# Seismic Response Analysis and Connection Performance Evaluation of a Hybrid Coupled PEC Wall System

Authors: Yun Shi; Mingzhou Su; Lu Jiang; Qiaoling Zhou; Lingyu Guan; Yukun Yang; Lili Zhang
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

This paper proposes a hybrid coupled partially encased composite (PEC) wall system, obtained through the connection of two PEC walls by means of the shear critical steel coupling beams with an innovative welded connection. This structural solution is designed to take advantage of both the stiffness of the PEC walls (required to limit building damage under frequent earthquakes) and the ductility of the steel coupling beams (necessary to dissipate energy under medium-intensity and high-intensity earthquakes). The connection performance of an innovative rigid joint with different configurations in this system is studied through pseudostatic analysis, and the seismic performance of the proposed hybrid coupled PEC wall system is evaluated through multirecord nonlinear dynamic analysis of a set of case studies. Adopted finite element models are developed and validated against the available experimental results. A summary of the results is presented and discussed to highlight the potential of the proposed hybrid coupled PEC wall systems. The key feature of this system is development of a reasonable two-level yielding mechanism (the first level is the yielding of the coupling beams, and the second level is the yielding of the PEC wall) without damage to the welded joints.


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## Body

## 1. Introduction

A partially encased composite (PEC) structure has been known for its attractive combination of high elastic stiffness and superior inelastic performance characteristics. It has great potential as a seismic-resistant solution if properly designed to exploit the stiffness contribution of the concrete material and the dissipative capacity of the steel components. Meanwhile, the PEC structure has excellent fire resistance and can be assembled directly in the field after processing in factories [1–4]. Currently, the behaviour of PEC columns and PEC beams has been widely studied [5–10]. An example of this structure is the PEC frame structure, in which PEC columns are connected by steel or PEC beams. It has been applied to the Meishanjiang project (Figure 1).Figure 1
PEC frame structures in the Meishanjiang project.
(a)
(b)Considering that PEC columns allow for stable hysteretic behaviour and excellent assembly performance, Zhang et al. proposed PEC walls to further exploit the potential of PEC structural solutions (Figure2). Full-scale tests on single PEC walls demonstrated the effectiveness of the adopted solution [11].Figure 2
PEC wall system. (a) Steel component. (b) Concrete component. (c) PEC wall.
(a)
(b)
(c)Subsequently, Yunan et al. developed a design procedure for the considered PEC wall system according to the results of the tests [12]. In this way, PEC structures could be utilized in midrise buildings in seismic regions. Nevertheless, single PEC walls have some common shortcomings in practical engineering, including heavy self-weight, difficulties in hoisting integral units, and high installation cost. As viable substitutes for single PEC walls, hybrid coupled PEC wall systems have been proposed in this paper. The proposed hybrid coupled PEC wall system is composed of two single PEC walls connected by means of steel coupling beams. Butt-welded connections are used between the coupling beams and the PEC walls (Figure 3).Figure 3
(a) Hybrid coupled PEC wall. (b) Steel component of the test. (c) Details of an innovative welded joint.
(a)
(b)
(c)In-depth explorations of the potential of the hybrid coupled wall system require the performance evaluation of innovative rigid joints and the elastoplasticity response analysis of the structure. Accordingly, this paper discusses the connection performance of the innovative rigid joints with different configurations in this system through pseudostatic analysis and investigates the seismic performance of the hybrid coupled PEC wall through multirecord nonlinear dynamic analysis. A set of case studies was used to gain insight into the seismic performance of structures both at the element level, e.g., local stress and strain in the rigid joints, and at the structural level, e.g., lateral displacements, yielding and damage sequence, and performance at assigned seismic intensities.


## 2. Hysteretic Analysis of Innovative Welded Connection

### 2.1. Simplified Calculation of Typical Connection

The construction of the weld joints in the hybrid coupled PEC system benefits from the research studies made for the beam-column connections in the hybrid coupled wall (HCW) system [13], given the similarities in their damage mechanism (ignoring the effect of the wall web on the bearing capacity of the joints in the hybrid coupled PEC system). Equations (1)–(4) are proposed to describe the capacity behaviour of the joints.The ultimate load-carrying capacity of the joint can be calculated as follows:(1)Vu=0.168fckbjhj+fytwhw3+fyvkAsvshb−ttb,where fck is the axial compressive strength of the concrete; bj and hj are the width and the height, respectively, of the effective section at the joints; fy is the yield strength of the steel; tw and hw are the thickness and height, respectively, of the steel plate at the joints; fyvk is the standard value of the shear yield strength of the steel; Asv and s are the area and the spacing, respectively, of the tie bar at the joints; and hb and tfb are the height and the thickness, respectively, of the coupling beam.JGJ99-2015 link classification [14] for eccentrically braced frames was considered, and the design was performed by enforcing the choice of shearing yield links due to their more stable hysteretic behaviour compared with bending yield links. The plastic shear-yielding capacity of the coupling beam can be calculated as follows:(2)Vp=0.58fyhwtw,where hw is the web depth, tw is the web thickness, and fy is the yield strength of the steel.When(3)Vu≥Vp,there is strong connection.When(4)Vu<Vp,there is weak connection.


