Shaking table test of reinforced concrete coupled shear walls with single layer of web reinforcement and inclined steel bars

Abstract

In this study, five 1/4 scaled shaking table tests were conducted to investigate the seismic performance of reinforced concrete coupled shear walls with single layer of web reinforcement and inclined steel bars. The five tested coupled shear walls included three models with normal opening ratio (19%) and two models with large hole ratio (27%). The three models with normal opening included one model with single layer of web reinforcement, two models with single layer of web reinforcement and 75° inclined steel bars in the limbs’ web or at the bottom. Two reinforced concrete coupled shear walls with large hole and single row of reinforcements also were tested with inclined reinforcements or without them. The dynamic characteristics, dynamic response, and failure mode of each model were compared and analyzed. The test and analysis results demonstrate that the inclined steel bars are identified as an efficient means of limiting overall deformation, increasing energy dissipation, and reducing the possible damage by earthquake for reinforced concrete coupled shear walls with single layer of web reinforcement. Thus, reinforced concrete coupled shear walls with inclined steel bars have better seismic performance than reinforced concrete coupled shear walls without inclined steel bars. With appropriate design, reinforced concrete coupled shear walls with single layer of web reinforcement and inclined steel bars can be applied in multi-story buildings.

Keywords

coupled shear wall dynamic damage mechanism inclined steel bars shaking table test single layer of web reinforcement

Introduction

In China, masonry structures, light steel structures, and frame structures are normal structures for the multi-story residential structure system (Wang and Li, 2001). Masonry structures have a very long applied history in China. But amount of weakness exists in masonry structures, such as low shear strength, weak seismic performance, poor energy saving effect (Jonaitis and Zavalis, 2013; Mohamad et al., 2007). What is more, to protect the decreasing cultivated land, the traditional clay brick multi-story residential structures have already been prohibited in most cities of China. The light steel structure is also used in multi-story residential structures in some areas of China. The steel has good capacity of plasticity, toughness, energy absorption, and ductility (Dudás, 2003). But the weakness of low corrosion resistance and poor fire resistance cannot be ignored for light steel structure (Wald et al., 2006). And the cost in the protection of light steel structure is higher than that of reinforced concrete structure, so it is not easy for popularization and application. For frame structures, the layout of the residential rooms is generally irregular and the columns are also hard to arrange in regular position. For rectangular frame columns in frame structures, the width of columns and beams is usually larger than the thickness of infilled walls, which affects the indoor appearance and the furniture layout (Pavese et al., 2016; Rossetto and Elnashai, 2005; Sasani, 2008). The infilled walls in frame structures are affected by the unfavorable factors such as temperature and material which result in cracking (Li et al., 2013; Tang et al., 2012; Yang et al., 2013). The reinforced concrete shear wall is a structure of good bearing capacity and seismic performance. It is a kind of effective structural system to resist lateral force, most commonly used in architectural design. In China, a lot of research results about the shear wall with single layer of web reinforcement have been made available in recent years (Cao et al., 2010a, 2010b, 2010c, 2011). Those research achievements provide reliable test data for the application of this shear wall in multi-story building structures which meet the basic seismic demand as the Code for Seismic design of Building (GB50011, 2010) required. The thin shear walls reinforced with single layer of deformed bars and welded-wire mesh are also used for one-to-two stories housing in several Latin American countries (Carrillo et al., 2015; Quiroz et al., 2013). Focusing on the function of inclined steel bars in seismic performance for shear walls (Salonikios et al., 1999, 2000, 2007), some results about static testing of single layer of web reinforcement and inclined steel bars (Zhang et al., 2016a, 2016d, 2017) have indicated that inclined steel bars can improve the hysteretic response of shear walls with single layer of web reinforcement.

The studies on seismic performance of reinforced concrete (RC) shear walls have made some progress about inclined steel bars and opening. These achievements include the study about the coupled walls with distributed crossover steel bars at the bottom (Sittipunt and Wood, 1995), the study about the large opening ratio impacting load capacity, ductility and failure mode of the shear wall for the ordinary multi-story buildings (Ali, 2006; Mosoarca, 2014), the study about the coupled shear walls with inclined steel bars in coupled beams and a performance-based design method for the coupled shear wall (Xuan et al., 2008), the study about the influence of the opening on the low-rise shear walls reinforced with single layer of deformed bars and welded-wire mesh (Carrillo and Alcocer, 2012), and the study about the coupled shear walls with single layer of web reinforcement and different inclined steel bars (Zhang et al., 2016b, 2016c). But majority of those experimental results were obtained by means of static testing. Experimental studies on dynamic behavior of structural RC shear walls with single layer of web reinforcement and inclined steel bars are fairly few.

