# Quasi-Static Cyclic Test on a Concrete-Encased Frame-Reinforced Concrete Tube Building Model

Authors: Lei Zeng; Yunfeng Xiao; Juan Chen; Yiguang Chen
Journal: Shock and Vibration
 (2018)

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## Abstract

This paper experimentally investigated the seismic behavior of a 1:5 reduced-scale model of concrete-encased steel frame-reinforced concrete core tube building. The quasi-static testing with multipoint loading was carried out, and mode-superposition response spectrum method was adopted to control the amplitude of displacement. The damage process, crack pattern, and failure mode were observed. Various parameters were obtained, including lateral deformation, hysteretic characteristics, strain distribution, ductility, and energy dissipation capacity. The test revealed the distributions of base shear between the core tube and frame. The result indicated that the core tube bears major loading and exhibited overturning failure, afterwards frame carry the surplus load and exhibited column tensile failure and joint panel shear failure. The characteristic of two seismic resistant systems are reflected by the excellent cooperation of core tube and frame.


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## Body

## 1. Introduction

Concrete-encased steel frame-reinforced concrete core tube (CS frame-RC core tube) buildings are becoming increasingly popular around the world in high-rise buildings [1–3]. This composite structural system consists of columns located on the periphery of the building and tube located on the center of the building. This arrangement embodies the design concept of two lines to resist shear force [4, 5]. The first line of defense is RC core tube with high lateral stiffness; it will bear most of the shear force caused by the horizontal earthquake. The second is CS frame, which mainly undertakes the vertical load and partial overturning moment caused by horizontal load. Meanwhile, when the stiffness and resistance of core tube degenerate under a strong earthquake, the framework will continue to bear the surplus loading. Compared with RC frame structure, the bearing capacity of this composite structural system is obviously improved, and the lateral deformation of the building can be limited to an expected level.As a distinctive component in this composite structural system, the CS member has been systematically studied. Li et al. [6] have conducted experiment for limit values of axial compression ratio for CS column. Chen et al. [7] explores an analytical model to predict the compressive bearing capacity. The core concrete is enhanced by the steel, which results in the higher bearing capacity. Meanwhile, the steel skeleton can improve the ductility [8, 9]. Thus, CS member is suitable for the frame of composite structural system. CS frame is proved to have the advantages of reducing cross-section area and excellent global stability [10]. In particular, the exterior joints with unsymmetrical section (T- and L-shaped steel section) can satisfy the nonuniform force state and save space [11, 12]. The failure mechanism of the frame is the beam-hinged mechanism, which satisfies the seismic design principle of strong column and weak beam. The ductility and energy dissipation capacity of CS frame are much better than RC frame [13]. The reinforced concrete core tube provides high initial stiffness and bears major shear. The deformation would be strictly controlled, and lateral instability is effectively prevented [14]. The CS frame-RC core tube buildings benefit from the two components with individual characteristics [15].There are only a limited number of researches about experiment on the composite structural system. Several shaking table tests were carried out and seismic performance was analyzed [16–18]. The results showed that the whole specimen generally exhibited bending failure. The damage mainly occurred at the bottom of core tube and joint. The lateral displacement was still under the safety limits regulated by Chinese Code. As an alternative, numerical simulation methods were also proposed. Some macroelement based models were established for seismic analysis of composite high-rise buildings aiming at predicting their global responses under earthquakes [19–22]. Static pushover analysis, dynamic time history analysis, and incremental dynamic analysis (IDA) method were applied to evaluate the nonlinear responses of composite high-rise buildings [23, 24].However the test models above are designed with small similarity ratio (1/20, 1/35) [16–18], which is restricted by the shaking table capacities. The disparity between the acceleration similarity ratio of earthquake actions and actual similarity ratio for gravity acceleration cannot be ignored [25]. In addition, lateral force caused by earthquake is expected to resist by both frame and core tube through composite action. Because there are remarkable differences in stiffness between frame and core tube [23, 24, 26], the frame columns may fail by shear and crush in resisting strong earthquakes and eventually leads to sudden collapse of whole structure [27, 28]. It is significant to evaluate the seismic performance of this composite structural system through specimen with a larger similarity ratio, which can represent the general behavior of the prototype. Mechanical behavior of the parts (the bottom of core tube and joint of frame) under complicated force state should be carefully analyzed.In this paper, a 1:5 reduced-scale model of concrete-encased steel frame-reinforced concrete core tube building is constructed, and quasi-static testing is conducted to assess the response under axial compression and cyclic horizontal load. The lateral load and corresponding displacement and strain of steel and concrete are measured. The crack pattern and failure mode of each component are observed. The seismic performance is evaluated by the obtained hysteretic curve, ductility, energy dissipation capacity, and stiffness degradation. The function of two seismic resistant systems of this structure is verified.


