# Configuration Features and Calculation Mechanisms of the Composite RC Column-Steel Beam (RCS) Joints: State of the Art

Authors: Liquan Xiong; Xingyue Pan; Zhen Jia; Zhengchao Guo; Linyan Li; Jian He
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Reinforced concrete and steel (RCS) composite moment frame structures consist of reinforced concrete (RC) columns and steel (S) beams. Such systems combined with several advantages of the two structural members have larger structural stiffness, lower cost, and faster construction speed than the traditional concrete or steel frame system to be a particularly well viable alternative for use in seismic risk regions. The calculation of joint shear capacity is an essential step in seismic design. This study introduces the typical configuration characteristics of the RCS connection and reviews the state of the art of the shear bearing capacity in terms of failure models, shear distribution mechanisms, calculation mechanisms, and requirements given in the experimental and theoretical study to provide reference and foundation for the subsequent study. Finally, the development of recommendations and further research studies on seismic performance of RCS composite frames are provided.


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## Body

## 1. Introduction

The reinforced concrete and steel (RCS) composite structure consisting of reinforced concrete columns (RC), steel beams (S), and concrete slabs with generally composite metal decking have gained increasing interest in the seismic region over the past decades. Compared with the conventional steel or RC frame systems, the RCS composite frames using RC rather than structural steel columns provide the superior attributes of large span, light self-weight, good fire resistance, excellent lateral stiffness, fast construction speed, and excellent seismic performance [1–4]. Such systems are particularly well viable alternative for use in mid-to-high-rise buildings in low to moderate seismic risk regions and low-to mid-rise buildings in moderate to high seismic risk regions [5, 6].The RCS composite frames began to gain popularity in both the United States and Japan in the late 1970’s and early 1980’s, respectively. In the United States, this system replacing the steel columns of traditional steel moment frames can provide high axial compressive loads to satisfy the building height and lateral stiffness (drift) criteria in engineering practice [7–9]. In Japan, the steel reinforced concrete (SRC) structure performed well in the 1923 Kanto earthquake, which made a contribution to the development of the prevalence of the composite system by the construction companies and occupants. Under this background, the RCS composite system was recommended to obtain the long-span capabilities and cost savings compared with the RC moment frames in high seismic zones [10–12].Compared with the members in the traditional steel or reinforced concrete moment frame structures in the seismic design, a primary challenge for the composite RCS frames focused on the reliable junction among the steel beams and RC columns. Many researchers [1, 5, 7, 13–19] conducted a series of experimental programs to investigate the joint details, failure modes, shear strength, high strength concrete, column-to-beam strength ratio, and axial force effect of the RCS connection. The results of those specimens have been presented as follows: (1) the RCS joints with proper details can provide stable, ductile, and predictable behavior under reversed cyclic loading, (2) basic mechanics provides understanding of the internal shear mechanisms and the failure modes that govern the RCS joint strength, and (3) the utilization of the details in RCS joints can enhance the strength and stiffness of subassemblies, which would reduce the joint distortion and rigid body rotation to increase the capacity of shear resistance. To study the composite effects of RCS joint with the RC slab, extensive data [3, 19–25] indicate that (1) the specimens following the strong column weak beam criterion formed the plastic hinges at the beam ends and showed a good cyclic performance (Figure 1); (2) the comparison of interior RCS subassemblies without the RC floor slab, the ultimate shear strength of the composite beam-slab sections was calculated, and 20% strength increase was seen in the specimen due to RC slab; (3) avoiding the high compressive stresses by the involvement of cast in situ slab in the joint region resulted in the area of concrete getting crushed near the corners of column, and guidelines and recommendations for the RCS connections with proper details, e.g., cover plates, band plates, and shear studs, were necessary for seismic design; and (4) effective flange width of the composite beam-slab sections has a significant effect on the capacity of beam moment and equivalent elastic moment of inertia values. To evaluate the behavior of the exterior RCS connections [17, 26–30], various details, such as end plates, shear keys, and extended cover plates, and the shear strength models have been proposed. Additionally, the influential factors of the RCS connections on the static performance including the axial compression ratio, steel insert length, the thickness of end plate, and the column concrete grade was also studied. Those results pointed out that RCS frames were suitable for getting recognized as an alternative to the high seismic risk zones. Besides, the novel type RCS connection weakening the extension beam end-joint was proposed to move the plastic hinge from the end of a beam to a weakened point and a novel through-column type with the details of H steel profile and plates in the joint which presented stable seismic performance [31, 32].Figure 1
Load-displacement curve (specimen 3) by Men et al. [3]: (a) specimen 3 and (b) load-displacement curve.
(a)(b)To learn more about the cyclic performance of RCS moment frames in the building structures, a series of tests have been conducted [33–39]. The results reported that (1) the frame structures with two joint details of through-beam type and through-column type had an excellent seismic performance, those of which presented the plastic hinge mechanisms that concentrated upon the end of steel beams and the bottom of RC columns to meet the strong-joint weak-component criterion; (2) the structure slightly damaged in frequent earthquake and presented the collapse prevention level under rare earthquake to further validate the reliability of this innovative system. However, the previously mentioned studies clearly show that the mass of experimental studies for the RCS joints have been done in comparison with the moment frames, and research studies on the behavior of the overall frame structures will be conducted further.RCS connections subjected to large shear forces under seismic loads are one of the key parts to form an efficient composite structure. The objective of this study is firstly to present the structural configuration features and failure models of composite RCS connections. Additionally, the state-of-the-art of shear bearing capacity models of the RCS connections in terms of shear distribution mechanisms, calculation mechanisms, and requirements given in the experimental and theoretical study was introduced. According to those studies, the research progress of shear bearing capacity formulas of the RCS joints focused on providing reference for the subsequent study.


## 2. Configuration and Damage Features of the RCS Joints

### 2.1. The Types of the RCS Joints

According to different design phenomena, the RCS connections are classified into beam-through type and column-through type, as illustrated in Figure2. For the beam-through type (Figure 2(a)), the steel beam which continuously passes through the RC column can eliminate welding at the maximum bending moment region or bolting the steel beam in the joint, and the proper details can strengthen the RCS joint to provide very stable and ductile behavior under reversed cyclic loading (Figure 3). In general, the small steel column is encased in concrete and the face bearing plates were connected to the steel web panel. The advantages of this RCS joint mainly include those as follows: (1) the steel beam was continuous through the RC column to mobilize the force transfer mechanism between the steel and concrete to avoid the fracture-critical joints and (2) the steel columns encased by reinforced concrete columns provide for an efficient vertical spread of the construction activity. Certainly, the details of the composite connection might cause the difficulties in some ways of assembling reinforcement and casting the concrete in engineering practice. To ensure construction quality, the steel beam flanges can extend to the joint which partly cuts off to keep the longitudinal reinforcement of the column passing through the connection to facilitate casting and vibrating the concrete [5]. As shown in Figure 2(a), the major distinction of “through-beam” vs. “through-column” type connections is that the steel flanges are interrupted at the joint to minimize the impact on construction. Through-column type connections combining conventional SRC concepts where encasing the end of the steel beam connected to the concrete column have been the preferred detail in Japan. Additionally, the connection details include inner or outer diaphragms, cover plates, and a transverse stiffener connected the steel panel zone to strengthen the strength and ductility capacity of the RCS joints (Figure 3) [40, 41]. However, the disadvantage of the connection with cutting the flange is that it might cause the reduction of bearing area in joint regions to decrease the stress transferring mechanisms [42, 43]. The primary goal of these tests nearly focused on validating specific joint details instead of quantifying the internal force transfer mechanisms of the joint (see Figure 4).Figure 2
RCS connections: (a) the beam-through type and (b) the column-through type.
(a)(b)Figure 3
The behavior of beam-through type connections by Cheng and Chen [15]: (a) the failure mode and (b) force-displacement loops.
(a)(b)Figure 4
Force-displacement loops of column-through type connection by Kuramoto and Nishiyama [41].