### 2.2. Refined Finite Element Model of Welded Connection

The seismic design philosophy of the joints aims to satisfy the strong joint-weak member concept in which a failure must occur in the coupling beams and be avoided in the joints. To verify the simplified formulas, 6 models were designed for detailed evaluation, as shown in Table1. Due to the structural symmetry with respect to the midplane at the beam web and the wall section, only half of the connection subassemblage was modelled to reduce the computational effort. The derivation of the structural boundary conditions is shown in Figure 4(a). The loading consisted of displacement-controlled cyclic loads on the beam ends and axial pressure loads on the wall. Based on a general-purpose nonlinear finite element analysis program ABAQUS, various configurations of the rigid joint were modelled and analysed. Figure 4(b) shows the finite element meshes and structural member dimensions of model PEC-1, which was modelled to represent the basic welded connection, while other models with various configurations were designed to clarify the effectiveness of the connection behaviour. Exactly how the design parameters affect the connection behaviour was also more closely examined. The finite element models of the connection subassemblage consisted of three-dimensional structural solid elements. The parts that were connected using a batten plate were defined as being in a contact relationship. The stress-strain relations of the structural steel and the weld were simulated based on bilinear isotropic hardening behaviour. To simulate the mechanical behaviour of the butt weld, the merge method with the perfect bond between two parts was adopted. The material exhibits elastic linear behaviour up to the yielding point (345 MPa). Beyond the yielding point, the strain-hardening effect starts with a slope of 0.01Es [15] up to the ultimate point. The stress-strain relations of the concrete were simulated based on a plastic-damage model with concrete grade C40 (characteristic compressive strength fcu = 40 MPa). The main failure mechanisms for the concrete material are cracking in tension and crushing in compression based on the fundamental assumption of the plastic-damage model. In particular, a rate-independent plasticity model was used to analyse the inelastic behaviour. Moreover, the plasticity of the models was determined using the von Mises yielding criterion with the associated flow rule. Furthermore, the kinematic hardening behaviour of the structural steel was assumed for cyclic analysis.Table 1
Structural member dimensions and design properties in the models.
Models
Coupling beam
PEC wall
Strong/weak connection
Axial compression ratio
Section
Span
t
f
t
w
Transverse stiffeners
PEC-1
H500 × 180 × 8 × 14
500
10
6
No
Strong
0.4
PEC-2
H500 × 180 × 8 × 14
500
10
6
Yes
Strong
0.4
PEC-3
H500 × 180 × 8 × 14
500
10
4
No
Weak
0.4
PEC-4
H500 × 180 × 8 × 14
500
10
4
Yes
Weak
0.4
PEC-5
H500 × 180 × 8 × 14
500
10
6
No
Strong
0.2
PEC-6
H500 × 180 × 8 × 14
500
10
6
No
Strong
0.6Figure 4
Basic welded connection (PEC-1). (a) Derivation of structural boundary conditions. (b) Structural boundary conditions and member dimensions in PEC-1.An example of calibration and validation of the adopted model is carried out using as a benchmark the experimental test for the single PEC wall shown in Figure5 [11]. The preliminary calibration of the material parameters was conducted on the basis of the experimental stress-strain relations measured during the specimen construction. The force-deformation results (Figure 6) showed a satisfactory agreement between the three-dimensional finite element model and the specimen, with the following values of the parameters: yield-bearing capacity Py = 678 kN, yield displacement Δy = 11.4 mm, and initial stiffness k = 98.1 kN/mm for the nonlinear finite element model and yield-bearing capacity Py = 631 kN, yield displacement Δy = 12.7 mm, and initial stiffness k = 126 kN/mm for the specimen. However, because the finite element model does not consider the fracture of the metal and welds, no stiffness or strength degradation of the model appeared. Meanwhile, the damage mechanism of the specimen is identical in the finite element analysis and the present experimental study in which the elastic and elastoplastic developing stages are witnessed. The primary failure deformation is identical to the experimental one. The typical deformation damage location is shown in Figure 7.Figure 5
Full-scale PEC wall test.Figure 6
Comparison of the force-deformation curves of the test in [5].Figure 7
Comparison of the failure modes of the test.
(a)
(b)
(c)
(d)


### 2.3. The Connection Performance Analysis

#### 2.3.1. Hysteretic Curve, Load-Bearing Capacity, and Ductility

The shear force-displacement curves of the models are illustrated in Figure8. Model backbone curves are presented in Figure 9. The theoretical and simulated values of the yield-bearing capacity of the models are presented in Table 2. From the chart, the following can be seen: (1) When the axial compression ratio is less than 0.4, all the models with strong joints were loaded up to 5Δy, while PEC-3 and PEC-4 with weak joints reached 4Δy, where Δy is the yield displacement. The displacement ductility coefficient of the strong connection models is notably higher than that of the weak connection models. However, when the axial compression ratio is greater than 0.4, the model has limited ductility capacity, even if the joint is strong by calculation. (2) Obviously, all the models with strong connections possess stable and expanding hysteretic loops with no deterioration in stiffness and load-carrying capacity, and it can, therefore, be inferred that the energy dissipation capacity of the models with strong connections designed by the above simplified calculation is very significant. (3) The data show a satisfactory agreement between the theoretical value and the simulated value. Meanwhile, the data indicate that the models with the transverse stiffeners reach a larger load-carrying capacity compared with the models without the transverse stiffeners in weak connections, although they have the same theoretical bearing capacity. The yield load value of model PEC-4 is 2.16% higher than that of model PEC-3.Figure 8
Shear force-displacement curves of the models. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Backbone curves of the models. (a) PEC-1, PEC-2, PEC-3, and PEC-4. (b) PEC-1, PEC-5, and PEC-6.
(a)
(b)Table 2
Comparison of yield load.
Models
FEM analysis results
Computational results
Error (%)
Yield load (kN)
Strong/weak connection
Yield load (kN)
Strong/weak connection
PEC-1
776
Strong
755
Strong
2.78
PEC-2
753
Strong
755
Strong
0.26
PEC-3
740
Weak
752
Weak
1.59
PEC-4
756
Weak
752
Weak
0.53
PEC-5
768
Strong
755
Strong
1.72
PEC-6
713
Weak
755
Strong
5.56


#### 2.3.2. Stiffness Degradation

The stiffness of all the models could be calculated as follows:(5)K=P++P−Δ++Δ−,where P+ and P− are the maximum lateral force in the positive and negative directions, respectively, in the same hysteretic loop and Δ+ and Δ− are the maximum displacement in the positive and negative directions, respectively, in the same hysteretic loop of P+ and P−.Figure10 shows the stiffness degradation curves of the models given by equation (5).Figure 10
Stiffness of the models. (a) PEC-1, PEC-2, PEC-3, and PEC-4. (b) PEC-1, PEC-5, and PEC-6.
(a)
(b)The curves show the following: (1) The stiffness of the models decreases with increasing cyclic series. With the cracking of the concrete, the stiffness decreases rapidly, and the stiffness degradation tends to be stable at the large displacement stage. (2) The initial stiffness of model PEC-3 is 11.9% lower than that of model PEC-1, and this phenomenon is due to the smaller web sections of the weak connection models, leading to lower lateral stiffness compared with that of the strong connection models. Meanwhile, the initial stiffness of the models with transverse stiffeners is higher than that of the models without the transverse stiffeners. For models PEC-1 and PEC-3 compared with models PEC-2 and PEC-4, the differences are 12.1% and 4.3%, respectively. (3) With the increase in the axial compression ratio, the initial stiffness of the models increases. However, the degradation rate of stiffness tends to be consistent in the later stage of loading.


