Experimental and numerical investigation on seismic performance of hollow floor interior slab-column connections

Abstract

This paper aims to investigate the seismic performance of hollow floor interior slab-column connection (HFISC). In this new connection system, several tube fillers are placed in slab to form hollow concrete. Moreover, locally solid zone, shear components, and hidden beam around the connections are installed to improve the bearing capacity and ductility of specimens. Three slab-column connections with different shear components were tested under cyclic loading and every specimen was constructed with parallel tube fillers in the north direction and orthogonal tube fillers in the south direction. The seismic behavior of specimens was evaluated according to the hysteretic response, skeleton curve, ductility, stiffness degradation, and energy dissipation. A finite element model was then developed and validated by a comparison with the experimental results. Based on experimental results and finite element analysis results, the relative effects of the hollow ratio of slab, the ratio of longitudinal reinforcement, the shear area of bent-up steel bars, and the arm length of welding section steel cross bridging were elucidated through parametric studies. This new slab-column connection showed better plastic deformation capacity while the bearing capacity was kept. Specimens with parallel tube fillers showed better seismic behavior than those of specimens with orthogonal tube fillers.

Keywords

hollow floor slab-column connection seismic behavior tube filler pattern shear component

Introduction

Flat-slab system has been widely used for residential and commercial buildings due to their easier construction and flexible partition. More importantly, this structural system shows lower story height in comparison to beam–column frame or bearing wall systems (Rha et al., 2014). However, the lack of beams requires a direct transfer of load from the slab to the columns, which makes the connections susceptible to punching shear failures. In some cases, the failure of a joint may cause the failure of the adjacent joints, triggering a progressive collapse of part or even the entire building (Meli and Rodriguez, 1988). In 2017, the Mexico earthquake produced the collapse of 46 structures which resulted in 219 deaths (Galvis et al., 2017). Most of the collapse buildings consisted of reinforced concrete buildings whose lateral resisting system consisted of flat slabs supported by reinforced concrete columns. This phenomenon highlights the necessity of research on the seismic performance of flat-slab system.

During the early phase of application, the flat plate was only used as a floor system primarily for resisting gravity load. Therefore, slab-column structures were constructed without any shear reinforcement. Increasing thickness of the slab was a frequent approach to ensure the shear strength of connection (Birkle and Dilger, 2008). Slab-column structure is a special structure system in which concrete slabs and columns are main members bearing load. Though increasing the thickness of slab can increase the bearing capacity of connection, on the other hand, the slab-column structure with thickness slab may aggravate shear failure of connection. In order to reduce weight, drop panel and column capital are used to resist shear stresses (Megally and Ghali, 2000).

The above approaches could increase the shear strength but not ductility. Recently, slab-column structures are often utilized in combination with either structural walls or special moment-resisting frames. The ductility of these systems is generally limited by the deformation capacity of slab-column connections. For this reason, many researches have been conducted to investigate various shear components to develop the shear strength and ductility of slab-column connections, such as, post-installed shear bolts (Bu and Polak, 2009; Fernández Ruiz et al., 2010), stirrups (Glikman et al., 2017; Song et al., 2012), continuous cages, two-leg stirrups, etc. (Einpaul et al., 2016), shear studs (Isufi et al., 2019; Matzke et al., 2015; Song et al., 2012), ductility reinforcement (Ghali, 2007), shear bands (Kang et al., 2017; Song et al., 2012), lattice shear reinforcement (Park et al., 2007), thin plate stirrups (Kang and Wallace, 2008), etc.

For flat-slab system, the lack of beams requires a direct transfer of load from the slab to the columns, which makes the connections susceptible to shear failures. Therefore, hollow floor slab-column structure system has been proposed to lighten self-weight of slabs. In addition, this system has the advantages of alleviating earthquake response, improving sound insulation and reducing structure cost, and so on (Araujo et al., 2011). But for another, hollow concrete will weaken the rigidity of floor slabs and decrease the shear strength of connections. In the literature, Wang et al. (2008) reported testing the results of 9 reinforced concrete hollow slabs and analysis results of 80 reinforced concrete solid slabs which were designed to against punching shear. The test results showed that the punching shear strength of connection decreased by 15%∼30% as the hollow ratio of slab was 10%. Gong et al. (2013) tested nine hollow slab-column connections under punching shear force in which thickness, rib width and hollow ratio were taken in account. As a continuation of this work, Zhu et al. (2018) tested six hollow slab-column connections subjected to unbalanced moments. It was also concluded that the punching shear strength of hollow floor decreased as hollow ratio increased. After that, a two-story hollow slab column structure, which was subjected to cyclic loading, was tested to investigate the seismic performance of the hollow slab-column structure (Zhu et al., 2019).

