Improving punching behavior of interior voided slab-column connections using steel sheets

Engineering Structures 199 (2019) 109614

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Improving punching behavior of interior voided slab-column connections using steel sheets

T

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Thaar S. Al-Gasham , Jasim M. Mhalhal, Hussain A. Jabir Civil Engineering Department, College of Engineering, University of Wasit, Iraq

A R T I C LE I N FO

A B S T R A C T

Keywords: Voided slabs Biaxial slabs Bubble decks Flat plate Punching strength Steel sheets ABAQUS Strengthening Energy absorption Ductility

In recent modern buildings, voided slabs have been extensively employed because of the high reduction in their self-weight up to 35%. Limited studies have been conducted on such slabs, and no significant drop in the flexural strength was reported due to introducing voids. In contrast, a considerable drop in the punching strength of the voided slabs was addressed. Therefore, this study presented a new and simple method for improving the punching shear strength and behavior of such slabs by employing steel sheets. Five half-scale specimens were fabricated. One slab was solid and kept as a reference specimen, while the others were voided slabs. They contained 96 spherical voids distributed uniformly throughout the slab area, three of them were strengthened by six embedded steel sheets, three sheets in each direction. The sheets were orthogonally configured and intersected below the column stub. The variable of the study was the sheet thickness (0.8 mm, 1.0 mm, and 1.2 mm). The specimens were subjected to a gradually concentrated load through the column up to collapse. The test results revealed that significant losses were recorded in the strength, stiffness, ductility, and energy absorption of the voided slab without sheets compared with the reference one. However, the strengthening of voided slabs by sheets was superior not only in retrieving these losses but also in exceeding them. Besides, FE analysis was conducted, utilizing the ABAQUS program, for profoundly illustrating the experimental findings and performing a parametric study. Based on the FE observations, the activation of sheets was found to be increased by enlarging their thickness, and the best activation was observed when gathering the sheets below or nearer the column stubs.

1. Introduction In the current reinforced concrete (RC) constructions, RC flat plates are frequently used where a slab is directly supported on columns without column capital, drop panel, or beams. The flat plates have several advantages, compared with other slab types, such as quicker construction period, relatively inexpensive formwork, smaller structural depth, and more suitability to architectural demands [1,2]. However, flat plates have a relatively low flexural stiffness, and they are more susceptible to punching failure in the zone of slab-column connections. Therefore, their depth should be increased, especially when long spans are desired. In this state, their self-weight augments, leading to several disadvantages like the high consumption of raw materials, and the need for larger columns’ sections and more massive footings. To get the required depth of flat plates with keeping their self-weight as light as possible, void formers can be inserted inside slabs forming voided slabs [3–5]. Voided slabs were first invented by Danish engineer Jørgen

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Breuning in 1990, in which a considerable amount of concrete is replaced by plastic voids positioned between the top and bottom reinforcement meshes before casting. These slabs are sometimes called bubble decks or biaxial slabs, and they can act as two-way slabs where loads can be transferred in any direction. The self-weight of voided slabs is about 30–35% lesser than that of solid slabs with the same flexural strength [6–8]. Furthermore, voided slabs are considered as green structures besides other benefits, including the high load-carrying capacity and material-saving [9,10]. In general, the flexural strength of such slabs was investigated by several researchers [11–15], they asserted that the voided slabs attained approximately the same flexural strength of the solid slabs with an identical depth, but voided slabs showed a slightly lower flexural stiffness than solid ones did. However, a noteworthy decrease in the one-way shear strength of the voided slabs was addressed, reaching 27–40% below that of the solid slab [16]. Furthermore, the one-way shear strength and the development of the shear cracks were found to be remarkably affected by the shape of voids, whereas the material of voids affected only the shear capacity

Corresponding author at: Rabee District/University City, Wasit-Kut 10013, Iraq. E-mail address: [email protected] (T.S. Al-Gasham).

https://doi.org/10.1016/j.engstruct.2019.109614 Received 30 May 2019; Received in revised form 23 August 2019; Accepted 29 August 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Engineering Structures 199 (2019) 109614

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altering the control perimeter of the well-known codes for calculating the punching strength of such slabs as well as on the configuration of a solid zone around columns. However, the introduction of a solid zone of complex shape requires significant attention from workers, which may lead to delay in the construction time or increase the number of workers. Thus, both the benefits and economy of the voided slabs will be reduced. Furthermore, the previous studies have not pointed out to a remarkable enhancement in either the punching shear strength or the failure mode of voided flat slabs. The brittle punching failure mode was reported despite adopting complex shapes of the solid zone around the column. Therefore, a new technique should be developed to enhance the punching strength of voided slabs significantly rather than introducing a solid area around the column.

