Seismic Performance of Embedded Connections for Precast Hybrid Coupled Wall Systems: Experimental Study and Theoretical Analysis

Abstract

The novel precast hybrid coupled wall structure system considers convenience requirements for the production and construction of prefabricated components. In this study, to determine the ultimate shear strength of embedded beam-to-wall connections, four full-scale specimens were meticulously designed using the “weak connections and strong components” methodology. Under low-cycle loading on a coupling steel beam, the experimental results indicated that the shear strength of the specimen was approximately twice that predicted by the Mattock–Gaafar mechanical model employed in Seismic Provisions for Structural Steel Buildings (ANSI/AISC 341-16). Therefore, a mechanical model was established to analyze the force transfer between the steel beam and concrete wall. Finally, design formulas for the shear strength were proposed, in addition to corresponding suggestions for construction reinforcement in the embedded area and adjacent zones.

1. Introduction

The hybrid coupled wall is a significant topic of research in the fifth-phase seismic research project, which was conducted by the 5th Joint Technical Coordinating Committee (JTCC) of the United States of America (US)–Japan Cooperation Program. Recently, numerous experimental and theoretical studies were conducted on structural systems and joint structures of hybrid coupled walls and have yielded promising results [1,2,3,4,5,6]. Research revealed that, compared with traditional reinforced concrete (RC) coupled shear walls, steel coupling beams in hybrid coupled wall systems leverage the working mechanism of the eccentrically braced energy-dissipating beam section to provide two advantages. First, the structure demonstrates favorable seismic performances, as it enters the elastic–plastic stage without significant degradation of the wall strength, stiffness, and energy dissipation capacity. Second, the structures can be readily repaired because seismic energy is absorbed by steel coupling beams instead of concrete shear walls, thus effectively reducing the development of cracks at the bottom of the walls. Numerous attempts have been made to enhance and investigate the seismic performance of hybrid coupled wall systems [7,8,9,10].

To promote the application of hybrid coupled wall systems in construction, in 2010, the Composite Structure Committee under the American Society of Civil Engineers (ASCE) systematically summarized the seismic design theory of hybrid coupled wall systems. Furthermore, the Recommendations for Seismic Design of Hybrid Coupled Wall Systems (RHCWS) [11] was published. The American Institute of Steel Construction (AISC) specified the structural and connection design of hybrid coupled walls in ANSI/AISC 341-16 [12]. The connection methods used for steel coupling beams and concrete shear walls primarily include an end plate, post-tensioning, steel-edge member-steel coupling beam, and embedded joints. Among these, the most common connection form in hybrid coupled wall structure systems is the embedded joint, which can effectively transmit the bending moment between the steel coupling beam and concrete wall due to its higher stiffness [13]. However, the structural complexity of the embedded connections between the steel coupling beam and shear wall hindered the widespread adoption of hybrid coupled wall systems.

Numerous improvements were made for the popularization and application of this structural system. One such approach involves simplifying the structure of embedded connections by precasting the shear wall with a steel beam in a factory to form a wall assembly unit (Figure 1). Briefly, at the construction site, the units are spliced to create a structural system. When a concrete wall does not require openings for doors or windows, adjacent embedded steel beams can be joined directly, and hollow blocks can be used to fill the lower vertical spaces. Alternatively, adjacent embedded steel beam sections can be connected to the steel coupling beams to meet the architectural requirements for doors or windows (Figure 2). This results in a novel structural system with a favorable seismic performance: the precast hybrid coupled wall structural system [14,15], as shown in Figure 3. Compared with an ordinary shear wall, a precast coupled wall has the following advantages:

(1) A longer wall can be split into several shorter walls of standard length, thus improving the standardization of precast components, which requires less utilization of the formwork and reduces the cost of a single precast wall.

(2) Vertical assembly wall units are connected by dry connections instead of traditional concrete cast-in-place connections, which improves the construction efficiency and reduces project costs.