#### 2.3.3. Failure Modes

Figures11 and 12 show the stress responses of the steel and the compressive damage of the concrete of the models at 4Δy. The figures show the following: (1) The stress of the steel and the compressive damage of the concrete in PEC-1 and PEC-3 are significantly less than those in PEC-2 and PEC-4, respectively. The analysis results indicate that the development of steel stress and concrete cracks can be effectively restrained by setting the transverse stiffeners along the flange of the coupling beams. In addition, for a strong connection, the stress values of the coupling beam were much higher than those of the joints, and only a few elements of the shear wall entered the plastic stage, while other elements of the wall were still in the elastic stage, which shows that the design method of strong connection is suitable. (2) With the increasing axial compression ratio, the yielding position of the model shifts from the web of the coupling beam to the wall, and the compressive damage of concrete in the PEC wall is more obvious than that in other models. Therefore, the maximum axial compression ratio of the wall should not exceed 0.4.Figure 11
Stress responses of the steel at 4Δy. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)Figure 12
Compressive damage of concrete at 4Δy. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)


## 2.1. Simplified Calculation of Typical Connection

The construction of the weld joints in the hybrid coupled PEC system benefits from the research studies made for the beam-column connections in the hybrid coupled wall (HCW) system [13], given the similarities in their damage mechanism (ignoring the effect of the wall web on the bearing capacity of the joints in the hybrid coupled PEC system). Equations (1)–(4) are proposed to describe the capacity behaviour of the joints.The ultimate load-carrying capacity of the joint can be calculated as follows:(1)Vu=0.168fckbjhj+fytwhw3+fyvkAsvshb−ttb,where fck is the axial compressive strength of the concrete; bj and hj are the width and the height, respectively, of the effective section at the joints; fy is the yield strength of the steel; tw and hw are the thickness and height, respectively, of the steel plate at the joints; fyvk is the standard value of the shear yield strength of the steel; Asv and s are the area and the spacing, respectively, of the tie bar at the joints; and hb and tfb are the height and the thickness, respectively, of the coupling beam.JGJ99-2015 link classification [14] for eccentrically braced frames was considered, and the design was performed by enforcing the choice of shearing yield links due to their more stable hysteretic behaviour compared with bending yield links. The plastic shear-yielding capacity of the coupling beam can be calculated as follows:(2)Vp=0.58fyhwtw,where hw is the web depth, tw is the web thickness, and fy is the yield strength of the steel.When(3)Vu≥Vp,there is strong connection.When(4)Vu<Vp,there is weak connection.


## 2.2. Refined Finite Element Model of Welded Connection

The seismic design philosophy of the joints aims to satisfy the strong joint-weak member concept in which a failure must occur in the coupling beams and be avoided in the joints. To verify the simplified formulas, 6 models were designed for detailed evaluation, as shown in Table1. Due to the structural symmetry with respect to the midplane at the beam web and the wall section, only half of the connection subassemblage was modelled to reduce the computational effort. The derivation of the structural boundary conditions is shown in Figure 4(a). The loading consisted of displacement-controlled cyclic loads on the beam ends and axial pressure loads on the wall. Based on a general-purpose nonlinear finite element analysis program ABAQUS, various configurations of the rigid joint were modelled and analysed. Figure 4(b) shows the finite element meshes and structural member dimensions of model PEC-1, which was modelled to represent the basic welded connection, while other models with various configurations were designed to clarify the effectiveness of the connection behaviour. Exactly how the design parameters affect the connection behaviour was also more closely examined. The finite element models of the connection subassemblage consisted of three-dimensional structural solid elements. The parts that were connected using a batten plate were defined as being in a contact relationship. The stress-strain relations of the structural steel and the weld were simulated based on bilinear isotropic hardening behaviour. To simulate the mechanical behaviour of the butt weld, the merge method with the perfect bond between two parts was adopted. The material exhibits elastic linear behaviour up to the yielding point (345 MPa). Beyond the yielding point, the strain-hardening effect starts with a slope of 0.01Es [15] up to the ultimate point. The stress-strain relations of the concrete were simulated based on a plastic-damage model with concrete grade C40 (characteristic compressive strength fcu = 40 MPa). The main failure mechanisms for the concrete material are cracking in tension and crushing in compression based on the fundamental assumption of the plastic-damage model. In particular, a rate-independent plasticity model was used to analyse the inelastic behaviour. Moreover, the plasticity of the models was determined using the von Mises yielding criterion with the associated flow rule. Furthermore, the kinematic hardening behaviour of the structural steel was assumed for cyclic analysis.Table 1
Structural member dimensions and design properties in the models.
Models
Coupling beam
PEC wall
Strong/weak connection
Axial compression ratio
Section
Span
t
f
t
w
Transverse stiffeners
PEC-1
H500 × 180 × 8 × 14
500
10
6
No
Strong
0.4
PEC-2
H500 × 180 × 8 × 14
500
10
6
Yes
Strong
0.4
PEC-3
H500 × 180 × 8 × 14
500
10
4
No
Weak
0.4
PEC-4
H500 × 180 × 8 × 14
500
10
4
Yes
Weak
0.4
PEC-5
H500 × 180 × 8 × 14
500
10
6
No
Strong
0.2
PEC-6
H500 × 180 × 8 × 14
500
10
6
No
Strong
0.6Figure 4
Basic welded connection (PEC-1). (a) Derivation of structural boundary conditions. (b) Structural boundary conditions and member dimensions in PEC-1.An example of calibration and validation of the adopted model is carried out using as a benchmark the experimental test for the single PEC wall shown in Figure5 [11]. The preliminary calibration of the material parameters was conducted on the basis of the experimental stress-strain relations measured during the specimen construction. The force-deformation results (Figure 6) showed a satisfactory agreement between the three-dimensional finite element model and the specimen, with the following values of the parameters: yield-bearing capacity Py = 678 kN, yield displacement Δy = 11.4 mm, and initial stiffness k = 98.1 kN/mm for the nonlinear finite element model and yield-bearing capacity Py = 631 kN, yield displacement Δy = 12.7 mm, and initial stiffness k = 126 kN/mm for the specimen. However, because the finite element model does not consider the fracture of the metal and welds, no stiffness or strength degradation of the model appeared. Meanwhile, the damage mechanism of the specimen is identical in the finite element analysis and the present experimental study in which the elastic and elastoplastic developing stages are witnessed. The primary failure deformation is identical to the experimental one. The typical deformation damage location is shown in Figure 7.Figure 5
Full-scale PEC wall test.Figure 6
Comparison of the force-deformation curves of the test in [5].Figure 7
Comparison of the failure modes of the test.
(a)
(b)
(c)
(d)


