Shaking table testing of the reinforced concrete staggered slab-column structure

Abstract

In order to study the seismic performance of the reinforced concrete staggered slab-column structure, one 1/7 scaled test specimen was fabricated and tested. The acceleration response, displacement distribution, dynamic characteristics, torsion responses, failure mechanism, shear force, and strain of test specimen were measured and evaluated. Test results indicated that the natural frequency and acceleration magnification factor of the test specimen gradually reduced, while the floor shear force and torsion response gradually increased. Meanwhile, the maximum inter-story drift angle of test specimen in the elastic and elastic-plastic stage was 1/196 and 1/78, respectively, indicating that the lateral stiffness of staggered slab-column structure was relatively small. The inter-story angles of the second and fifth floors were larger than adjacent floors. It was suggested that the stiffness of the test specimen was inhomogeneously distributed due to staggered slabs and a lack of frame beams. The damage of columns between staggered slabs was obviously larger than other columns. The plastic hinges were successively observed at slab-column junctions on the first and second floor and bottom of columns. Finally, the plastic hinges at slab-column junctions lost their capacity, followed by plastic hinges at the bottom of columns, and the test specimen collapsed. The failure process of the staggered slab-column structure exhibited undesirable brittle failure mode. Based on the experimental results, several design suggestions were proposed to improve the overall seismic behavior of the staggered slab-column structure. Such comprehensive research helps enhance understanding of this newly developed type of structure.

Keywords

shaking table test seismic performance staggered slab-column structure dynamic characteristic nonlinear response

Introduction

As the combination of staggered structure and slab-column structure, the staggered slab-column structure has advantages such as reduction in story height and flexibility in space utilization (Ping, 2014). By virtue of remarkable economic benefits and conveniences, this newly developed structure has been gradually applied in urban constructions. However, the slab in the same layer was divided into several parts, which undermined the integrity and stiffness of the structure. In addition, the columns between staggered slabs were prone to short column effect due to their limited effective length (Shahrour and Allouzi, 2020). Such deficiencies would result in an adverse impact on the seismic performance of staggered slab-column structures.

Up to now extensive studies have been conducted to analyze the seismic behavior of the staggered structures and slab-column structures. The outcomes concerning staggered structure were mainly focused on the seismic behavior and mechanical properties of joints. Dang et al. (2020a) investigated the seismic behavior of staggered joints between CFST columns and RC beams. The experimental results showed that the shear deformation of joints was small, and the plastic hinges were formed at beams. Jian et al. (2021) conducted an experimental and analytical study to investigate the seismic performance and failure mode of staggered joints between CFRST columns and RC beams. Three typical failure modes and the discriminant ratio between different failure modes were determined. Xla et al. (2021) studied the seismic behavior of the CFST frame with staggered beam-to-column joints. The frame exhibited a beam hinge failure mechanism, and its seismic behavior was inferior to CFST frame conventional joints. Wang et al. (2021) investigated the seismic behavior of staggered joints between SRC columns and RC beams. It was indicated from the experimental results that joints with staggered height had higher capacity and stiffness. The concrete compression strut mechanism was still applicable in this type of joint. In the meantime, the punching-shear behavior and seismic behavior of slab-column connections had been widely studied in recent years. Various shear components had been applied to develop the shear strength and ductility of slab-column connections, such as post-installed shear bolts (Bu et al., 2009), stirrups (Glikman et al., 2017; Song et al., 2012), shear studs (Isufi et al., 2019; Matzke et al., 2015), ductility reinforcement (Johannes et al., 2007), shear bands (Kang et al., 2017), thin plate stirrups (Kang and Wallace, 2008), and shear components combined with hidden beams (Pang et al., 2018), etc. To further understand the seismic performance of slab-column connections, Dang et al. (2020b) tested three hollow floor interior slab-column connections, and the results showed that this new type of connection showed favorable seismic performance.