### 2.2. Typical Joint Details

The beam-column joints play a key role in a composite reinforced concrete column-to-steel beam frame system. Compared with the conventional concrete or steel frame, the mechanical feature of RCS joints shows a complex condition due to the unique connection between the steel beam and the reinforced concrete column. The previously mentioned studies clearly focused on the design of the composite RCS beam-column connections, especially for the configurations, to quantify the internal force transfer mechanisms and maintain displacement compatibility of the joints. 3D representation of the typical features of RCS connection details is shown in Figure5. The details in Figures 5(a)–5(f) are so-called “through-beam” type connections. In Figure 5(a), face bearing plates (FBPs) located at the face of the concrete column are fillet welded to the steel beam web and flanges to mobilize the shear resistance of the concrete in the joint region. In general, stirrups passing through the web of the steel beam were also used to stabilize the vertical column reinforcements and constrain the concrete in the joint. In Figure 5(b), the transverse beam was welded to the beam web orthogonally. From Figure 5(c), we can see that FBPs can vary in width and may be either in full height or split for fabrication ease, such as broaden and extended face bearing plates (E-FBPs) to avoid the concrete crushing in the high-bearing stresses zone located just above and below the steel beam flanges [7]. Additionally, the similar details include vertical reinforcements, shear studs, and band plates (Figure 5(d)) which connected to the beam flanges are convenient to enhance the vertical bearing strength in the continuous direction [15, 17, 44, 45]. Figure 5(e) shows that cover plates wrapping around the RC column region constrained the concrete in the core regions to form the excellent confinement conditions. Small steel columns, as shown in Figure 5(f), are welded to the beam flanges and embedded in the RC column, and these act as the erection columns to provide for an efficient vertical support for construction and are also used for shear transfer purposes. The details in Figures 5(g)–5(i) are so-called “through-column” type connections. Figure 5(g)shows that the vertical stiffener forms an octagon-shaped joint region encompassing the column to simplify constructability. These stiffener plates were field welded to the extended FBPs by means of full penetration welding. Joint detailing consisted of cover plates and a horizontal stiffener to strengthen the joint region, as shown in Figure 5(h). Figure 5(i) is an example of hybrid detail, combining conventional SRC concepts by encasing the inner or outer diaphragm. It is noteworthy that these types of connection details can be used alone or in conjunction with each other to effectively mobilize joint force.Figure 5
Typical features of joint detail by Nishiyama et al. [43]: (a) face bearing plates, (b) transverse beam, (c) extended face bearing plates, (d) band plates, (e) cover plates, (f) small steel column, (g) vertical stiffener, (h) horizontal stiffener, and (i) diaphragm.
(a)(b)(c)(d)(e)(f)(g)(h)(i)


### 2.3. Failure Models of the RCS Joint

#### 2.3.1. Typical Failure Models

According to the research of Sheikh et al. [7, 46], the typical failure model of the RCS connections is characterized by the panel shear failure and vertical bearing failure, as shown in Figure 6. Those failure modes of RCS connections were accepted by the scholars in this field and ASCE Seismic Provisions [47]. From a series of tests on the behavior of internal RCS connections with proper details as mentioned previously, the characteristics of the panel shear failure (Figure 6(a)) consisted of the yield of steel beam web, concrete cracking, and crushing, which are typically similar to the steel or reinforced concrete joints. A bearing failure (see in Figure 6(b)) occurs when the concrete in the column regions adjacent to the beam flanges crushes due to high-bearing strains. At the same time, rigid body rotation of the steel beam in the joint located just above and below the steel flanges was presented. It is desirable for engineers to design RCS connections to possess a bearing strength larger than shear strength in order to gain stable ductile performance. As described, those details which include small steel column, band plates, shear studs, and vertical joint reinforcements, as shown in Figure 5, are some means of strengthening for bearing strength in the joint.Figure 6
Two types of joint failure models [1, 5, 46]: (a) panel shear failure and (b) vertical bearing failure.
(a)(b)


#### 2.3.2. Other Failure Modes

Based on the results of experiments [1, 5], other failure modes of the interior RCS joints exhibited local shear failure and joint-beam mixed failure from Figure 7. For simple construction, the steel beam flanges were partly cut off in the joint proposed by Men et al. [5]. Additionally, the specimens followed the design philosophy of the strong-component weak-joint criterion to evaluate the seismic performance. However, the local shear failure of the specimens 2 and 4 was observed since the details could not confine concrete in the joint to carry tension forces associated with the compression field mechanism. As shown in Figure 7(a), the features of the local shear failure are a combination of panel shear failure and vertical bearing failure. The damage phenomena of those specimens include the local yield of steel web, concrete cracking in the joint, and the rigid body rotation of the steel beam within the concrete column which resulted in concrete crushing along the margin of the steel flanges. At the same time, the similar failure features were recorded by other tests [13, 49]. In general, the relative participation of each failure depends upon joint detailing, as discussed previously. However, from the behavior of those specimens, local shear failure (Figure 7(a)) showed good seismic performance with stable load versus displacement response, excellent strength, and deformation capacity to meet the requirement for earthquake resistant structures.Figure 7
Other failure features: (a) local shear failure [5] and (b) joint-beam mixed failure [1].
(a)(b)An example representative of tests with joint-beam mixed failure shown by Lee et al. [1] on the details of specimens include FBPs, transverse beams, and headed studs according to the ASCE guidelines (ASCE 1994) [47]. Furthermore, the closely spaced ties installed in the joint to protect the highly stressed bearing region support the strut-and-tie action of the outer compression field. Four interior beam column joints were designed with the strong column-weak beam concept. Nevertheless, the unfavorable failure mode of those specimens reported that the beam column connection became severely damaged and the plastic hinges were developed until the end of testing due to the absence of strengthening details to mobilize the shear mechanism of the outer panel. The damage features were similar to that of specimens OB1-1, OBJS1-1, and OBJS2-0 conducted by Kanno [13]. The characteristics of joint-beam mixed failure consisted of the yield of steel web, the oblique concrete cracks, and the flange flexural yielding which penetrated the joint panel (Figure 7(b)). The reason for the joint-beam mixed failure might be that the plastic hinge zone is spread over a relatively large length rather than being concentrated at the column face because the shear strength of the joint is equivalent to that of the flexural or local buckling capacity of the steel beam. Meanwhile, the joint-beam mixed failure model seemed to be the limit state of the plastic hinge region of the steel beam and local shear failure of the joint. Nevertheless, these specimens had good strength and deformation capacity (Figure 7(b)) to be used for the low to moderate seismic design of RCS joints. Based on the mentioned failure models, the connection details of the RCS joints consisted of FBPs or E-FBPs, band plates, or shear keys, and cover plates should be installed to transfer of member forces to satisfy in the design practice.


## 2.1. The Types of the RCS Joints

According to different design phenomena, the RCS connections are classified into beam-through type and column-through type, as illustrated in Figure2. For the beam-through type (Figure 2(a)), the steel beam which continuously passes through the RC column can eliminate welding at the maximum bending moment region or bolting the steel beam in the joint, and the proper details can strengthen the RCS joint to provide very stable and ductile behavior under reversed cyclic loading (Figure 3). In general, the small steel column is encased in concrete and the face bearing plates were connected to the steel web panel. The advantages of this RCS joint mainly include those as follows: (1) the steel beam was continuous through the RC column to mobilize the force transfer mechanism between the steel and concrete to avoid the fracture-critical joints and (2) the steel columns encased by reinforced concrete columns provide for an efficient vertical spread of the construction activity. Certainly, the details of the composite connection might cause the difficulties in some ways of assembling reinforcement and casting the concrete in engineering practice. To ensure construction quality, the steel beam flanges can extend to the joint which partly cuts off to keep the longitudinal reinforcement of the column passing through the connection to facilitate casting and vibrating the concrete [5]. As shown in Figure 2(a), the major distinction of “through-beam” vs. “through-column” type connections is that the steel flanges are interrupted at the joint to minimize the impact on construction. Through-column type connections combining conventional SRC concepts where encasing the end of the steel beam connected to the concrete column have been the preferred detail in Japan. Additionally, the connection details include inner or outer diaphragms, cover plates, and a transverse stiffener connected the steel panel zone to strengthen the strength and ductility capacity of the RCS joints (Figure 3) [40, 41]. However, the disadvantage of the connection with cutting the flange is that it might cause the reduction of bearing area in joint regions to decrease the stress transferring mechanisms [42, 43]. The primary goal of these tests nearly focused on validating specific joint details instead of quantifying the internal force transfer mechanisms of the joint (see Figure 4).Figure 2
RCS connections: (a) the beam-through type and (b) the column-through type.
(a)(b)Figure 3
The behavior of beam-through type connections by Cheng and Chen [15]: (a) the failure mode and (b) force-displacement loops.
(a)(b)Figure 4
Force-displacement loops of column-through type connection by Kuramoto and Nishiyama [41].