In this study, the connection configuration of steel beams embedded in concrete walls for precast hybrid coupled wall systems was studied based on previous research results, considering the convenient requirements of production in factories and installation at construction sites. The transfer mechanism between steel beams and shear walls at the connections was studied by conducting four full-scale seismic performance tests. Finally, a design formula for the connection shear strength of was proposed, in addition to construction requirements. The remainder of this paper is organized as follows. Section 2 describes the specimen design and material characteristics. Section 3 presents the experimental procedure. Section 4 presents an analysis of the experimental results, including a description of the crack pattern, hysteresis response, stiffness characteristics, and strain distribution. Based on the aforementioned analysis, Section 5 proposes a mechanical model based on the test results, and Section 6 provides relevant design recommendations. Finally, Section 7 presents the conclusions of the study.

2. Specimen Design and Fabrication

2.1. Prototype Structure

The prototype structure had a total height of 52.2 m, including 1 basement floor and 18 stories aboveground. Each floor aboveground had a height of 2.9 m. The length of the coupling beam was 900 mm, and the thickness of the wall was 250 mm. In this study, the design process was in accordance with a performance-based approach, wherein the steel coupling beam was designed based on the requirements of the eccentrically braced energy-dissipating beam section in ANSI/AISC 341-16.

2.2. Specimens Design

Based on the requirements of RHCWS and ANSI/AISC 341-16, four full-scale joint-failure (JF) series specimens were designed and improved to satisfy the requirements of fabrication, transportation, and installation. In practical applications, the embedded steel beam and steel coupling beam are spliced using a screw connection, as shown in Figure 2. The main focus of this research was joint failure. The connection between the embedded steel beam and the steel beam had no influence on the test results. Therefore, the entire steel beam was used to facilitate processing.

Half of the specimens served as research objects, and featured a wall length, height, and thickness of 1600 mm, 2900 mm, and 250 mm, respectively, whereas the length of the steel coupling beam was 450 mm. The research specimen shown in Figure 3, which is surrounded by dotted lines, included the upper precast wall, cast-in-place concrete part, steel coupling beam, and lower precast wall. In contrast to the structural design concept of “strong connections and weak components” employed in traditional construction, the JF series specimens adopted the concept of “weak connections and strong components” to obtain the ultimate shear strength and stress mechanism of the connections. Specifically, when the concrete stress in the connection area reached its ultimate strength, the steel coupling beam remained in an elastic or nearly elastic state.

The steel coupling beam section size of the JF series of specimens was H350 × b × 8 × 16 mm. The ratio of the shear wall thickness, t, to the steel coupling beam flange width, b, is an essential factor that influences the connection shear strength. Therefore, the flange widths of the steel coupling beams in specimens JF-S1, JF-S2, and JF-S3 were set to 100 mm, 120 mm, and 140 mm, respectively, as shown in Figure 4. The embedded length of the steel coupling beams in the JF series of specimens was 435 mm. Since the connection shear strength did not consider the beneficial effects of the auxiliary reinforcement, no auxiliary reinforcement was included in the design. Both the RHCWS and ANSI/AISC 341-16 used the Mattock–Gaafar mechanical model [16], which was employed in the preliminary design of the connection shear strength of the JF series specimens and satisfied the following equations:

$$V_{\mathrm{p}}=\eta V_l$$

(1)

$$V_{\mathrm{p}}=4.05\sqrt{f_{\mathrm{c}}}{\left({\displaystyle \frac{t}{b}}\right)}^{0.66}{\beta }_{1}b{l}_{\mathrm{e}}\left[{\displaystyle \frac{0.58-0.22{\beta }_1}{0.88+a/l_{\mathrm{e}}}}\right]$$

(2)

$$V_l=\min \left[0.6d_{\mathrm{w}}{t}_{\mathrm{w}}{f}_{\mathrm{y}},M_{l\mathrm{p}}/\left(2a\right)\right]$$

(3)

$$M_{l\mathrm{p}}=f_{\mathrm{y}}{Z}_{\mathrm{p}}$$

(4)

where V_p is the predicted shear strength of the coupling steel beam connection to the wall pier, η is the ratio of shear strength of the connection to the coupling steel beam, V_l is the shear yield strength of the coupling steel beam, f_c is the specified compressive strength of concrete, t is the width of the column or thickness of the shear wall, b is the width of the flange for a beam, β₁ is the factor relating the depth of the equivalent rectangular compressive stress block to the depth of the neutral axis, l_e is the length of the embedment of the steel coupling beam in the concrete shear wall, a is the distance from the concentrated load to the face of the column or shear wall, d_w is the depth of the web for a beam, t_w is the thickness of the web for a beam, f_y is the specified minimum yield stress of the steel or reinforcement, M_lp is the moment corresponding to the plastic stress distribution over a link section, and Z_p is the plastic section modulus about the axis of bending.