In defense of comprehensive research outcomes for the staggered joints and slab-column joint, the reports concerning the seismic performance of the whole staggered slab-column structure were relatively limited. Zhou et al. (2010) carried out shaking table tests on a 1/4-scale 4-story post-tensional pre-stressed concrete hollow slab-column structure. The experimental results demonstrated that the key effect of seismic response was low-order vibration mode and the first-order mode shape showed shear characteristics in the elastic stage. Zhu et al. (2019) tested a two-story hollow slab-column structure. The results showed that the structure has better ductility and bearing capacity, while the energy dissipation ability is limited.

The above research results indicated that the seismic behavior and force mechanism of the staggered joint and slab-column structure was different from conventional structures. The studies on the staggered slab-column structures were very limited. Therefore, the seismic performance and failure mode of the staggered slab-column structure needs to be further studied. This paper presented and discussed the results of the shaking table tests program on one 1/7 scaled staggered slab-column structure. The tests were conducted at the Key Laboratory of Concrete and Pre-stressed Concrete Structures of the Ministry of Education. This study aimed to develop a fundamental understanding of the seismic performance and give constructive design suggestions to this newly developed staggered slab-column structure.

Description of the shaking table test

Prototype

The prototype of the shaking table test was a garage assumed to be located in Jiangning-District, Nanjing, and is a 6-story building. The overall dimensions of the prototype were 24 m × 24 m in plan and 9.8 m in elevation. The plane layout of the prototype was determined mainly considering the garage design requirements, such as turning radius, parking density, and driving route. The story of the prototype was determined as six, considering both the public policy and the adverse effect of staggered slabs. Figure 1 shows the architectural chart of the garage.

Figure 1.

Architectural chart of the garage.

According to the GB50011-2016 (2010), the seismic precautionary intensity was 7, the site category was II, and the seismic design group was the first group. The corresponding peak ground acceleration (PGA) value of the design earthquake (i.e., probability of exceedance of 10% in 50 years) is 100 cm/s². The value of the characteristic site period and maximum value of the seismic influence coefficient are 0.35s and 0.08, respectively. The design wind load is 0.45 kN/m².

Test specimen and test setup

To meet the physical limitations of the shaking table, the prototype was scaled to a 1/7 scale model. The test specimen was designed and fabricated under the laws of similarity. The details of the plan and elevation views of the test structures are shown in Figure 2(a) and (b). The model was 1.4 m tall, and its plan dimensions were 3.248 m (x-direction, or east-west direction) × 3.249 m (y-direction, or north-south direction). Figure 2(a) shows the structural arrangement of the first floor. Frame beams were set between side columns, and slab-column caps were set between intermediate columns and slabs. The structural arrangement of adjacent floors was symmetrically distributed. The story height of the second floor was 0.6 m, and the story height of the other floors was 0.4 m. Figure 2(c) shows the geometry and reinforcement details of the test specimen. The cross-sectional dimensions of the columns were 71.5 mm × 71.5 mm, and the cross-sectional dimensions of the beams were 35.7 mm × 85.7 mm. The thickness of the slab was 34.3 mm.

Figure 2.

Details of test specimen: (a) Plan view; (b) Elevation view; (c) Section view; (d) Details of experimental setup (unit in mm).

The experimental setup for the shaking table test is shown in Figure 2(d). The test specimen can be rigidly anchored to the shaking table through its base, which was placed at the bottom of the test specimen. Anti-slip devices were employed to prevent relative slip between test specimen and shaking table device during the test procedure. The weight of the test specimen and its base were 3.17 t and 6.90 t, respectively. To meet the requirements of laws of similarity, a total of 6.53 t additional mass was added uniformly on each floor.

Material properties

According to the work of Sabnis et al. (1999), the materials employed in the experimental model should maintain a similar stress–strain relationship and have lower Young’s and higher density than that used in prototype building. The model was made of micro concrete, iron wire (as reinforcement). The mean values of cube compressive strength (side length-70.7 mm) and elastic modulus of the micro concrete used for constructing the models are 14.29 MPa and 7034.5 MPa, respectively. The material properties of iron wire are listed in Table 1.