From the above researches, it was noticed that shear reinforcements were usually used in solid flat slab. However, there were few reports on the seismic behavior of hollow floor slab-column connection with shear reinforcement, available in the literature. To ensure the ultimate bearing capacity and improve plastic deformation capacity of hollow floor slab-column connection, a new hollow floor slab-column connection, which considered shear components and locally solid zone of slab around the column simultaneously, were proposed. Six connections subjected to vertical load had been tested (Pang et al., 2019). This paper is aim to investigate the seismic performance of hollow floor slab-column connections with shear components. Three specimens were tested subjected to cyclic loading. In addition, a finite element model was established to predict the seismic behavior of connection and a parametric study was performed.

Experimental program

Specimen designs

In this study, a total of three specimens with a scale of 1:2 to the prototype structure were tested, the first one made with hidden beam only, the second one made with hidden beam and bent-up steel bars (BSB), and the last one made with hidden beam and welding section steel cross bridging (WSSCB), as shown in Figure1. To improve the shear strength of HFISC, all specimens were constructed with a solid zone around the column, which was 220 mm wide, as shown in Figure 1(a). According to the Chinese code of JGJ T268-2012 (2012), the hollow ratio of all specimens was 32.96%. In order to mitigate the bending load-carrying capacity of connections in-plane two directions, the south side of specimens was constructed with orthogonal tube fillers. The north side of specimens was constructed with parallel tube fillers to investigate the seismic behavior of specimens with different tube filler pattern, as shown in Figure 1(a).

Figure 1.

Details of the specimens: (a) tube fillers pattern of slab, (b) constructional detail of HFISC1, (c) constructional detail of HFISC2, and (d) constructional detail of HFISC3.

More details of the slab-column connections were given in Table 1 and Figure 2. The distance from the top column and bottom column to slab were all 700 mm. The slabs were longitudinally reinforced with bidirectional C8@100 at the top and bottom of slab, respectively. Hidden beam was arranged along the vertical and horizontal axis of the column. Within the range of 0 to 300 mm from the column face, the stirrups of hidden beam were spaced at 50 mm intervals with C6 to strengthen the connection. The other stirrups were spaced at 100 mm intervals with C6. For specimen HFISC2, the connection was constructed with six 8 mm BSBs along the vertical and horizontal axis of the column. For specimen HFISC3, the WSSCB was welded with 6.3# steel channel, which was consist of 63 × 4.8 mm flange and two 40 × 4.8 mm webs. The shear studs were also arranged to prevent bond slippage between concrete and WSSCB.

Table 1.

Main parameters of specimens.

Specimen	Column			Slab			Hidden beam		Shear component
Specimen	Length/mm	Section/mm	Longitudinalrebars	Span/mm	Section/mm	Longitudinalrebars	stirrup	Section/mm	Shear component
HFISC1	1540	300 × 300	8C16	2400	140 × 1400	C8@100	C6@100 (50)	300 × 300	/
HFISC2	1540	300 × 300	8C16	2400	140 × 1400	C8@100	C6@100 (50)	300 × 300	BSB
HFISC3	1540	300 × 300	8C16	2400	140 × 1400	C8@100	C6@100 (50)	300 × 300	WSSCB

Figure 2.

Details of shear components, column and hidden beam: (a) photo and sketch map of BSB, (b) photo and sketch map of WSSCB, (c) column, and (d) hidden beam.

Material properties

According to Chinese code of GB/T228.1-2010 (2010), mechanical properties of reinforcing bars and WSSCB, as shown in Table 2, were obtained by tensile testing of three coupons. In Table 2, f_y, f_u, and ε_u represent the yield strength, ultimate strength and yield strain, respectively.

Table 2.

Material properties of steel.

Type	f_y/MPa	f_u/MPa	ε _u	Elongation (%)
6 mm deformed steel bar	530.00	656.67	2650.00	16.32
8 mm deformed steel bar	535.00	666.67	2675.00	19.60
16 mm deformed steel bar	463.33	643.33	2316.67	17.27
4.8 mm flange of WSSCB	296.67	355.00	1483.33	28.34

All specimens were constructed using ready mixed concrete of grade C30. In Chinese code of GB50010-2010 (2010), this implies that the cube compressive strength of concrete can reach 30 MPa at 28 days. Three standard cubes (150 × 150 × 150 mm) were compressed on the day of testing specimen. The measured values of compressive strength of specimen HFISC1, HFISC2 and HFISC3 were 31.26, 30.48, and 33.05 MPa, respectively.