## 2.3. The Connection Performance Analysis

### 2.3.1. Hysteretic Curve, Load-Bearing Capacity, and Ductility

The shear force-displacement curves of the models are illustrated in Figure8. Model backbone curves are presented in Figure 9. The theoretical and simulated values of the yield-bearing capacity of the models are presented in Table 2. From the chart, the following can be seen: (1) When the axial compression ratio is less than 0.4, all the models with strong joints were loaded up to 5Δy, while PEC-3 and PEC-4 with weak joints reached 4Δy, where Δy is the yield displacement. The displacement ductility coefficient of the strong connection models is notably higher than that of the weak connection models. However, when the axial compression ratio is greater than 0.4, the model has limited ductility capacity, even if the joint is strong by calculation. (2) Obviously, all the models with strong connections possess stable and expanding hysteretic loops with no deterioration in stiffness and load-carrying capacity, and it can, therefore, be inferred that the energy dissipation capacity of the models with strong connections designed by the above simplified calculation is very significant. (3) The data show a satisfactory agreement between the theoretical value and the simulated value. Meanwhile, the data indicate that the models with the transverse stiffeners reach a larger load-carrying capacity compared with the models without the transverse stiffeners in weak connections, although they have the same theoretical bearing capacity. The yield load value of model PEC-4 is 2.16% higher than that of model PEC-3.Figure 8
Shear force-displacement curves of the models. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Backbone curves of the models. (a) PEC-1, PEC-2, PEC-3, and PEC-4. (b) PEC-1, PEC-5, and PEC-6.
(a)
(b)Table 2
Comparison of yield load.
Models
FEM analysis results
Computational results
Error (%)
Yield load (kN)
Strong/weak connection
Yield load (kN)
Strong/weak connection
PEC-1
776
Strong
755
Strong
2.78
PEC-2
753
Strong
755
Strong
0.26
PEC-3
740
Weak
752
Weak
1.59
PEC-4
756
Weak
752
Weak
0.53
PEC-5
768
Strong
755
Strong
1.72
PEC-6
713
Weak
755
Strong
5.56


### 2.3.2. Stiffness Degradation

The stiffness of all the models could be calculated as follows:(5)K=P++P−Δ++Δ−,where P+ and P− are the maximum lateral force in the positive and negative directions, respectively, in the same hysteretic loop and Δ+ and Δ− are the maximum displacement in the positive and negative directions, respectively, in the same hysteretic loop of P+ and P−.Figure10 shows the stiffness degradation curves of the models given by equation (5).Figure 10
Stiffness of the models. (a) PEC-1, PEC-2, PEC-3, and PEC-4. (b) PEC-1, PEC-5, and PEC-6.
(a)
(b)The curves show the following: (1) The stiffness of the models decreases with increasing cyclic series. With the cracking of the concrete, the stiffness decreases rapidly, and the stiffness degradation tends to be stable at the large displacement stage. (2) The initial stiffness of model PEC-3 is 11.9% lower than that of model PEC-1, and this phenomenon is due to the smaller web sections of the weak connection models, leading to lower lateral stiffness compared with that of the strong connection models. Meanwhile, the initial stiffness of the models with transverse stiffeners is higher than that of the models without the transverse stiffeners. For models PEC-1 and PEC-3 compared with models PEC-2 and PEC-4, the differences are 12.1% and 4.3%, respectively. (3) With the increase in the axial compression ratio, the initial stiffness of the models increases. However, the degradation rate of stiffness tends to be consistent in the later stage of loading.


### 2.3.3. Failure Modes

Figures11 and 12 show the stress responses of the steel and the compressive damage of the concrete of the models at 4Δy. The figures show the following: (1) The stress of the steel and the compressive damage of the concrete in PEC-1 and PEC-3 are significantly less than those in PEC-2 and PEC-4, respectively. The analysis results indicate that the development of steel stress and concrete cracks can be effectively restrained by setting the transverse stiffeners along the flange of the coupling beams. In addition, for a strong connection, the stress values of the coupling beam were much higher than those of the joints, and only a few elements of the shear wall entered the plastic stage, while other elements of the wall were still in the elastic stage, which shows that the design method of strong connection is suitable. (2) With the increasing axial compression ratio, the yielding position of the model shifts from the web of the coupling beam to the wall, and the compressive damage of concrete in the PEC wall is more obvious than that in other models. Therefore, the maximum axial compression ratio of the wall should not exceed 0.4.Figure 11
Stress responses of the steel at 4Δy. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)Figure 12
Compressive damage of concrete at 4Δy. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)