Table 1.

Material properties of iron wire.

Material	Size	d/mm	A_s/mm²	f_y/MPa	f_u/MPa	E_s/MPa
Iron wire	12#	2.87	6.48	341.71	384.08	2.08 × 10⁴
Iron wire	14#	2.31	4.19	348.97	384.90	2.32 × 10⁴
Iron wire	16#	1.80	2.55	232.51	346.08	1.69 × 10⁴
Iron wire	18#	1.34	1.41	259.39	375.29	2.68 × 10⁴

Note. d is the diameter of the iron wire; A_s is the sectional area of the iron wire; f_y is the yield stress; f_u is the extensive stress; E_s is the elasticity modulus of the iron wire.

Model similitude

The scaled building model was often used in the shaking table tests due to the limitation of equipment capacity. The shaking table test was the most effective test in reflecting the actual seismic performance of a complex structure (Lu et al., 2016). In this paper, the scale of the test specimen was chosen as 1/7, and the model similitude rules were developed from well-established scaling theory (Sabnis, 1983). According to Buckingham’s Pi theorem, three independent basic quantities should be determined to fully describe the dynamic behavior when designing a model. The basic scaling factors of geometry, elastic modulus, and acceleration were chosen as 1/7, 1/4, and 1, respectively. Other parameters were deduced by these three basic factors. The main similitude relationships of the test model are shown in Table 2.

Table 2.

Scaling parameters for model.

Parameter	Relationship	Model/prototype
Length	S L	0.143
Stress	S σ	0.25
Elastic modulus	S E = S σ	0.25
Mass	S m = S2 LS E/S a	0.005
Acceleration	S a	1
Force	S F = S ES2 L	0.005
Time	S t = S0.5 lS-0.5 a	0.378
Frequency	Sf = S-0.5 lS0.5 a	2.65

Shake table characteristic.

The dynamic tests were performed on the earthquake simulation facility of the Key Laboratory of Concrete and Pre-stressed Concrete Structures of Ministry of Education. The shake table is composed of a 4 m × 6 m platform, and the basic capacities are listed in Table 3.

Table 3.

Shake table characteristics.

Parameter	Value	units
Dimensions	4.0 × 6.0	m
Payload	30.0	tons
Maximum displacement	250.0	mm
Maximum velocity	6.0	m/s
Maximum acceleration	1.5 (full load)/3.0 (empty)	g
Frequency range	0.1–50.0	Hz

Test procedure

Considering the factors of the characteristic period, peak acceleration, duration of seismic wave, and requirement of Chinese Code for seismic design of buildings, three earthquake records were selected as input excitations: El Centro wave, Taft wave, and Shanghai artificial wave SHW4. Figure 3 summarizes the time history and acceleration response spectrum of these three seismic signals.

Figure 3.

The acceleration time history of the input seismic signals: (a) El Centro wave; (b) Taft wave; (c) SHW4 wave; (d) Acceleration response spectrum of seismic waves.

To observe the structural behavior under different levels of earthquake intensity, the ground motions were input with different amplitudes of PGA. The probability of exceedance within 50 years of frequent, basic, and rare earthquakes were 63%, 10%, and 2–3%, respectively. Due to that the shaking table device currently operated in single-degree-of-freedom, all ground motions were considered to act only in the x-direction (east-west direction) to study the effect of staggered slabs. White noises were used to scan the test specimen before and after the input of different levels of seismic waves to measure the dynamic parameters. The details of shaking table inputs are listed in Table 4.

Table 4.

Load cases for shaking table test.