## 2. Experimental Program

### 2.1. Test Model Design

A typical multistory CS frame-RC core tube building prototype was designed in accordance with the Code for Seismic Design of Buildings of China (GB50023-2009). The effects of vertical loads (live- and dead-loads) and lateral loads were provided referring to the Technical Specification for Concrete Structures of Tall Building (JGJ3-2002). The prototype building was designed based on an 8-degree seismic fortification intensity zone and a II-type of site classification. The design basic acceleration of ground motionag was 0.20g, which was with a reference probability of exceedance, 10% in 50 years. The site was classified according to the equivalent shear-wave velocity of soil and the site overlying depth, the design characteristic period of ground motion Tg was 0.35s for a II-type of site. It should be noted that the seismic intensity and response spectrum used during the design were those given in the Chinese seismic code.The frame is composed of CS columns and steel beams with I cross-section, while the core tube is made of reinforced concrete. Considering the laboratory conditions, a 1:5 reduced-scale model was constructed for the quasi-static tests. The model was 10 stories with square cross-sections, with 20 beams and 12 columns in each story. The total height of the model was 8700 mm. The depth of the foundation, the first story, and the rest of the stories were 500 mm, 1000 mm, and 800 mm, respectively. Two holes were arranged on each story for elevator doors. The details and dimensions of the specimen are shown in Figure1. It should be mentioned that the selected span is small because of the limitation of laboratory conditions. Compared with typical building, the linear stiffness ratio of beams and floor system increases. The capacity of shear transferring between core tube and frame is enlarged. It may lead to less damage degree of beams and floor system.Figure 1
Dimensions of specimen (units: mm).
(a)
Cross-section (b)
ElevationBased on the requirements of Architectural Structure Load Standards (GB50009-2001) of China, the live- and dead-loads for the test model are 2.0 kN/m2 and 1.6 kN/m2, respectively. A certain amount of sandbags is stacked on floors to simulate the uniform load. Because it is difficult and dangerous in construction, only the tenth-floor slab is not constructed. But the columns, beams, and core tube are still constructed, and the ninth-floor slab is defined as the top of specimen. The removed dead load is added by the additional sandbags in the ninth floor. The materials used for the test model were identical to those of the prototype structure, thereby indicating that the scaling factor of the elastic modulus was SE = 1. Table 1 shows the similarity relationships.Table 1
Similarity relationship of the model.
Physical quantity Dimensions Ratio of similitude Length L S L = 1/5 Young's modulus FL−2 S E = 1 Mass FT2L−1 S m = 1/25 Stress FL−2 S σ = 1 Time T S T = Poisson ratio 1 ν = 1 Force F S F=1/25


### 2.2. Test Model Construction

The CS columns had a square cross-section of 100 mm × 100 mm. Figure2 shows the configurations and skeleton of the CS columns. The cross-shaped structural steel used in the columns consisted of several hot-rolled steel plates. The steel plates were welded to create a cross-shaped steel section. Figure 3 shows the steel beams and configurations of beam-column joints. An I cross-section was adopted in the steel beams. The beams steel plates were welded to the columns steel skeleton.Figure 2
Configurations and skeleton of CS columns (units: mm).
(a)
Column (b)
Steel skeletonFigure 3
Details of joint and beam (units: mm).
(a)
Joint (b)
BeamThe composite slab was adopted. The slab system was composed of thin steel plate, concrete, steel bar, and stud connectors. Single-layer mesh reinforcement is used, and 10 mm length stud connectors were welded to the steel plate to strengthen the bond between the steel plate and concrete. A sectional view and details of the reinforcements are shown in Figure4.Figure 4
Composite slab system (units: mm).A square cross-section is used for the core tube, and the dimensions are shown in Figure5. The thickness is 60 mm for the first two floors and 40 mm for the rest. Double-layer mesh reinforcing is arranged in the tube, including four 12mm diameter bars in the corners. For the actual structure, the cross-section indeed decreases along with the height. As the scale of specimen is reduced by similarity ratio, there is a small difference in dimension. For the convenience of construction, the using cross-section is identical.Figure 5
Detail of core tube (units: mm).
(a)
Dimension of the north and south wall (b)
Dimension of the east and west wall (c)
Reinforcement of section 1-1 (d)
Reinforcement of section 2-2


### 2.3. Material Properties

The material properties of the steel plate and reinforcement were tested as shown in Table2. The spot mixed concrete was used for the CS columns, composite slabs, and core tube. The measured cube compressive strength (fcu) before test was 41.5 N/mm2.Table 2
Materials properties of steel.
Material Yield Strength Ultimate Strength Elastic Modulus f y (N/mm2) f u (N/mm2) E s (N/mm2) Φ4 bars 305 424 2.1 × 105 Φ12 bars 347 451 2.1×105 Steel plate 327 463 2.0 × 105