[17]. Similarly, a significant drop in the punching strength of the voided slabs was registered [18] due to replacing a large amount of concrete by voids in the critical section responsible of resisting the enormous punching stresses induced around the column [19,20]. There are various definitions for the critical section of the solid slabs in the well-known international codes [21,22]. In the ACI 318-14 code [23], the critical section is defined at a distance of d/2 from a column face (d is the effective slab depth). According to the Euro code 2 [24], EC2, the critical section is positioned at a distance 2d from the column face. In the voided slabs, the definition of the critical section is so complicated since it substantially changes with varying the arrangement and shape of voids [19,20]. In the last two decades, relatively few studies have been conducted on the punching strength of voided slab-column connections. They mainly focused on defining the location and shape of the critical section and enhancing the punching strength by leaving a solid area around columns without voids. Various shapes of voids were used like oval, donut, cuboid, and spherical. In 2002, Schnellenbach-Held et al. [3] performed an experimental study on six voided flat plate specimens with varying thickness (240 mm and 450 mm). They showed that columns punched out the slabs through a section placed d/2 from the edge of the column and the voided slabs attained the same punching strength of solid slabs when voids were positioned beyond the control perimeter of ACI-code. In contrast to this, other studies [25,26] highlighted a drop in the punching strength of voided slab, about 34–50% in comparison with a solid slab despite voids were shifted beyond the control perimeter at a distance, equal to 1.5 times the slab thickness, from the column face. Therefore, a solid zone (without voids) was proposed to realize the same punching strength of a solid slab. According to [25], the solid zone should be expanded at a spacing of three times the slab thickness measured from the column face while it should be extended 2d from the column face based on the proposal of Kwak et al. [26]. Further recommendations were reported in [5,27] to adjust the ACI 318-14 [23] equations for determining the punching capacity of voided flat slabs by considering an additional control perimeter besides that of the ACI-code. Han and lee [5] suggested the additional perimeter to be at a section resulting in the lowest punching shear strength. The additional control perimeter, proposed by Lee et al. [27], locates at the internal face (nearer to column) of voids, which are sorted at the first row. In 2017, Valivonis et al. [19] attempted to enhance the punching shear strength of the voided slab with shear bolts through introducing a solid zone around the column face, two configurations for the solid zone were adopted: rectangular and cross shapes. They stated that the cross shape was the best in improving the punching strength of the voided slabs by about 18% compared with slab having voids along the entire area. Additionally, they proposed an adjustment on the procedure of EC2 code to evaluate the punching strength of the voided slabs; the proposed method predictions were in a good agreement with the experimental results. More complex shapes of the solid zone were suggested by Chung et al. in 2018 [20]. They arranged the donut voids around the columns based on the critical perimeter of ACI-code [23], so zero, four, or eight voids intersected the critical perimeter, and the results were compared with a solid slab. The maximum reported loss in the punching strength was 13%. It is essential to mention that the reduction percent in the punching strength of the voided slabs, with respect to the solid counterpart, was different among the performed studies [5,18,20,28–31]. This percent ranged from 4% to 50%, depending on the shape of voids and their arrangement around the column. The smallest percent was reported for the spherical voids, while the largest one was for the cylinder-shaped voids. Generally, these studies are very few, although the punching failure represents the most critical case facing the voided slabs, which are often constructed in the form of flat slabs. They all primarily focused on

2. Significance of research This study proposed a new and simple solution for improving the punching shear behavior of the voided slabs using steel sheets. A total of six sheets were embedded in each voided slab, three sheets in each direction. The sheet thickness was variable (0.8, 1.0, and 1.2 mm). The activeness of the proposed method was verified through an experimental comparison with a voided slab having no sheets and a solid slab. After that, a numerical analysis was implemented to explain the enhancement mechanism of sheets besides performing a parametric study. Two parameters were assessed: the thickness and arrangement of the sheets. 3. Test program 3.1. Description of experimental specimens In order to fulfill the goal of this investigation, five half-scale specimens were constructed. They represent an interior central column connected to a slab bordered by the lines of contra-flexure. The slabs were square in the plane, measuring 1000 × 1000 mm, with a total depth of 90 mm. The central column was also square with dimensions of 120 mm × 120 mm with a 280 mm height, extending from the top surface of the slab, Fig. 1. It is worth mentioning that the dimensions of the specimens are approximately comparable to those adopted by Binici and Bayrak [32]. Although the use of linearly scaled specimens in the experimental programs of reinforced concrete members is common because of laboratory limitations, the nominal shear stress in scaled-down specimens is higher than that in the corresponding full-scale one due to the size effect [33,34]. However, the size effect on the thin slabs (thickness is smaller than 400 mm) is limited and depends, in addition to the thickness of the slab, on the ability of a member to redistribute internal forces owing to yielding of reinforcement and cracking [35].

Fig. 1. Dimensions of specimen. 2

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Fig. 2. Arrangement of inserts inside the specimen.

22% of the height of the sheet) to make the cut area from sheets as smaller as possible. The distance between holes in one line was approximately equal to 2d; this means the sheets were to be bonded into the slab at an interval of d (the distance between two successive holes). Moreover, the six steel strips were assembled at the intersection zone in the center of slabs by making slots extended approximately to the mid-height of strips. These slots were in opposite directions, where they were at the top of strips placed in a specific direction and at the bottom of strips positioned in the orthogonal direction. Then, the assembly was asserted by overlapping the slots each other, and the overlapping lines were welded (Fig. 3d) to ascertain a rigid connection among those six strips. The slabs were symmetrically reinforced in the bottom and top, using 22Ø 6 mm deformed steel bars with a yield strength of 511 MPa and ultimate strength of 633 MPa. The clear concrete cover was 10 mm, producing an average effective depth (d) of 74 mm. Accordingly, the average ratio of the tensile reinforcement was 0.84%; this ratio was selected to ensure the failure to be in the punching mode [33]. The bars were distributed at the top and bottom meshes in a configuration shown in Fig. 4 for fixing voids in their planned positions. For the column stub, 4-Ø10mm deformed bars were used as the main reinforcement with a yield strength of 484 MPa. These bars were 90° hooked directly above the bottom steel mesh. Besides, Ø6mm deformed bars stirrups were provided at a spacing of 60 mm center-tocenter, as shown in Fig. 4d. Usually, obstacles in voided slabs are more than in solid slabs, making a reach of concrete into available narrow spaces more complex. Therefore, the self-compacting concrete was adopted in producing all five specimens. The raw materials used were ordinary Portland cement, well-graded crushed gravel, sand, water, and superplasticizer. The maximum size of crushed gravel was 6.7 mm, which was less than of 3/ 4 the clear cover. All specimens were cast from one concrete batch for averting the variation in the concrete strength. The average 28-day cylinder concrete compressive strength was 28.2 MPa.