Serial number	Peak acceleration (g)	Seismic record	Direction
1	0.02 (White noise sweeping-1)	WN1	x (east-west direction)
2–4	0.035	El/Taft/SHW4	x (east-west direction)
5	0.02 (White noise sweeping-2)	WN2	x (east-west direction)
6–8	0.05	El/Taft/SHW4	x (east-west direction)
9	0.02 (White noise sweeping-3)	WN3	x (east-west direction)
10–12	0.07	El/Taft/SHW4	x (east-west direction)
13	0.02 (White noise sweeping-4)	WN4	x (east-west direction)
14–16	0.10	El/Taft/SHW4	x (east-west direction)
17	0.02 (White noise sweeping-5)	WN5	x (east-west direction)
18–20	0.14	El/Taft/SHW4	x (east-west direction)
21	0.02 (White noise sweeping-6)	WN6	x (east-west direction)
22–24	0.22	El/Taft/SHW4	x (east-west direction)
25	0.02 (White noise sweeping-7)	WN7	x (east-west direction)
26–27	0.40	El/SHW4	x (east-west direction)

Note: El = El Centro wave; Taft = Taft wave; SHW4 = Shanghai artificial wave; WN = white noise.

Instrumentation

In order to monitor the global response and local state of the model structure during the test, a variety of instrumentations were installed on the model structure in advance. The accelerations, displacements, and strain were measured by variable capacitance accelerometers, electromagnetic displacement, and strain gauges, respectively. The accelerometers A1–A8 were attached to the surface of the frame floor to measure the absolute acceleration response. The electromagnetic displacement transducers D1–D7 were attached to the external edge of the beam to measure the displacement of each floor. The electromagnetic displacement transducers D8–D9 were set to the corner of the top layer to measure the torsion response of the test specimen. The arrangement of accelerometers and displacement transducers are shown in Figure 4(a) and (b). The strain gauges of Column 5, Column 6, Column 9, and Column 11 are shown in Figure 4(c). The plan view of columns with strain gauges is shown in Figure 4(d).

Figure 4.

Typical floor plan of the measuring points: (a) Axis ① perspective; (b) Axis ⑤ perspective; (c) Distribution of strain gauges; (d) Columns with strain gauges. Note. A = Accelerometer, D = displacement transducers.

Experimental results and discussion

Test phenomena

(1) The PGA = 0.035 g: The test specimen responded slightly, and no obvious cracks were found after earthquake excitations. The fundamental frequency of the test specimen was almost the same as before testing, indicating that the test specimen was still in the elastic stage, which met the “undamaged under minor earthquakes” design attributes.

(2) The PGA of 0.07 g and 0.1 g: No obvious cracks were found after earthquake excitations. Meanwhile, the fundamental frequency of the test specimen decreases. The second white noise scan displayed a reduction of the natural frequency, indicating that the structural rigidity had decreased as a result of internal damage.

(3) The PGA of 0.14 g: The test specimen responded with increasing amplitude, and tiny vertical cracks were observed at beam-column junctions on the first and third floors (Figure 5(a)). No obvious torsion response was observed during the earthquake excitation. The white noise scan displayed a reduction of the natural frequency, which indicated that the structural rigidity has decreased as a result of cracks.

(4) The PGA of 0.22 g: The test specimen responded with violent amplitude. Visible cracks were observed at junctions between side beams and columns (Figure 5(b) and (c)). The width of existing cracks continued to develop, and new cracks gradually appeared. The plastic hinges gradually appeared and developed at slab-column junctions on the first and second floors. The test specimen started to incline.

(5) The PGA of 0.4 g (El Centro seismic wave): The response amplitude of the model outdistanced that previously. The observed cracks were mainly concentrated at beam-column junctions. The damage of slab-column junctions on the first, second, and third floor developed more sufficient compared with those on the fourth, fifth, and sixth floor. Spalling of concrete accompanied by successive crisp sounds was recorded in slab-column junctions on the first floor, resulting in exposure of stirrups and longitudinal iron wires (Figure 5(d)). The damage of columns between staggered slabs was more obvious compared with other columns. The plastic hinges at the bottom of the columns gradually appeared, and the plastic hinges at slab-column junctions almost lost their capacity, resulting in obvious inclination on the test specimen.