## 2.2. Typical Joint Details

The beam-column joints play a key role in a composite reinforced concrete column-to-steel beam frame system. Compared with the conventional concrete or steel frame, the mechanical feature of RCS joints shows a complex condition due to the unique connection between the steel beam and the reinforced concrete column. The previously mentioned studies clearly focused on the design of the composite RCS beam-column connections, especially for the configurations, to quantify the internal force transfer mechanisms and maintain displacement compatibility of the joints. 3D representation of the typical features of RCS connection details is shown in Figure5. The details in Figures 5(a)–5(f) are so-called “through-beam” type connections. In Figure 5(a), face bearing plates (FBPs) located at the face of the concrete column are fillet welded to the steel beam web and flanges to mobilize the shear resistance of the concrete in the joint region. In general, stirrups passing through the web of the steel beam were also used to stabilize the vertical column reinforcements and constrain the concrete in the joint. In Figure 5(b), the transverse beam was welded to the beam web orthogonally. From Figure 5(c), we can see that FBPs can vary in width and may be either in full height or split for fabrication ease, such as broaden and extended face bearing plates (E-FBPs) to avoid the concrete crushing in the high-bearing stresses zone located just above and below the steel beam flanges [7]. Additionally, the similar details include vertical reinforcements, shear studs, and band plates (Figure 5(d)) which connected to the beam flanges are convenient to enhance the vertical bearing strength in the continuous direction [15, 17, 44, 45]. Figure 5(e) shows that cover plates wrapping around the RC column region constrained the concrete in the core regions to form the excellent confinement conditions. Small steel columns, as shown in Figure 5(f), are welded to the beam flanges and embedded in the RC column, and these act as the erection columns to provide for an efficient vertical support for construction and are also used for shear transfer purposes. The details in Figures 5(g)–5(i) are so-called “through-column” type connections. Figure 5(g)shows that the vertical stiffener forms an octagon-shaped joint region encompassing the column to simplify constructability. These stiffener plates were field welded to the extended FBPs by means of full penetration welding. Joint detailing consisted of cover plates and a horizontal stiffener to strengthen the joint region, as shown in Figure 5(h). Figure 5(i) is an example of hybrid detail, combining conventional SRC concepts by encasing the inner or outer diaphragm. It is noteworthy that these types of connection details can be used alone or in conjunction with each other to effectively mobilize joint force.Figure 5
Typical features of joint detail by Nishiyama et al. [43]: (a) face bearing plates, (b) transverse beam, (c) extended face bearing plates, (d) band plates, (e) cover plates, (f) small steel column, (g) vertical stiffener, (h) horizontal stiffener, and (i) diaphragm.
(a)(b)(c)(d)(e)(f)(g)(h)(i)


## 2.3. Failure Models of the RCS Joint

### 2.3.1. Typical Failure Models

According to the research of Sheikh et al. [7, 46], the typical failure model of the RCS connections is characterized by the panel shear failure and vertical bearing failure, as shown in Figure 6. Those failure modes of RCS connections were accepted by the scholars in this field and ASCE Seismic Provisions [47]. From a series of tests on the behavior of internal RCS connections with proper details as mentioned previously, the characteristics of the panel shear failure (Figure 6(a)) consisted of the yield of steel beam web, concrete cracking, and crushing, which are typically similar to the steel or reinforced concrete joints. A bearing failure (see in Figure 6(b)) occurs when the concrete in the column regions adjacent to the beam flanges crushes due to high-bearing strains. At the same time, rigid body rotation of the steel beam in the joint located just above and below the steel flanges was presented. It is desirable for engineers to design RCS connections to possess a bearing strength larger than shear strength in order to gain stable ductile performance. As described, those details which include small steel column, band plates, shear studs, and vertical joint reinforcements, as shown in Figure 5, are some means of strengthening for bearing strength in the joint.Figure 6
Two types of joint failure models [1, 5, 46]: (a) panel shear failure and (b) vertical bearing failure.
(a)(b)


### 2.3.2. Other Failure Modes

Based on the results of experiments [1, 5], other failure modes of the interior RCS joints exhibited local shear failure and joint-beam mixed failure from Figure 7. For simple construction, the steel beam flanges were partly cut off in the joint proposed by Men et al. [5]. Additionally, the specimens followed the design philosophy of the strong-component weak-joint criterion to evaluate the seismic performance. However, the local shear failure of the specimens 2 and 4 was observed since the details could not confine concrete in the joint to carry tension forces associated with the compression field mechanism. As shown in Figure 7(a), the features of the local shear failure are a combination of panel shear failure and vertical bearing failure. The damage phenomena of those specimens include the local yield of steel web, concrete cracking in the joint, and the rigid body rotation of the steel beam within the concrete column which resulted in concrete crushing along the margin of the steel flanges. At the same time, the similar failure features were recorded by other tests [13, 49]. In general, the relative participation of each failure depends upon joint detailing, as discussed previously. However, from the behavior of those specimens, local shear failure (Figure 7(a)) showed good seismic performance with stable load versus displacement response, excellent strength, and deformation capacity to meet the requirement for earthquake resistant structures.Figure 7
Other failure features: (a) local shear failure [5] and (b) joint-beam mixed failure [1].
(a)(b)An example representative of tests with joint-beam mixed failure shown by Lee et al. [1] on the details of specimens include FBPs, transverse beams, and headed studs according to the ASCE guidelines (ASCE 1994) [47]. Furthermore, the closely spaced ties installed in the joint to protect the highly stressed bearing region support the strut-and-tie action of the outer compression field. Four interior beam column joints were designed with the strong column-weak beam concept. Nevertheless, the unfavorable failure mode of those specimens reported that the beam column connection became severely damaged and the plastic hinges were developed until the end of testing due to the absence of strengthening details to mobilize the shear mechanism of the outer panel. The damage features were similar to that of specimens OB1-1, OBJS1-1, and OBJS2-0 conducted by Kanno [13]. The characteristics of joint-beam mixed failure consisted of the yield of steel web, the oblique concrete cracks, and the flange flexural yielding which penetrated the joint panel (Figure 7(b)). The reason for the joint-beam mixed failure might be that the plastic hinge zone is spread over a relatively large length rather than being concentrated at the column face because the shear strength of the joint is equivalent to that of the flexural or local buckling capacity of the steel beam. Meanwhile, the joint-beam mixed failure model seemed to be the limit state of the plastic hinge region of the steel beam and local shear failure of the joint. Nevertheless, these specimens had good strength and deformation capacity (Figure 7(b)) to be used for the low to moderate seismic design of RCS joints. Based on the mentioned failure models, the connection details of the RCS joints consisted of FBPs or E-FBPs, band plates, or shear keys, and cover plates should be installed to transfer of member forces to satisfy in the design practice.


## 2.3.1. Typical Failure Models

According to the research of Sheikh et al. [7, 46], the typical failure model of the RCS connections is characterized by the panel shear failure and vertical bearing failure, as shown in Figure 6. Those failure modes of RCS connections were accepted by the scholars in this field and ASCE Seismic Provisions [47]. From a series of tests on the behavior of internal RCS connections with proper details as mentioned previously, the characteristics of the panel shear failure (Figure 6(a)) consisted of the yield of steel beam web, concrete cracking, and crushing, which are typically similar to the steel or reinforced concrete joints. A bearing failure (see in Figure 6(b)) occurs when the concrete in the column regions adjacent to the beam flanges crushes due to high-bearing strains. At the same time, rigid body rotation of the steel beam in the joint located just above and below the steel flanges was presented. It is desirable for engineers to design RCS connections to possess a bearing strength larger than shear strength in order to gain stable ductile performance. As described, those details which include small steel column, band plates, shear studs, and vertical joint reinforcements, as shown in Figure 5, are some means of strengthening for bearing strength in the joint.Figure 6
Two types of joint failure models [1, 5, 46]: (a) panel shear failure and (b) vertical bearing failure.
(a)(b)


## 2.3.2. Other Failure Modes

Based on the results of experiments [1, 5], other failure modes of the interior RCS joints exhibited local shear failure and joint-beam mixed failure from Figure 7. For simple construction, the steel beam flanges were partly cut off in the joint proposed by Men et al. [5]. Additionally, the specimens followed the design philosophy of the strong-component weak-joint criterion to evaluate the seismic performance. However, the local shear failure of the specimens 2 and 4 was observed since the details could not confine concrete in the joint to carry tension forces associated with the compression field mechanism. As shown in Figure 7(a), the features of the local shear failure are a combination of panel shear failure and vertical bearing failure. The damage phenomena of those specimens include the local yield of steel web, concrete cracking in the joint, and the rigid body rotation of the steel beam within the concrete column which resulted in concrete crushing along the margin of the steel flanges. At the same time, the similar failure features were recorded by other tests [13, 49]. In general, the relative participation of each failure depends upon joint detailing, as discussed previously. However, from the behavior of those specimens, local shear failure (Figure 7(a)) showed good seismic performance with stable load versus displacement response, excellent strength, and deformation capacity to meet the requirement for earthquake resistant structures.Figure 7
Other failure features: (a) local shear failure [5] and (b) joint-beam mixed failure [1].
(a)(b)An example representative of tests with joint-beam mixed failure shown by Lee et al. [1] on the details of specimens include FBPs, transverse beams, and headed studs according to the ASCE guidelines (ASCE 1994) [47]. Furthermore, the closely spaced ties installed in the joint to protect the highly stressed bearing region support the strut-and-tie action of the outer compression field. Four interior beam column joints were designed with the strong column-weak beam concept. Nevertheless, the unfavorable failure mode of those specimens reported that the beam column connection became severely damaged and the plastic hinges were developed until the end of testing due to the absence of strengthening details to mobilize the shear mechanism of the outer panel. The damage features were similar to that of specimens OB1-1, OBJS1-1, and OBJS2-0 conducted by Kanno [13]. The characteristics of joint-beam mixed failure consisted of the yield of steel web, the oblique concrete cracks, and the flange flexural yielding which penetrated the joint panel (Figure 7(b)). The reason for the joint-beam mixed failure might be that the plastic hinge zone is spread over a relatively large length rather than being concentrated at the column face because the shear strength of the joint is equivalent to that of the flexural or local buckling capacity of the steel beam. Meanwhile, the joint-beam mixed failure model seemed to be the limit state of the plastic hinge region of the steel beam and local shear failure of the joint. Nevertheless, these specimens had good strength and deformation capacity (Figure 7(b)) to be used for the low to moderate seismic design of RCS joints. Based on the mentioned failure models, the connection details of the RCS joints consisted of FBPs or E-FBPs, band plates, or shear keys, and cover plates should be installed to transfer of member forces to satisfy in the design practice.