The studies of the shaking table test usually investigate the overall response and the dynamic properties of structures. And the shaking table tests of full structure systems are generally performed on small-scale models due to the size limitations of the shaking tables and are focused on limited aspects of the problem in general. Because of the influence of the small-scale factor, the material properties, and the complicated constructional measures, also the dynamic responses of the single number are always ignored. Appling the shaking table test to the single member rather than the whole structure, the large-scale simulation can be applied. And the dynamic damage mechanism of single members is clearer. This article presents the results of an experimental investigation of the dynamic performance of RC coupled shear walls with single layer of web reinforcement. Five RC coupled shear walls with single layer of web reinforcement were tested through the use of shaking table, and the research focused on the influence of the different forms of the inclined steel bars. The experiment result shows inclined steel bars can improve the seismic capacity of RC coupled shear walls with single layer of web reinforcement.

Experimental details

Test specimens

Five 1/4 scaled coupled shear wall models were designed according to the load capacity of the shaking table used, labeled as CSWD-1, CSWXD-2, CSWXD-3, CSWD-4, and CSWXD-5. As presented in Table 1, CSWD-1 and CSWD-4 had single layer of web reinforcement with normal opening hole (19%) or large opening hole (27%), CSWXD-2 and CSWXD-3 had single layer of web reinforcement and 75° inclined steel bars in the limbs’ web or at the bottom with normal opening hole (19%). CSWXD-5 had single layer of web reinforcement and 75° inclined steel bars in the limbs’ web with large opening hole (27%). All walls had limbs of T-shaped cross section with a thickness of 50 mm considering the influence of adjoining members. The simplified boundary element around the opening was 2Ø6 longitudinal bars, while the simplified boundary element in the limb was the column concealed with the triangular stirrups, placed 2Ø6 and 1Ø4 longitudinal bars (Zhang et al., 2009). The dimensions and reinforcement layout of the specimens are shown in Figure 1. In order to explore its basic seismic performance, web reinforcement was designed according to the seismic code of China (GB50011, 2010), using the minimum reinforcement ratio of the request 0.25%. As shown in Figure 1, the first floor height of the five specimens was all 710 mm according to the scaling factors (i.e. geometry scale factor, S_L = 1/4). The opening hole dimension of CSWD-1, CSWXD-2, and CSWXD-3 was all 300 mm × 450 mm. The opening hole dimension of CSWD-4 and CSWXD-5 was both 380 mm × 500 mm. Specimens were built with the same materials of the prototype (i.e. materials properties were not changed) and only the dimensions of the models were altered. The layout of the steel bars of the specimens was arranged according to the reinforcement ratio of the prototypes. The stirrup ratio of boundary element for the prototypes was 2.5%. Stirrups in the simplified boundary element of five specimens were all Ø4 at 70 mm.

Table 1.

Design parameters of specimens.

Wall	CSWD-1	CSWXD-2	CSWXD-3	CSWD-4	CSWXD-5
Opening geometry	19%	19%	19%	27%	27%
Web reinforcement ratio of wall limbs	0.25%	0.25%	0.25%	0.25%	0.15%
Inclined reinforcement of wall limbs	–	4Ø4 (0.1%)	6Ø4 (0.1%)	–	4Ø4 (0.1%)
Style of inclined reinforcement	–	75°	75°	–	75°
Inclined reinforcement of coupled beams	–	2Ø6	2Ø6	–	–

Figure 1.

Dimensions and reinforcement of specimens: (a) CSWD-1, (b) CSWXD-2, (c) CSWXD-3, (d) CSWD-4, and (e) CSWXD-5.

The design concrete strength grade for the wall was C30. The specimens in test were made by fine stone concrete and the maximum grain size of the coarse aggregate was 10 mm. The cubic compressive strength of concrete was 37.8 MPa. Specific dry weight of the concrete for five specimens was 23.25 kN/m³. Elastic modulus of the concrete for five specimens was 24.43 GPa. The weight of CSWD-1, CSWXD-2 and CSWXD-3 was approximately 1.74 kN. The weight of CSWD-4 and CSWXD-5 was approximately 1.65 kN. The weight of five specimens was close. The mechanical properties of the steel bars are listed in Table 2.

Table 2.

Mechanical properties of steel bars.

Steel reinforcementdiameter (mm)	Yield strength(MPa)	Ultimate strength(MPa)	Elastic modulus (GPa)	Elongation (%)	Yield strain(×10^–6)
Ø4	730.3	903.0	190.6	3.0	3928
Ø6	394.5	578.3	220.7	22.0	1787

Test setup

The experiment was conducted at the Key Laboratory of Urban and Engineering Safety and Disaster Reduction in Beijing University of Technology, China. The dimension of the table is 3 m × 3 m; the maximum load capacity is 10 ton; the frequency is 0.1–50 Hz; the acceleration can reach 2.5g without load or 1.0g with full load. The similitude coefficient of specimens is provided in Table 3.

Table 3.

Similitude coefficient for specimens.