### 2.4. Test Setup and Loading Histories

The structural vibration induced by earthquakes is contributed by all modal responses. The mode-superposition response spectrum method is an effective and accurate method, which can consider the influence of higher mode shapes [29]. The contribution of each mode shape is different in the total response; thus the participation coefficient η is introduced to describe this proportion. The loading program is detailed as follows.(1) Reference [5] has carefully described the program about measuring dynamic characteristics. Several vibration pickup sensors were installed as shown in Figure 6(a). A signal acquisition system with at most six channels was connected to record the data; however it was enough for measuring the mode shapes. The details of vibration pickup sensors and acquisition process are shown in Figure 7.Figure 6
The test setup.
(a)
Loading and measuring device (b)
Picture of specimenFigure 7
Measurement for dynamic characteristics.
(a)
Vibration pickup sensors and DASP system (b)
Measuring process(2) Based on the dynamic characteristics, Data Acquisition and Signal Processing (DASP) program was adopted to carry out the modal analysis (see Figure7(b)). The higher mode shapes and corresponding participation coefficientη were obtained. According to Code for Seismic Design of Buildings (GB 50011-2010), the number of selected mode shapes is determined by the sum ofη, which should be more than 90%. Table 3 shows theη of first five modes; the sum has already satisfied the requirement. The density of used material should be enlarged to five times based on the scale effect. However the steel and concrete material with 5-fold density are not available, and the mass missing is not considered. But the required live- and dead-loads are taken into account and calculated by scale factors. This part of mass (including the mass of removed 10th-floor slabs) is applied by sandbags. The missing mass due to scaled material density leads to the decrease of effective floor masses and total mass. The mode shapes and participation coefficients are influenced.Table 3
Participation coefficients of mode shapes.
Mode shape 1st-order 2nd-order 3rd-order 4th-order 5th-order Participation coefficientηi/% 74.41 14.26 5.50 2.82 1.49(3) The reverse cyclic loading applied by multipoint is proved to accurately consider the influence of higher mode shapes [19]. According to existing experimental equipment, two actuators were set up at the 4th- and 9th-floor slabs (see Figure 6). The displacement-controlled method was adopted, and Figure 8 shows the first five mode shapes. The amplitude of displacement is defined by (1) [29] and finally Δ9/Δ4=1.5:1. In the loading program, displacement increment at 9th floor is 8 mm per level, and three cycles are applied at each level as shown in Figure 9. Once the bearing capacity falls to 85% of the ultimate lateral load, or the specimen is unable to continue bearing axial forces, the test is regarded as finished.(1)Δ9Δ4=∑i=1NηiΔ9,i∑i=1NηiΔ4,ii=1,2,3,4,5where Δ9 and Δ4 are the actual displacement applied on 9th and 4th floor; Δ9,i and Δ4,i are lateral displacement ofi-th mode shape as shown in Figure 8; ηi is participation coefficients ofi-th mode shapes.Figure 8
The first five mode shapes.Figure 9
The history of loading program.


### 2.5. Instrumentation

The measuring points were defined to capture the overall response of the test model during loading as well as any local effects, such as CS columns and core tube yielding. Displacement sensors were mounted on the slabs of each story at the loading side. Due to the symmetry of cross-section, the components at 1st and 2nd floor in Figure10(a) were selected for attaching strain gauges as shown in Figure 10(b), and the detail is shown in Figure 11.Figure 10
The arrangement of strain gauges.
(a)
The selected component for attachment of strain gauges (b)
Strain gauges for concrete and steelFigure 11
Arrangement of strain gauges and rosettes at the first and second floors (units: mm).
(a)
Strain of steel skeleton (b)
Strain of concrete


## 2.1. Test Model Design

A typical multistory CS frame-RC core tube building prototype was designed in accordance with the Code for Seismic Design of Buildings of China (GB50023-2009). The effects of vertical loads (live- and dead-loads) and lateral loads were provided referring to the Technical Specification for Concrete Structures of Tall Building (JGJ3-2002). The prototype building was designed based on an 8-degree seismic fortification intensity zone and a II-type of site classification. The design basic acceleration of ground motionag was 0.20g, which was with a reference probability of exceedance, 10% in 50 years. The site was classified according to the equivalent shear-wave velocity of soil and the site overlying depth, the design characteristic period of ground motion Tg was 0.35s for a II-type of site. It should be noted that the seismic intensity and response spectrum used during the design were those given in the Chinese seismic code.The frame is composed of CS columns and steel beams with I cross-section, while the core tube is made of reinforced concrete. Considering the laboratory conditions, a 1:5 reduced-scale model was constructed for the quasi-static tests. The model was 10 stories with square cross-sections, with 20 beams and 12 columns in each story. The total height of the model was 8700 mm. The depth of the foundation, the first story, and the rest of the stories were 500 mm, 1000 mm, and 800 mm, respectively. Two holes were arranged on each story for elevator doors. The details and dimensions of the specimen are shown in Figure1. It should be mentioned that the selected span is small because of the limitation of laboratory conditions. Compared with typical building, the linear stiffness ratio of beams and floor system increases. The capacity of shear transferring between core tube and frame is enlarged. It may lead to less damage degree of beams and floor system.Figure 1
Dimensions of specimen (units: mm).
(a)
Cross-section (b)
ElevationBased on the requirements of Architectural Structure Load Standards (GB50009-2001) of China, the live- and dead-loads for the test model are 2.0 kN/m2 and 1.6 kN/m2, respectively. A certain amount of sandbags is stacked on floors to simulate the uniform load. Because it is difficult and dangerous in construction, only the tenth-floor slab is not constructed. But the columns, beams, and core tube are still constructed, and the ninth-floor slab is defined as the top of specimen. The removed dead load is added by the additional sandbags in the ninth floor. The materials used for the test model were identical to those of the prototype structure, thereby indicating that the scaling factor of the elastic modulus was SE = 1. Table 1 shows the similarity relationships.Table 1
Similarity relationship of the model.
Physical quantity Dimensions Ratio of similitude Length L S L = 1/5 Young's modulus FL−2 S E = 1 Mass FT2L−1 S m = 1/25 Stress FL−2 S σ = 1 Time T S T = Poisson ratio 1 ν = 1 Force F S F=1/25