Test setup

Specimens were tested at the Structural Laboratory of Henan University of Urban Construction in Henan Province, China. As shown in Figure 3, three actuators were connected with reaction frame. Two of them, with 500 kN capacity and ±250 mm stroke, applied cyclic loading on the edge of slabs to simulate earthquake actions. Another actuator with 600 kN was used to apply vertical load at the upper surface of column. A polytetrafluoroethylene (PTFE) plate with butter, which was used to decrease the effect of micro deformation on the seismic behavior of specimens, was placed between steel blocks. Four hand jacks were used to fix the bottom of hinged support. The column was inserted into the hinged support, as shown in Figure 3(a). In addition, to prevent specimens from losing the out-of-plane stability, a lateral herringbone brace was installed between reaction frame and specimens. It could be seen from Figure 3 that the lateral brace was welded with two circular steel tubes and three plates with cross stiffener. One plate was connected at the tip of column head, the other was connected to reaction frame.

Figure 3.

Test setup: (a) sketch map, (b) photo of test setup.

Test content

According the Chinese code of JGJ/T 101-2015 (2015), an axial load of 350 kN, which represented an axial compression ratio of 0.13, was applied to the column and maintained constant throughout the test. To ensure full contact between specimens and test setup, the preload was applied before formal loading. The loading scheme was composed of load-controlled phase and displacement-controlled phase. During the load-controlled phase, cyclic loading was applied for one cycle until the strain of critical position increased to yield strain. After that, the displacements of hydraulic jacks were selected as the initial displacement (Δ_y) in displacement-controlled phase. Each specimen was gradually loaded to displacement of 1Δ_y, 2Δ_y, 3Δ_y, 4Δ_y, 5Δ_y, … and each displacement was three cycles. After the load decreased to 85% of the peak load, specimens were considered destroyed.

In order to better predict the yield displacement of specimens, several electrical gauges were attached to critical longitudinal reinforcement bars to measure strains, as shown in Figure 4(a). Seven strain gauges were installed to measure strains in the middle of BSBs, as shown in Figure 4(b). Also, a number of strain gauges were installed at the flange the WSSCB, as shown in Figure 4(c).

Figure 4.

The layout of strain gauges: (a) strain gauges in reinforcement bars at the bottom of slab, (b) strain gauges in BSBs, and (c) strain gauges in flange of WSSCB.

Test results and discussion

Cracking pattern and failure Mode

All of the specimens had a flexure failure according to test results. Although specimen HFISC2 and specimen HFISC3 were conducted with BSBs and WSSCB, the crack form and failure modes were similar to specimen HFISC1. The failure process for connections could be classified as four stages: initial cracking stage, cracking stage, ultimate stage, and failure stage. Specimen HFISC1 was selected to illustrate the whole failure process and the failure mode of all specimens was shown in Figure 5, which was obtained using the software AutoCAD from the photos of specimens at failure stage. Note that the red lines represent the main cracks or the concrete spalling. For ease of description, HFISC1-N represents the northern slab of HFISC1 which constructed with parallel tube fillers, HFISC1-S represents the southern slab of HFISC1 which constructed with orthogonal tube fillers, as shown in Figure 1(a).

Initial cracking stage: This stage was from the beginning of the test to the occurrence of the first cracks. But even with different tube layout, the first cracks of HFISC1-S and HFISC1-N occurred near the column and were parallel to the short side of slab. The cracking displacement was 0.33 time and 0.28 time of yield displacement for HFISC1-S and HFISC1-N. The corresponding load was about 30.77% and 28.30% of peak load for HFISC1-S and HFISC1-S.

Through cracking stage: As the applied load increased, the initial cracks extended continuously and more parallel cracks were observed. Simultaneously, some diagonal cracks were formed at the western and eastern area of slab. Then, the parallel cracks grew wider but not formed the main cracks. When the load increased to 27.2 kN for HFISC1-S and 36 kN for HFISC1-N, the strains of longitudinal bars near the column, where the maximum bending moment occurred, reached the yield strain. This implied that specimen HFISC1 reached the yield stage. The yield displacements were 10.5 and 14.5 mm for HFISC1-S and HFISC1-N, respectively. During the earlier stage of displacement-controlled phase, the number of cracks and crack width increased with increasing loads and HFISC1-N formed a V-shaped fracture distribution. When the cyclic displacement increased to two times of yield displacement, some parallel transverse cracks were observed for HFISC1-N. In addition, more diagonal cracks occurred at the bottom and top of slab for HFISC1-S, which propagated diagonally to the edges of slab to form a V-shaped fracture distribution. Soon afterwards, the width of initial cracks continued to increase and a small number of cracks were observed at three times of yield displacement. Specimens formed plastic hinges at the slab-column connections.