## 3. Shear Mechanisms of the RCS Joints

### 3.1. Force Distribution of the RCS Joints

Force distribution of the interior RCS joints is illustrated in Figure8. As shown in Figure 8, the forces of the joint include the bending moments, shear forces, and axial forces transmitted from the RC column ends and the right and left sides of the steel beams, which caused the joint region to be placed in a state of compression-bending-shear composite stress. Because of the small axial force of the steel beam, they are generally negligible to simplify the force calculation model. For the axial pressure of the column, although some tested results indicated that the axial force has a certain influence on the mechanical performance of the joint [13, 50], most of the current researches did not consider the axial force. At the same time, this study assumes that the bending moment and shear force from the right and left beam ends are equal, and the bending moment and shear force from the upper and lower column ends are also equal.Figure 8
Force transfer mechanisms of the interior RCS joint.According to the force equilibrium condition of the interior RCS joints (see in Figure8), the shear capacity Vjt in the core area of the joint can be obtained as(1)Vjt=Mbl+Mbrhbw1−hbwhc−hb,where Mbl and Mbr are the bending moments at the root of the left and right beam, hb is the beam section height, hc is the distance between the inflection points of the upper and lower column ends of the joint, hbw is the distance between the flanges of the steel beam, and hbw is equal to (hb − tf), where tf is the thickness of the steel flange.


### 3.2. Mechanisms for RCS Joint Shear Resistance

#### 3.2.1. Beam-Through Type Joint

As shown in Figure8, force transfer mechanisms of the beam-through type RCS joint with the proper details indicated that the effective joint region consisted of the inner element and outer element to meet the bearing capacity and compatibility of deformation. The width of FBPs, E-FBPs, steel flange, and studs determined that of inner element and the details of band plates, cover plates, and small steel column affected the outer element width in the joint, respectively. Based on the damage features of the experimental and finite element models results [1, 2, 7, 16, 18], the load resistance mechanisms for joint shear capacity in the beam-through RCS joints is generally provided by three mechanisms: steel web panel, inner concrete diagonal strut, and outer concrete compression field, as shown in Figure 9. In the RCS joints, the behavior of the steel web panel similar to that, in the steel frames is idealized as carrying pure shear stress over a portion of the joint region, as shown in Figure 9(a), which is dependent on the location and distribution of vertical bearing stresses. The inner concrete diagonal strut in the inner element region is activated by squeezing the concrete between the steel beam flanges and FBPs or E-FBPs welded the steel beam flanges, as shown in Figure 9(b), which is similar to the mechanism model to resist shear in reinforced concrete connections. In general, the outer concrete compression field is composed of several compression struts since horizontal reinforcements which welded the steel web form a truss mechanism in the joint region (Figure 9(c)), which was often used for establishing the shear model in reinforced concrete beams. In addition, the concrete horizontal strut is developed in the region of column concrete outside the steel beam flanges (Figure 9(d)). Since shear force is transferred horizontally from the beam flanges into the compression field due to the joint details of the embedded small steel column, stiffeners extended above and below the steel beam, shear studs, or reinforcements welded to the beam flanges. The research results [1, 51] indicated that the sum of the contributions of the steel web and inner concrete strut is approximately 60% for the shear strength of RCS joints and that of the outer concrete compression filed is approximately 40%, respectively. Certainly, shear capacity of the outer element in the joint region could decrease because the difference depends on the absence of strengthening joint details to mobilize the shear mechanism of the outer panel.Figure 9
Mechanisms for beam-through type joint shear resistance: (a) steel web panel, (b) inner concrete diagonal strut, (c) outer concrete compression field, and (d) concrete horizontal strut.
(a)(b)(c)(d)


#### 3.2.2. Column-Through Type Joint

As mentioned before (see in Figure5), the details of column-through type joint generally include cover plates, orthogonal steel web, and diaphragm to keep the longitudinal reinforcement through the connection to simplify constructability; at the same time, the joint details also guarantee stress transferring mechanisms for composite reinforced concrete and steel joint. According to the experimental results by Kuramoto and Nishiyama [41], four mechanisms for beam-through type joint shear resistance are shown in Figures 10(a)–10(d). From Figures 10(a) and 10(b), the stress transferring mechanisms consisted of steel web panel, concrete diagonal strut, and concrete horizontal strut in the joint. The steel web panel mechanism and concrete diagonal strut mechanism formed in the inner element are similar with those of the beam-through type joint. The concrete horizontal strut mechanism which transferred the concrete compressive stresses through the inner element to the outer element included concrete horizontal strut-1 and concrete horizontal strut-2. The first one formed the concrete horizontal struts to mobilize compressive stresses from steel beam flanges to FBPs in the outer panel (Figure 10(c)). Additionally, the second concrete horizontal strut mechanism was developed between the intersection point of the web panels in the core area of joints and the corner of cover plates and then mobilized the outer diagonal concrete struts, cover plates, and the bond stresses between reinforcing bars in the joint to contribute the shear capacity.Figure 10
Mechanisms for beam-through type joint shear resistance [41]: (a) steel web panel, (b) concrete diagonal strut, (c) concrete horizontal strut-1, and (d) concrete horizontal strut-2.
(a)(b)(c)(d)


## 3.1. Force Distribution of the RCS Joints

Force distribution of the interior RCS joints is illustrated in Figure8. As shown in Figure 8, the forces of the joint include the bending moments, shear forces, and axial forces transmitted from the RC column ends and the right and left sides of the steel beams, which caused the joint region to be placed in a state of compression-bending-shear composite stress. Because of the small axial force of the steel beam, they are generally negligible to simplify the force calculation model. For the axial pressure of the column, although some tested results indicated that the axial force has a certain influence on the mechanical performance of the joint [13, 50], most of the current researches did not consider the axial force. At the same time, this study assumes that the bending moment and shear force from the right and left beam ends are equal, and the bending moment and shear force from the upper and lower column ends are also equal.Figure 8
Force transfer mechanisms of the interior RCS joint.According to the force equilibrium condition of the interior RCS joints (see in Figure8), the shear capacity Vjt in the core area of the joint can be obtained as(1)Vjt=Mbl+Mbrhbw1−hbwhc−hb,where Mbl and Mbr are the bending moments at the root of the left and right beam, hb is the beam section height, hc is the distance between the inflection points of the upper and lower column ends of the joint, hbw is the distance between the flanges of the steel beam, and hbw is equal to (hb − tf), where tf is the thickness of the steel flange.