Quantity	Equation	Scale factor	Quantity	Equation	Scale factor
Length (L)	S _L	1/4	Density (ρ)	S_σ/(S_aS_L)	4
Stress (σ)	S _σ	1	Force (F)	S _σ S _L ²	1/16
Acceleration (a)	S _a	1	Period (T)	S_L^1/2S_a^–1/2	1/2
Strain (ε)	1	1	Frequency (f)	S _L ^–1/2 S _a ^1/2	2
Mass (m)	S _ρ S _L ³	1/16	Elastic modulus (E)	1	1

The designed axial compression ratio of the shear wall was 0.1; therefore, the added mass on the top of the specimen was 7.485 ton. The gravity load trough was fixed to the specimen by bolts, and construction measures were carefully taken to make sure that there was no relative displacement between the load trough and the specimen. To maintain in-plane stability of the shear wall during the test, four supporting poles were installed around the specimen and were connected to the load trough by slide bolts. The specific test device can be seen in Figures 2 and 3.

Figure 2.

Schematic diagram of test setup: (a) whole loading device and (b) connection device for load beam.

Figure 3.

Schematic diagram of transducer arrangement.

Test procedure and measurements

In order to observe the damage caused by the actual seismic wave in an ideal failure mode, the actual seismic record should be inputted to the specimens on the shaking table. Therefore, the El-Centro (1940) N-S wave was selected. The scaled values of time interval and duration of time of the earthquake motions were then 0.02×0.5=0.01s and 53.74×0.5=26.87s, respectively. The time history acceleration and response spectra for scaled earthquake motion are shown in Figure 4.

Figure 4.

Inputted earthquake: (a) time history acceleration for specimens and (b) response spectra for specimens.

According to the static test results of RC coupled shear walls with single layer of web reinforcement (Zhang et al., 2016b, 2016c), seven earthquake hazard levels were selected. The T-1, T-2, and T-3 were designed according to the design basic acceleration of ground motion for precautionary intensity of 7°, 8°, and 9° in the seismic code of China (GB50011, 2010), respectively. T-4, T-5, T-6, and T-7 were designed to investigate the severe dynamic damage state for RC coupled shear walls with single layer of web reinforcement. The actual PGA acquired on the surface of the shaking table during the experimental procedure is shown in Table 4.

Table 4.

Test procedure.

Record	PGA (g)
Record	CSWD-1	CSWXD-2	CSWXD-3	CSWD-4	CSWXD-5
T-1	0.189	0.191	0.151	0.163	0.165
T-2	0.388	0.330	0.328	0.296	0.370
T-3	0.524	0.492	0.484	0.411	0.556
T-4	0.615	0.650	0.527	0.606	0.602
T-5	0.815	0.782	0.778	0.726	0.780
T-6	1.155	0.875	0.919	1.033	0.857
T-7	1.219	1.126	1.153	1.270	1.111

PGA: peak ground acceleration.

The absolute acceleration response on each floor and on the important positions of the coupled shear wall was collected. The test measurements also included each story’s shear drift, the strain at the end of the longitudinal reinforcement in wall limbs, and the strain at the end and in the middle of the longitudinal reinforcement of coupled beams. The strain gauge arrangement for steel bars of specimen CSWXD-2 can be seen in Figure 5.

Figure 5.

Strain gauge arrangement for steel bars of specimen CSWXD-2.

Experimental results and interpretation

Natural frequency and damping ratio

The natural frequency of each specimen measured in different stages is listed in Table 5 and Figure 6. In Figure 6, A is amplitude (g) from the result curve of transfer function and A_max is maximum amplitude corresponding to the natural frequency of each specimen. The change of the natural frequency reflects variation characteristics of the specimens’ stiffness. The results from Figure 6 indicate that the natural frequency of the five specimens started to decrease and damping ratio increased gradually with the increase of specimens’ damage level. The reason is that the diagonal cracks continually developed and the plastic deformations gradually increased as the experiment progresses. The natural frequency decrement of CSWXD-2 and CSWXD-3 was lower than that of CSWD-1. The reason is that the pin function of the inclined steel bars stayed and restricted the development of diagonal cracks so that the stiffness decrement of CSWXD-2 and CSWXD-3 was slower than that of CSWD-1. For coupled shear walls with large opening, the natural frequency decrement of CSWD-4 was larger than that of CSWXD-5 in the final condition. This shows that inclined steel bars can also limit stiffness degradation for coupled shear walls with large openings. In the final condition, natural frequency for CSWD-1 and CSWD-4 suddenly dropped; thus, stiffness and load capacity of CSWD-1 and CSWD-4 lost suddenly. The load capacity of CSWXD-2, CSWXD-3, and CSWXD-5 was not completely lost in the ultimate test conditions, especially with CSWXD-3 the least damaged.

Table 5.

Test results of natural frequency and damping ratio.