Ultimate stage: New cracks were not observed as the displacement reached four times of yield displacement. Besides, the concrete cover warping of slabs appeared near the slab-column connections. Then, the vertical load of HFISC1-S and HFISC1-N increased to the peak load at five times of yield displacement. Subsequently, some concrete blocks spalled from the slab.

Failure stage: After reaching the peak load, the specimen continued to apply load. The bearing capacity of HFISC1-S and HFISC1-N slowly decreased. During this period, more concrete blocks spalled and reinforcing steel bar leaked. After the bearing capacity declined to about 85% of peak load, the test ended.

Some fracture distribution rules could be got from Figure 5(a): Tube fillers weaken the flexural rigidity of slab. Therefore, the number of cracks in the area with tube fillers was more than those of areas with hidden beam and without tube fillers, which formed a V-shaped fracture distribution. Figure 5(b): Specimen HFISC2 and specimen HFISC3 had similar crack patterns and failure modes to specimen HFISC1. However, the main parallel cracks of specimen HFISC3 moved outward and the slabs around the column exhibited more severe damage. Figure 5(c): In the north area of HFISC, the cracks of were symmetric along the long side of slab. In the southwest area of HFISC, cracks propagated diagonally because tube fillers pattern was perpendicular to the direction of bending moment. However, the cracks in the southeast area of HFISC were similar to the cracks in the north area of HFISC. Therefore, the cracks in the south area of slab were asymmetric.

Figure 5.

Crack patterns of specimens: (a) top slab of HFISC1, (b) bottom slab of HFISC1, (c) top slab of HFISC2, (d) bottom slab of HFISC2, (e) top slab of HFISC3, and (f) bottom slab of HFISC3.

Moment versus drift ratio hysteretic curves

The vertical load was applied using two hydraulic jacks, and each one was connected with the edge of slab. For evaluating the seismic performance of buildings in terms of displacements, structural engineers use typically the story drift of connection, mainly including the deformation of slab and the column (Drakatos et al., 2016). Compared with the deformation of slab, the contribution of the deformation of column to the story drift can be negligible. Based on the internal force equilibrium method, the lateral moment-drift ratio curves of all specimens can be obtained from the vertical loads and displacements of hydraulic jacks.

Figure 6 illustrates the lateral moment-drift ratio curves of each specimen. which marks the cracking point, the reinforcing bar or shear components yield points, the yield point of specimen, the peak lateral moment points, the cover concrete spalling point, and the steel bars leaking point.

Figure 6.

Lateral moment-drift ratio hysteretic curves of the specimens: (a) HFISC1, (b) HFISC2, and (c) HFISC3.

Figure 6(a) shows the lateral moment-drift ratio curves of specimen HFISC1. The first cracks appeared in specimen HFISC1 at a drift ratio of 0.58%, and the corresponding lateral moment was 33.18 kN·m. The first longitudinal reinforcing bar yielded at a drift ratio of 2.38%, and the corresponding lateral moment was 66.36 kN·m. At a drift ratio of 6.72%, specimen reached the peak lateral moment (110.87 kN·m). After that, the lateral moment of the specimen decreased slowly in response to the concrete spalling and the steel bars yielding.

Figure 6(b) illustrates the lateral moment-drift ratio curves of specimen HFISC2. The first cracks appeared in specimen HFISC2 at a drift ratio of 0.67%, and the corresponding lateral moment was 43.68 kN·m, which was 32% higher than those of specimen HFISC1. This implied that BSBs can increase the cracking load of HFISC. The first longitudinal reinforcing bar yielded at a drift ratio of 3.05%, and the corresponding lateral moment was 80.85 kN·m, which was larger the values of specimen HFISC1. This indicated that BSBs can delay the yielding of reinforcing bars and improve the yield strength of specimen. After the specimen reached to the yielding stage, the BSBs firstly yielded at a drift ratio of 4.23%, the corresponding lateral moment was 108.22 kN·m. At a drift ratio of 9.14%, specimen reached the peak lateral moment (121.65 kN·m). Then, the lateral moment of the specimen decreased slowly in response to the concrete spalling and the steel bars yielding.

Figure 6(c) shows the lateral moment-drift ratio curves of specimen HFISC3. The first cracks appeared in specimen HFISC3 at a drift ratio of 0.84%, and the corresponding lateral load was 39.27 kN·m, which was 18% higher than those of specimen HFISC1. This implied that WSSCB can also increase the cracking loading of HFISC, but with a smaller improvement than specimen HFISC2. The first longitudinal reinforcing bar yielded at a drift ratio of 0.40%, and the corresponding lateral load was 105 kN·m, which were much larger than the those of specimen HFISC1 and HFISC2. After the specimen reached to the yielding stage, the WSSCB yielded firstly at a drift ratio of 5.54%, the corresponding lateral moment was 134.25 kN·m. At a drift ratio of 11.90%, specimen reached the peak lateral moment (148.29 kN·m). Then, the lateral moment of the specimen decreased slowly in response to the concrete spalling and the steel bars yielding.

