrid steel-BFRP bars.

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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.

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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 **punching** **shear** 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.

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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 **punching** **shear** capacity under premature loading tests. This effect is clearly observed in Tables 2-3 and Figure 4c for Group 3 specimens. The **punching** **shear** capacity was affected by the time of loading, even for the specimens with accelerating admixture, but the **punching** **shear** 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.

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Abstract **Punching** **shear** reinforcement systems such as studs and stirrups are used to improve the **punching** **shear** 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 **punching** **shear** reinforcement. Several important parameters are incorporated in the **analysis**, namely the column size, the slab thickness and the **punching** **shear** 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 **punching** **shear** behavior to an acceptable accuracy.

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A more realistic rational model was previously pro - posed by Shehta [10] and Shehta and Regan [11]. 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. **Reinforced** **concrete** flat **slabs** are widely employed in structural systems. The location of the slab - column connection is the most sensitive part of the flat slab [12]. Although, several theoretical models are proposed in the literature to compute the **punching** strength of the **reinforced** **concrete** **slabs** [13] and only a few research projects have been conducted on the **punching** **shear** strength of **concrete** **slabs**. Theoretical approaches proposed by few researchers [6, 8] are quite complicated. Different approaches like Truss Analogy [14], Fracture **Analysis** [15], Finite Element **Analysis** [16, 17] and the modified mechanical model [18] have also been proposed. Eas ier methods were proposed [19, 20] for calculating the **punching** **resistance** of simple and high strength **concrete** **slabs** respectively.

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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

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Sharaf et al. [4] studied the effect of strengthening by externally CFRP strips on full-scale slab-columns failed in **punching** **shear**. 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 **punching** **shear** **resistance** 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. [5]). **Punching** **shear** 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. [5] 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 **punching** **shear** failure. Guan [6] and Moe [7] investigated the case of failure in footing and **reinforced** **concrete** **slabs** in **shear**. A wide range of tests was conducted on a diversity of **slabs** with openings close to the columns.

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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 **punching** **shear** **resistance** of high strength **concrete** **slabs** 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 **punching** **shear** strength

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It was also demonstrated that an increase in the post- cracking stiffness of the slabs provided by the higher steel fibre dosage decrease the angle of the inclined punchi[r]

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Ospina et al. (2003) [3] 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 [5] 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**-**shear** **resistance** of the FRP-RC slab-column connections. Zhang et al. [7] 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**.

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strength of **concrete** **slabs**: 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 **punching** **shear** **resistance** for **reinforced** **concrete** slab-column connection may be needed. The strengthening of slab-column connection against **punching** **shear** **resistance** 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** [6]. The present study aims to evaluate the using of FRP materials to increase the **punching** **shear** **resistance** of **concrete** slab-column. The values of **punching** **shear** 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.

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was reached on average (Faria et al. 2012). A similar solution for improving **punching** **shear** **resistance** 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 **punching** **shear** **resistance** increase of up to 114% was observed in the ductile case.

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A series of the elements tested by Swamy and Ali [5] were selected to gain a better understanding of the predicted effect of the steel ﬁbre volume on the **punching** **shear** 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 **punching** **shear** 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 **punching** **shear** strength for elements tested by Swamy and Ali ( [5] are shown in Fig. 9 b, with an excellent correlation ob- served between the model predictions and the test results. 5. Code-like formulation

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After the war in Kosovo buildings are often constructed using **reinforced** **concrete** 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 **punching** **shear** 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.

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