Record	CSWD-1		CSWXD-2		CSWXD-3		CSWD-4		CSWXD-5
Record	f (Hz)	ζ (%)	f (Hz)	ζ (%)	f (Hz)	ζ (%)	f (Hz)	ζ (%)	f (Hz)	ζ (%)
Initial	8.25	1.79	8.30	1.43	8.59	1.88	8.20	1.63	8.15	1.62
T-1	8.06 (BC)	2.72	7.86	2.28	8.10	2.24	8.11 (BC)	1.82	7.76 (BC)	1.96
T-2	7.42	3.88	7.13 (BC)	3.21	8.01 (BC)	2.99	7.52 (LC)	2.53	7.13 (LC)	2.46
T-3	7.28 (LC)	4.05	5.69	3.41	7.91	3.04	7.47	3.12	7.08	2.59
T-4	6.74	5.23	5.66 (LC)	3.74	6.74	3.49	7.37	3.89	6.69	2.77
T-5	5.56	5.58	5.63	3.98	6.35 (LC)	4.11	6.93	4.61	5.91	3.4
T-6	4.49	6.72	5.62	4.47	6.34	4.91	5.27	4.71	5.42	4.93
T-7	2.83	12.34	5.08	5.80	6.25	4.95	1.51	14.63	4.44	8.64

f: frequency; ζ: damping ratio; BC: beam crack occurred; LC: limbs crack occurred.

Figure 6.

Frequency attenuation diagram of white noise transfer function: (a) CSWD-1, (b) CSWXD-2, (c) CSWXD-3, (d) CSWD-4, and (e) CSWXD-5.

Displacement response

The measured results of the maximum first and second story drift of each specimen in different stages are listed in Tables 6 and 7, respectively. The shear deformation of each specimen in first story drift can be seen in Figure 7.

Table 6.

Maximum first story drift and first story drift angle.

Record	CSWD-1		CSWXD-2		CSWXD-3		CSWD-4		CSWXD-5
Record	D_FS (mm)	θ_FS (rad)	D_FS (mm)	θ_FS (rad)	D_FS (mm)	θ_FS (rad)	D_FS (mm)	θ_FS (rad)	D_FS (mm)	θ_FS (rad)
T-1	0.27	1/2629	0.34	1/2088	0.27	1/2629	0.27	1/2629	0.28	1/2535
T-2	0.67	1/1059	0.73	1/972	0.57	1/1246	0.66	1/1075	0.74	1/959
T-3	1.05	1/676	1.88	1/378	0.82	1/866	0.91	1/780	0.90	1/789
T-4	1.42	1/500	3.05	1/233	0.94	1/755	1.30	1/546	1.50	1/473
T-5	3.75	1/189	3.45	1/206	1.19	1/597	3.50	1/202	3.34	1/213
T-6	6.74	1/105	4.04	1/176	4.29	1/165	6.84	1/104	4.32	1/164
T-7	–	–	6.29	1/112	6.50	1/109	–	–	6.28	1/113

D_FS: first story drift; θ_FS: first story drift angle.

Table 7.

Maximum second story drift and second story drift angle.

Record	CSWD-1		CSWXD-2		CSWXD-3		CSWD-4		CSWXD-5
Record	D_SS (mm)	θ_SS (rad)	D_SS (mm)	θ_SS (rad)	D_SS (mm)	θ_SS (rad)	D_SS (mm)	θ_SS (rad)	D_SS (mm)	θ_SS (rad)
T-1	0.23	1/3087	0.23	1/3087	0.21	1/3381	0.21	1/3381	0.21	1/3381
T-2	0.57	1/1246	0.63	1/1127	0.41	1/1732	0.54	1/1315	0.58	1/1224
T-3	0.97	1/732	1.45	1/490	0.68	1/1044	0.89	1/798	0.77	1/922
T-4	1.15	1/617	2.43	1/292	0.79	1/899	1.05	1/676	1.21	1/587
T-5	3.44	1/206	3.05	1/233	0.93	1/763	3.36	1/211	2.55	1/278
T-6	6.41	1/111	3.61	1/197	3.18	1/223	6.91	1/103	4.51	1/157
T-7	–	–	5.03	1/141	5.58	1/127	–		–	–

D_SS: second story drift; θ_SS: second story drift angle.

Figure 7.

The first story shear deformation of the specimen: (a) CSWD-1, (b) CSWXD-2, (c) CSWXD-3, (d) CSWD-4, and (e) CSWXD-5.

Under the ground motions, the maximum first story drift angle θ_FS and second story drift angle θ_SS of each specimen can be determined as follows

θ_{FS} = \frac{D_{FS}}{H_{FS}}

(1)

θ_{SS} = \frac{D_{SS}}{H_{SS}}

(2)