In this study, the value of η was set to approximately 0.56 to ensure that the specimen satisfied the design test objective. During the design stage, the compressive strength of the concrete, yield strength of the web and stiffener, yield strength of the flange, and tensile yield strength of the steel bars were set to 26.6, 235, 345, and 400 MPa, respectively. The main design parameters of the specimens are listed in

Table 1. Main design parameters of the specimens.

Specimen Name	Beam Section h × b × tw × tf (mm)	a (mm)	le (mm)	t (mm)	t/b	fc (MPa)	fyw (MPa)	fyf (MPa)	Inverted U-Shaped Rebar
JF-S1	350 × 100 × 14 × 16	450	435	250	2.50	26.6	235	345	YES
JF-S2	350 × 120 × 14 × 16				2.08				YES
JF-S3	350 × 140 × 14 × 16				1.79				YES
JFS3-NU	350 × 140 × 14 × 16				1.79				NONE

Note: h is the height of the steel coupling beam; t_f is the thickness of the flange; f_yf is the specified minimum yield stress of the steel beam flange; f_yw is the specified minimum yield stress of the steel beam web.

.

Vertically connected bars between the upper and lower precast walls were held in place with semi-grouted sleeves installed at the bottom of the upper precast wall. Additionally, a horizontal reinforcement densification zone with a height of 500 mm was incorporated into the design to further restrain the semi-grouted sleeves [17].

A 150 mm-thick horizontal joint strip was poured with on-site concrete between the upper and lower wall assembly units; however, this process typically produces cold joints, which negatively impact the shear strength of the joint. To address the disadvantages of cold joints, inverted U-shaped rebars with a spacing and diameter of 125 and 6 mm, respectively, and a top side that was 70 mm higher than the upper flange surface of the steel beam, were distributed along the length of the wall. The JFS3-NU specimen had the same design parameters as JF-S3, except for the absence of inverted U-bars, to evaluate the impact of these rebars on the shear strength of the joint between the wall and the embedded steel beam. Six vertical steel bars with diameters of 18 mm were placed in the embedded area of the steel coupling beam along the wall length. Two horizontal stirrups with diameters of 8 mm were arranged between the upper and lower flanges of the steel coupling beam in the embedded area. Additionally, three layers of horizontal stirrups with diameters of 8 mm and horizontal spacings of 100 mm were distributed in the upper and lower regions of the area where the steel coupling beam was embedded. The distance between the horizontal stirrups adjacent to the steel beam was 25 mm from the outer flange surface. The remaining wall reinforcements are illustrated in Figure 4.

2.3. Manufacturing Process

To simulate the construction process of a precast hybrid coupled wall and facilitate the installation of the sensors, the specimens were constructed in four main steps, as illustrated in Figure 5. First, the top beam of the upper wall and the foundation of the lower wall were poured separately to realize the layout of the steel sleeves, steel beams, sensors, and other components of the wall. Second, concrete was poured to complete the upper and lower walls. Third, a 130 mm-thick layer of concrete was poured over the steel beam of the lower wall to simulate the construction of a floor slab between the upper and lower walls. Finally, after the upper and lower walls were spliced together, the bottom of the upper wall was plugged, and the grouting material was filled to a thickness of 20 mm. This approach allowed for a realistic simulation of the construction process and the testing of various aspects of the hybrid coupled wall system.

2.4. Measured Material Properties

The specimens were constructed in three batches, and the mechanical properties of the concrete at the foundation, wall, and horizontal joints are listed in

Table 2. Test values of the mechanical properties of the concrete.

Specimen Name	Compressive Strength/MPa	Tensile Strength/ MPa	Elastic Modulus/ MPa	Pour Batch
C1	30.2	3.00	32,554	Foundation and top beam
C2	33.0	3.14	33,338	Wall
C3	29.0	2.93	32,171	Horizontal seam

. Additionally, the mechanical properties of the grouting material, steel, and steel bars were examined in detail, as listed in

Table 3. Test values of the mechanical properties for grouting material.