## 2.2. Test Model Construction

The CS columns had a square cross-section of 100 mm × 100 mm. Figure2 shows the configurations and skeleton of the CS columns. The cross-shaped structural steel used in the columns consisted of several hot-rolled steel plates. The steel plates were welded to create a cross-shaped steel section. Figure 3 shows the steel beams and configurations of beam-column joints. An I cross-section was adopted in the steel beams. The beams steel plates were welded to the columns steel skeleton.Figure 2
Configurations and skeleton of CS columns (units: mm).
(a)
Column (b)
Steel skeletonFigure 3
Details of joint and beam (units: mm).
(a)
Joint (b)
BeamThe composite slab was adopted. The slab system was composed of thin steel plate, concrete, steel bar, and stud connectors. Single-layer mesh reinforcement is used, and 10 mm length stud connectors were welded to the steel plate to strengthen the bond between the steel plate and concrete. A sectional view and details of the reinforcements are shown in Figure4.Figure 4
Composite slab system (units: mm).A square cross-section is used for the core tube, and the dimensions are shown in Figure5. The thickness is 60 mm for the first two floors and 40 mm for the rest. Double-layer mesh reinforcing is arranged in the tube, including four 12mm diameter bars in the corners. For the actual structure, the cross-section indeed decreases along with the height. As the scale of specimen is reduced by similarity ratio, there is a small difference in dimension. For the convenience of construction, the using cross-section is identical.Figure 5
Detail of core tube (units: mm).
(a)
Dimension of the north and south wall (b)
Dimension of the east and west wall (c)
Reinforcement of section 1-1 (d)
Reinforcement of section 2-2


## 2.3. Material Properties

The material properties of the steel plate and reinforcement were tested as shown in Table2. The spot mixed concrete was used for the CS columns, composite slabs, and core tube. The measured cube compressive strength (fcu) before test was 41.5 N/mm2.Table 2
Materials properties of steel.
Material Yield Strength Ultimate Strength Elastic Modulus f y (N/mm2) f u (N/mm2) E s (N/mm2) Φ4 bars 305 424 2.1 × 105 Φ12 bars 347 451 2.1×105 Steel plate 327 463 2.0 × 105


## 2.4. Test Setup and Loading Histories

The structural vibration induced by earthquakes is contributed by all modal responses. The mode-superposition response spectrum method is an effective and accurate method, which can consider the influence of higher mode shapes [29]. The contribution of each mode shape is different in the total response; thus the participation coefficient η is introduced to describe this proportion. The loading program is detailed as follows.(1) Reference [5] has carefully described the program about measuring dynamic characteristics. Several vibration pickup sensors were installed as shown in Figure 6(a). A signal acquisition system with at most six channels was connected to record the data; however it was enough for measuring the mode shapes. The details of vibration pickup sensors and acquisition process are shown in Figure 7.Figure 6
The test setup.
(a)
Loading and measuring device (b)
Picture of specimenFigure 7
Measurement for dynamic characteristics.
(a)
Vibration pickup sensors and DASP system (b)
Measuring process(2) Based on the dynamic characteristics, Data Acquisition and Signal Processing (DASP) program was adopted to carry out the modal analysis (see Figure7(b)). The higher mode shapes and corresponding participation coefficientη were obtained. According to Code for Seismic Design of Buildings (GB 50011-2010), the number of selected mode shapes is determined by the sum ofη, which should be more than 90%. Table 3 shows theη of first five modes; the sum has already satisfied the requirement. The density of used material should be enlarged to five times based on the scale effect. However the steel and concrete material with 5-fold density are not available, and the mass missing is not considered. But the required live- and dead-loads are taken into account and calculated by scale factors. This part of mass (including the mass of removed 10th-floor slabs) is applied by sandbags. The missing mass due to scaled material density leads to the decrease of effective floor masses and total mass. The mode shapes and participation coefficients are influenced.Table 3
Participation coefficients of mode shapes.
Mode shape 1st-order 2nd-order 3rd-order 4th-order 5th-order Participation coefficientηi/% 74.41 14.26 5.50 2.82 1.49(3) The reverse cyclic loading applied by multipoint is proved to accurately consider the influence of higher mode shapes [19]. According to existing experimental equipment, two actuators were set up at the 4th- and 9th-floor slabs (see Figure 6). The displacement-controlled method was adopted, and Figure 8 shows the first five mode shapes. The amplitude of displacement is defined by (1) [29] and finally Δ9/Δ4=1.5:1. In the loading program, displacement increment at 9th floor is 8 mm per level, and three cycles are applied at each level as shown in Figure 9. Once the bearing capacity falls to 85% of the ultimate lateral load, or the specimen is unable to continue bearing axial forces, the test is regarded as finished.(1)Δ9Δ4=∑i=1NηiΔ9,i∑i=1NηiΔ4,ii=1,2,3,4,5where Δ9 and Δ4 are the actual displacement applied on 9th and 4th floor; Δ9,i and Δ4,i are lateral displacement ofi-th mode shape as shown in Figure 8; ηi is participation coefficients ofi-th mode shapes.Figure 8
The first five mode shapes.Figure 9
The history of loading program.