where D_FS and D_SS are the first story drift and the second story drift, respectively. H_FS and H_SS are both the height of 710 mm. It can be seen from Table 6 that when the five specimens subjected to the same level of sixth time shaking table motion, the maximum first story drift of CSWXD-2 and CSWXD-3 decreased by 40.1% and 36.4%, respectively, compared with that of CSWD-1. It indicates that the inclined steel bars can decrease the drift response significantly for coupled shear walls of normal opening after the concrete cracking. The maximum first story drift of CSWXD-5 decreased by 36.8% compared with that of CSWD-4. Therefore, for coupled shear walls of large opening, the inclined steel bars can also decrease the drift response. It can be seen from Table 7 that the second story drift was less than the first story drift for RC coupled shear walls with single layer of web reinforcement and with normal opening when subjected to the same level of sixth and seventh time shaking table motion. While for RC coupled shear walls with single layer of web reinforcement and with large opening, the second story drift was slightly larger than the first story drift when subjected to the same level of sixth and seventh time shaking table motion. From Figure 7, it can be noted that the maximum shear deformation response in first story drift increased with test procedure for the RC coupled shear walls with single layer of web reinforcement. The inclined steel bars had insignificant influence on the shear deformation responses of the first story in the early test procedure for five specimens. The maximum shear deformation responses in first story drift decreased significantly by installing inclined steel bars for coupled shear walls of normal opening at the failure stages. And the inclined steel bars restricted shear deformation in the first story drift of the coupled shear walls with large opening at the failure stages to some extent. The reason is that the inclined steel bars can restrict the development of diagonal cracks and shear slipping at the bottom of shear walls.

Acceleration and base shearing force response

The measured maximum absolute roof acceleration responses of the five specimens are listed in Table 8. The comparison of roof acceleration history responses among five specimens subjected to the strongest earthquake excitation for 3 s, before and after concrete cracking as well as initial cracks appearing in the coupled beam or wall limbs, is shown in Figure 8. It can be noted from Table 8 and Figure 8 that the inclined steel bars did not have a significant effect on the acceleration responses in early test stages. After the development of the wall limbs’ cracks, the acceleration response of CSWXD-2 and CSWXD-3 was higher than that of CSWD-1 under the same peak acceleration for the excitation of the shaking table. It shows that the seismic performance of RC coupled shear walls increases by installing the inclined steel bars. The reason is that the inclined steel bars have the pin function and restrict the development of diagonal cracking. In later test stages, the acceleration responses of CSWXD-5 were similar with that of CSWD-4. The seismic performance of CSWD-4 and CSWXD-5 was close.

Table 8.

Maximum roof acceleration responses and maximum base shears of specimens.

Record	CSWD-1		CSWXD-2		CSWXD-3		CSWD-4		CSWXD-5
Record	PRA (g)	BS (kN)	PRA (g)	BS (kN)	PRA (g)	BS (kN)	PRA (g)	BS (kN)	PRA (g)	BS (kN)
T-1	0.186	13.92	0.197	14.74	0.188	14.07	0.174	13.02	0.184	13.77
T-2	0.435	32.56	0.346	25.89	0.404	30.23	0.375	28.06	0.423	31.66
T-3	0.498	37.28	0.408	30.54	0.605	45.28	0.456	34.13	0.450	33.68
T-4	0.620	46.41	0.617	46.40	0.833	62.35	0.632	47.31	0.677	50.67
T-5	1.157	86.60	0.941	70.43	0.845	63.24	0.815	61.00	0.959	71.78
T-6	1.166	87.28	1.047	78.36	1.204	90.12	1.097	82.11	1.080	80.84
T-7	0.987	–	1.250	93.56	1.257	94.09	0.775	–	1.144	85.63

PRA: peak roof acceleration; BS: base shear.

Figure 8.

Time histories comparison of roof accelerations: (a) Test T-1, (b) Test T-2, and (c) Test T-4.

Under the ground motions, the maximum nominal base shear of each specimen at the moment t, F_i(t)_max, can be determined as follows

F_{i} (t)_{max} = {| - m a_{i} (t) |}_{max}

(3)

where m is the centralized mass at roof of the specimen and a_i is the acceleration for the ‘i’ time excitation. The maximum values of the base shear are listed in Table 7. It can be noted that the inclined steel bars increased the earthquake resistance capacity of coupled shear walls with single layer of web reinforcement. When the maximum roof drift angle of first story for CSWD-1, CSWXD-2, and CSWXD-3 reached 1/105, 1/112, and 1/109, the maximum base shear of CSWXD-2 and CSWXD-3 increased 7.2% and 7.8%, respectively, compared to CSWD-1. Thus, the earthquake resistance capacity of coupled shear walls of normal opening increased with the inclined steel bars. However, when the maximum roof drift angle of first story for CSWD-4 and CSWXD-5 reached 1/104 and 1/113, the maximum base shear of CSWXD-5 was similar to that of CSWD-4. It indicates that inclined steel bars have little effect on the earthquake resistance capacity of coupled shear walls with large opening.

Energy dissipation

A series of cyclic loading tests of RC coupled shear walls with single layer of web reinforcement and inclined steel bars were conducted to investigate the function of inclined steel bars (Zhang et al., 2016b, 2016c). The hysteresis loops of specimens in cyclic loading tests are shown in Figure 9. Hysteresis loops can reflect the energy dissipation capacity of specimens. From Figure 9, it can be found that inclined steel bars at the bottom of the shear wall limbs and in the middle of coupled beams improved the energy dissipation capacity significantly for RC coupled shear walls with single layer of web reinforcement and with normal opening hole. For RC coupled shear walls with single layer of web reinforcement and with large opening hole, the arrangement of inclined steel bars could improve the energy dissipation capacity to some extent.