Figure 7 shows a comparison between the vertical load-displacement hysteretic curves of the north direction and the south direction of specimens HFISC1, HFISC2, and HFISC3, where HFISC-N and HFISC-S represent the hydraulic jack connecting the north slab and the south slab of specimen, respectively. It could be observed that the hysteretic curves of HFISC-S exhibited obvious pinching behavior than those of HFISC-N. In addition, the hysteretic loops of HFISC-N were larger and fatter than those of HFISC-S. This indicated that specimen with parallel tube fillers showed better seismic behavior, including higher peak load, better energy-dissipating and ductility factor, et al, than those of specimens with orthogonal tube fillers. This can be attributed to the reason that parallel tube fillers can help specimen provide bear larger moment due to a larger inertia moment than orthogonal tube fillers.

Figure 7.

Comparison of lateral load-displacement hysteretic curves: (a) comparison between HFISC1-N and HFISC1-S, (b) comparison between HFISC2-N and HFISC2-S, and (c) comparison between HFISC3-N and HFISC3-S.

Skeleton curves and bearing capacity

Figure 8 illustrates the horizontal load-displacement curves of hysteresis loops for all specimens. The cracking load to peak load for all specimens was about 26%~35%. Table 3 shows the characteristic load and characteristic displacement for all specimens. As evidenced in Table 3, HFISC3 showed the highest peak load, a result of constructing with WSSCB. The average peak load of HFISC2 reached 72.52 kN, which was only higher than those HFISC1 by about 5.92% due to a smaller shear area of BSBs in specimen HFISC2. The average peak load of HFISC3 was higher than those of HFISC1 by about 36.99%, and this indicated that WSSCB may be served as a more effective shear component than BSBs.

Figure 8.

Skeleton curves of specimens.

Table 3.

Load characteristic values and displacement characteristic values of specimens.

Specimen	Direction	P_cr/kN	Δ_cr/mm	P_y/kN	Δ_y/mm	P_m/kN	Δ_m/mm	P_u/kN	Δ_u/mm	μ	μ_a
HFISC1	Positive	21.55	3.48	49.35	15.40	72.81	42.89	61.89	71.34	4.63	4.36
HFISC1	Negative	–21.55	–2.95	–48.66	–17.36	–64.13	–42.89	–54.51	–71.35	4.09	4.36
HFISC2	Positive	28.36	4.05	61.24	17.39	79.00	54.86	67.15	72.67	4.18	4.08
HFISC2	Negative	–28.36	–4.06	–53.36	–18.28	–66.03	–54.85	–56.13	–72.67	3.98	4.08
HFISC3	Positive	25.50	5.06	78.79	23.17	97.80	47.80	83.13	71.42	3.08	3.22
HFISC3	Negative	–25.50	–4.15	–71.01	–26.86	–89.80	–47.79	–76.33	–70.10	3.36	3.22

P _cr represents the crack load; Δ_cr represents the crack displacement; P_y represents the yield load; Δ_y represents the yield displacement; P_m represents the peak load; Δ_m represents the displacement corresponding to peak load; P_u represents the ultimate load; Δ_u represents the ultimate displacement; µ represents the ductility factor; µ_a represents average value of ductility factor in positive and negative direction.

Measured strains

Based on the obtained mechanical properties of reinforcing bars, the yield strain of reinforcing bars and BSBs was about 2675µε, and the yield of WSSCB was 1483.33µε. Figure 9 presents the strain variations in the reinforcing bars, BSBs and WSSCB with respect to the horizontal displacement of specimens.

Figure 9.

Measuring strains in the reinforcing bars, BSBs and WSSCB of specimens: (a) S5 for reinforcing bars of all specimens, (b) S10, S8, and S6 for reinforcing bars of HFISC1, (c) S13, S14, and S15 for BSBs of HFISC2, (d) S17, S18, and S19 for BSBs of HFISC2, (e) S21 and S22 for top flange of WSSCB of HFISC3, and (f) S26 and S27 for bottom flange of WSSCB of HFISC3.