## 2.3.1. Hysteretic Curve, Load-Bearing Capacity, and Ductility

The shear force-displacement curves of the models are illustrated in Figure8. Model backbone curves are presented in Figure 9. The theoretical and simulated values of the yield-bearing capacity of the models are presented in Table 2. From the chart, the following can be seen: (1) When the axial compression ratio is less than 0.4, all the models with strong joints were loaded up to 5Δy, while PEC-3 and PEC-4 with weak joints reached 4Δy, where Δy is the yield displacement. The displacement ductility coefficient of the strong connection models is notably higher than that of the weak connection models. However, when the axial compression ratio is greater than 0.4, the model has limited ductility capacity, even if the joint is strong by calculation. (2) Obviously, all the models with strong connections possess stable and expanding hysteretic loops with no deterioration in stiffness and load-carrying capacity, and it can, therefore, be inferred that the energy dissipation capacity of the models with strong connections designed by the above simplified calculation is very significant. (3) The data show a satisfactory agreement between the theoretical value and the simulated value. Meanwhile, the data indicate that the models with the transverse stiffeners reach a larger load-carrying capacity compared with the models without the transverse stiffeners in weak connections, although they have the same theoretical bearing capacity. The yield load value of model PEC-4 is 2.16% higher than that of model PEC-3.Figure 8
Shear force-displacement curves of the models. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Backbone curves of the models. (a) PEC-1, PEC-2, PEC-3, and PEC-4. (b) PEC-1, PEC-5, and PEC-6.
(a)
(b)Table 2
Comparison of yield load.
Models
FEM analysis results
Computational results
Error (%)
Yield load (kN)
Strong/weak connection
Yield load (kN)
Strong/weak connection
PEC-1
776
Strong
755
Strong
2.78
PEC-2
753
Strong
755
Strong
0.26
PEC-3
740
Weak
752
Weak
1.59
PEC-4
756
Weak
752
Weak
0.53
PEC-5
768
Strong
755
Strong
1.72
PEC-6
713
Weak
755
Strong
5.56


## 2.3.2. Stiffness Degradation

The stiffness of all the models could be calculated as follows:(5)K=P++P−Δ++Δ−,where P+ and P− are the maximum lateral force in the positive and negative directions, respectively, in the same hysteretic loop and Δ+ and Δ− are the maximum displacement in the positive and negative directions, respectively, in the same hysteretic loop of P+ and P−.Figure10 shows the stiffness degradation curves of the models given by equation (5).Figure 10
Stiffness of the models. (a) PEC-1, PEC-2, PEC-3, and PEC-4. (b) PEC-1, PEC-5, and PEC-6.
(a)
(b)The curves show the following: (1) The stiffness of the models decreases with increasing cyclic series. With the cracking of the concrete, the stiffness decreases rapidly, and the stiffness degradation tends to be stable at the large displacement stage. (2) The initial stiffness of model PEC-3 is 11.9% lower than that of model PEC-1, and this phenomenon is due to the smaller web sections of the weak connection models, leading to lower lateral stiffness compared with that of the strong connection models. Meanwhile, the initial stiffness of the models with transverse stiffeners is higher than that of the models without the transverse stiffeners. For models PEC-1 and PEC-3 compared with models PEC-2 and PEC-4, the differences are 12.1% and 4.3%, respectively. (3) With the increase in the axial compression ratio, the initial stiffness of the models increases. However, the degradation rate of stiffness tends to be consistent in the later stage of loading.


## 2.3.3. Failure Modes

Figures11 and 12 show the stress responses of the steel and the compressive damage of the concrete of the models at 4Δy. The figures show the following: (1) The stress of the steel and the compressive damage of the concrete in PEC-1 and PEC-3 are significantly less than those in PEC-2 and PEC-4, respectively. The analysis results indicate that the development of steel stress and concrete cracks can be effectively restrained by setting the transverse stiffeners along the flange of the coupling beams. In addition, for a strong connection, the stress values of the coupling beam were much higher than those of the joints, and only a few elements of the shear wall entered the plastic stage, while other elements of the wall were still in the elastic stage, which shows that the design method of strong connection is suitable. (2) With the increasing axial compression ratio, the yielding position of the model shifts from the web of the coupling beam to the wall, and the compressive damage of concrete in the PEC wall is more obvious than that in other models. Therefore, the maximum axial compression ratio of the wall should not exceed 0.4.Figure 11
Stress responses of the steel at 4Δy. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)Figure 12
Compressive damage of concrete at 4Δy. (a) PEC-1. (b) PEC-2. (c) PEC-3. (d) PEC-4. (e) PEC-5. (f) PEC-6.
(a)
(b)
(c)
(d)
(e)
(f)


## 3. Seismic Response Analysis of the Hybrid Coupled PEC Wall

### 3.1. Design of Case Studies

The design of the considered case studies is an 18-floor residential building selected as a prototype structure. A hybrid coupled PEC shear wall structure is selected for this project. In this structure, the PEC shear wall is the primary lateral resistance component and the steel beam is the horizontal bearing component. Beams and PEC walls were designed according to relevant Chinese codes [14, 16, 17] using steel grade Q345 (nominal yield stress fy = 345 MPa) and concrete grade C40 (characteristic compressive strength fcu = 40 MPa). The floor was assumed to be made of corrugated sheets and a concrete slab, with a thickness of 130 mm; hence, the floor can be considered a rigid diaphragm. Representative values of gravity G could be computed using the formula 1D + 0.5L, where D and L are dead and live loads, respectively. The total mass of the model was 12,649t.Moderately firm ground conditions of GB50011-2010 with a design peak ground acceleration (PGA) of 0.05 g (with a 10% exceedance probability in a 50-year period) were considered the seismic input. An 18-story hybrid coupled PEC wall system was designed using the elastic design method according to the current Chinese code by GBS Co., Ltd. Figure13 depicts the arrangement in the structures. On the basis of the connection solutions, a strong weld connection was adopted on the wall side.Figure 13
Arrangement in the structures.In this paper, elastic-plastic time history analysis of the hybrid coupled PEC wall system is accomplished by the program ABAQUS to evaluate the global response and component deformation of the structure.