Furthermore, Dönmez and Bažant [36] reported that the size effect is significant when the thickness of a member is greater than 500 mm, and for the smaller size, this influence can be ignored. In this paper, the study is limited on the thin slab and therefore scaling down the slab thickness by a factor of ½ (from 180 mm to 90 mm) seems to be acceptable to generalize conclusions due to the limited effect of the size. In general, one specimen (S) was made with a solid cross-sectional area and kept as a reference specimen. The others were voided slabs and contained 96 spherical voids with a 70 mm diameter inserted inside the slabs at the depth center, see Fig. 2. These inserts were uniformly distributed throughout the entire plane area at a spacing of 90 mm on center. A small distance, 40 mm, was left between the column edges and the closest face of the first row voids; it represents nearly d/2 to avoid possible segregation that could happen in this zone, where the available rooms were relatively narrow. The concrete ribs in between voids were 20 mm wide, and the concrete flanges located above and below the inserts were 10 mm thick, as shown in Fig. 2. Three of the voided slabs were equipped with six steel sheet strips for enhancing their punching strength, three strips at both longitudinal and transverse directions. In each direction, the three strips were placed at the center of the three central ribs and introduced along the specimen length, 1000 mm, to provide the required development length. Moreover, these six strips were connected orthogonally to each other directly below the column stub, as illustrated in Fig. 3. Also, these strips were inserted directly between the top and bottom steel meshes with a height of 46 mm and a variable thickness of (0.8, 1.0, and1.2 mm). The yield strength of these sheets was approximately identical, equal to on average 243 MPa. The remaining one voided slab was without strips. Thus, the voided slabs were named by a designation comprising a letter (V) followed by a number referring to a thickness of the steel strip (i.e., V0 = voided slab without strips and V0.8 = voided slab with strips of a 0.8 mm thickness). Table 1 displays the properties of the five experimental specimens. To anchor sheets into slabs, they were perforated with two rows of 10 mm-holes to allow passage of aggregate. The holes were regularly distributed along the length of sheets in a staggered arrangement with a distance of 150 mm on center, and a spacing between the two rows was 16 mm on center, see Fig. 3c. It is essential to state that the idea of anchoring the sheets using holes was suggested by Lameiras et al. [37]. They embedded glass-fiberreinforced polymer plates in concrete blocks, and then pull-out tests were performed. They stated that the diameter of the holes should be larger than the maximum aggregate size, and the bond strength enhanced as the hole number increased. However, no recommendation on the distance between holes was given. In this investigation, the holes’ diameter was selected to be nearly 50% greater than the maximum aggregate size (6.7 mm), and this diameter seems to be suitable (nearly

3.2. Test configuration and instrumentation On the same day (28 days after casting), all slabs were tested under the effect of a concentrated load applied through the column stub, as shown in Fig. 5. This load was subjected gradually by a hydraulic jack with a capacity of 2000 kN up to the collapse of the specimen. The displacement-controlled scheme was adopted in applying the concentrated load with a speed rate of 0.5 mm/min. The specimens were positioned into the testing frame and rested simply on roller lines along four edges (square perimeter) with a clear span of 900 mm. Thus, the corners of the specimens were free to uplift during the test. This setup is convincing for representing an interior slab-column connection 3

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Fig. 3. Details of steel sheets, (a) arrangement of voids and steel sheets inside specimens, (b) orthogonal connection of steel sheets, (c) dimensions of steel sheets and (d) welding line.

span (directly below the column center). Furthermore, the strain of tension bar was monitored using electric strain gauges mounted on the central bottom bars in both longitudinal and transverse directions. They were five gauges in each direction distributed at a distance, measured from the column face, ranged from 0.0d to 2.0 d at an interval of 0.5d. Likewise, the strain of central steel sheets was observed at their mid-height in both directions through five strain gauges, which were placed at an angle of 45° with their length at a spacing ranging from 0.0d to 2.0d with an interval of 0.5d. Fig. 6 shows the location of strain gauges for both reinforcing bar and steel sheet. To trace the crack propagation in the bottom specimen face (tension face), a high accuracy camera, endoscope camera, was utilized. This camera is a handheld type connected to a computer. Finally, all instrumentations used for observing the test results were connected to a data logger, Data taker G85, which registered readings

Table 1 Properties of the experimental specimens. Designation

Cross-section type

Thickness of steel sheets (mm)

S V0.0 V0.8 V1.0 V1.2

solid voided voided voided voided

– – 0.8 1.0 1.2

restricted by the lines of contra-flexure where the moment is zero. This setup has been adopted in the most punching shear investigations since the 1950s [34]. The applied load was recorded by a load cell situated between the column stub and the piston of the hydraulic jack. Also, the central deflection of specimens was registered using a linear variable differential transducer (LVDT) placed underneath specimens at the mid4

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Fig. 4. Details of reinforcement, (a) 3D view, (b) front view, (c) top view and (d) column reinforcement.

cracks were integrated, and the specimen exhibited the sudden and brittle punching shear failure mode (see Fig. 7a). On the tension face, the punching shear failure surface formed at a distance of 2.9 d (233.5 mm) measured on average from the column edges. The voided specimen without steel sheets (V0.0) also failed in the punching shear mode. Generally, this specimen displayed much fewer cracks than those seen in the solid specimen (S), and the diagonal cracks did not develop more in this specimen, as illustrated in Fig. 7b, due to the inverse relationship between cracks and voids number [5]. Besides, the shear failure perimeter of V0.0 specimen appeared nearer to the column face than that of S specimen did, at an average spacing of 160 mm (2d). This distance indicates that the punching cracks passed through the voids of the first row and reached the tension face of the V0.0 specimen at a point located approximately below the center of voids of the second row.

at each second of the test event and then transferred these readings directly to a computer.