Figure 9.

Hysteresis loops of specimens in static tests: (a) CSW-1, (b) CSWX-2, (c) CSW-3, and (d) CSWX-4.

For the shaking table test of RC coupled shear walls with single layer of web reinforcement, the accumulated hysteretic dissipated energy under different earthquake excitations can be obtained by the curve between the base shear and story drift. According to the effect of earthquake, the accumulated hysteretic dissipated energy E of each specimen in shaking table tests can be determined as follows

E = \sum_{i = 1}^{s} \frac{1}{2} F_{i} (t_{k}) [x_{i} (t_{k + 1}) - x_{i} (t_{k - 1})]

(4)

where F_i(t_k) is the nominal base shear of each specimen at the moment t_k. x(t_k + 1) and x(t_k + 1) are the story drift at the moment t_k + 1 and t_k − 1, respectively. s is the total number of sampling points under different earthquake excitations. Figure 10 reflects the variation of accumulated hysteretic dissipated energy for each specimen with time t under different earthquake excitations. From Figure 10, it can be found that inclined steel bars had no obvious effect on the energy dissipation of RC coupled shear walls with single layer of web reinforcement in test T-1 and test T-2 for each specimen. In test T-4, the accumulated hysteretic dissipated energy of CSWXD-2 and CSWXD-3 increases 21% and 12%, respectively, compared to CSWD-1 (323 kN mm). While the accumulated hysteretic dissipated energies of CSWD-4 and of CSWXD-5 were 310 and 318 kN mm, respectively, in test T-4. Inclined steel bars can improve the energy dissipation capacity of RC coupled shear walls with single layer of web reinforcement and with large opening hole to some extent.

Figure 10.

Accumulated hysteretic dissipated energy of earthquake action: (a) CSWD-1, (b) CSWXD-2, (c) CSWXD-3, (d) CSWD-4, and (e) CSWXD-5.

Stress and strain analysis

Figure 11 shows reinforcement strain damage processes of longitudinal reinforcement at the wall limbs edge of the coupled shear wall before the final damage. ZZ1–ZZ4 are strain gauges located at the bottom of longitudinal bars in the simplified boundary element which can be seen in Figure 5. From Figure 11, we can find:

With the increase of the peak acceleration of the record, reinforcement strain at the wall limbs edge increased gradually and finally entered the yield stage. The development of the strain in the early stage is similar, while the yielding stage usually happens in the later stage.

Compared with specimen CSWD-1, specimen CSWD-4’s reinforcement strain at the wall limbs edge developed rapidly into the yielding stage. The increase of the flexural deformation for CSWD-4 can make the reinforcement strain at the wall limbs edge rise, and the yield stage may go ahead.

Compared with specimen CSWD-1, specimen CSWXD-2 and CSWXD-3’s yielding strain at the wall limbs edge appeared relatively late, and the process of strain at the wall limbs edge developing into failure was longer. By arranging the inclined steel bars, the yield of the reinforcement can be delayed and the stress of the reinforcement can be reduced, providing that the inclined steel bars play an effective role in controlling the damage process.

The development of reinforcement strain at the edge of the beam was significantly faster than that of the wall limbs edge. In the process of testing, compared with the web reinforcement, the strain growth amplitude of inclined steel bars was relatively larger, which can play the first seismic fortification line in the coupled beam.

Figure 11.

Strain development of longitudinal reinforcement in edge members of specimens: (a) CSWD-1, (b) CSWXD-2, (c) CSWXD-3, (d) CSWD-4, and (e) CSWXD-5.

Failure characteristics

After the test T-6, the crack diagram of each model is shown in Figure 12. The failure mode of each specimen is shown in Figure 13. It can be found.

Figure 12.

Crack diagram of specimens after test T-6: (a) CSWD-1, (b) CSWXD-2, (c) CSWXD-3, (d) CSWD-4, and (e) CSWXD-5.

Figure 13.

Failure modes of specimens: (a) CSWD-1, (b) CSWXD-2, (c) CSWXD-3, (d) CSWD-4, and (e) CSWXD-5.

In CSWD-1 model, after earthquake excitation with the PGA of 0.189g, vertical cracks appeared at the joint areas between the coupled beam and wall limbs. After earthquake excitation with the PGA of 0.388g, the crack continued to appear in the coupled beam with the width of the crack reaching to 0.12 mm. After earthquake excitation with the PGA of 0.524g, horizontal cracks appeared at the lower wall limbs first. After earthquake excitation with the PGA of 0.615g, the concrete on the coupled beam began to peel off, and the wall limb cracks developed to the inclined shear cracks. After earthquake excitation with the PGA of 0.815g, the first incline cracks began to appear in the coupled beam. After earthquake excitation with the PGA of 1.155g, a large area of concrete peeled off in the corner of the coupled beam. The obvious inclined cracks development could be seen in the lower limbs of the wall. The phenomenon of wall limb concrete peeling off happened. The width of the crack in the coupled beam and wall limbs reached to 0.3 and 0.24 mm, respectively. After earthquake excitation with the PGA of 1.219g, the large area of concrete in the coupled beam fell off, leaking out of the internal reinforcement. The concrete at the corner of the lower wall limbs was crushed, so the bearing capacity of the beam was lost.