### 3.2. Finite Element Model of the Hybrid Coupled PEC Wall

To better observe the behaviour of PEC walls, composite shell elements were used for the shear walls that were meshed by using the software’s “Structure” mesh type and beam elements were used for other structural members. Figure14 shows the finite element model used in ABAQUS. The material constitutive relation is consistent with the connection model.Figure 14
Finite element model used in ABAQUS.


### 3.3. Vibration Analysis

Prior to the nonlinear dynamic analyses, vibration analysis was performed in order to evaluate the dynamic properties in the linear behaviour range of the designed case studies. The eigen analysis was based on the structural inertia properties derived from the design loads, i.e., self-weight and permanent and live loads. The lowest six vibration modes are shown in Figure15, and the natural period of vibration calculated by ABAQUS and YJK is reported in Table 3. The response results show a satisfactory agreement between the period of vibration calculated by ABAQUS and that calculated by YJK.Figure 15
The lowest six vibration modes. (a)T1 = 3.39 s. (b) T2 = 3.17 s. (c) T3 = 2.74 s. (d) T4 = 1.04 s. (e) T5 = 0.90 s. (f) T6 = 0.78 s.
(a)
(b)
(c)
(d)
(e)
(f)Table 3
Natural period of vibration calculated by ABAQUS and YJK.
Vibration
Natural period of vibration (s)
Vibration modes
YJK
ABAQUS
Error (%)
1
3.38
3.39
0.29
X-directional first-order translation
2
3.01
3.17
5.3
Y-directional first-order translation
3
2.67
2.74
2.6
First-order reverse
4
1.01
1.04
3.0
X-directional second-order translation
5
0.85
0.90
5.9
X-directional second-order translation
6
0.76
0.78
2.6
Second-order reverse


### 3.4. Multirecord Dynamic Analysis at the Design Seismic Level

#### 3.4.1. Ground Motion Records and Base Shear

Nonlinear dynamic analyses were performed using two natural ground motion records and artificial ground motion records as the seismic input according to the comments in GB50011-2010. The ground motion records selected are listed in Table4. To consider the effects of seismic excitation intensity on the seismic performance of the models, the maximum time history of accelerations was scaled to 125 cm/s2 in high-intensity earthquake events (the earthquake with the exceedance probability of 2% in a 50-year period). Figure 16 compares the acceleration response spectra and the design acceleration spectrum. The design acceleration spectrum is based on normative data. The elastic-plastic base shear-time history curve of the structures is shown in Figure 17. The maximum base shear and the ratio of base shear to effective weight are shown in Table 5. From the point of view of the response spectrum, the ratio of base shear in time history under high-intensity earthquakes and CQC (complete quadratic combination) under low-intensity earthquake is approximately 4∼6 times, which is in a reasonable range. Meanwhile, the ratio of base shear to effective weight is between 3.6% and 6.2%, which is in a reasonable range. This also proves that the selected seismic wave is suitable.Table 4
Ground motion records.
No.
Earthquake
Occurrence time
Recording station
Magnitude
TR1
Imperial Valley
1979.10.15
EI Centro Array, CA
6.9
TR2
Long Ling Aftershock
1976.6.9
Longlin, Yunnan, China
6.2
RG
Artificial ground motions fitting moderately firm ground conditionsFigure 16
Design spectra and scaled earthquake spectra.Figure 17
Elastic-plastic base shear-time history curve of structures. (a) TR1-X. (b) TR2-X. (c) RG-X.
(a)
(b)
(c)Table 5
The maximum base shear.
Seismic wave
RG (kN)
TR1 (kN)
TR2 (kN)
X-direction
Y-direction
X-direction
Y-direction
X-direction
Y-direction
Time history under high-intensity earthquakes
7885
6980
5958
4612
5899
5371
CQC under frequent earthquakes
1034
1075
1034
1075
1034
1075
High-intensity earthquakes/frequent earthquakes
7.62
6.49
5.76
4.29
5.70
4.99
Ratio of base shear to effective weight
6.2%
5.5%
4.7%
3.6%
4.7%
4.2%


#### 3.4.2. Global Deformations

The roof horizontal displacements are shown in Figure18, and the mean maximum interstory drifts (d/h) are shown in Figure 19. The designed hybrid coupled PEC walls had good lateral stiffness at the design seismic input, with roof displacements always below H = 300 mm, and the mean maximum interstory drifts were less than the limitation for seismic walls in GB50011-2010. Under the three seismic ground motion records, the mean maximum interstory drifts show similar variation trends, and there is no obvious phenomenon of deformation concentration.Figure 18
Roof horizontal displacement. (a) TR1. (b) TR2. (c) RG.
(a)
(b)
(c)Figure 19
Mean maximum interstory drifts. (a) TR1. (b) TR2. (c) RG.
(a)
(b)
(c)


#### 3.4.3. Main Structure Performance

Figure20 shows the stress responses of the steel of the model in the RG wave. The numerical model accurately estimated the location of the plastic hinge. Under high-intensity earthquakes, a few coupling beams and frame beams in the middle of the floors were inelastic first with increasing durations. Then, the other coupling beams at the upper and lower floors gradually entered the inelastic state, and the shear walls remained elastic. With the increasing lateral loads, the shear plastic hinge will be formed in the steel coupling beams before the formation of the flexural plastic hinge in the PEC wall members. In a hybrid coupled PEC wall system, coupling beams dissipate the energy induced by earthquake loads through inelastic deformation. The structure could resist the loads by severe earthquakes, and there was no danger of structure collapse.Figure 20
Stress responses of the steel of the model. (a) 3 s. (b) 9 s. (c) 15 s. (d) 20 s.