Figure 9(a) shows the strains of measuring point S5 at the bottom of slab for all specimens. It can be found that the reinforcing bars of all specimens yielded except for specimen HFISC1. The max strains of S5 were 4985µε, 3291µε, 2328µε for specimen HFISC1, HFISC2, and HFISC3, respectively. This implied that shear components could help reinforcement bars share the bending moment of connections. Figure 9(b) provides the strains of S10, S8, and S6 at the bottom of slab for specimen HFISC1. The strain of S10 was higher than those of S8 and S6, indicating that the strains decreased with the distance from the measuring point to the edge of column increasing.

Figure 9(c) and (d) represent the strain variations in the BSBs with respect to the horizontal displacement of specimen HFISC2. It can be observed that only S15, which was installed along with the short edge of slab, reached yield strain. However, S17, S18, and S19, which are installed along with the long edge of slab, all yielded. This indicated that only three BSBs, installing along with the long edge of slab, mainly help the specimen dissipate energy under unidirectional earthquake motion. Hence, BSBs had a little effect on improving the seismic behavior of HFISC.

Figure 9(e) and (f) represent the strain variations in the flange of WSSCB for specimen HFISC3. WSSCB was welded as a whole by several steel channels. Therefore, although the specimen HFISC3 was tested subjected unidirectional earthquake motion, the WSSCB can have a better working performance. From Figure 9(e) and (f), it can be observed that, these measuring points, whether were installed along the long or short edge of slab, all reached the yield strain. Based on the above analysis about the strains of WSSCB, it was concluded that the flanges of WSSCB yielded during the test process, indicating that the WSSCB was an effective shear component in HFISC.

Ductility factor

The ductility factor (µ) is defined as the ratio of between the ultimate displacement (Δ_u) to the displacement at first yield (Δ_y) (JGJ/T 101-2015, 2015), which can be used as a measure of deformation capability of the specimens. The ultimate displacement (Δ_u) is defined by points corresponding to the applied load declined to 85% of the maximum load. Table 3 shows the ductility factor of specimens. The ductility factor of specimen HFISC2 and HFISC3 was 4.08 and 3.22, which was smaller than those of specimen HFISC1 by about 6.42% and 26.15%. This implied that although BSBs and WSSCB can increase the bearing capacity, but decrease the ductility factor of connection due to the shorter plastic stage. In addition, the ductility factors of all specimens were all higher than 3, which were far larger than the suggested ductility for reinforced concrete structure (µ_a is larger than or equal to 2) (Zhou, 1991). This meant that the ductility factor of slab-column connections were about 1.61 times to 2.18 times of that reinforced concrete structure, showing excellent deformation capacity.

Energy dissipation

The equivalent viscous damping coefficient (h_e) is often used to evaluate the energy dissipation capacity of specimens, and can be calculated by:

h_{e} = \frac{S_{ABC} + S_{CDA}}{2 π (S_{OBF} + S_{ODE})}

(1)

Where S_ABC and S_CDA are the area of arc ABC and CDA in Figure10. Similarly, S_OBF and S_ODE are the area of triangle OBF and ODE, respectively.

Figure 10.

Idealized hysteretic loop.

Figure 11 shows the h_e versus the displacement of all specimens. It was seen that, the h_e of specimens increased continuously with displacement at the elastic stage. The h_e of specimen HFISC1 was higher than those of specimen HFISC2 and HFISC3 before the specimens reached the yield stage, implying that specimen HFISC1 showed better energy-dissipating capacity than those of specimen HFISC2 and HFISC3. This was because that more longitudinal steel bar yielded for dissipating energy for HFISC1. At this point, the h_e was 0.144, 0.122, and 0.103 for specimen HFISC1, HFISC2, and HFISC3, respectively. When the specimen reached the failure mode, it was noticed that the h_e of specimen reached 0.125 to 0.176 and specimen HFISC1 showed lowest h_e. In comparison to HFISC1, the h_e of HFISC2 and HFISC3 was higher than those of specimen HFISC1 by about 12.59% and 40.69%. This was because BSBs and WSSCB yielded to help specimen dissipate energy. According to the suggested value (GB 50936-2014, 2014), the h_e is approximately equal to 0.1 for reinforced concrete structure. This meant that specimens had better energy dissipation ability.

Figure 11.

h _e of specimens.

Finite element modeling

General

To further investigate the seismic performances of HFISC, a FE model was formulated by a commonly FE program ABAQUS (version 6.11-3). Following its validation with the experimental results, a parametric study was performed by varying critical parameters.

In this FE model, the concrete was modeled by the 3D eight-node solid reduced-integration element C3D8R. The steel bars, BSBs and WSSCB were modeled by truss element T3D2, and embedded in the concrete. The effects of the relative bond and slip of the reinforcement with respect to the concrete were ignored. Hollow concrete was used to for modeling tube filler. RP-1, which was coupled with the top surface of column, was used to apply axial load. RP-2, which was coupled with the bottom surface of column, was used to simulate the hinged support. RP-3 and RP-4, coupling with the top and bottom surface of slab, was used to apply cyclic loading, as shown in Figure 12(a).