4. Test results and discussion 4.1. Cracking pattern and failure modes In the solid specimen (S), the flexural cracks were observed early on the tension surface (bottom face). Cracking initiated firstly as fine flexural cracks in the central zone of the specimen, perpendicular to the direction of steel bars. By increasing the applied load, more radial and tangential cracks occurred and extended toward the specimen edges. As the load was augmented further, a set of diagonal cracks appeared, developing from or near the column corners, and oriented to the external edges and corners of the specimen. At the collapse, the diagonal 5

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were almost identical and comprised two stages, pre-cracking, and postcracking stages, respectively. The pre-cracking stage started from the beginning of the experiment up to initiation of the first flexural crack. Subsequently, the second stage (post-cracking stage) commenced and continued until reaching the ultimate limit state, in which cracking led to a reduced stiffness (as expected). Finally, the load-carrying capacity dramatically declined due to punching the column stub through the slab depth; the nature of this failure was brittle. For the three specimens with steel sheets (V0.8, V1.0, and V1.2), the load-deflection responses were entirely different from that recently has been explained due to the presence of the steel sheets. In these responses, four stages were distinguished. The first two stages were comparable to those observed in the S and V0.0 specimens. The third stage represents the descent in the load-carrying capacity of voided slabs, at which the loads gradually dropped from the ultimate loads to forces, corresponding nearly 85%−86% of the peak loads. This behavior can be attributed to the full cracking of the concrete below the column stub that was unable to resist a further load and to the complete yielding of steel sheets in the central zone below and near the column stub. These sheets, however, prevented the column from penetrating the slabs suddenly, and they also redistributed the applied load to the remote parts that could carry an additional load. Then, the fourth stage was noticed where the central deflection enormously rose without substantial change in the subjected load. This stage is known as the plastic plateau zone, which refers to the remarkable enhancement in the ductility of voided slabs because of employing the steel sheets in strengthening against the punching shear failure. At the end of tests, these three specimens failed in a more ductile and gradual mode that was a combined flexural-punching failure. It is worth highlighting that in the voided slabs with steel sheets, the ultimate load and the failure load were not equal, where the failure loads were approximately 85–86% of the corresponding the ultimate ones. In contrast, these two loads were the same for both S and V0.0 specimens.

Fig. 5. Test set-up.

Fig. 6. Positions of strain gauges.

The remaining three specimens (V0.8, V1.0, and V1.2) with embedded steel sheets of (0.8 mm, 1.0 mm, and 1.2 mm) thickness, respectively, experienced approximately the same crack distribution that was utterly different from what was noticed in S and V0.0 specimens, in which more diagonal cracks grew from the center of the specimens and propagated towards the specimen edges and corners. However, their width was much smaller than that of cracks observed in the solid specimen (S). As the applied load increased, additional diagonal cracks developed and the oldest ones extended further to the supporting lines as well as the column stub penetrated excessively the specimens, approximately into half the slab depth before failure. This was due to the presence of steel sheets, which were able to sustain the column stub and transfer its load into other parts of the slab that still could resist more load. Just before the collapse, several tangential cracks connected in an irregular shape around the column beyond the outer face of the first row voids. After that, the three specimens were failed in the combined punching-flexural failure mode that was gradual and ductile, as seen in Fig. 7c. Based on visual inspection on the area where concrete spalled off, no remarkable slip between sheets and concrete was observed in the strengthened slabs. Thus, the use of embedded steel sheets was of excellent effectiveness in improving the failure mode. This mode changed to ductile one rather than the brittle shear failure that always appears in voided slabs, even if voids are shifted far away from the column faces or shear bolts are used [5,19,20].

4.2.2. Ultimate loads Table 2 summarizes the ultimate loads of all specimens, and these values are also plotted in Fig. 9 versus the thickness of the steel sheets. Closer inspection of the figure shows that introducing 96 voids along the entire area of the V0.0 specimen caused a drop in the ultimate load of about 22% compared to the solid slab (S). This finding was expected due to an excessive reduction in the critical cross-sectional area around the column that is mainly accountable for resisting the punching stresses induced in this zone. Furthermore, Fig. 9 highlights that the strengthening of the voided slabs by steel sheets not only improved their strength but also succeeded in recovering and passing the lost strength due to inserting voids along the whole area of the slab-column connection. Compared to the solid specimen (S), the three specimens with 0.8 mm, 1.0 mm, and 1.2 mm sheets realized larger ultimate loads by about 17%, 20%, and 28%, respectively. Concerning the voided slab V0.0, the enhancement in the ultimate load for these specimens was 50%, 54%, and 64%, respectively. This enhancement in strength could be attributed to several factors. The first factor is that the steel sheets played an important role in confining the concrete in between them and hence arresting the propagation and expansion of both diagonal and flexural cracks. The second one returns to the large vertical forces provided by these sheets, these forces significantly contributed to resist the applied punching force. The third factor was the ability of these sheets to covey the subjected load from the extremely damaged zone below and near the column stub to the farther ones. In addition, the sheets were supported on four edges, and thus they could provide to some extent direct strutting, leading to transferring a part of the applied load directly to the supporting lines. In the real situation, the case is opposite to the test setup where the loads are transferred from slab to the supporting

4.2. Load-deflection behavior 4.2.1. General behavior Fig. 8 compares the load- central deflection response of the five experimental slab-column connections. It can be revealed that the use of embedded steel sheets in the strengthening of the voided slabs led to a distinct change in the response of these slabs compared to other ones having no sheets (S, and V0.0). The response of S and V0.0 specimens 6

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(a) Specimen S(corrsponding deflection= 10.7 mm)

(b) Specimen V0.0 (corrsponding deflection= 7.0 mm)

(c) Specimen V1.2 (corrsponding deflection= 41.0 mm) Fig. 7. Crack patterns at failure loads.