## 2.5. Instrumentation

The measuring points were defined to capture the overall response of the test model during loading as well as any local effects, such as CS columns and core tube yielding. Displacement sensors were mounted on the slabs of each story at the loading side. Due to the symmetry of cross-section, the components at 1st and 2nd floor in Figure10(a) were selected for attaching strain gauges as shown in Figure 10(b), and the detail is shown in Figure 11.Figure 10
The arrangement of strain gauges.
(a)
The selected component for attachment of strain gauges (b)
Strain gauges for concrete and steelFigure 11
Arrangement of strain gauges and rosettes at the first and second floors (units: mm).
(a)
Strain of steel skeleton (b)
Strain of concrete


## 3. Experimental Results

### 3.1. Experimental Phenomena

Figures12–15 show the development of crack pattern. In the initial stage, the specimen exhibited elastic state after loading and unloading. As the top displacement reached 16 mm, horizontal cracks primarily occurred at the boundaries along the wall height, and microcracks developed at the bottom of column on the first floor. Then the cracks gradually extended with opening and closing. When the top displacement reached 32 mm, diagonal cracks with 45° angle were observed on the west and east of core tube on the first floor. As the top displacement reached 56 mm, shear cracks appeared in column-beam joints, and local bulge occurred on the profiled steel sheets on 4th, 7th, 8th, and 9th floors. The diagonal cracks on the core tube eventually developed to X-shaped intersecting cracks. Once top displacement reached 88 mm, concrete at wall edges seriously spalled and crushed. The longitudinal reinforcements were exposed, which were accompanied by the buckling and fracture. At present the core tube was regarded as overturning failure, and the frame continued to bear the surplus loading. Horizontal cracks were found on the surfaces of the 1st- and 2nd-floor slabs, massive spalling of concrete occurred in the joint, and the steel skeleton was deformed. Once the top displacement reached 136 mm, the load reduced to 85% of the ultimate bearing capacity, the specimen was severely damaged, and experiment was concluded.Figure 12
Cracks on core tube at the first floor.
(a)
The south wall (b)
The north wall (c)
The west wall (d)
The east wallFigure 13
Cracks on columns at the first floor.
(a)
The interior column (b)
The corner columnFigure 14
Cracks on joints at the second floor.
(a)
The interior joint (b)
The exterior jointFigure 15
Cracks on slab at the second floor.Each component of the specimen exhibited various failure modes. The core tube exhibited relatively wide cracks and severe concrete crushing localized at the bottom. There were two types of cracks as shown in Figure12; one was horizontal tension cracks, which mainly occurred on the north and south of core tube (perpendicular to the loading direction). Under the action of tension and compression, the concrete was seriously crushed, and the width of the cracks was approximately 10 mm (see Figures 12(a) and 12(b)). The other was oblique shear cracks, which mainly occurred on the west and east of core tube (parallel to the loading direction). Cracks gradually extended at 45° angle and eventually formed X-shaped intersecting cracks (see Figures 12(c) and 12(d)).Compared with the core tube, frame exhibited relatively few cracks as shown in Figures13 and 14. Horizontal tension cracks occurred at the bottom of the column, with a small amount of concrete spalling. Shear cracks were observed in the joints particularly on the 1st and 2nd floors, which were accompanied by severe concrete crushing. The longitudinal reinforcements and steel skeleton were exposed and bent. As shown in Figure 15, horizontal cracks mainly occurred on the floor slabs. Concrete was crushed at the boundary between floor slabs and the core tube, and the steel plate was compressed and exhibited locally bulging.In general the core tube characterized by large lateral stiffness had borne major loading and worked as first seismic resistant system. Once it failed by overturning, the frame supported the structure as the second seismic resistant system.


### 3.2. Deformation and Strains

The lateral displacement of each floor at stages of Δ9=±8 mm, ±24 mm, ±56 mm, ±88 mm, and ±136 mm is shown in Figure 16. Interstory drift ratio θi is defined as follows:(2)θi=Δi-Δi-1hii=1,2,3,…,9where Δi is lateral displacement of thei-th floor andhi is the height ofith floor.Figure 16
Lateral deformation.
(a)
Absolute displacements (b)
Story drift ratiosThe absolute displacements and story drift ratios are shown in Figure16. According to (2) and measured data, the maximum story drift ratio isθ4. During the loading process, the damage patterns at 4th floor presented previously. As the lateral displacement increased, the stiffness at 4th floor obviously degenerated, and the damage degree was larger than other floors. According to Technical Specification for Concrete Structures of Tall Building (JGJ3-2002) of China, the limiting value of elastic-plastic interstory ratio for frame-core tube structure is 0.01. It is clear that when Δ9 reached 32 mm, the specimen begins to enter the plastic stage.The strain of steel skeleton in columns is at range of 1974–3148με, which gets into the yielding stage. The strain of steel skeleton in beam is generally less than 500με, and it remains in the elastic stage. The concrete strain is 1284–3539με, exceeding the ultimate compressive strain of 0.003. In general, under the action of cyclic loading, both of the columns and core tube mainly bear lateral loads.