Specimen Name	Compressive Strength/ MPa	Flexural Strength/ MPa
CG1	107.3	11.5

,

Table 4. Test values of the mechanical properties of the steel materials.

Specimen Name	Thickness/ mm	Yield Strength/ MPa	Ultimate Strength/ MPa	Strength to Yield Ratio	Elongation/%	The Tested Place
P1	8	326	469	1.44	33	Web
P2	10	325	458	1.41	35	Stiffeners
P3	12	320	449	1.40	36	Stiffener
P4	14	284	442	1.56	38	Web
P5	16	269	436	1.62	37	Stiffeners
P6	16	382	589	1.54	31	Flange
P7	20	261	419	1.60	43	Stiffeners

and

Table 5. Test values of the mechanical properties of the steel bars.

Specimen Name	Diameter/ mm	Yield Strength/MPa	Ultimate Strength/MPa	Strength to Yield Ratio	Elongation/ %
B1	6	501	632	1.44	17
B2	8	532	654	1.23	24
B3	10	451	601	1.33	27
B4	12	513	684	1.33	26
B5	16	452	634	1.40	34
B6	18	476	654	1.37	26
B7	20	489	687	1.40	22

, respectively.

3. Experimental Procedure

To conduct the load test, a jack device and hydraulic servo actuator were employed, as illustrated in Figure 6. A vertical load was applied to the force-distribution steel beam, which was placed at the top of the specimen to simulate the axial pressure on the wall.

A hydraulic servo actuator with a maximum loading capacity of 1000 kN was fixed to the lower flange of the reaction steel frame, which was situated approximately 450 mm away from the outer edge of the shear wall. The actuator applied vertical cyclic loads to simulate the seismic load on a steel coupling beam. The shear strength of each specimen was measured using the built-in pressure sensor of the actuator, and the vertical deformation of the steel beam was measured using an external displacement meter. To ensure the precise motion of the steel beam, two rigid rods connected to the displacement meter were fastened to the outer edge of the support stiffener due to interference from the loading fixture. The vertical deformation of the steel beam was calculated as the average of two displacement values.

A pre-load test was conducted to verify the stability of the support and normal functioning of the testing equipment before commencing the main test. The axial pressure on the wall was increased to 1000 kN and the operating conditions of the test device were observed to ensure no abnormalities occurred. Thereafter, the load was increased to 2000 kN, and a cyclic load was applied to the steel coupling beam while maintaining a constant axial pressure on the wall throughout the test. A cyclic load was applied using the load–displacement mixed control loading method. The loading process was repeated once for each stage before the initial cracks appeared and three times for each stage after the initial cracks appeared, as shown in Figure 7. The Δ/Δ_y represents the ratio of loading displacement to yield displacement, while the T represents the cyclic period. The test was terminated when the load dropped below 85% of the ultimate load or if the specimen failed.

4. Experimental Results

4.1. Crack Pattern and Damage

As depicted in Figure 8, the specimen was divided into various parts to describe the development of wall cracks. The intersecting face of the shear wall and steel coupling beam was designated as the wall side, whereas the faces perpendicular to the side of the wall were labeled as the wall front and wall back. A portion of the steel beam embedded in the shear wall was identified as the embedded area and the left side of this region was referred to as the embedded area root.

The concrete cracking and failure modes of the specimens in the JF series were similar. Initially, a horizontal crack appeared at the junction between the shear wall side and bottom surface of the steel coupling beam. As the load increased, oblique cracks developed in the embedded area and its lower area, whereas vertical cracks appeared on the embedded area root, as shown in Figure 9a (considering specimen JF-S3 as an example). Over time, cracks gradually spread to the joint center and neighboring areas and eventually formed crescent-shaped cracks. When approaching completion, the wall surrounding the embedded area of the steel coupling beam protruded outward, and a portion of the concrete spalled off, as shown in Figure 9b. This was particularly evident on the side of the wall that adjoined the steel beam. The upper and lower wings of the steel beam were clearly separated from the neighboring concrete. The loading test was terminated when the concrete in the embedded area of the steel beam lost its shear strength. No significant damage or residual deformation occurred in the coupled steel beam excavated from the wall, as shown in Figure 10. This indicates that the experiment effectively accomplished its intended objectives.