## 3.2. Mechanisms for RCS Joint Shear Resistance

### 3.2.1. Beam-Through Type Joint

As shown in Figure8, force transfer mechanisms of the beam-through type RCS joint with the proper details indicated that the effective joint region consisted of the inner element and outer element to meet the bearing capacity and compatibility of deformation. The width of FBPs, E-FBPs, steel flange, and studs determined that of inner element and the details of band plates, cover plates, and small steel column affected the outer element width in the joint, respectively. Based on the damage features of the experimental and finite element models results [1, 2, 7, 16, 18], the load resistance mechanisms for joint shear capacity in the beam-through RCS joints is generally provided by three mechanisms: steel web panel, inner concrete diagonal strut, and outer concrete compression field, as shown in Figure 9. In the RCS joints, the behavior of the steel web panel similar to that, in the steel frames is idealized as carrying pure shear stress over a portion of the joint region, as shown in Figure 9(a), which is dependent on the location and distribution of vertical bearing stresses. The inner concrete diagonal strut in the inner element region is activated by squeezing the concrete between the steel beam flanges and FBPs or E-FBPs welded the steel beam flanges, as shown in Figure 9(b), which is similar to the mechanism model to resist shear in reinforced concrete connections. In general, the outer concrete compression field is composed of several compression struts since horizontal reinforcements which welded the steel web form a truss mechanism in the joint region (Figure 9(c)), which was often used for establishing the shear model in reinforced concrete beams. In addition, the concrete horizontal strut is developed in the region of column concrete outside the steel beam flanges (Figure 9(d)). Since shear force is transferred horizontally from the beam flanges into the compression field due to the joint details of the embedded small steel column, stiffeners extended above and below the steel beam, shear studs, or reinforcements welded to the beam flanges. The research results [1, 51] indicated that the sum of the contributions of the steel web and inner concrete strut is approximately 60% for the shear strength of RCS joints and that of the outer concrete compression filed is approximately 40%, respectively. Certainly, shear capacity of the outer element in the joint region could decrease because the difference depends on the absence of strengthening joint details to mobilize the shear mechanism of the outer panel.Figure 9
Mechanisms for beam-through type joint shear resistance: (a) steel web panel, (b) inner concrete diagonal strut, (c) outer concrete compression field, and (d) concrete horizontal strut.
(a)(b)(c)(d)


### 3.2.2. Column-Through Type Joint

As mentioned before (see in Figure5), the details of column-through type joint generally include cover plates, orthogonal steel web, and diaphragm to keep the longitudinal reinforcement through the connection to simplify constructability; at the same time, the joint details also guarantee stress transferring mechanisms for composite reinforced concrete and steel joint. According to the experimental results by Kuramoto and Nishiyama [41], four mechanisms for beam-through type joint shear resistance are shown in Figures 10(a)–10(d). From Figures 10(a) and 10(b), the stress transferring mechanisms consisted of steel web panel, concrete diagonal strut, and concrete horizontal strut in the joint. The steel web panel mechanism and concrete diagonal strut mechanism formed in the inner element are similar with those of the beam-through type joint. The concrete horizontal strut mechanism which transferred the concrete compressive stresses through the inner element to the outer element included concrete horizontal strut-1 and concrete horizontal strut-2. The first one formed the concrete horizontal struts to mobilize compressive stresses from steel beam flanges to FBPs in the outer panel (Figure 10(c)). Additionally, the second concrete horizontal strut mechanism was developed between the intersection point of the web panels in the core area of joints and the corner of cover plates and then mobilized the outer diagonal concrete struts, cover plates, and the bond stresses between reinforcing bars in the joint to contribute the shear capacity.Figure 10
Mechanisms for beam-through type joint shear resistance [41]: (a) steel web panel, (b) concrete diagonal strut, (c) concrete horizontal strut-1, and (d) concrete horizontal strut-2.
(a)(b)(c)(d)


## 3.2.1. Beam-Through Type Joint

As shown in Figure8, force transfer mechanisms of the beam-through type RCS joint with the proper details indicated that the effective joint region consisted of the inner element and outer element to meet the bearing capacity and compatibility of deformation. The width of FBPs, E-FBPs, steel flange, and studs determined that of inner element and the details of band plates, cover plates, and small steel column affected the outer element width in the joint, respectively. Based on the damage features of the experimental and finite element models results [1, 2, 7, 16, 18], the load resistance mechanisms for joint shear capacity in the beam-through RCS joints is generally provided by three mechanisms: steel web panel, inner concrete diagonal strut, and outer concrete compression field, as shown in Figure 9. In the RCS joints, the behavior of the steel web panel similar to that, in the steel frames is idealized as carrying pure shear stress over a portion of the joint region, as shown in Figure 9(a), which is dependent on the location and distribution of vertical bearing stresses. The inner concrete diagonal strut in the inner element region is activated by squeezing the concrete between the steel beam flanges and FBPs or E-FBPs welded the steel beam flanges, as shown in Figure 9(b), which is similar to the mechanism model to resist shear in reinforced concrete connections. In general, the outer concrete compression field is composed of several compression struts since horizontal reinforcements which welded the steel web form a truss mechanism in the joint region (Figure 9(c)), which was often used for establishing the shear model in reinforced concrete beams. In addition, the concrete horizontal strut is developed in the region of column concrete outside the steel beam flanges (Figure 9(d)). Since shear force is transferred horizontally from the beam flanges into the compression field due to the joint details of the embedded small steel column, stiffeners extended above and below the steel beam, shear studs, or reinforcements welded to the beam flanges. The research results [1, 51] indicated that the sum of the contributions of the steel web and inner concrete strut is approximately 60% for the shear strength of RCS joints and that of the outer concrete compression filed is approximately 40%, respectively. Certainly, shear capacity of the outer element in the joint region could decrease because the difference depends on the absence of strengthening joint details to mobilize the shear mechanism of the outer panel.Figure 9
Mechanisms for beam-through type joint shear resistance: (a) steel web panel, (b) inner concrete diagonal strut, (c) outer concrete compression field, and (d) concrete horizontal strut.
(a)(b)(c)(d)


## 3.2.2. Column-Through Type Joint

As mentioned before (see in Figure5), the details of column-through type joint generally include cover plates, orthogonal steel web, and diaphragm to keep the longitudinal reinforcement through the connection to simplify constructability; at the same time, the joint details also guarantee stress transferring mechanisms for composite reinforced concrete and steel joint. According to the experimental results by Kuramoto and Nishiyama [41], four mechanisms for beam-through type joint shear resistance are shown in Figures 10(a)–10(d). From Figures 10(a) and 10(b), the stress transferring mechanisms consisted of steel web panel, concrete diagonal strut, and concrete horizontal strut in the joint. The steel web panel mechanism and concrete diagonal strut mechanism formed in the inner element are similar with those of the beam-through type joint. The concrete horizontal strut mechanism which transferred the concrete compressive stresses through the inner element to the outer element included concrete horizontal strut-1 and concrete horizontal strut-2. The first one formed the concrete horizontal struts to mobilize compressive stresses from steel beam flanges to FBPs in the outer panel (Figure 10(c)). Additionally, the second concrete horizontal strut mechanism was developed between the intersection point of the web panels in the core area of joints and the corner of cover plates and then mobilized the outer diagonal concrete struts, cover plates, and the bond stresses between reinforcing bars in the joint to contribute the shear capacity.Figure 10
Mechanisms for beam-through type joint shear resistance [41]: (a) steel web panel, (b) concrete diagonal strut, (c) concrete horizontal strut-1, and (d) concrete horizontal strut-2.
(a)(b)(c)(d)


## 4. Calculation Mechanism of the RCS Joint Shear Capacity

The RCS joints subjected to large shear forces under seismic loads usually play a major role in the ultimate limit state of the capacity of whole frame structure. Therefore, the calculation of joint shear capacity is an essential step in seismic design. Based on experimental and theoretical analysis, the shear capacity calculation formulas were recommended from the different countries standards and many researchers, e.g., the American standard of ASCE, the Japanese standard of AIJ, and the Chinese standard of JGJ 138-2016, those of which indicated a noticeable difference to apply the seismic design. The design guidelines of the shear model were derived from two alternative seismic design approaches, namely, the strength-based capacity design procedure and deformation-based capacity design procedure. This section systematically reviews the state of the art in the calculation formula and discusses the contribution of the various components of the joint region to the shear capacity of the RCS joint. Additionally, a comparison between the outputs of the models was also conducted.