In the CSWXD-2 model, the initial crack was located on the upper coupled beam after earthquake excitation with the PGA of 0.330g with the width of the crack reaching to 0.02 mm. After earthquake excitation with the PGA of 0.650g. The first inclined cracks began to appear in the coupled beam and slight cracks appeared at the upper wall limbs first. After earthquake excitation with the PGA of 0.875g, crossed inclined cracks appeared in the beam, the width of beam diagonal crack was 0.20 mm, and the maximum crack width for the upper wall limbs was 0.08 mm. At the joint areas between the coupled beam and wall limbs, a little concrete fell off. After earthquake excitation with the PGA of 1.126g, inclined shear cracks more seriously appeared in the coupled beam and a slight amount of concrete fell off in the wall limbs, but the load capacity of CSWXD-2 still maintained.

In CSWXD-3 model, after earthquake excitation with the PGA of 0.330g, the first slight cracks appeared on both sides of the coupled beam and the width of the crack in the coupled beam reached to 0.04 mm. After earthquake excitation with the PGA of 0.527g, the width of the crack reached to 0.10 mm. After earthquake excitation with the PGA of 0.778g, inclined cracks appeared in the coupled beam for the first time. A slight crack appeared at the upper wall limbs for the first time. After earthquake excitation with the PGA of 0.919g, the crack width in the wall limbs reached to 0.10 mm. In the final stage of destruction of 1.153g, the surface of the concrete at the intersection of the coupled beam fell off, while inclined cracks partially appeared on the wall limbs, which has less impact on the bearing capacity of the specimen.

In the CSWD-4 model, after earthquake excitation with the PGA of 0.163g, the vertical cracks occurred in the coupled beam. After earthquake excitation with the PGA of 0.296g, the width of the crack reached to 0.18 mm and a little crack appeared in the middle area of the wall limbs. After earthquake excitation with the PGA of 0.606g, a wider area of cracks developed. Along with cracks of coupled beam extension, the width of cracks developed to 0.2 mm. After 0.726g, the inclined cracks appeared on the upper wall limbs, and crack width of coupled beams reached to 0.4 mm, where most vertical cracks were. After earthquake excitation with the PGA of 1.033g, the inclined crack began to appear in the coupled beam. After earthquake excitation with the PGA of 1.270g, significant peeling at the junction of the beam and the limbs occurred. The wall limbs were damaged seriously, with a large area of concrete peeling off and internal steel disrupted. The ultimate strength was lost.

In the CSWXD-5 model, vertical cracks first appeared at both sides of the coupling beam after earthquake excitation with the PGA of 0.165g. After earthquake excitation with the PGA of 0.370g, the first incline cracks began to appear in the coupled beam with a width of 0.06 mm and slight cracks could be seen in the upper wall limbs. After earthquake excitation with the PGA of 0.602g, new development for the cracks of the coupled beam and a new piece of inclined crack appeared with the width of 0.08 mm. After earthquake excitation with the PGA of 0.780g, shear cracks began to appear on the wall limbs, while cracks of the coupled beam continued to develop, up to 0.54 mm, even the concrete started to peel off. After earthquake excitation with the PGA of 0.857g, the concrete also began to peel off in the wall limbs. The max diagonal crack width reached to 0.85 mm in the coupled beam. After earthquake excitation with the PGA of 1.111g, CSWXD-5 model was eventually destroyed and the wall limbs suffered the obvious shear damage.

The failure characteristics in the test show the following:

All the specimens’ failure characteristics are that cracking first occurred in the coupled beams. And then cracks appeared in the wall limbs. The final failure mode of each specimen with normal opening ratio showed that the damage of coupled beams was more serious than that of the wall limbs. This embodies the design ideas of “two seismic fortification lines” in the coupled shear wall of normal opening ratio.

When the coupled shear wall failure occurred, cracks of CSWD-1 were more concentrated in the lower part of the wall limbs and a significant amount of concrete peeled off. However, because of the effect of the inclined steel bars in the walls, the development of cracks in CSWXD-2 and CSWXD-3’s lower wall limbs was restricted, and the initial cracks were intermittent. Finally, cracks were less developed and were concentrated in the upper part of the wall.

When the initial cracks occurred to the wall limbs, the shaking table’s peak acceleration for CSWXD-2 and CSWXD-3 increased by 24.0% and 48.5%, respectively, compared with that of CSWD-1. The shaking table’s peak acceleration for CSWD-4 and CSWXD-5 decreased by 43.5% and 29.4%, respectively, compared with that of CSWD-1.