The final state of the JF series joint failure is shown in Figure 9c–f. The cracks exhibited a K-shaped pattern, spanning from JF-S1 to JF-S3 on the right-hand side of the embedded area’s root. Conversely, the left side exhibited an inverted K-shaped configuration that extended from JF-S1 to JF-S3. Additionally, the K-shaped cracks spanning JF-S1 to JF-S3 were increasingly noticeable in sequential order. The width and length of the cracks differed significantly between the upper and lower portions of the embedded area due to the higher densification of the horizontal steel bars in the bottom area of the upper wall. The degree of damage to the JFS3-NU specimen was more significant than that of the JF-S3 specimen, particularly in and above the embedded area, as it lacked the inverted U-shaped reinforcement.

4.2. Hysteresis Response

Figure 11 presents the hysteresis curves and their corresponding skeleton curves for the JF series specimens. The distribution of the hysteresis curves exhibited a notable pinching phenomenon, which was principally similar across all specimens. This was primarily due to the relative sliding of the concrete and steel bar at the connection under cyclic loading, which resulted in a decrease in the restraining effect of the concrete on the steel beam, particularly when the ultimate load was applied. Consequently, when the load was reduced to approximately 0 kN, the steel beam lost a significant amount of stiffness.

Table 6. Test results for each loading stage of the specimen.

Specimen Name	Loading Direction	Cracking Value		Yield Value		Ultimate Value		Vp	Vcr/Vu	Vy/Vu	Vu/Vp
		Δcr/mm	Vcr/ kN	Δy/ mm	Vy/ kN	Δu/ mm	Vu/ kN
JF-S1	Positive	—	—	6.7	544.5	11.6	619.1	298.9	—	0.88	2.08
	Negative	−1.8	−275.5	−6.7	−531.9	−11.9	−625.6		0.44	0.85
JF-S2	Positive	—	—	8.3	608.4	14.9	708.7	318.0	—	0.86	2.22
	Negative	−2.5	−316.5	−7.9	−590.2	−14.6	−701.1		0.45	0.84
JF-S3	Positive	—	—	7.3	620.0	17.8	728.3	335.1	—	0.85	2.15
	Negative	−2.2	−357.8	−8.6	−623.2	−14.7	−712.9		0.50	0.87
JFS3-NU	Positive	—	—	6.9	630.2	14.8	729.3	335.1	—	0.86	2.15
	Negative	−2.3	−357.3	−6.9	−606.5	−14.7	−709.1		0.50	0.86

Note: Δ_cr is the vertical displacement corresponding to V_cr; Δ_y is the vertical displacement corresponding to V_y; Δ_u is the vertical displacement corresponding to V_u.

summarizes the test results for the JF series of specimens, including the crack, yield, ultimate, and predicted values. The crack value was obtained by observing the initial crack during the test, and the yield value was calculated using the equivalent elastoplastic energy method based on the skeleton curve. The ultimate value was determined by analyzing the skeleton curve, whereas the predicted value was calculated using the Mattock–Gaafar mechanical model and the measured material-mechanical parameters. All specimens exhibited cracking under negative loading: the average yield displacements of JF-S1, JF-S2, JF-S3, and JFS3-NU were 6.7, 8.1, 8.0, and 6.9 mm, and the corresponding ductility values for the ultimate load coefficients were 1.75, 1.83, 2.04, and 2.14, respectively. The relationship between the ductility of each specimen and its loading displacement was demonstrated using two coordinate values, as shown in Figure 11. As the flange widths increased, the ultimate loads of JF-S1, JF-S2, and JF-S3 increased significantly and reached 622.4 kN, 704.9 kN, and 720.6 kN, respectively. The ratio of the cracking load, V_cr, to ultimate load, V_u, increased significantly as the flange width increased, with a difference of only 6% between the maximum and minimum values. Conversely, the ratio of the yield load, V_y, to V_u decreased as the flange width increased, with a 10% difference between the maximum and minimum values. These data demonstrated that significant relationships existed between the cracking, yield, and ultimate loads. The mean value of the ratio of V_u to the predicted shear strength, V_p, was 2.15 for all specimens, thus indicating that the connection shear strength predicted by the Mattock–Gaafar mechanical model was excessively conservative. The cracking, yielding, and ultimate bearing capacities of JF-S3 and JFS3-NU were almost identical, thus demonstrating that the setting of the inverted U-shaped reinforcement at the flange of the steel beam had a negligible influence on the shear strength of the connection.