### 4.1. American Calculation Methods

To learn about the behavior of the RCS joint, Sheikh et al. [7] performed a series of tests on 15 two-thirds scale specimens under monotonic and cyclic loading. The results have shown that the internal shear mechanisms and modes of failure governed the joint strength, and significant strength increases were achieved using straightforward details, such as FBPs, small steel column, and shear studs. Based on the tested results, Deierlein et al. [46] recommended a design model to calculate the nominal strength of the interior composite beam-column joints. It is worth mentioning that the model provides the calculated nominal joint strength corresponding to measure values at 1% joint distortion. Based on the distinct failure modes and stress transfer mechanisms between an inner and outer elements of the RCS joint, the model recognized that the joint behavior is characterized. Additionally, the American standard of ASCE [47] presented the guidelines for composite beam-column connection design according to the joint shear strength mechanic model mainly proposed by Deierlein et al. [46], as shown in Figure 9. The shear resistance model consists of steel web panel, inner diagonal concrete strut, and outer strut concrete compression filed, and the model for calculating the horizontal shear strength of the interior joint is given as follows:(2)Vj=0.6Fysptspjh+1.7fc′bph+0.4fc′boh+0.9AshFyshhsh,where Vj is suitable for calculating the shear capacity of interior composite joint, Fysp and tsp are the yield strength and thickness of the steel panel, jh is the effective web panel length associated with the external load imposed on the joint, fc′ is the concrete compressive strength (MPa), bp and bo are the FBPs width (inner element) and the effective width of outer concrete panel (out element), h is the depth of concrete column measured parallel to beam, Ash is the cross-sectional area of reinforcing bars in each layer spaced at sh through the beam depth, and Fysh is the yield strength of the stirrups. In addition, to achieve the strong-joint weak-component criterion, the details of E-FBPs or band plates rather than only installing the FBPs in the joints should be used to attain the full plastic hinge of the steel beam ends since the local concrete crushing would cause the unexpected joint-beam mixed failure [1]. However, the shear model was primarily based on experimental results obtained from testing of interior connections, and the accuracy of such design to calculate the strength of exterior and top RCS subassemblies still remained skeptical. The design provisions of connections in RCS frames was only suitable for use in low to moderate seismic risk zones.Kanno [13] performed tests on composite RCS subassemblies to evaluate the failure models, the detail features, and bearing strength. Based on those tested datum and the ASCE specification [14], the shear model conducted by Kanno and Deierlein [51] were used for those as follows: (1) address unique failure modes and stress transfer mechanisms in the interior joints and (2) extend the precious model to consider a broader set of connection details. To recognize the possibility of shear failure and bond failure in the outer element simultaneously with vertical bearing failure in the inner panel, the revised strength model for the through-beam joints was proposed. This shear model presented the significant difference between the failure of the inner element and the overall joint. The shear calculation model consisting of the strength of inner and outer elements is calculated as follows:(3)Vj=minVswe,Vbe+minVscf,Vb0,Vswe=Fysp3tsp0.8h+1.65fc′bih,Vbe=0.47fc′bih+FyAy,Vscf=AshFysh0.9hsh+1.05fc′bih≤1.65fc′bih,Vbo=1.16fc′φbxmr,where Vswe and Vbe are the panel shear and vertical bearing strengths of the inner element, Vbo and Vscf are the strengths of the outer elements failing in bond and shear, respectively, bi is equal to the width of the inner element corresponding to the maximum widths of FBPs (bp) and steel flange (bf) in Figure 9, Fy and Ay is the yield strength and total area of vertical reinforcements welded the steel beam flanges, respectively, φb is the total perimeter length of one set of the reinforcing bars in the joint, and xmr is the center distance of vertical column reinforcement. Compared with that of the ASCE guidelines [47], the revised shear model modified to be better account for the joint failure model was applicable for joint details, such as transverse beams and tie reinforcement within the joint. The minimum requirements of the tie reinforcement might be relaxed to reduce the contribution of shear strength. To ensure adequate deformation capability and toughness necessary for seismic design, the tie requirements, joint geometries, and strength resistance factors of the composite RCS joints were needed to further be studied.To accurately predict the shear strength of exterior joints using the ASCE design guidelines, a new model to predict the shear force and stirrup and concrete strains at any level of shear distortion in the beam-through RCS joints was presented by Parra-Montesinos and Wight [52]. Based on the joint shear deformation level of 1.2% corresponding to moderate damage and significant damage, the ultimate shear strength of exterior and interior RCS connections would be calculated for use in zones of high seismicity. The model presented herein all the three mechanisms discussed previously (see in Figure 9) according to different details and contribution of the inner and outer concrete strut in the joint. The mechanic model of shear capacity similarly to that of ASCE [47] is given as(4)Vj=kwFysptsph3+kifc′−0.0048fc′+1.13k1k2hbf−tsp+kofc′−0.0048fc′+1.13k1k2k3hbo,where kw is 0.9 and 0.8 for interior and exterior joints, respectively; ki and ko are strength factors of 0.21, 0.34, 0.32, and 0.16 for interior and exterior joints, respectively; bf is the width of the beam flange. k1, k2, and k3 listed in Table 1 are strength factors. However, the three types of confinement which consisted of U-shaped stirrups, steel band plate, and cover plate were considered in this model and other details in the joint, such as small column and shear studs, were not contributed.Table 1
k1, k2, and k3 factors [52].
FactorInterior jointExterior jointJoint detailsk11.01.0FBPs and hoops1.21.1FBPs and SBP1.41.2FBPs, SBP and hoops or SCPk21.0/1.51.0/1.5No transverse beams or transverse beamsk31.11.1FBPs and hoops1.3/1.51.3/1.5SBP or hoops and SBP2.02.0SCPNote. SBP = steel band plate; SCP = steel cover plate.According to the tested results of the beam-through RCS roof levelT-connections with details of FBPs and steel band plates, ultimate horizontal joint shear strength was given by the contributions from the steel web panel and the inner and outer diagonal strut [29]. The shear force versus shear distortion envelope responses of the RCS roof T-connections referred to that of Parra-Montesinos et al. [22]. The shear strength equation can be can be determined as follows:(5)Vj=0.8Fysp3tsph+0.29fc′−0.0048fc′+1.13hbf−tw+0.5fc′−0.0048fc′+1.13hbo,where bf is the width of steel beam flange, bo is the outer panel width, bo = 12tbp, and tbp is the thickness of the steel band plate. However, it should be pointed out that the applicable scope of this shear design equation is small as it depends on the scope of the experimental data, and the predicted shear strength of the joint is questionable due to severe bond stress degradation experienced by the column longitudinal bars.


### 4.2. Japanese Calculation Method

Based on a large number of the interior beam-through type and column-through type joints from the analytical studies and the Japanese standard of AIJ [53], the proposed shear design equation of RCS joints is given by Nishiyama et al. [43]. A comparison of the shear resistance mechanisms in the joint between the ASCE [47] and Nishiyama et al. [43] indicates that the ultimate shear strength consisted of steel web panel, cover plates, transverse reinforcement, and concrete compression in the joint region. The failure mechanism of the RCS subassemblies followed the weak beam-strong column criterion based on the working stress design method. The model for calculating the horizontal shear strength is given as(6)Qp=c1Awσwy3+0.5Afσfy3+0.25pwσrybcdmc+0.04c2c3bcσBδjDc,where Aw and Af are sectional area of steel web and cover plates, σwy, σfy, and σry are the yield stress of steel web, cover plates, and transverse reinforcement, respectively, Pw is the transverse reinforcement ratio in the joint region, bc and Dc are the width and depth of the column, dmc is the maximum distance between tensile and compressive reinforcement, σB is the concrete compressive strength in the joint region, δj is a shape factor with values of the interior, exterior and top-interior, and top-corner joints being 3.0, 2.0, and 1.0, respectively, and c1, c2, and c3 are factors depending on the details of the RCS joints (see in Figure 5), as shown in Table 2. Compared to other shear models originated from the ASCE guideline [47], the proposed shear mode is suitable for the column-through type RCS joints to focus on the contribution of the cover pates and transverse reinforcement. Besides, the difference between the concrete damage mechanism and stress transferring mechanism predicted that joint shear strength was obvious. The web panel mechanism consists of a steel web panel and transfers shear stresses from steel beam flanges and RC columns (see in (6)). The concrete mechanisms included the concrete horizontal strut and diagonal strut mechanism, which were considered in (6) according to the different details at the RCS joints.Table 2
Detail coefficients [43].
FactorsCoefficientDetail of jointc10.8With neither FBP nor cover plates0.9With stirrups, FBP, or cover platec20.8With neither FBP nor cover plate1.0With stirrups, FBP, or cover plates1.1Extended FBP or steel column and interior band plates1.5Exterior band plate, FBP and vertical reinforcement, and transverse stiffeners1.6Diaphragms, wide FBP, and transverse stiffenersc30.9Without transverse beam1.0Transverse beamBased on the similar shear resistance mechanisms of the ASCE [47] and AIJ [53] specifications, Choi et al. [6] proposed a new shear model to consider the contribution of detailed effect of shear keys, E-FBPs, transverse beams, and cover plates in the interior RCS joints. The calculation method for the shear capacity of the RCS joints can be given as(7)Vj=Vs+Vn++Vn′+Vcp,Vs=Fysptspjh3,Vn=1.65fc′bph,Vn′=1.05fc′boh+0.9hAsh.Fyshsh,Vcp=2αFyc3tc,where Vs, Vn, Vn’, and Vcp are the shear strength of steel beam web, inner element concrete, outer element external concrete, and cover plate, respectively, α is the strength coefficient, and Fyc and tc are the thickness and yield stress of cover plate. The test results indicated that the recommended formulas are suitable to evaluate the shear strength for the interior RCS connections. Compared with other models, the proposed equation focused on the mobilization coefficients for beam-column connections and the shear contribution of the cover plates. Additionally, the confining effect of the outer element concrete in the joint by the detail of cover plates was also considered to fully understand the load transfer mechanism [49].