(6) The PGA of 0.4 g (Shanghai artificial seismic wave SHW4): The response amplitude of the test specimen increased significantly, and the characteristic period of the test specimen increased. The plastic hinges at the bottom of the columns were fully developed and almost lost their capacity. The rupture was firstly observed at the slab-column junction between Column 12 and slab of the first floor, and ruptures at other junctions on the first and second floors were successively observed. The failure of the bottom vertical members rendered them unable to support the whole test specimen, and the test specimen lost its balance and collapsed. The impact force between the first floor and shaking table triggered a progressive collapse to the rest floors of the test specimen (Figure 5(e)). It was indicated from the failure mode that the beams and slabs of the test specimen remained complete, while the vertical members were damaged seriously.

Figure 5.

Typical damage of test model: (a) First crack; (b) Cracks at beam-column junction; (c) Damage of outer frame; (d) Damage of column; (e) Collapse of test specimen.

The collapse mechanism of the test specimen is illustrated in Figure 6. The whole collapse process could be summarized as the following stages: ① The plastic hinge gradually appeared and developed at slab-column junctions on the first and second floors, and the test specimen started to tilt (Figure 6(a)). ② With increasing earthquake excitations, the plastic hinges at junctions were fully developed. The plastic hinges gradually appeared at the bottom of columns (Figure 6(b)). ③ The plastic hinges at the bottom of the columns were fully developed, and the plastic hinges at slab-column junctions almost lost their capacity. The whole test specimen was significantly inclined (Figure 6(c)). ④ Ruptures of slab-column junctions were observed, and the plastic hinges at the bottom of the columns lost their capacity. The failure of bottom vertical members rendered them unable to support the whole test specimen, and the test specimen started to collapse (Figure 6(d)). ⑤ The impact force between the first floor and shaking table triggered a progressive collapse to the rest floors of the test specimen (Figure 6(e) and (f)).

Figure 6.

Failure mechanism of test specimen: (a) Plastic hinges appeared; (b) Plastic hinges fully developed; (c) Plastic hinge almost lost capacity; (d) Rupture of slab-column junctions; (e) Progressive collapse of test specimen; (f) Test specimen totally collapsed.

Dynamic response

Before and after each earthquake excitation test level, the dynamic properties of the test specimen were estimated by white noise excitation. The low-intensity white noise has a 0.5–50 Hz frequency band and a root-mean-square for a duration of 120 s. The natural frequencies were determined through transfer functions based on the acceleration response of the test specimen and the base motion. The damping ratios of the test specimen were determined using the well-known half-power bandwidth method applied to the peaks of the transfer functions. The frequencies and damping ratio of the model are obtained, as shown in Table 5.

Table 5.

Frequencies and damping ratios under different stages.

Test stage	First vibration frequency (Hz)/damping ratio (%)		Second vibration frequency (Hz)/damping ratio (%)		Third vibration frequency (Hz)/damping ratio (%)
Initial stage	6.38	0.98	16.35	0.51	22.75	0.41
After inputs of 0.035 g	6.25	1.02	16.23	0.63	22.00	0.42
After inputs of 0.05 g	6.25	1.02	16.17	0.62	21.88	0.44
After inputs of 0.07 g	6.13	1.04	16.13	0.67	21.56	0.49
After inputs of 0.10 g	5.88	1.85	15.88	0.73	21.38	0.52
After inputs of 0.14 g	5.75	1.85	15.63	0.74	20.63	0.59
After inputs of 0.22 g	3.50	1.23	15.38	0.89	20.5	0.68

The first three fundamental model frequencies were 6.38 Hz, 16.35 Hz, and 22.75 Hz, respectively, and remained stable until the PGA was 0.07 g. It was indicated that no apparent damage occurred after these earthquake excitations. When the PGA was 0.1 g, the fundamental frequencies of the model began to drop, indicating the formation of minor damage inside the test specimen. The fundamental frequencies of test specimen kept declining with the increase of PGA, accompanied by the development of cracks and the formation of plastic hinges. When the PGA was 0.4 g, the first three fundamental frequencies were 3.50 Hz, 15.38 Hz, and 17.50 Hz, respectively. The three fundamental frequencies were reduced to 54.85%, 94.06%, and 76.92% of its initial frequencies, which indicated that the test specimen underwent a certain degree of damage and stiffness degradation after earthquake excitations.