4.3. Stiffness Characteristics

The secant stiffness, k_s, which was calculated by measuring the slope of the peak line connecting the positive and negative loads in the first cycle of each load level on the hysteresis curve, was employed to assess the degradation of connection stiffness as the load value increased. The initial stiffness values of JF-S1, JF-S2, and JF-S3 were 176, 210, and 262 kN/mm, respectively, as shown in Figure 12. The initial stiffness of JFS3-NU was 247 kN/mm, which was slightly lower than that of JF-S3. The stiffness of JF-S2 was greater than that of JF-S1 when the load did not reach the crack value, whereas the stiffnesses of JF-S2 and JF-S3 were relatively consistent when the load exceeded the yield load. However, JF-S3 remained more rigid than JF-S1 and JF-S2 throughout the test. Additionally, the stiffness of JF-S3 was greater than that of JFS3-NU when the load did not reach the crack value; however, both were relatively consistent when the load exceeded the yield load.

4.4. Strain Distribution

The strains of the horizontal stirrups in both the embedded area and its upper region, in addition to the inverted U-shaped reinforcement, were monitored to investigate the stress distribution of the reinforcement adjacent to the steel beam. The yield strain values for diameters of 6 and 8 mm, as shown in Figure 13, were 2505 με and 2660 με, respectively, which were obtained from the test data on the mechanical properties of the steel bars in Table 5. Notably, the strain values corresponding to the negative load on the steel beam were provided, considering that the hysteresis curve was essentially symmetrical.

The horizontal stirrup strain gauges were placed along the length of the steel beam in the embedded area. The strain values corresponding to V = 0, V_cr, V_y, and V_u are shown in Figure 13a. It should be noted that the specimen was exposed only to axial pressure from the wall when V was zero. The strain distribution indicated that the maximum strain of each specimen was less than 200 με when the load was zero or V_cr. As the load increased toward V_y, the stirrups of each specimen transitioned into an elastic state; however, the stresses at Point A in JF-S3 and JFS3-NU remained almost equal to the yield value. As the load continued to increase toward V_u, a significant difference in the horizontal stirrup strain values was observed between the specimens. This caused Point A in JF-S3, in addition to Points A and B in JFS3-NU, to transit into the elastic–plastic phase, whereas the horizontal stirrups of the other specimens remained in the elastic state.

The horizontal stirrup strain values along the wall thickness direction are shown in Figure 13b at the time of V_u. As the width of the steel coupling beam flange increased, the strain values at Points C, D, and E increased. From a comparison of all the specimens, the strain difference was significant at Point C, whereas it was extremely remote at Point E. For each specimen, the strain values, particularly for JF-S3 and JFS3-NU, decreased rapidly along the height of the wall. Point C for all the specimens, except for Specimen JF-S1, was in an elastic–plastic state, whereas Points D and E for all the specimens remained in an elastic phase.

Due to the damage to the strain gauges at time V_u, the strain values of the inverted U-bar along the direction of the wall height are shown in Figure 13c at time V_y. The strain distribution for each specimen, particularly JF-S1, exhibited a linear pattern. The interaction between the steel beam and concrete wall in the embedded area conformed to the plane section assumption under the action of a shear force on the steel beams. Furthermore, all the measurement points, except Point K, were in the elastic phase.

5. Mechanics Models

5.1. Comparison of Current Mechanical Models and Experimental Results

From the 1970s onward, researchers investigated connection mechanisms of steel beams embedded in concrete columns and shear walls. In addition to the Mattock–Gaafar mechanical model, which is typically employed to predict the shear strength of specimens, several other mechanical models have been proposed, such as the PCI, Marcakis–Mitchell, Minami, and Park–Yun models [13].

Table 7. Experimental and predicted values of the strength.