Table 2 Test results of specimens. Specimen

Ultimate load, Pu, (kN)

Yield deflection, Δy, (mm)a

ultimate deflection, Δu, (mm)b

Ductility index

Toughness kN mm

S V0.0 V0.8 V1.0 V1.2

138.8 108.2 162.6 166.4 177.3

4.76 4.05 4.26 5.79 5.52

10.34 5.43 33.06 38.02 35

2.17 1.34 7.76 6.57 6.34

1145.97 515.87 4876.8 5609.4 5914.01

a Calculated based on the method of equivalent elasto-plastic energy absorption. b Calculated based on the fracture method.

4.2.3. Deflection The divergence in the deflection of the five specimens became remarkable after developing the first cracking, as can be seen in Fig. 8. Before cracking at the linear stage, all specimens gave almost similar deflection. Next, the voided slab V0.0, among the tested specimens, exhibited the softest load-deflection response, whereas the strengthened voided slabs displayed the stiffest behavior. In general, the enhancement in the stiffness seemed to be not proportional to the thickness of sheets where the V0.8 sample registered lower deflection than

Fig. 8. Force- central deflection curve of specimens.

columns. In other words, this means that the sheets can also provide direct strutting in the real situation since they are rested on the supporting columns. Finally, the steel sheets also acted as flexural reinforcement and accordingly the flexural strength of the voided slabs notably enriched.

7

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Fig. 10. Park definition for displacements [43], (a) definition of yield displacement based on equivalent elasto-plastic energy absorption, and (b) definition of the ultimate deflection based on the first fracture of an element. Fig. 9. Ultimate load versus sheet thickness.

reference specimen S, nearly 38%. This means that the ability of voided slabs to absorb the energy resulting from an earthquake is low. Consequently, special attention should be paid in case of constructing such slabs in seismic zones. However, this drop in the ductility index was found to be overcome by strengthening the voided slabs using steel sheets. Thus, using steel sheets, as proposed, is an excellent solution for voided slabs vulnerable to earthquake loading. In general, the ductility enhancement decreased with increasing the sheet thickness since the sheets worked as additional flexural reinforcement, this addition got more significant with enlarging the sheet thickness, leading to delay the yielding of the tension bars. The ductility improvement for the V0.8, V1.0, and V1.2 specimens were 257%, 202%, and 192% compared to the S slab, respectively.

V1.0 and V1.2 samples up to a force of 155 kN. For a more precise explanation, it is more suitable to discuss the deflection at the same load. Herein, two levels are considered; 70% of the peak load of the solid specimen (97.2 kN) that represents the service load [38–40], and at the peak load of the S slab (138.8 kN). For the V0.0 specimen, the deflection at the service load was 64% greater than that of S specimen. However, this specimen collapsed at load far below 138.8 kN. This consequence points out that the stiffness of the voided slab-column connection was highly degraded due to the rapid expansion and extension of cracks across these voids. In specimen V1.0 strengthened by 1.0 mm thick sheets, the deflection at the service load was equal to that of S specimen. At peak load, it realized deflection 42% lower than that registered in the S sample. For the remaining two specimens V0.8 and V1.2, the deflections at the service stage were 7% and 14% below that of S specimen, while at peak stage these percentages increased to 61% and 51%, respectively. These results indicate that the negative effect of the voids on the stiffness of slabs was entirely omitted by steel sheets that restricted the growth and propagation of both flexural and shear cracks. Moreover, these sheets worked simultaneously as shear and flexural reinforcement, and hence improving the effective moment of inertia of specimens, leading to a significant enhancement in the stiffness that reflected in reducing the deflection values. For the eventual deflection recorded at the collapse of specimens, the V0.0 specimen experienced a deflection exceeding that of the S specimen by about 35%. In the strengthened specimens, the eventual deflections were much higher, reaching 293%, than that of the solid specimen due to the more ductile failure they showed.

4.2.5. Energy absorption Energy absorption is equal to the area enclosed by the load-displacement curve. It represents a measure of the absorbed energy by structural elements before collapse [40,41]. Table 2 lists the energy absorption values of all specimens. Additionally, these values are depicted in Fig. 11 versus the thickness of the steel sheets. Inspection of these results reveals that the presence of voids in the specimen (V0.0) led to an enormous decline in the energy absorption capacity, reaching 55% compared to the solid slab (S). In the concrete members, the energy absorption is directly related to the ability of concrete to resist cracking and fractures. In the voided slabs, a large amount of concrete was replaced by voids, and as a consequence, their energy absorption declined. On the other hand, the use of steel sheets in the strengthening of the voided slab was superior in upgrading their energy absorption due to the activation of the sheets in restricting the growth of the cracks and delaying the concrete fracture. Referring to Fig. 11, the rate of energy absorption development became slower with augmenting the sheet thickness. The energy absorption of the V0.8, V1.0, and V1.2 were

4.2.4. Ductility The ductility concept defines the ability of a structural element to experience a considerable inelastic deformation before the collapse and is considered an essential characteristic for structures constructed in the seismic zone [41]. The ductility index is measured as the ratio of the ultimate deflection (Δu) to the yield deflection (Δy). In literature, there are various methods for evaluating the yield and ultimate deflections, and the selection of the most suitable method is crucial, especially for seismic design [42]. Park [43] defined four methods for calculating the yield displacement. Among them, Hashemi et al. [42] used the method of equivalent elasto-plastic energy absorption for determining the ductility of bubbled members. In this method, the measured load-deflection curve is idealized into an elasticperfectly plastic curve with the identical energy absorption as the actual system (Fig. 10a). This definition seems reasonable, and thus, it is adopted herein. For the ultimate deflection, Park [43] also described four procedures. The procedure, which is based on the first fracture of an element (Fig. 10b), was chosen as done by Hashemi et al. [42]. Table 2 lists the determined ultimate and yield deflections as well as the ductility index. The presence of voids in the slab-column connection resulted in a notable reduction in the ductility when compared to