## 3.1. Design of Case Studies

The design of the considered case studies is an 18-floor residential building selected as a prototype structure. A hybrid coupled PEC shear wall structure is selected for this project. In this structure, the PEC shear wall is the primary lateral resistance component and the steel beam is the horizontal bearing component. Beams and PEC walls were designed according to relevant Chinese codes [14, 16, 17] using steel grade Q345 (nominal yield stress fy = 345 MPa) and concrete grade C40 (characteristic compressive strength fcu = 40 MPa). The floor was assumed to be made of corrugated sheets and a concrete slab, with a thickness of 130 mm; hence, the floor can be considered a rigid diaphragm. Representative values of gravity G could be computed using the formula 1D + 0.5L, where D and L are dead and live loads, respectively. The total mass of the model was 12,649t.Moderately firm ground conditions of GB50011-2010 with a design peak ground acceleration (PGA) of 0.05 g (with a 10% exceedance probability in a 50-year period) were considered the seismic input. An 18-story hybrid coupled PEC wall system was designed using the elastic design method according to the current Chinese code by GBS Co., Ltd. Figure13 depicts the arrangement in the structures. On the basis of the connection solutions, a strong weld connection was adopted on the wall side.Figure 13
Arrangement in the structures.In this paper, elastic-plastic time history analysis of the hybrid coupled PEC wall system is accomplished by the program ABAQUS to evaluate the global response and component deformation of the structure.


## 3.2. Finite Element Model of the Hybrid Coupled PEC Wall

To better observe the behaviour of PEC walls, composite shell elements were used for the shear walls that were meshed by using the software’s “Structure” mesh type and beam elements were used for other structural members. Figure14 shows the finite element model used in ABAQUS. The material constitutive relation is consistent with the connection model.Figure 14
Finite element model used in ABAQUS.


## 3.3. Vibration Analysis

Prior to the nonlinear dynamic analyses, vibration analysis was performed in order to evaluate the dynamic properties in the linear behaviour range of the designed case studies. The eigen analysis was based on the structural inertia properties derived from the design loads, i.e., self-weight and permanent and live loads. The lowest six vibration modes are shown in Figure15, and the natural period of vibration calculated by ABAQUS and YJK is reported in Table 3. The response results show a satisfactory agreement between the period of vibration calculated by ABAQUS and that calculated by YJK.Figure 15
The lowest six vibration modes. (a)T1 = 3.39 s. (b) T2 = 3.17 s. (c) T3 = 2.74 s. (d) T4 = 1.04 s. (e) T5 = 0.90 s. (f) T6 = 0.78 s.
(a)
(b)
(c)
(d)
(e)
(f)Table 3
Natural period of vibration calculated by ABAQUS and YJK.
Vibration
Natural period of vibration (s)
Vibration modes
YJK
ABAQUS
Error (%)
1
3.38
3.39
0.29
X-directional first-order translation
2
3.01
3.17
5.3
Y-directional first-order translation
3
2.67
2.74
2.6
First-order reverse
4
1.01
1.04
3.0
X-directional second-order translation
5
0.85
0.90
5.9
X-directional second-order translation
6
0.76
0.78
2.6
Second-order reverse


## 3.4. Multirecord Dynamic Analysis at the Design Seismic Level

### 3.4.1. Ground Motion Records and Base Shear

Nonlinear dynamic analyses were performed using two natural ground motion records and artificial ground motion records as the seismic input according to the comments in GB50011-2010. The ground motion records selected are listed in Table4. To consider the effects of seismic excitation intensity on the seismic performance of the models, the maximum time history of accelerations was scaled to 125 cm/s2 in high-intensity earthquake events (the earthquake with the exceedance probability of 2% in a 50-year period). Figure 16 compares the acceleration response spectra and the design acceleration spectrum. The design acceleration spectrum is based on normative data. The elastic-plastic base shear-time history curve of the structures is shown in Figure 17. The maximum base shear and the ratio of base shear to effective weight are shown in Table 5. From the point of view of the response spectrum, the ratio of base shear in time history under high-intensity earthquakes and CQC (complete quadratic combination) under low-intensity earthquake is approximately 4∼6 times, which is in a reasonable range. Meanwhile, the ratio of base shear to effective weight is between 3.6% and 6.2%, which is in a reasonable range. This also proves that the selected seismic wave is suitable.Table 4
Ground motion records.
No.
Earthquake
Occurrence time
Recording station
Magnitude
TR1
Imperial Valley
1979.10.15
EI Centro Array, CA
6.9
TR2
Long Ling Aftershock
1976.6.9
Longlin, Yunnan, China
6.2
RG
Artificial ground motions fitting moderately firm ground conditionsFigure 16
Design spectra and scaled earthquake spectra.Figure 17
Elastic-plastic base shear-time history curve of structures. (a) TR1-X. (b) TR2-X. (c) RG-X.
(a)
(b)
(c)Table 5
The maximum base shear.
Seismic wave
RG (kN)
TR1 (kN)
TR2 (kN)
X-direction
Y-direction
X-direction
Y-direction
X-direction
Y-direction
Time history under high-intensity earthquakes
7885
6980
5958
4612
5899
5371
CQC under frequent earthquakes
1034
1075
1034
1075
1034
1075
High-intensity earthquakes/frequent earthquakes
7.62
6.49
5.76
4.29
5.70
4.99
Ratio of base shear to effective weight
6.2%
5.5%
4.7%
3.6%
4.7%
4.2%


### 3.4.2. Global Deformations

The roof horizontal displacements are shown in Figure18, and the mean maximum interstory drifts (d/h) are shown in Figure 19. The designed hybrid coupled PEC walls had good lateral stiffness at the design seismic input, with roof displacements always below H = 300 mm, and the mean maximum interstory drifts were less than the limitation for seismic walls in GB50011-2010. Under the three seismic ground motion records, the mean maximum interstory drifts show similar variation trends, and there is no obvious phenomenon of deformation concentration.Figure 18
Roof horizontal displacement. (a) TR1. (b) TR2. (c) RG.
(a)
(b)
(c)Figure 19
Mean maximum interstory drifts. (a) TR1. (b) TR2. (c) RG.
(a)
(b)
(c)


### 3.4.3. Main Structure Performance

Figure20 shows the stress responses of the steel of the model in the RG wave. The numerical model accurately estimated the location of the plastic hinge. Under high-intensity earthquakes, a few coupling beams and frame beams in the middle of the floors were inelastic first with increasing durations. Then, the other coupling beams at the upper and lower floors gradually entered the inelastic state, and the shear walls remained elastic. With the increasing lateral loads, the shear plastic hinge will be formed in the steel coupling beams before the formation of the flexural plastic hinge in the PEC wall members. In a hybrid coupled PEC wall system, coupling beams dissipate the energy induced by earthquake loads through inelastic deformation. The structure could resist the loads by severe earthquakes, and there was no danger of structure collapse.Figure 20
Stress responses of the steel of the model. (a) 3 s. (b) 9 s. (c) 15 s. (d) 20 s.