### 3.3. Hysteretic Curve

The hysteretic curve of the specimen indicates the relationship between base shear and top displacement. The hysteresis curve shape is between the spindle and the “S” form, as shown in Figure17. The specimen generally exhibited three stages: yielding, ultimate, and failure stage. In the initial stage of loading, the specimen remains elastic, the loading and unloading curves are straight, and minor residual deformation occurs. With increasing horizontal displacement, the specimen reaches the elastic-plastic stage, and the area of the hysteresis loops increases. The peak loads of the subsequent two cycles, at one displacement level, gradually decline. When top displacement reaches 32 mm, the hysteresis loop inclines toward the horizontal axis, and obvious stiffness degradation and residual deformation indicate that the specimen attains yielding stage. The specimen reaches the ultimate stage at 88 mm, where the maximum load is 356 kN. The core tube completely fails at this point, the frames have varying levels of damage, and the bearing capacity of the specimen begins to decrease. As the top displacement reaches 136 mm the specimen moves into the failure stage.Figure 17
Hysteretic curve.The damage process of different components can be described as follows (zones a–e as shown in Figure17): (a) when Δ9 was less than 16 mm, no damage occurred and the specimen was intact. Then minor damage occurred on the columns at first floor. (b) When Δ9 reached 32 mm, the core tube began to get damaged; however the columns did not develop further damage. (c) When Δ9 reached 56 mm, the core tube seriously got damaged; meanwhile the joints and floor slabs slightly got damaged. (d) When Δ9 reached 88 mm, the core tube failed and the damage degree of joints and slabs was aggravated. (e) When Δ9 reached 136 mm, the frame got into failure stage.According to the Specification of Testing Methods for Earthquake Resistant Building (JGJ101-96) of China, the degradation of bearing capacity can be described by coefficientλi in (3), shown in Table 4. (3)λi=PiPi-1wherePi is the peak load ati-th displacement level.Table 4
Degradation of bearing capacity.
Top displacement /mm 88 96 104 112 120 128 λ i/% Positive 1 0.97 0.98 0.98 0.96 0.96 Negative 1 0.97 0.97 0.97 0.94 0.95The peak loads of the specimen during the second and third cycles of each displacement level are both lower than the previous ones, and, finally, the bearing capacity degenerates by about 5%.


### 3.4. Envelope Curve

The skeleton curve of the specimen is symmetrical in both positive and negative directions as shown in Figure18. In order to confirm the yield and damage points, the equivalent energy method is adopted, as shown in Figure 19.A1 andA2 are the shaded areas. The loads and displacements at the yield point, limit point, and failure point are presented in Table 5, where Py, Δy, Pmax, Δmax, Pu, and Δu are the loads and displacements at yielding, ultimate, and failure points, respectively.Table 5
Yielding, ultimate and failure point of specimen.
Stage Yielding Ultimate Failure P y/kN Δ y/mm P m a x/kN Δ m a x/mm P u/kN Δ u/mm Positive 238.49 32.15 351.72 87.93 298.46 136.27 Negative -243.52 -31.39 -356.12 -86.55 -304.95 -133.92Figure 18
Skeleton curve.Figure 19
Equivalent energy method.The skeleton curve shows the elastic-, plastic-, and degradation-stages. In the initial stage, the curve is a straight line, bearing capacity increases rapidly, and stiffness remains stable. With increasing loads, concrete cracks and steel yields, and the skeleton curve gradually inclines toward the horizontal axis. The maximum base shear is 356 kN at the ultimate stage. The bearing capacity then decreases to 298 kN at failure owing to the serious damage of the core tube and frame.


### 3.5. Ductility and Energy Dissipation

The displacement ductility coefficient,μ, is calculated by (4), and an equivalent viscous coefficient, he, to evaluate the energy dissipation of specimen, is calculated by (5).(4)μ=ΔuΔy(5)he=12π·SΔABC+ΔCDASΔOBE+ΔODFwhere Δu and Δy are parameters as described in Table 5, S(ΔABC+ΔCDA) is the area of one hysteretic loop as shown in Figure 20, and S(ΔOBE+ΔODF) is the total area of ΔOBE and ΔODF.Figure 20
Hysteretic loop and energy dissipation capacity.The displacement ductility coefficientμ is 4.27. The equivalent viscous coefficient he is shown in Figure 21, and the maximum value is 0.374 when Δ9 reaches 88 mm. It meets the requirement ofμ≥3 in Code for Seismic Design of Buildings (GB50011-2010). Compared with the results of other frames (L-shaped column composed of concrete-filled steel tubes frame [30]), the mentioned parameters areμ=3.31 and he=0.336. It is proved that specimen for CS frame-RC core tube building allows larger inelastic deformation.Figure 21
Energy dissipation capacity.


### 3.6. Stiffness Degradation

The stiffness of specimen can be described by secant stiffnessKi, as calculated by (6)Ki=+Pi+-Pi+Δi+-ΔiwherePi and Δi are the peak load and corresponding displacement ati-th displacement level of 9th floor, respectively.The stiffness degradation is shown in Figure22. It can be seen that the stiffness of the specimen remains constant in the initial stage, but it degenerates rapidly once the core tube damage. Platform segment shows the elastic stage of specimen, and the degradation reveals the cumulative damage of structure. Finally the stiffness degenerates for about 67.49%. Compared with the result of [30], in which stiffness degradation is 79.07%, CS frame-RC core tube buildings maintain larger stiffness even at failure stage.Figure 22
Degradation of stiffness.