Specimen Name	JF-S1	JF-S2	JF-S3	JFS3-NU
bi/mm	86	106	126	126
b/mm	100	120	140	140
Vu/kN	622.4	704.9	720.6	719.2
Vp(PCI)	287.4	316.2	316.2	316.2
Vu/Vn(PCI)	2.17	2.23	2.28	2.27
Vp(Marcakis)/kN	377.3	377.3	377.3	377.3
Vu/Vp(Marcakis)	1.65	1.87	1.91	1.91
Vp(Mattock)/kN	323.6	353.4	372.4	372.4
Vu/Vp(Mattock)	1.92	2.05	1.99	1.98
Vp(Minami)/kN	416.1	499.0	582.6	582.6
Vu/Vp(Minami)	1.50	1.41	1.24	1.23
Vp(Park)/kN	283.7	329.4	350.4	350.4
Vu/Vp(Park)	2.19	2.14	2.06	2.05
Vn(theory)/kN	320.9	389.9	458.9	458.9
Vu/Vn(theory)	1.94	1.81	1.57	1.57
Vn(calc.)/kN	629.0	672.7	710.8	710.8
Vu/Vn(calc.)	0.99	1.05	1.01	1.01
Vn(proposed)/kN	627.8	671.4	709.4	709.4
Vu/Vn(proposed)	0.99	1.05	1.02	1.01

For all specimens: l_e = 420 mm; a = 465 mm; f_c = 32.6 MPa; β₁ = 0.81.

compares the results of the calculation with the test ultimate shear strength of the specimens based on the expressions of the connection shear strength for various mechanical models. The comparison revealed the following: (1) the calculated result of the PCI was the most conservative, and the average value of V_u∕V_p(PCI) of the four specimens was 2.24, and (2) the results of the Minami calculation were close to the experimental results, but the average value of V_u∕V_p(Minami) reached 1.34, and a significant discrepancy was noted between the calculated results and measured values. Although the calculation formulas for the shear strength were verified through the experimental results, the construction of the embedded area influenced the load transfer mechanism. Therefore, these formulas have their application scope. In this study, the force transfer mechanism was altered by incorporating a horizontal stirrup into the connection, which prevented the direct application of previous findings. Therefore, a novel mechanical model was developed, which considers the test results, and a formula for calculating the shear strength of the connection was proposed.

5.2. Proposed Mechanical Model

A mechanical model of this connection was developed by Yu Q [18]. The strength of the connection was constrained by horizontal steel bars set in the embedded area and its upper and lower areas, which allowed for the concrete inside and outside the core area to be fully exerted. The resulting mechanical model is shown in Figure 14. The assumptions made in this study include the following: (1) The concrete strains in both the inner and outer compression zones of the steel beam section were in accordance with a linear distribution. (2) The maximum compressive strain, ε_cu, of the front compression zone, which had an equivalent rectangular distribution with a stress value of 0.85f_c and shape coefficient of β₁, was 0.003. (3) The maximum compressive strain, ε_b, in the rear compression zone was 0.002, and the stress distribution was parabolic with a value that can be calculated using Equation (5). (4) In terms of front compression, the forces acting on the steel beam section inside and outside the area were recorded as C_if and C_of, respectively. These values were determined by point-position agreement, and their corresponding action positions were in agreement. Furthermore, the positions and corresponding action positions of C_ib and C_ob were congruent.

$${\sigma }_{\mathrm{c}}=1000f_{\mathrm{c}}\left(\epsilon -250{\epsilon }^2\right)$$

(5)

where σ_c represents the concrete compressive stress, and ε represents the concrete compressive strain.

The resultant force, C_b, acting on the inner and outer sides of the steel coupling beam flange by the concrete in the rear compression zone is expressed as follows:

$$C_{\mathrm{b}}=C_{\mathrm{ob}}+C_{i\mathrm{b}}={\displaystyle \frac{f_{\mathrm{c}}\left(b+b_i\right)\left(2.25c^3-5.25c^2{l}_{\mathrm{e}}+3.75c{l}_{\mathrm{e}}^2-0.75l_{\mathrm{e}}^3\right)}{c^2}}$$

(6)

where b_i is the width of the flange deducting web thickness, and c is the length of the compression zone at the back of the connection.