## 3.4.1. Ground Motion Records and Base Shear

Nonlinear dynamic analyses were performed using two natural ground motion records and artificial ground motion records as the seismic input according to the comments in GB50011-2010. The ground motion records selected are listed in Table4. To consider the effects of seismic excitation intensity on the seismic performance of the models, the maximum time history of accelerations was scaled to 125 cm/s2 in high-intensity earthquake events (the earthquake with the exceedance probability of 2% in a 50-year period). Figure 16 compares the acceleration response spectra and the design acceleration spectrum. The design acceleration spectrum is based on normative data. The elastic-plastic base shear-time history curve of the structures is shown in Figure 17. The maximum base shear and the ratio of base shear to effective weight are shown in Table 5. From the point of view of the response spectrum, the ratio of base shear in time history under high-intensity earthquakes and CQC (complete quadratic combination) under low-intensity earthquake is approximately 4∼6 times, which is in a reasonable range. Meanwhile, the ratio of base shear to effective weight is between 3.6% and 6.2%, which is in a reasonable range. This also proves that the selected seismic wave is suitable.Table 4
Ground motion records.
No.
Earthquake
Occurrence time
Recording station
Magnitude
TR1
Imperial Valley
1979.10.15
EI Centro Array, CA
6.9
TR2
Long Ling Aftershock
1976.6.9
Longlin, Yunnan, China
6.2
RG
Artificial ground motions fitting moderately firm ground conditionsFigure 16
Design spectra and scaled earthquake spectra.Figure 17
Elastic-plastic base shear-time history curve of structures. (a) TR1-X. (b) TR2-X. (c) RG-X.
(a)
(b)
(c)Table 5
The maximum base shear.
Seismic wave
RG (kN)
TR1 (kN)
TR2 (kN)
X-direction
Y-direction
X-direction
Y-direction
X-direction
Y-direction
Time history under high-intensity earthquakes
7885
6980
5958
4612
5899
5371
CQC under frequent earthquakes
1034
1075
1034
1075
1034
1075
High-intensity earthquakes/frequent earthquakes
7.62
6.49
5.76
4.29
5.70
4.99
Ratio of base shear to effective weight
6.2%
5.5%
4.7%
3.6%
4.7%
4.2%


## 3.4.2. Global Deformations

The roof horizontal displacements are shown in Figure18, and the mean maximum interstory drifts (d/h) are shown in Figure 19. The designed hybrid coupled PEC walls had good lateral stiffness at the design seismic input, with roof displacements always below H = 300 mm, and the mean maximum interstory drifts were less than the limitation for seismic walls in GB50011-2010. Under the three seismic ground motion records, the mean maximum interstory drifts show similar variation trends, and there is no obvious phenomenon of deformation concentration.Figure 18
Roof horizontal displacement. (a) TR1. (b) TR2. (c) RG.
(a)
(b)
(c)Figure 19
Mean maximum interstory drifts. (a) TR1. (b) TR2. (c) RG.
(a)
(b)
(c)


## 3.4.3. Main Structure Performance

Figure20 shows the stress responses of the steel of the model in the RG wave. The numerical model accurately estimated the location of the plastic hinge. Under high-intensity earthquakes, a few coupling beams and frame beams in the middle of the floors were inelastic first with increasing durations. Then, the other coupling beams at the upper and lower floors gradually entered the inelastic state, and the shear walls remained elastic. With the increasing lateral loads, the shear plastic hinge will be formed in the steel coupling beams before the formation of the flexural plastic hinge in the PEC wall members. In a hybrid coupled PEC wall system, coupling beams dissipate the energy induced by earthquake loads through inelastic deformation. The structure could resist the loads by severe earthquakes, and there was no danger of structure collapse.Figure 20
Stress responses of the steel of the model. (a) 3 s. (b) 9 s. (c) 15 s. (d) 20 s.


## 4. Conclusions

A hybrid coupled partially encased composite (PEC) wall system was proposed. FEM models were established by ABAQUS to study the connection performance of an innovative rigid joint with different configurations in this system and the seismic performance of the proposed hybrid coupled PEC wall system. Adopted finite element models are developed and validated with experimental tests. The following conclusions can be drawn within the limitations of the research:(1)
In the designs made with strong welded joints in this system, the strong joints had reliable load-bearing and ductility capacities under cyclic loads, and the hysteretic loops were very plump. The models with strong joints possessed stable and expanding hysteretic loops with no deterioration in the load-bearing capacity. This indicated that the design objective of strong joints was satisfied.(2)
The connection performance of joints with transverse stiffeners was slightly higher than that without transverse stiffeners under the same design conditions. Moreover, away from the hysteresis curve, the axial compression ratio can significantly affect the connection performance, and the joint performs best when the axial compression ratio does not exceed 0.4.(3)
In the hybrid coupled PEC wall system, all the steel beams yielded while the PEC wall was still in its elastic range. The shear coupling beams dissipated the earthquake energy through inelastic shear deformation. The PEC wall could still resist the lateral loads when the coupling beams were damaged, which indicated that the hybrid coupled PEC wall system was a safe and dual system. Meanwhile, the performance of the hybrid coupled PEC wall system could meet the limitation requirements in the design codes.



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*Source: 8139697-2020-01-31.xml*