## 3.1. Experimental Phenomena

Figures12–15 show the development of crack pattern. In the initial stage, the specimen exhibited elastic state after loading and unloading. As the top displacement reached 16 mm, horizontal cracks primarily occurred at the boundaries along the wall height, and microcracks developed at the bottom of column on the first floor. Then the cracks gradually extended with opening and closing. When the top displacement reached 32 mm, diagonal cracks with 45° angle were observed on the west and east of core tube on the first floor. As the top displacement reached 56 mm, shear cracks appeared in column-beam joints, and local bulge occurred on the profiled steel sheets on 4th, 7th, 8th, and 9th floors. The diagonal cracks on the core tube eventually developed to X-shaped intersecting cracks. Once top displacement reached 88 mm, concrete at wall edges seriously spalled and crushed. The longitudinal reinforcements were exposed, which were accompanied by the buckling and fracture. At present the core tube was regarded as overturning failure, and the frame continued to bear the surplus loading. Horizontal cracks were found on the surfaces of the 1st- and 2nd-floor slabs, massive spalling of concrete occurred in the joint, and the steel skeleton was deformed. Once the top displacement reached 136 mm, the load reduced to 85% of the ultimate bearing capacity, the specimen was severely damaged, and experiment was concluded.Figure 12
Cracks on core tube at the first floor.
(a)
The south wall (b)
The north wall (c)
The west wall (d)
The east wallFigure 13
Cracks on columns at the first floor.
(a)
The interior column (b)
The corner columnFigure 14
Cracks on joints at the second floor.
(a)
The interior joint (b)
The exterior jointFigure 15
Cracks on slab at the second floor.Each component of the specimen exhibited various failure modes. The core tube exhibited relatively wide cracks and severe concrete crushing localized at the bottom. There were two types of cracks as shown in Figure12; one was horizontal tension cracks, which mainly occurred on the north and south of core tube (perpendicular to the loading direction). Under the action of tension and compression, the concrete was seriously crushed, and the width of the cracks was approximately 10 mm (see Figures 12(a) and 12(b)). The other was oblique shear cracks, which mainly occurred on the west and east of core tube (parallel to the loading direction). Cracks gradually extended at 45° angle and eventually formed X-shaped intersecting cracks (see Figures 12(c) and 12(d)).Compared with the core tube, frame exhibited relatively few cracks as shown in Figures13 and 14. Horizontal tension cracks occurred at the bottom of the column, with a small amount of concrete spalling. Shear cracks were observed in the joints particularly on the 1st and 2nd floors, which were accompanied by severe concrete crushing. The longitudinal reinforcements and steel skeleton were exposed and bent. As shown in Figure 15, horizontal cracks mainly occurred on the floor slabs. Concrete was crushed at the boundary between floor slabs and the core tube, and the steel plate was compressed and exhibited locally bulging.In general the core tube characterized by large lateral stiffness had borne major loading and worked as first seismic resistant system. Once it failed by overturning, the frame supported the structure as the second seismic resistant system.


## 3.2. Deformation and Strains

The lateral displacement of each floor at stages of Δ9=±8 mm, ±24 mm, ±56 mm, ±88 mm, and ±136 mm is shown in Figure 16. Interstory drift ratio θi is defined as follows:(2)θi=Δi-Δi-1hii=1,2,3,…,9where Δi is lateral displacement of thei-th floor andhi is the height ofith floor.Figure 16
Lateral deformation.
(a)
Absolute displacements (b)
Story drift ratiosThe absolute displacements and story drift ratios are shown in Figure16. According to (2) and measured data, the maximum story drift ratio isθ4. During the loading process, the damage patterns at 4th floor presented previously. As the lateral displacement increased, the stiffness at 4th floor obviously degenerated, and the damage degree was larger than other floors. According to Technical Specification for Concrete Structures of Tall Building (JGJ3-2002) of China, the limiting value of elastic-plastic interstory ratio for frame-core tube structure is 0.01. It is clear that when Δ9 reached 32 mm, the specimen begins to enter the plastic stage.The strain of steel skeleton in columns is at range of 1974–3148με, which gets into the yielding stage. The strain of steel skeleton in beam is generally less than 500με, and it remains in the elastic stage. The concrete strain is 1284–3539με, exceeding the ultimate compressive strain of 0.003. In general, under the action of cyclic loading, both of the columns and core tube mainly bear lateral loads.


## 3.3. Hysteretic Curve

The hysteretic curve of the specimen indicates the relationship between base shear and top displacement. The hysteresis curve shape is between the spindle and the “S” form, as shown in Figure17. The specimen generally exhibited three stages: yielding, ultimate, and failure stage. In the initial stage of loading, the specimen remains elastic, the loading and unloading curves are straight, and minor residual deformation occurs. With increasing horizontal displacement, the specimen reaches the elastic-plastic stage, and the area of the hysteresis loops increases. The peak loads of the subsequent two cycles, at one displacement level, gradually decline. When top displacement reaches 32 mm, the hysteresis loop inclines toward the horizontal axis, and obvious stiffness degradation and residual deformation indicate that the specimen attains yielding stage. The specimen reaches the ultimate stage at 88 mm, where the maximum load is 356 kN. The core tube completely fails at this point, the frames have varying levels of damage, and the bearing capacity of the specimen begins to decrease. As the top displacement reaches 136 mm the specimen moves into the failure stage.Figure 17
Hysteretic curve.The damage process of different components can be described as follows (zones a–e as shown in Figure17): (a) when Δ9 was less than 16 mm, no damage occurred and the specimen was intact. Then minor damage occurred on the columns at first floor. (b) When Δ9 reached 32 mm, the core tube began to get damaged; however the columns did not develop further damage. (c) When Δ9 reached 56 mm, the core tube seriously got damaged; meanwhile the joints and floor slabs slightly got damaged. (d) When Δ9 reached 88 mm, the core tube failed and the damage degree of joints and slabs was aggravated. (e) When Δ9 reached 136 mm, the frame got into failure stage.According to the Specification of Testing Methods for Earthquake Resistant Building (JGJ101-96) of China, the degradation of bearing capacity can be described by coefficientλi in (3), shown in Table 4. (3)λi=PiPi-1wherePi is the peak load ati-th displacement level.Table 4
Degradation of bearing capacity.
Top displacement /mm 88 96 104 112 120 128 λ i/% Positive 1 0.97 0.98 0.98 0.96 0.96 Negative 1 0.97 0.97 0.97 0.94 0.95The peak loads of the specimen during the second and third cycles of each displacement level are both lower than the previous ones, and, finally, the bearing capacity degenerates by about 5%.