In the initial stage, the damping ratio of the test specimen was relatively small. With the increasing amplitude of earthquake excitations, the damping ratio gradually increased due to the development of cracks and the formation of plastic hinges. The energy dissipation ability of the test specimen increased gradually.

According to the equation (1), the structural stiffness k is proportional to the square of the fundamental frequency f under the condition that the mass m of the model is consistent (Xue and Xu, 2018). The stiffness degradation rate η is defined as equation (2)

f = (\frac{1}{2 Π}) \cdot \sqrt{\frac{k}{m}}

(1)

η = \frac{(k - k_{0})}{k_{0}} = \frac{(f^{2} - f_{0}^{2})}{f_{0}^{2}}

(2)

where k₀ and k are the initial stiffness and the stiffness during the test, respectively. f₀ and f are the initial frequency and the frequency during the test, respectively.

Figure 7 illustrates the degradation of the lateral stiffness of the test specimen. It can be seen that the overall stiffness of the test specimen degenerated to a great extend with the increase of PGA input. The lateral stiffness degradation rate η was 7.68% when the PGA reached 0.1 g, corresponding to the phenomenon that no obvious cracks were observed. When the PGA reached 0.22 g, the lateral stiffness degradation rate η increased to 18.77%, and large amounts of cracks were observed all over the test specimen. The rate η reached 69.9% when the PGA reached 0.4 g, indicating that the test specimen lost its lateral stiffness, and this was consistent with the collapse of the test specimen observed in the earthquake excitation.

Figure 7.

Lateral stiffness degradation of test model.

Figure 8 shows the first two vibration mode shapes of the test specimen. The first two modes of the structure have a convex tendency, and the response of the test specimen was mainly translational.

Figure 8.

Elastic modal shapes of test model.

Acceleration response

The experimental results showed that the acceleration responses of the test specimen under different seismic waves were not similar. This was attributed to that the characteristic periods of seismic waves were different. The acceleration responses depend on the dynamic characteristics of the properties of the excitations. The acceleration amplification factors (β, the ratio of the floor acceleration to the ground acceleration) of each floor under different earthquakes are plotted in Figure 9. It can be observed that the parameter β basically kept increasing with the increase in height under the same PGA, and the β ranged from 1.33 to 2.14 under different earthquake excitations. The acceleration response of the second floor was remarkably larger than the adjacent floors. This could be attributed to the following: (1) the effective length of the column in the second floor was larger than adjacent floors; (2) the lateral stiffness of the test specimen was inhomogeneously distributed. The dynamic amplification factor β of the test specimen decreased gradually with the increase in PGA, which implied that the stiffness of the test specimen degraded progressively. Moreover, the acceleration responses of the test specimen under the SHW4 wave were larger than that under the El Centro and Taft waves when PGA was relatively high. This was attributed to that the frequency of the test specimen, which underwent a significant reduction in rigidity after earthquake excitations, was close to the frequency of the SHW4 wave.

Figure 9.

Acceleration amplification factors of each floor: (a) El Centro wave; (b) Taft wave; (c) SHW4 wave.

Maximum relative displacement

Figure 10 shows the maximum relative displacement between each layer and the base of the test specimen under different earthquake excitations. The relative displacements gradually increased with the increase in the amplitude of earthquake excitations. The displacement distribution trends of the test specimen under the El Centro and the Taft waves were similar. There were two obvious turning points at the second and fifth floor, indicating that the max relative displacements of the second and fifth floor were larger than that of adjacent floors (Figure 10(a) and (c)). It was indicated that the lateral stiffness of the test specimen was inhomogeneously distributed due to staggered slabs and a lack of frame beams. When the PGA reached 0.4 g, the maximum relative displacement of the second floor was significantly larger than that of other floors. It was indicated that the second floor was a weak layer in the test specimen, and this was consistent with the phenomenon that the collapse started from column-slab junctions on the second floor (Figure 10(b)). The displacement distribution trends of the test specimen under the SHW4 wave were similar to that under two other seismic waves when PGA was less than 0.07 g, and two turning points were observed at the second and fifth floor. With the increase of PGA, the lateral stiffness of the third floor degraded sharply, and an obvious turning point was observed at the third floor when PGA was larger than 0.14 g (Figure 10(d)). It was indicated that the lateral stiffness of the test specimen was inhomogeneously distributed, and the local damage under earthquake excitations was obvious.