Fig. 11. Energy absorption versus sheet thickness. 8

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Fig. 12. Steel strain profiles, (a) at service load, and (b) at ultimate loads.

distance of 2d from the column edge. This illustrates why the strengthened slabs witnessed a slight drop in the load-carrying capacity just beyond the ultimate load. The ability of sheets to attain the yield strain indicated that they were well bonded into slabs. In these profiles, the strains suddenly jumped at a location of 0.5 d, indicating that the punching shear cracks passed through this point and high stresses were directly transferred to the sheets. After that, the strain value decreased due to the ability of concrete at these locations to carry a share of the applied load. In general, a comparison between the two parts of Fig. 13 reveals that the contribution of the steel sheets in the strengthening of the voided slabs became more recognizable as the cracks increased and widened. Finally, at both load levels, the thinner sheets gave higher strain values.

326%, 389%, and 416% over that of the S specimen, respectively. 4.3. Reinforcing bar strains As previously mentioned, the strain of tension bar was investigated along a spacing of 2.0 d from the column edge through five strain gauges attached to the central bar. The strain profiles for all specimens were compared in Fig. 12 at two load levels. The first one (Fig. 12a) was similar for all slabs, 97.2 kN, that represents the service load of the control specimen S. The second force (Fig. 12b) was different for all specimens that equal to the ultimate load attained by each slab. The horizontal dashed line in these figures clarifies the yield strain of steel bar. It is evident from both figures that the steel strains were inversely proportional to the spacing measured from the column face. At the service load, no slabs exhibited the yield strain, and the voided slab V0.0 showed the highest strain of all. In this slab, the adopted service load was almost 90% of its failure load. This means the cracks to be propagated deeper through the slab thickness, resulting in shifting the neutral axis nearer the top surface of the slab, which reflected on increasing the steel strain. The other slabs displayed convergent strain profiles, confirming that the steel sheets were efficient in restricting the growth and extension of the cracks as aforementioned. Then, all the slabs (except V0.0 slab) yielded at a force corresponding 78.6–88.0% of the ultimate load. The first yield was recorded at the nearer strain gauge to the column edge. At the ultimate loads, Fig. 12b, all the strain profiles, except for that of the V0.0 slab, entered into the plastic stage. Besides, the yielding distance was found to be longer in the strengthened voided slabs than that in the solid specimen. This distance was nearly 0.5 d measured from the column face in the solid slab S. In the voided slabs with steel sheets, the yielding distance extended up to the center of the first line voids, about 75 mm from the column face. Despite reaching the steel strain to a high level in the strengthened slabs, the failure modes did not change totally to the flexural mode.

5. Numerical investigation Based on the experiment results, the use of steel sheets in the voided slabs was found to be an excellent solution for improving the overall behavior of such slabs and eliminating the adverse effects of the voids, compared with solid slabs. However, the improvement mechanism is complicated due to the extraordinary geometry of the voided slabs. In order to get a more and explicit explanation about this mechanism as well as investigating additional parameters without conducting further expensive tests, numerical simulation using the finite element (FE) method was performed. 5.1. Finite element model The ABAQUS program was employed in implementing the nonlinear FE analysis. Three-Dimensional modeling was adopted to simulate the behavior of the slabs. In this modeling, the concrete was represented by hexahedral elements, C3D8R, with eight nodes and the steel bars were modeled by truss elements, T3D2, which has two nodes, whereas shell elements with four nodes, S4R, were utilized in meshing the steel sheets. A perfect bond was assumed between the concrete and both steel bars and sheets. Therefore, the holes in sheets were removed to ease the mesh mapping. The assumption of the perfect bond was based on: (1) the sheets were extended beyond the contra-flexure lines, and accordingly, the required development length was realized; (2) they were perforated along their length, and the efficiency of this connection technique was proved [37]; (3) they were placed in direct contact with top and bottom steel meshes, and thus the bond was improved due to friction forces, developing between the sheet edges and ribs of rebars; and (4) the sheets were rigidity connected each other

4.4. Steel sheet strains Similar to the previous section, the strain profiles at the mid-height of steel sheets for strengthened specimens are plotted in Fig. 13a and b at the service and ultimate loads, respectively. Fig. 13a states that the steel sheets were in the elastic state at the service loads, the strains augmented until a location of d from the column edge, and then they rapidly decreased. At the ultimate loads, Fig. 13b, the strain profiles of sheets fundamentally altered and entered into the plastic state along a 9

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Fig. 13. Sheet strain profiles, (a) at service load, and (b) at ultimate loads.

and V0.0 specimens, respectively. This load rose to 43–47 kN for specimens, having steel sheets. Thereafter, the cracking grew and traveled to the external edges of specimens in the same way of the tests. According to CDPM, the cracking appears when the tensile equivalent plastic strain (PEEQT) at a point is greater than zero [44,50]. PEEQT is plotted in Fig. 15 to show the crack pattern at failure load for specimens S, V0.0, and V1.2, respectively. The crack pattern of FE was also compared to that of the experiment, represented by black lines in Fig. 15 on the tension face of slabs and a satisfactory similarity was found between them. Referring to Fig. 15a, the cone of punching shear in the solid slab S appeared at a 280 mm from the column face, and this distance is very close to that of the experiment, which was 290 mm. For voided specimen V0.0, the FE confirmed the experiment finding that the punching crack passed across the nearer void to the column face and intersected the tension face at a point located approximately below the center of the second-row voids (Fig. 15b). Moreover, the punching cone initiated at a distance of 150 mm from the column edge, corresponding 160 mm in the test. Finally, the combined flexural-punching failure was apparent in specimen V1.2 (Fig. 15c) where the cracks distributed along the overall length of the specimen without an explicit the punching shear cone.