The failure mode of CSWD-4 and CSWXD-5 was mainly the upper left wall shear failure with serious diagonal cracks to the shear wall edge. According to concrete structure design code of China (GB50010, 2010), the bending strength and the shear strength of wall limbs can be calculated. CSWD-4 and CSWXD-5 have wall limbs of T-shaped cross section. The calculated bending strength can be obtained according to the internal force equilibrium ΣN = 0 and ΣM = 0. The calculated bending strengths of CSWD-4’ and CSWXD-5’ upper wall limbs are 25.6 and 24.9 kN, respectively. The calculated shear strength can be obtained according to equation (5). The calculated shear strengths of CSWD-4’ and CSWXD-5’ upper wall limbs are 22.2 and 18.1 kN, respectively

\begin{matrix} V = \frac{1}{λ - 0.5} 0.5 f_{t} b_{w} h_{w 0} + 0.13 N \frac{A_{w}}{A} \\ + f_{yh} \frac{A_{sh}}{s} h_{w 0} + f_{yb} A_{sb} \cos θ \end{matrix}

(5)

where $λ$ is the shear span ratio; f_t is the tensile strength of concrete; h_w0 is the applied height of the cross section; b_w is the section width of shear wall; N is the axial force; A_w is the area of the wall web; A is the area of the wall; f_yh is the yield strength of horizontal web reinforcement; A_sh is the area of horizontal web reinforcement; s is the space of horizontal web reinforcement; f_yb is tension yield strength of inclined steel bars; A_sb is area of inclined steel bars; and θ is the angle of the inclined steel bars in the horizontal direction.

It can be found that the shear strength of the upper wall limbs was weaker than its bending strength for the coupled shear walls with the large opening. Due to the vertical pouring of concrete during the construction of the models, the concrete properties of the upper wall limbs were slightly weaker than that of the lower wall limbs. Because of this, the shear damage first happened in the upper wall limbs for CSWD-4 and CSWXD-5. Therefore, this failure mode is able to be avoided through reasonable design in potential engineering structure.

To sum up, the configuration of the inclined steel bars can improve the seismic performance of the coupled shear wall with normal opening ratio. And for the coupled shear wall of large opening ratio, it is necessary to take measures such as installing inclined steel bars on the upper wall limbs or improving the web reinforcement ratio of the wall limbs, so as to ensure that the shear strength is higher than that of the bending strength for the coupled shear walls with single layer of web reinforcement and large opening.

Summary and conclusion

The inclined steel bars have no obvious effect on increasing the specimens’ initial stiffness. After the concrete cracking, the stiffness degradation of the RC coupled shear wall with single layer of web reinforcement decreases with the installing of the inclined steel bars, resulting in a decrease of the reduced degree of natural frequency. Because the inclined steel bars restrict the development of diagonal cracks, the final stiffness decrement of the RC coupled shear wall with single layer of web reinforcement and inclined steel bars is less than that of the shear walls without inclined steel bars.

When initial cracks appear in the wall limbs, the shaking table’s peak acceleration of the RC coupled shear wall with single layer of web reinforcement is lower than that of the RC coupled shear wall with single layer of web reinforcement and inclined steel bars, while it reduces with the increase of opening ratio. When the level of ground motion is basically the same after cracks developed in the wall limbs, the acceleration response of the RC coupled shear wall with single layer of web and inclined steel bars is higher, and the acceleration response of the RC coupled shear wall of large opening is slightly lower than that of the RC coupled shear wall of normal opening.

During the failure of the shear walls, when the level of ground motion is basically the same, the first floor lateral drift response of the RC coupled shear wall with single layer of web reinforcement is greater than that of the RC coupled shear wall with inclined steel bars. Use of inclined steel bars in coupled shear walls can reduce the shear deformation response. For coupled shear walls with the large hole opening, the use of the inclined steel bars can also reduce the drift response.

The failure mechanism of the RC coupled shear walls with single layer of web reinforcement of the same opening ratio is basically similar. Under the same peak acceleration of the shaking table, the damage degree of the RC coupled shear walls with different arrangements is closed. The damage degree of the RC coupled shear walls without inclined steel bars is relatively severe. Because of the inclined steel bars, the development of the cracks is restricted. More cracks appeared with smaller width and were concentrated in the middle or upper part of the wall. The load-carrying capacity and ductility of the coupled shear walls are significantly improved.

The seismic capacity of RC coupled shear wall with single layer of web reinforcement can meet the requirements of seismic design in Chinese Code GB50011 (2010). The inclined steel bars can improve the seismic capacity of the RC coupled shear wall with single layer of web reinforcement and they are suitable to be used in multi-story structures. For the RC coupled shear wall with large opening, the shear strength of the overall wall limbs needs to be strengthened to prevent shear failure prior to flexural failure.

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: The authors are grateful for the funding provided by the National Natural Science Foundation of China (51378029), the Science and Technology Key Project of Beijing Municipal Education Commission (KZ20171000 5003), and the Key Laboratory of Urban Security and Disaster Engineering MOE, Beijing University of Technology.

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