### 4.3. Chinese Calculation Methods

The formula for the shear capacity of steel reinforced concrete column-steel beam joints is specified by the Chinese standard for design of composite structures (JGJ 138-2016) [54]. This type of the joints can be regarded as a special case of the interior beam-through type RCS joint, which presented the small steel column as a detail that is embedded in the concrete column. Compared with that of the ASCE guideline [47], the concrete resistance mechanism of the proposed shear model in the joint ignored the contribution of outer concrete compression field to easily calculate the seismic design. The model is given by(8)Vj=0.58Fysptsphw+1.8ϕjftbjhj+FyshAshh0−as′sh,where hw is the height of steel web, ft is concrete axis tensile strength (MPa), ϕj is a shape factor, and the values are taken to be 1.0, 0.6, and 0.3 for the interior joints, exterior and top-interior joints, and top-corner joints, respectively, bj is the effective joint length, which is equal to half the width of column, hj is the column depth, h0 is the distance between the resultant force of the tension flange and longitudinal tension reinforcement to the compression edge of the concrete section, and as′ is the concrete cover in the column. This specified shear model was applicable for the calculation of the shear capacity of joints at different locations and joint types in the frame. Besides, the design formulas considered the details of cover plates, band plates, and stirrups in the joint. However, the calculated values of Chinese standard of JGJ 138-2016 [54] does not take into consideration the impact of the axial pressure in the RC column to meet the structural safety in engineering practice.To evaluate the shear capacity considering the effect of axial compression ratio and RC slab width, Chu et al. [19] performed tests on six interior column-steel beam joints with or without RC slabs. The results presented that the details of X-reinforcement at the joint had little effect on the shear capacity and the width and thickness of the RC slab might obviously increase the shear strength. At the same time, the RCS joint with the higher axial compression ratio showed a slight increase in the shear capacity. However, the existing shear equations as mentioned before did not consider the effect of the RC slab on the shear capacity, which can facilitate to achieve the ideal shear failure mode in the joint with the RC slab in engineering practical. Therefore, the shear model for calculating the shear capacity of the RCS joints with the RC slab was proposed according to the Chinese standard of JGJ 138-2016 [54]. The shear formula can be obtained through the experimental results and finite element simulation as follows:(9)Vj=Fysptsphw3+1.8αϕjftbjhj+FyshAshh0−as′sh,α=0.232bs+8.38hs+2.272,where αj is the influence coefficient of the RC slab and bs and hs are the width and height of the RC slab, respectively. The proposed formula calculated values agreed well with the experimental values to provide a reference for the RCS composite system in the seismic design. However, the calculating accuracy of shear formulas for the RCS joint with the RC slab was further studied due to the limitations of the experimental specimens and finite element simulation conditions.


## 4.1. American Calculation Methods

To learn about the behavior of the RCS joint, Sheikh et al. [7] performed a series of tests on 15 two-thirds scale specimens under monotonic and cyclic loading. The results have shown that the internal shear mechanisms and modes of failure governed the joint strength, and significant strength increases were achieved using straightforward details, such as FBPs, small steel column, and shear studs. Based on the tested results, Deierlein et al. [46] recommended a design model to calculate the nominal strength of the interior composite beam-column joints. It is worth mentioning that the model provides the calculated nominal joint strength corresponding to measure values at 1% joint distortion. Based on the distinct failure modes and stress transfer mechanisms between an inner and outer elements of the RCS joint, the model recognized that the joint behavior is characterized. Additionally, the American standard of ASCE [47] presented the guidelines for composite beam-column connection design according to the joint shear strength mechanic model mainly proposed by Deierlein et al. [46], as shown in Figure 9. The shear resistance model consists of steel web panel, inner diagonal concrete strut, and outer strut concrete compression filed, and the model for calculating the horizontal shear strength of the interior joint is given as follows:(2)Vj=0.6Fysptspjh+1.7fc′bph+0.4fc′boh+0.9AshFyshhsh,where Vj is suitable for calculating the shear capacity of interior composite joint, Fysp and tsp are the yield strength and thickness of the steel panel, jh is the effective web panel length associated with the external load imposed on the joint, fc′ is the concrete compressive strength (MPa), bp and bo are the FBPs width (inner element) and the effective width of outer concrete panel (out element), h is the depth of concrete column measured parallel to beam, Ash is the cross-sectional area of reinforcing bars in each layer spaced at sh through the beam depth, and Fysh is the yield strength of the stirrups. In addition, to achieve the strong-joint weak-component criterion, the details of E-FBPs or band plates rather than only installing the FBPs in the joints should be used to attain the full plastic hinge of the steel beam ends since the local concrete crushing would cause the unexpected joint-beam mixed failure [1]. However, the shear model was primarily based on experimental results obtained from testing of interior connections, and the accuracy of such design to calculate the strength of exterior and top RCS subassemblies still remained skeptical. The design provisions of connections in RCS frames was only suitable for use in low to moderate seismic risk zones.Kanno [13] performed tests on composite RCS subassemblies to evaluate the failure models, the detail features, and bearing strength. Based on those tested datum and the ASCE specification [14], the shear model conducted by Kanno and Deierlein [51] were used for those as follows: (1) address unique failure modes and stress transfer mechanisms in the interior joints and (2) extend the precious model to consider a broader set of connection details. To recognize the possibility of shear failure and bond failure in the outer element simultaneously with vertical bearing failure in the inner panel, the revised strength model for the through-beam joints was proposed. This shear model presented the significant difference between the failure of the inner element and the overall joint. The shear calculation model consisting of the strength of inner and outer elements is calculated as follows:(3)Vj=minVswe,Vbe+minVscf,Vb0,Vswe=Fysp3tsp0.8h+1.65fc′bih,Vbe=0.47fc′bih+FyAy,Vscf=AshFysh0.9hsh+1.05fc′bih≤1.65fc′bih,Vbo=1.16fc′φbxmr,where Vswe and Vbe are the panel shear and vertical bearing strengths of the inner element, Vbo and Vscf are the strengths of the outer elements failing in bond and shear, respectively, bi is equal to the width of the inner element corresponding to the maximum widths of FBPs (bp) and steel flange (bf) in Figure 9, Fy and Ay is the yield strength and total area of vertical reinforcements welded the steel beam flanges, respectively, φb is the total perimeter length of one set of the reinforcing bars in the joint, and xmr is the center distance of vertical column reinforcement. Compared with that of the ASCE guidelines [47], the revised shear model modified to be better account for the joint failure model was applicable for joint details, such as transverse beams and tie reinforcement within the joint. The minimum requirements of the tie reinforcement might be relaxed to reduce the contribution of shear strength. To ensure adequate deformation capability and toughness necessary for seismic design, the tie requirements, joint geometries, and strength resistance factors of the composite RCS joints were needed to further be studied.To accurately predict the shear strength of exterior joints using the ASCE design guidelines, a new model to predict the shear force and stirrup and concrete strains at any level of shear distortion in the beam-through RCS joints was presented by Parra-Montesinos and Wight [52]. Based on the joint shear deformation level of 1.2% corresponding to moderate damage and significant damage, the ultimate shear strength of exterior and interior RCS connections would be calculated for use in zones of high seismicity. The model presented herein all the three mechanisms discussed previously (see in Figure 9) according to different details and contribution of the inner and outer concrete strut in the joint. The mechanic model of shear capacity similarly to that of ASCE [47] is given as(4)Vj=kwFysptsph3+kifc′−0.0048fc′+1.13k1k2hbf−tsp+kofc′−0.0048fc′+1.13k1k2k3hbo,where kw is 0.9 and 0.8 for interior and exterior joints, respectively; ki and ko are strength factors of 0.21, 0.34, 0.32, and 0.16 for interior and exterior joints, respectively; bf is the width of the beam flange. k1, k2, and k3 listed in Table 1 are strength factors. However, the three types of confinement which consisted of U-shaped stirrups, steel band plate, and cover plate were considered in this model and other details in the joint, such as small column and shear studs, were not contributed.Table 1
k1, k2, and k3 factors [52].
FactorInterior jointExterior jointJoint detailsk11.01.0FBPs and hoops1.21.1FBPs and SBP1.41.2FBPs, SBP and hoops or SCPk21.0/1.51.0/1.5No transverse beams or transverse beamsk31.11.1FBPs and hoops1.3/1.51.3/1.5SBP or hoops and SBP2.02.0SCPNote. SBP = steel band plate; SCP = steel cover plate.According to the tested results of the beam-through RCS roof levelT-connections with details of FBPs and steel band plates, ultimate horizontal joint shear strength was given by the contributions from the steel web panel and the inner and outer diagonal strut [29]. The shear force versus shear distortion envelope responses of the RCS roof T-connections referred to that of Parra-Montesinos et al. [22]. The shear strength equation can be can be determined as follows:(5)Vj=0.8Fysp3tsph+0.29fc′−0.0048fc′+1.13hbf−tw+0.5fc′−0.0048fc′+1.13hbo,where bf is the width of steel beam flange, bo is the outer panel width, bo = 12tbp, and tbp is the thickness of the steel band plate. However, it should be pointed out that the applicable scope of this shear design equation is small as it depends on the scope of the experimental data, and the predicted shear strength of the joint is questionable due to severe bond stress degradation experienced by the column longitudinal bars.