## 3.4. Envelope Curve

The skeleton curve of the specimen is symmetrical in both positive and negative directions as shown in Figure18. In order to confirm the yield and damage points, the equivalent energy method is adopted, as shown in Figure 19.A1 andA2 are the shaded areas. The loads and displacements at the yield point, limit point, and failure point are presented in Table 5, where Py, Δy, Pmax, Δmax, Pu, and Δu are the loads and displacements at yielding, ultimate, and failure points, respectively.Table 5
Yielding, ultimate and failure point of specimen.
Stage Yielding Ultimate Failure P y/kN Δ y/mm P m a x/kN Δ m a x/mm P u/kN Δ u/mm Positive 238.49 32.15 351.72 87.93 298.46 136.27 Negative -243.52 -31.39 -356.12 -86.55 -304.95 -133.92Figure 18
Skeleton curve.Figure 19
Equivalent energy method.The skeleton curve shows the elastic-, plastic-, and degradation-stages. In the initial stage, the curve is a straight line, bearing capacity increases rapidly, and stiffness remains stable. With increasing loads, concrete cracks and steel yields, and the skeleton curve gradually inclines toward the horizontal axis. The maximum base shear is 356 kN at the ultimate stage. The bearing capacity then decreases to 298 kN at failure owing to the serious damage of the core tube and frame.


## 3.5. Ductility and Energy Dissipation

The displacement ductility coefficient,μ, is calculated by (4), and an equivalent viscous coefficient, he, to evaluate the energy dissipation of specimen, is calculated by (5).(4)μ=ΔuΔy(5)he=12π·SΔABC+ΔCDASΔOBE+ΔODFwhere Δu and Δy are parameters as described in Table 5, S(ΔABC+ΔCDA) is the area of one hysteretic loop as shown in Figure 20, and S(ΔOBE+ΔODF) is the total area of ΔOBE and ΔODF.Figure 20
Hysteretic loop and energy dissipation capacity.The displacement ductility coefficientμ is 4.27. The equivalent viscous coefficient he is shown in Figure 21, and the maximum value is 0.374 when Δ9 reaches 88 mm. It meets the requirement ofμ≥3 in Code for Seismic Design of Buildings (GB50011-2010). Compared with the results of other frames (L-shaped column composed of concrete-filled steel tubes frame [30]), the mentioned parameters areμ=3.31 and he=0.336. It is proved that specimen for CS frame-RC core tube building allows larger inelastic deformation.Figure 21
Energy dissipation capacity.


## 3.6. Stiffness Degradation

The stiffness of specimen can be described by secant stiffnessKi, as calculated by (6)Ki=+Pi+-Pi+Δi+-ΔiwherePi and Δi are the peak load and corresponding displacement ati-th displacement level of 9th floor, respectively.The stiffness degradation is shown in Figure22. It can be seen that the stiffness of the specimen remains constant in the initial stage, but it degenerates rapidly once the core tube damage. Platform segment shows the elastic stage of specimen, and the degradation reveals the cumulative damage of structure. Finally the stiffness degenerates for about 67.49%. Compared with the result of [30], in which stiffness degradation is 79.07%, CS frame-RC core tube buildings maintain larger stiffness even at failure stage.Figure 22
Degradation of stiffness.


## 4. Conclusions

The seismic behavior of CS frame-RC core tube building was investigated, the damage process, crack pattern, and failure mode were observed, and the following was concluded.(1) In the quasi-static test, the specimen failed mainly by the overturning mode. As the first seismic resistant system, the core tube carried the major load and suffered extensive damage. Major horizontal tension cracks and X-shaped oblique shear cracks occurred at the bottom of core tube. Once the core tube got damaged, the frame played the role of second seismic resistant system and continued to carry the surplus load. The joint experienced shear failure and the column experienced tensile failure, and the floor slabs failed in compression. The structure design satisfied the concept of “two seismic resistant systems.”(2) The hysteresis curve shape was between the spindle and the S form, and the skeleton curve of the specimen was symmetrical in both positive and negative directions. The specimen generally exhibited yielding, ultimate, and failure stages. The specimen began to enter the plastic stage at top displacement 32 mm. The structural maximum lateral bearing capacity was 356 kN at 88 mm and failed at 132 mm.(3) The strain of steel skeleton in columns and concrete at the bottom of core tube exceeded 3000με. However strain of beams was generally less than 500με and did not yield in the experiment. The frame design conformed to the seismic principles of “strong columns and weak beams” and “strong joints and weak members.”(4) The displacement ductility coefficientμ was 4.27, which had met the requirement ofμ≥3 in Code for Seismic Design of Buildings. The equivalent viscous coefficient he was 0.374, and the stiffness decreased by approximately 67.49% at failure stage. Compared with the result of similar structure, CS frame-RC core tube building allowed larger inelastic deformation, indicating the excellent seismic performance.



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*Source: 5643872-2018-06-13.xml*