below the column stub. Further, the sheets realized the yield stress, making this assumption reasonable. Due to the symmetry of slabs, only one-quarter of the specimen and half-thickness of the central steel sheet were modeled in the FE analysis to reduce the running time. The Concrete Damaged Plasticity Model (CDPM) was used for defining the two main mechanisms of concrete failure: tensile cracking and compressive crushing [44]. The CDPM was fed stress-strain values in the compression and tension, relying on the test compressive strength of concrete, by applying the standard formulas of Euro code (EN 19921-1) [24]. Besides, the softening part of the stress-strain curve of concrete in tension, which reflects the interactions between concrete and steel bars, was introduced using the formula of Wang and Hsu [45]. The procedure, used in building the CDPM herein, is described in details by [46]. The steel bars were modeled as a bi-linear material while the steel sheets were represented as an elastic-perfectly plastic material. Finally, the specimens were simply supported along four edges where the only vertical displacement was prevented, and the uplift of corners was allowed as the experimental case, and the load was applied through the column stub using the displacement-controlled method. 5.2. Validation of the adopted model The correlation between the load-deflection curve of the FE analysis and that of the test is considered the critical aspect in achieving the validation of FE model since this curve includes the response parameters like yield and ultimate loads, maximum deflection, ductility, stiffness, and energy absorption [47]. To reach this goal, two out of five CDPM parameters (dilation angle and viscosity) as well as the mesh size, were investigated carefully. After a sensitive analysis, the mesh size of 15 mm was adopted while the dilation angle and viscosity were selected to be 20° and 0.005, respectively. For remaining three parameters of CDPM, which are eccentricity, shape factor and stress ratio, the default values were chosen, which are 0.1, 1.16 and 0.67, respectively, as followed by previous numerical investigations conducted on the punching shear in flat slab [48,49]. Fig. 14 compares the load-deflection responses of the FE analysis with those of tests for the five specimens. It is evident that the FE analysis results are in an acceptable agreement with the test results. The ratio of the predicated to experimental ultimate loads for the slabs ranged from 0.95 to 1.06, as listed in Table 3. Furthermore, the cracking initiation and propagation in the FE were comparable to those observed in tests. In FE analysis, the first cracking was seen at the column corners at a load of 27.9 kN and 25.1 kN for S

5.3. Influence of steel sheets In the experimental program, the negative effect of voids on the overall behavior of slab-column connections was found to be wholly eliminated by introducing steel sheets. However, the experiments did not give an obvious explanation about how these sheets enhanced the behavior of such slabs. However, the FE analysis can provide a clear demonstration of the enhancement mechanism after acquiring the validation with the test results. According to the ABAQUS program, the maximum principal plastic strain (PE) represents the development of the cracking in the concrete members. Therefore, the PE can be adopted in stating the influence of steel sheets on restricting the cracking propagation and expansion, as plotted in Fig. 16. This figure defines the PE values at the center of an element located directly next to the column face on the tension surface of the specimen. It is worth highlighting that the bounds of Fig. 16 are limited to be slightly higher than that of V0.0 slab in order to make the comparison clearer. For the same reason, the results were briefed on the S, V0.0, and V1.2 samples. Fig. 16 clarifies that the PE values for the three specimens were similar up to a load of 47 kN. Then, the difference in the PE values was noticeable where the PE values rapidly increased in the V0.0 specimen, compared with the 10

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Fig. 14. Experimental and numerical load-deflection response of five specimens.

punching cone yielded, and the collapse of the specimen happened after spreading the yield along the length of the central sheets (located directly below the column). The third result can be attributed to acting the steel sheets as integrity reinforcement as well as they were directly supported on the roller lines of the test setup.

Table 3 Comparison between FE and test results. Specimen

Test ultimate load, Ptest, (kN)

FE ultimate load, PFE, (kN)

PFE/Ptest

S V0.0 V0.8 V1.0 V1.2

138.8 108.2 162.6 166.4 177.3

139.1 114.4 159.2 165.0 168.3

1.00 1.06 0.98 0.99 0.95

5.4. Parametric study Since the experiments conducted in this investigation were limited, a parametric study, based on the validated FE model, was implemented. Two variables, related directly to the study topic, were investigated, which were steel sheets’ thickness and their arrangement inside the slabs. The other properties of slabs were kept similar to those described in the test program.