## 4.2. Japanese Calculation Method

Based on a large number of the interior beam-through type and column-through type joints from the analytical studies and the Japanese standard of AIJ [53], the proposed shear design equation of RCS joints is given by Nishiyama et al. [43]. A comparison of the shear resistance mechanisms in the joint between the ASCE [47] and Nishiyama et al. [43] indicates that the ultimate shear strength consisted of steel web panel, cover plates, transverse reinforcement, and concrete compression in the joint region. The failure mechanism of the RCS subassemblies followed the weak beam-strong column criterion based on the working stress design method. The model for calculating the horizontal shear strength is given as(6)Qp=c1Awσwy3+0.5Afσfy3+0.25pwσrybcdmc+0.04c2c3bcσBδjDc,where Aw and Af are sectional area of steel web and cover plates, σwy, σfy, and σry are the yield stress of steel web, cover plates, and transverse reinforcement, respectively, Pw is the transverse reinforcement ratio in the joint region, bc and Dc are the width and depth of the column, dmc is the maximum distance between tensile and compressive reinforcement, σB is the concrete compressive strength in the joint region, δj is a shape factor with values of the interior, exterior and top-interior, and top-corner joints being 3.0, 2.0, and 1.0, respectively, and c1, c2, and c3 are factors depending on the details of the RCS joints (see in Figure 5), as shown in Table 2. Compared to other shear models originated from the ASCE guideline [47], the proposed shear mode is suitable for the column-through type RCS joints to focus on the contribution of the cover pates and transverse reinforcement. Besides, the difference between the concrete damage mechanism and stress transferring mechanism predicted that joint shear strength was obvious. The web panel mechanism consists of a steel web panel and transfers shear stresses from steel beam flanges and RC columns (see in (6)). The concrete mechanisms included the concrete horizontal strut and diagonal strut mechanism, which were considered in (6) according to the different details at the RCS joints.Table 2
Detail coefficients [43].
FactorsCoefficientDetail of jointc10.8With neither FBP nor cover plates0.9With stirrups, FBP, or cover platec20.8With neither FBP nor cover plate1.0With stirrups, FBP, or cover plates1.1Extended FBP or steel column and interior band plates1.5Exterior band plate, FBP and vertical reinforcement, and transverse stiffeners1.6Diaphragms, wide FBP, and transverse stiffenersc30.9Without transverse beam1.0Transverse beamBased on the similar shear resistance mechanisms of the ASCE [47] and AIJ [53] specifications, Choi et al. [6] proposed a new shear model to consider the contribution of detailed effect of shear keys, E-FBPs, transverse beams, and cover plates in the interior RCS joints. The calculation method for the shear capacity of the RCS joints can be given as(7)Vj=Vs+Vn++Vn′+Vcp,Vs=Fysptspjh3,Vn=1.65fc′bph,Vn′=1.05fc′boh+0.9hAsh.Fyshsh,Vcp=2αFyc3tc,where Vs, Vn, Vn’, and Vcp are the shear strength of steel beam web, inner element concrete, outer element external concrete, and cover plate, respectively, α is the strength coefficient, and Fyc and tc are the thickness and yield stress of cover plate. The test results indicated that the recommended formulas are suitable to evaluate the shear strength for the interior RCS connections. Compared with other models, the proposed equation focused on the mobilization coefficients for beam-column connections and the shear contribution of the cover plates. Additionally, the confining effect of the outer element concrete in the joint by the detail of cover plates was also considered to fully understand the load transfer mechanism [49].


## 4.3. Chinese Calculation Methods

The formula for the shear capacity of steel reinforced concrete column-steel beam joints is specified by the Chinese standard for design of composite structures (JGJ 138-2016) [54]. This type of the joints can be regarded as a special case of the interior beam-through type RCS joint, which presented the small steel column as a detail that is embedded in the concrete column. Compared with that of the ASCE guideline [47], the concrete resistance mechanism of the proposed shear model in the joint ignored the contribution of outer concrete compression field to easily calculate the seismic design. The model is given by(8)Vj=0.58Fysptsphw+1.8ϕjftbjhj+FyshAshh0−as′sh,where hw is the height of steel web, ft is concrete axis tensile strength (MPa), ϕj is a shape factor, and the values are taken to be 1.0, 0.6, and 0.3 for the interior joints, exterior and top-interior joints, and top-corner joints, respectively, bj is the effective joint length, which is equal to half the width of column, hj is the column depth, h0 is the distance between the resultant force of the tension flange and longitudinal tension reinforcement to the compression edge of the concrete section, and as′ is the concrete cover in the column. This specified shear model was applicable for the calculation of the shear capacity of joints at different locations and joint types in the frame. Besides, the design formulas considered the details of cover plates, band plates, and stirrups in the joint. However, the calculated values of Chinese standard of JGJ 138-2016 [54] does not take into consideration the impact of the axial pressure in the RC column to meet the structural safety in engineering practice.To evaluate the shear capacity considering the effect of axial compression ratio and RC slab width, Chu et al. [19] performed tests on six interior column-steel beam joints with or without RC slabs. The results presented that the details of X-reinforcement at the joint had little effect on the shear capacity and the width and thickness of the RC slab might obviously increase the shear strength. At the same time, the RCS joint with the higher axial compression ratio showed a slight increase in the shear capacity. However, the existing shear equations as mentioned before did not consider the effect of the RC slab on the shear capacity, which can facilitate to achieve the ideal shear failure mode in the joint with the RC slab in engineering practical. Therefore, the shear model for calculating the shear capacity of the RCS joints with the RC slab was proposed according to the Chinese standard of JGJ 138-2016 [54]. The shear formula can be obtained through the experimental results and finite element simulation as follows:(9)Vj=Fysptsphw3+1.8αϕjftbjhj+FyshAshh0−as′sh,α=0.232bs+8.38hs+2.272,where αj is the influence coefficient of the RC slab and bs and hs are the width and height of the RC slab, respectively. The proposed formula calculated values agreed well with the experimental values to provide a reference for the RCS composite system in the seismic design. However, the calculating accuracy of shear formulas for the RCS joint with the RC slab was further studied due to the limitations of the experimental specimens and finite element simulation conditions.


## 5. Summary and Conclusions

Hybrid reinforced concrete columns (RC) and steel beams (S) moment frame structures have gained popularity in seismic risk regions due to their effective combination of the advantages of the two structural members during the past several decades. Correspondingly, a significant amount of research studies on the performance and design approaches or guidelines of the RCS joints and whole frames have been conducted by the scholars and engineers. This study has summarized representative recent research projects focusing on shear capacity of the RCS joints: configuration features, failure models, mechanisms for joint shear resistance, and calculation formulas. According to the different detail features and design approaches of the RCS joints, the four typical failure models consisted of panel shear failure, vertical bearing failure, local shear failure, and joint-beam mixed failure. For the beam-through type RCS joints, three mechanisms for joint shear resistance include steel web panel, inner concrete diagonal strut, and outer concrete compression field. The only difference compared with those of the beam-through type joints is the concrete horizontal strut mechanism due to the details of the cover plates and diaphragms. Finally, the guidelines and recommendations of shear calculation formulas were recommended from the different countries standards and many researchers to provide a reference for the designers and the researchers. The limitations of this research include that (1)the types of joint details focused on the typical forms and other details, such as X-reinforcement, shear key, and PC stud, were less involved and (2) the standards and recommendations of shear capacity calculation mainly concentrated on those of American, Japanese, and Chinese origin.However, from the existing research results of the RCS joints or moment frames, the specific research studies on the seismic design provisions of the RCS joints or moment frames still developed in the future include those as follows:(i)
The number of tests on three dimensional joints with the orthogonal beams and composite slab to be consistent with the engineering practice was limited. In addition, the local shear failure and joint-beam mixed failure of the RCS joints are needed for further study.(ii)
The finite element analysis on behavior of the RCS joints should be further enhanced due to the restrictions of laboratory, test equipment, specimen number, and economic reasons. Finite element analysis can be used as an effective mean to provide a comprehensive and objective understanding of the shear calculation mechanisms, which is needed to be studied further.(iii)
Because of the test and theoretical study on the RCS structure systems are mainly the composite joints, the number of quasi-static, pseudo-dynamic, and shaking table test of RCS frames will be likely to be considered for future study.(iv)
To improve the seismic performance and achieve rapid return to occupancy under predetermined levels of lateral load, the novel damage installations in the RCS joints or whole frame systems consisting of rocking devices, replaceable members, and self-centering mechanisms were developed; at the same time, the application and research of the relevant damage characteristics and design guidelines of performance based design method were also evaluated.



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*Source: 4626392-2022-11-09.xml*