Figure 10.

The maximum relative displacement of the test specimen: (a) El Centro wave; (a) El Centro wave (PGA = 0.4 g); (c) Taft wave; (d) SHW4 wave.

Inter-story drift angle response

Inter-story drift angel is an effective indicator, or investigative tool, to examine the seismic behavior of structure during an earthquake. Table 6 presents the peak inter-story drift angles of the model under different earthquake excitations. According to the Chinese code for seismic design of buildings (2016), the elastic and elastic-plastic inter-story drift angles for frame structure were 1/550 and 1/50, respectively. The maximum inter-story drift angles of the test specimen gradually increased with the increase in the amplitude of earthquake excitations. When the PGA reached 0.035 g, the maximum inter-story drift angle of the test specimen under the El Centro wave, the Taft wave, and the SHW4 wave were 1/252, 1/229, and 1/196, respectively. The inter-story drift angles of the test specimen all exceeded the limits for frame structure (1/550). This indicated that the stiffness of the staggered slab-column frame structure was relatively small compared with normal frame structures. When the PGA reached 0.22 g, the maximum inter-story drift angle of the structure under the SHW4 wave was 1/78, which met the standard requirements. When the PGA reached 0.40 g, the maximum inter-story drift angle was 1/45, which exceeded the elastic-plastic inter-story drift angle for frame structure (1/50). The test specimen underwent collapse in the following excitation. This indicated that the elastic-plastic inter-story drift angle was applicable to evaluate the seismic performance of reinforced concrete staggered slab-column frame structure.

Table 6.

The maximum inter-story drift angle of model.

Earthquake excitation	Peak of acceleration inputs/g
Earthquake excitation	0.035 g	0.05 g	0.07 g	0.10 g	0.14 g	0.22 g	0.40 g
El Centro	1/252	1/224	1/211	1/212	1/212	1/200	1/45
Taft	1/229	1/216	1/207	1/203	1/184	1/169	-
SHW4	1/196	1/195	1/153	1/175	1/114	1/78	-

Shear force response

The inter-story shear force, which reflects the magnitude of the structure internal force, can be obtained through the measured accelerations and mass distribution of the test specimen. Figure 11 shows the inter-story shear force distribution of the test specimen. The shear forces gradually increased with the increase in the amplitude of earthquake excitation. The shear forces presented a triangular distribution pattern. When the PGA reached 0.4 g (El Centro wave), the shear force on the second floor increased obviously compared with other floors (Figure 10(a)), and this was consistent with the phenomenon that the collapse started from column-slab junctions on the second floor.

Figure 11.

Shear force: (a) El Centro wave; (b) Taft wave; (c) SHW4 wave.

Torsion response

The test specimen is asymmetrical in the x-direction (east-west direction), and symmetrical in the y-direction (north-south direction). In this paper, the time-histories method was used to analyze the torsion response of the test specimen. Figure 12 shows the comparison between displacement time-histories of the transducers D8 and D9 under different earthquake excitations. The displacement amplitude of D8 and D9 were obviously different, resulting in a relatively noticeable twist. One factor was that the lateral stiffness of the test specimen was inhomogeneously distributed, arising from architectural asymmetry arrangement. Another factor was that the structural stiffness center gradually changed due to asynchronous damage of the test specimen. The maximum value of the displacement time difference is illustrated in Table.7. It can be seen that the torsion effect gradually increased with the increase in the amplitude of earthquake excitations. Moreover, the torsion responses under the SHW4 wave were obviously larger than those under the El Centro and Taft waves.