solid sample, emphasizing that the cracks expanded faster due to the voids. Nevertheless, the specimen with 1.2 mm steel sheets displayed the least PE values of all; this means that the steel sheets were superior in restricting the crack widening and extension, and their efficiency became more remarkable beyond the initiation of the first crack. Likewise, Fig. 17 is plotted, depending on the ABAQUS results, to relate the stress of the tension bar at the center of an element located at the slab center with the applied load. One can note from the figure that, at the same load level, the V1.2 slabs experienced the smallest steel bar stress, indicating that the steel sheets also acted as longitudinal reinforcement that reflected on reducing the steel bar stress compared to the V0.0 slab. As shown in Fig. 17, there was a marginal increase in the rebar stress with increasing the applied load after reaching the yield stress (511 MPa) due to modeling the steel bars as bi-linear material in ABAQUS. Finally, the Von-Mises stresses distribution throughout the steel sheets is shown in Fig. 18 at three load levels, cracking, ultimate, and failure loads, respectively. The colors from red to blue correspond the stress value from higher to lower, respectively. At the cracking load, the activation of the steel sheet just began, and hence, lower values of stress were recorded (Fig. 18a). As the applied load increased to the ultimate, the stress values heightened fast, and the region below the column stub yielded, the yielding spread to a distance of 2d from the column face approximately, Fig. 18b. This distance corresponds to the formation of the punching cone. Therefore, the specimens were not able to carry a further load, and the applied load started to decline gradually. At failure, the yielding extended along the length of central steel sheets (the outer sheets in Fig. 18c) up to the supporting edges. It is essential to conclude three results from Fig. 18, those are the contribution of sheets launched beyond occurring of first cracking, the specimens reached their ultimate strength when sheets at the area of

5.4.1. Influence of sheet thickness In addition to the three thicknesses of steel sheets previously modeled (0.8 mm, 1.0 mm, and 1.2 mm), two new values (2.4 mm, and 3.6 mm) were analyzed. The arrangement of these sheets was similar to the experiments. The obtained results are plotted in Fig. 19. This figure asserts that both the strength and stiffness of voided slabs improved with increasing the sheet thickness in comparison with the V0.0 slab and all the analyzed slabs exhibited the ductile failure. Also, Fig. 20 relates the improvement in the strength of the voided slab to the sheet’s thickness. The strength enhancement with the thickness seems to be under proportional with a high relation factor, approaching 1.0. 5.4.2. Influence of sheets arrangement In order to explore the influence of steel sheets’ arrangement on the behavior of the voided slabs, nine steel sheets of 1.2 mm thickness were introduced at each slab direction in three configurations. In the first one (C1), the sheets were regularly distributed along the slab side at a distance of 90 mm center to center, as stated in Fig. 21a. In the second arrangement (C2), every three sheets were gathered in one bundle of 3.6 mm thickness, and thus each direction had three bundles spaced 90 mm each other like the experimental program (Fig. 21b). Finally (C3), all nine sheets were assembled by one bundle with a thickness of 10.8 mm, which was positioned at the slab center for each direction (Fig. 21c). The three configurations were analyzed by FE, and the results are depicted in Fig. 22a. It is clear that the C1 arrangement was of the least activation among the investigated configurations. This could 11

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At cross-section area

on the tension surface

(a) S slab

(b) V0.0 slab

(c) V1.2 slab Fig. 15. FE crack patterns at failure load.

arrangement offered results very similar to those of C2 arrangement. This consequence announced that the best efficiency of sheets was obtained when the sheets are placed below or near the column stub, where both the flexural and punching stresses are high.

be attributed to keeping a considerable number of steel sheets away from the zone of high-stress concentration near the column stub. The other arrangements (C2 and C3) showed nearly the same results. It is necessary to check the efficiency of the C3 arrangement when fewer sheets are introduced (a smaller thickness for bundle). Therefore, three sheets of a 1.2 mm thickness were analyzed in accordance with C2 and C3 arrangements, and the results are depicted in Fig. 22b. Again, C3

12

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Fig. 16. Load-PE curve.

Fig. 19. Load-deflection response of voided slabs having different sheet thickness.

Fig. 17. Load-Steel bar stress curve obtained from FE analysis.

6. Conclusions

Fig. 20. Enhancement in the strength of the voided slabs versus sheet thickness.

This study introduced a new and simple solution for improving the punching strength and the behavior of reinforced concrete voided slabcolumn connections using steel sheets embedded inside the slabs. An experimental program was conducted, in which five specimens were constructed and tested up to failure by subjecting a concentrated force through the column stub. One slab was fabricated with a solid crosssection, and the remaining slabs were voided by spreading 96 spherical voids regularly inside them. Three of them were strengthened by steel sheets with different thickness (0.8 mm, 1.0 mm, and 1.2 mm). Also, FE analysis was implemented to illustrate the experimental observations

and perform a parametric study as well. Based on the experimental and FE findings, the followings are essential conclusions; 1. The solid slab and the voided one without steel sheets were failed by the sudden and brittle punching shear mode, while those contained steel sheets exhibited a more ductile failure (combined flexuralpunching mode). 2. Compared with the solid specimen S, the voided slab V0.0 lost 22% of its strength. However, using the steel sheets succeeded in

Fig. 18. Von-Mises stress distribution on steel sheets, (a) at cracking load, (b) at ultimate load, and (c) at failure load. 13

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Fig. 21. Arrangement of steel sheets inside the voided slabs, (a) C1, (b) C2, and (c) C3.

ductility and energy absorption where the enhancement for these two criterions approached 257% and 416% above those of the reference slab S without voids, respectively. 5. According to FE analysis, the efficiency of the steel sheets was verified in restricting the growth and extension of cracks. Furthermore, they were observed to be working as flexural and shear reinforcements simultaneously. In addition, the load-carrying capacity of the strengthened specimens slightly dropped after the steel sheets below the column stubs had yielded. When the yielding of the central sheets arrived at the supported edge, the specimens collapsed. 6. Based on the parametric study, the activation of steel sheets was found to be augmented with increasing their thickness; the enhancement trend was under proportional. Finally, the best activation of the sheets was observed when the sheets were introduced below or near the column stub, where the stress concentration is relatively high.

(a) Nine 1.2 mm-thick sheets are introduced

Declaration of Competing Interest The authors declare that they have no conflict of interest. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.engstruct.2019.109614. References

(b) Three 1.2 mm-thick sheets are introduced

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Fig. 22. Effect of steel sheet’s arrangement on the behavior of voided slabs.

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