Figure 12.

FE model of HFISC: (a) the layout of reference points, (b) the meshed model.

On account of the computation time and computation accuracy, the mesh dimension of columns and slabs was 100 and 50 mm, as shown in Figure 12(b). The mesh dimension of reinforcing bars, BSBs and WSSCB was 50 mm.

Materials properties

A bilinear kinematic hardening model considering the stiffness degradation was used to simulate WSSCB. The hardening modulus E_s was taken as E_s = 0.01 E, where E was the elastic modulus of the steel. To fully simulate the cooperative work performance between concrete and reinforcements, the modified-Clough hysteresis model considering stiffness degradation of reinforcements was used to model the reinforcement (Qu and Ye, 2011). The damaged plasticity model for concrete in ABAQUS was utilized to simulate cracking, tension stiffening, the shear capacity of cracked concrete and crushing in compression, as shown in Figure 13. The stress-strain model for concrete proposed by Chinese code of GB50010-2010 (2010) was used to model the tensile and compressive behavior of concrete. The compressive damage parameter (d_c) and the tensile damage parameter (d_t) were used to represent the damage of concrete under cyclic loading. And the strain ratio was adopted to calculate damage parameter, which can be calculated by equations (2) and (3) (Birtel and Mark, 2006):

d_{c} = \frac{(1 - β_{c}) {\tilde{ε}}_{c}^{in} E_{c}}{σ_{c} + (1 - β_{c}) {\tilde{ε}}_{c}^{in} E_{c}}

(2)

d_{t} = \frac{(1 - β_{t}) {\tilde{ε}}_{t}^{in} E_{c}}{σ_{t} + (1 - β_{t}) {\tilde{ε}}_{t}^{in} E_{c}}

(3)

Figure 13.

The damaged plasticity model for concrete.

Where ${\tilde{ε}}_{in}^{c}$ and ${\tilde{ε}}_{in}^{t}$ represent the compressive and tensile inelastic and creaking strain; E_c represent the elastic modulus; β_c represent the ratio of compressive plastic strain to compressive creaking strain; β_t represent the ratio of tensile plastic strain to tensile creaking strain; ω_c and ω_t represent the compressive stiffness recovery factor and tensile stiffness recovery factor, which are between 0 and 1; σ_c0 and σ_t0 represent the compressive and tensile yield stress.

Comparison of test results and FEM results

For specimen HFISC1, Figure 14(a) illustrates the concrete damage nephogram of slab in tension and the red area presents the cracks. It could be seen that the damage distributing area was V-shaped, which was in agreement with the test results, as shown in Figure 5(b). The skeleton curves obtained from FE tests were compared to the experimental observations as shown in Figure 14(b). It can be noticed that the curves of FE model showed higher stiffness than the test results of specimen. This can be attributed to a perfectly ideal FE model comparing with test specimens, which didn’t take into account the bond-slip behavior, the defect of specimen and loading error. However, FE model predicted almost the same ultimate load and good plastic deformation capacity. Therefore, in the view of bearing capacity, though the numerical skeleton curves showed prior yield load and ultimate load, this model could be considered acceptable and was used for a further study.

Figure 14.

The FEM results: (a) the concrete damage nephogram in tension, (b) comparison of the skeleton curves for HFISC1-N.

Parametric studies

According to the discussions of the test results and FE results, a parametric study was performed to predict the bearing capacity of hollow floor slab-column connections with varying critical parameters, which included the hollow ratio of slab (ρ_h), the ratio of longitudinal reinforcement (ρ_l), the ratio of BSBs (ρ_b) and the arm length of WSSCB (l_w). ρ_b is defined as the ratio of S_b to S_h, where S_b represents the cross-sectional area of BSBs, and So WSSCB is, S_h is the product of the length (300 mm) and width (140 mm) of hidden beam. Specimen HFISC1 (ρ_l = 0.55%, ρ_h = 32.96%) was used as comparative reference to investigate the effect of ρ_h and ρ_l. Specimen HFISC2 (ρ_b = 0.36%) and HFISC3 (l = 800 mm) were used as comparative reference to analyze the effects of ρ_b and l_w, respectively.