Figure 12.

Displacement-comparison between the transducers D9 and D10 under different earthquake excitations: (a) El Centro wave (PGA = 0.10 g); (b) El Centro wave (PGA = 0.14 g); (c) El Centro wave (PGA = 0.22 g); (d) Taft wave (PGA = 0.10 g); (e) Taft wave (PGA = 0.14 g); (f) Taft wave (PGA = 0.22 g); (g) SHW4 wave (PGA = 0.10 g); (h) SHW4 wave (PGA = 0.14 g); (i) SHW4 wave (PGA = 0.22 g).

Table 7.

Maximum values of the displacement time difference.

Earthquake excitation	Peak of acceleration inputs/g
Earthquake excitation	0.10 g	0.14 g	0.22 g
El Centro	0.53	1.02	2.13
Taft	0.49	1.07	1.28
SHW4	0.59	1.49	4.28

Strain analysis

The maximum strains of micro concrete and iron wire, which were embedded in vertical members of the test specimen, under various earthquake excitations are plotted in Figures 13 and 14, respectively. It can be found that the strains of micro concrete and iron wire gradually increased with the increase in the amplitude of earthquake excitation and presented a similar distribution pattern. The maximum strains of micro concrete were mainly located at the top and bottom of the first floor. The maximum strains of iron wire were mainly located at the bottom of the first floor and second floor. The growth rate of strains aggravated remarkably when the PGA reached 0.22 g, and this could be attributed to the degradation of lateral stiffness of the test specimen.

Figure 13.

Maximum strains of microconcrete: (a) El Centro wave; (b) Taft wave; (c) SHW4 wave.

Figure 14.

Maximum strains of iron wire: (a) El Centro wave; (b) Taft wave; (c) SHW4 wave.

Figure 15 shows the strain time history of micro concrete in Column 5, Column 6, and Column 9 under different earthquake excitations when PGA reached 0.14 g. It can be found that the strain of Columns 6 was relatively larger than that of Columns 5. This can be attributed to that Column 6 was lack of restrains provided by the frame beam. Moreover, the strains of Column 9 were obviously larger than that of Column 5 and Column 6. It was indicated that Column 9 was subjected to higher internal force, and this was consistent with the phenomenon that the collapse started from columns between staggered slabs.

Figure 15.

Strain time-history of three columns under different earthquake excitations (PGA = 0.14 g): (a) El Centro wave; (b) Taft wave; (c) SHW4 wave.

Conclusion

The seismic performance of the staggered slab-column structure was investigated through the shaking table test. Based on the experimental analysis, the following conclusions can be drawn:

(1) The maximum inter-story drift angle of the test specimen was 1/196 when PGA reached 0.035 g, which outstood the limit of the Chinese design code. It was indicated that the lateral stiffness of the staggered slab-column structure was relatively small. The inter-story displacements of the second and fifth floors were significantly larger than that of adjacent floors. The stiffness of the test specimen was inhomogeneously distributed both vertically and horizontally. Meanwhile, obvious torsional effects were observed under earthquake excitations.

(2) The collapse of the test specimen started from the rupture of slab-column junctions on the first floor, followed by failure at the bottom of the columns. The failure process of the test specimen presented brittle failure mode, and the seismic performance of the test specimen was undesirable.

(3) The lateral stiffness of the staggered slab-column structure should be improved by increasing the sectional area of vertical members. The plan configuration should be properly addressed, and beams should be added between columns to reduce torsion response.

(4) To avoid brittle failure mode, reasonable design attributes “strong column-weak beam, strong joint-weak member” should be achieved by improving the capacity of columns between staggered slabs and enhancing the junctions between columns and slabs.

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 research paper was financially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions [grant numbers. CE02-2-47], and the National Natural Science Foundation for Young Scientists of China [grant number 51908336].

ORCID iDs

Shuting Liang

Longji Dang

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