It was noticed from Figure 15(a) that the bearing capacity of HFISC1 was slightly smaller than those of solid slab-column connection (SSC). But after the peak load, the bearing capacity of SSC decreased faster, which indicated that HFISC1 showed better plastic deformation capacity. Figure 15(b) shows the skeleton curves of specimens with different ρ_l. It could be observed that, the bearing capacity of specimen can be substantially improved with the increase of ρ_l. The bearing capacity increased by about 55.87% as the ρ_l increased from 0.55% to 1.13%. This implied that the ratio of longitudinal bars was a critical parameter, and it cannot be ignored in hollow floor slab-column structure design.

Figure 15.

Influence of critical parameters on skeleton curves: (a) ρ_h of HFISC1-N, (b) ρ_l of HFISC1-N, (c) ρ_b of HFISC2-N, (d) l_w of HFISC3-N.

On account of lower cross-sectional area for BSBs, it can be concluded from test results that the effect of BSBs on the seismic behavior was small for specimens HFISC2. Figure 15(c) provides the simulated results of specimens with different ρ_b. It can be noticed that the bearing capacity can reached to 75.9 kN as ρ_b increase to 1.91%, which was higher than those of specimen HFISC2 by 23.01%. This indicated that BSBs with higher ρ_b can improve the seismic performance of hollow floor slab-column connection.

Compared with BSBs, WSSCB was a more effective shear component. According to Chinese code (GB50010-2010, 2010), the side length of most unfavorable section for HFISC3 is 540 mm. Therefore, l_w = 600, 700, and 800 mm were selected as key parameters to analyze the seismic performance of HFISC3, and the corresponding skeleton curves as shown in Figure 15(d). As expected, the longer l_w the higher bearing capacity, and the bearing capacity increased by 16.9% when l_w increased from 600 to 800 mm. However, compared with ρ_l and ρ_b, the effect of l_w was smaller.

Based on the test results and numerical results, it was concluded that the hollow floor slab-column connections with hidden beams exhibited the similar seismic behavior in comparison to solid slab-connections. Besides, the parallel tube fillers, medium reinforcement ratio and WSSCB with basic arm length were adopted to achieve better seismic performance in the seismic design of hollow floor slab-column structures.

Conclusion

This paper presented a new slab-column connection system, which was composed of tube fillers, hidden beam, and shear components. To investigate the seismic behavior of this connection, three half-scale specimens were tested subjected to cyclic loading. Then, a finite element model was established to simulate the failure process of connections. On account of the effects of variation of the connections, a parameter study was conducted through the numerical approach. The conclusions of this study are summarized as follows:

The failure modes of specimens with different punching components were similar. The spalling of concrete and leaking of reinforcing bars around the connection occurred in each specimen. Since tube fillers weaken the flexural rigidity of slab, the number cracks of area without tube fillers were less than those of areas with tube fillers due to the reason that and the slabs of specimens showed a V-shaped fracture distribution rule.

Under unidirectional earthquake, both of BSBs and WSSCB can improve the seismic performance, including the bearing capacity, stiffness and energy-dissipating capacity. In comparison to BSBs, WSSCB can significantly increase the bearing capacity of HFISC. The bearing capacity of specimen HFISC2 and HFISC3 was higher than those of specimen HFISC1 by about 5.92% and 36.99%.

The ductility factor of slab-column connections could reach to 3.22 to 4.36 while the bearing capacity was kept. However, the ductility factor of specimen without shear components was higher than those of specimen with BSBs and WSSCBs. The ductility factor of specimen HFISC2 and HFISC3 was smaller than those of specimen HFISC1 by about 6.42% and 26.15%.

The arrangement of tube fillers significantly affected the seismic behavior of specimens. The hysteretic curves of specimen with orthogonal tube fillers showed obvious pinching behavior. In contrast to specimen with orthogonal tube fillers, specimens with parallel tube fillers showed higher bearing capacity, stiffness, ductility, and energy-dissipating capacity.

Before the specimens reached the yield stage, specimen HFISC1 showed better energy-dissipating capacity than specimen HFISC2 and HFISC3. As the specimen reached the failure stage, the h_e of specimens reached 0.125 to 0.176, and the h_e of HFISC2 and HFISC3 was higher than those of specimen HFISC1 by about 12.59% and 40.69%.

Based on the test results and numerical results, increasing the hollow ratio of slab, the ratio of longitudinal reinforcement, the ratio of BSBs and the arm length of WSSCB can increase the bearing capacity of hollow floor slab-column connection. The ratio of longitudinal bars was a critical parameter, and it cannot be ignored in hollow floor slab-column structure design.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (no. 51778214), the Postgraduate Research &Practice Innovation Program of Jiangsu Province under Grant (no. KYCX18_0122), the Scientific and Technological Project of Henan Province (no. 152102210066), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (no. CE02-2-47), which are gratefully acknowledged.

ORCID iDs

Longji Dang

Rui Pang

Shuting Liang

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