The position x_b of the resultant force in the rear compression zone can be expressed as follows:

$$x_{\mathrm{b}}={\displaystyle {\int }_0^{l_{\mathrm{e}}-c}{\sigma }_{\mathrm{c}}bx\mathrm{d}x/C_{\mathrm{ob}}}={\displaystyle \frac{0.69{\left(l_{\mathrm{e}}-c\right)}^3\left(c-0.36l_{\mathrm{e}}\right)}{c^3-2.33c^2{l}_{\mathrm{e}}+1.67c{l}_{\mathrm{e}}^2-0.33l_{\mathrm{e}}^3}}$$

(7)

where x_b represents the distance from the back of the embedded member to the neutral axis.

The resultant force, C_f, of the concrete in the front compression zone acting on the inner and outer sides of the steel coupling girder flange is expressed as follows:

$$C_{\mathrm{f}}=C_{i\mathrm{f}}+C_{\mathrm{of}}=0.85f_{\mathrm{c}}{\beta }_{1}c\left(b_i+b\right)$$

(8)

where C_if is the resultant compressive force acting inside the flange at the front of the connection, and C_of is the resultant compressive force acting outside the flange at the front of the connection.

Determining the torque equilibrium equation on V_n yields the following:

$$C_{\mathrm{f}}{l}_{\mathrm{v}}-C_{\mathrm{b}}\left(l_{\mathrm{v}}+Z\right)=0$$

(9)

where l_v represents the distance from the concentrated load to the resultant compression force, C_f, and Z represents the distance between the resultant concrete compressive forces C_b and C_f.

Substituting Equations (6)–(8) and the geometric relationships $l_{\mathrm{v}}=\left(a+{\beta }_{1}c/2\right)$ and $Z=a+l_{\mathrm{e}}-l_{\mathrm{v}}-\left(l_{\mathrm{e}}-c-x_{\mathrm{b}}\right)$ into Equation (9) yields the following:

$$\begin{gathered} \left(-2.65a-0.81c+a{\beta }_1+0.5c{\beta }_1^2\right)c^3+6.18a{l}_{\mathrm{e}}{c}^2+\left(-4.41a+3.09c\right)l_{\mathrm{e}}^{2}c \\ +\left(0.88a-2.94c\right)l_{\mathrm{e}}^3+0.66l_{\mathrm{e}}^4=0 \end{gathered}$$

(10)

Considering that Equation (10) is related only to the four parameters a, l_e, β₁, and c, the corresponding c value can be obtained by substituting the first three parameters of the JF series specimens. Four solutions were obtained for the value of c: c₁ = −3087 mm, c₂ = 152.5 mm, c₃ = 247.5 mm, and c₄ = 910 mm. According to Mattock, c = c₃ = 247.5 mm is an appropriate interpretation of Equation (10).

Determining the torque equilibrium equation on C_b yields the following:

$$V_{\mathrm{n}}\left(l_{\mathrm{v}}+Z\right)-C_{\mathrm{f}}Z=0$$

(11)

where V_n is the nominal shear strength of the coupling steel beam connection to the wall pier.

Substituting c/l_e = 247.5/420 = 0.589 into Equation (11) and simplifying it yields Equation (12), as follows:

$$V_{\mathrm{n}\left(\mathrm{theory}\right)}=V_{\mathrm{n}}={\displaystyle \frac{0.85f_{\mathrm{c}}\left[0.59{\beta }_1{l}_{\mathrm{e}}b\left(1+b_i/b\right)\left(0.84-0.29{\beta }_1\right)\right]}{0.84+a/l_{\mathrm{e}}}}$$

(12)

Moreover, Equation (12) proposes a theoretical model for calculating the shear strength of the connection. The calculation results and their ratios to the test results are listed in

Table 8. Variation of c/l_e with f_c and a/l_e.

a/le	c/le
	fc = 27.6 MPa (4000 psi)	fc = 34.5 MPa (5000 psi)	fc = 41.4 MPa (6000 psi)	fc = 48.3 MPa (7000 psi)	fc = 55.2 MPa (8000 psi)	Average
0.2	0.649	0.661	0.674	0.678	0.700	0.643
0.4	0.624	0.636	0.648	0.661	0.674
0.6	0.607	0.618	0.631	0.643	0.656
0.8	0.594	0.606	0.618	0.630	0.643
1.0	0.584	0.596	0.608	0.621	0.633	0.594
1.2	0.576	0.588	0.600	0.613	0.626
1.4	0.570	0.582	0.594	0.607	0.620
1.6	0.565	0.577	0.589	0.602	0.615
1.8	0.560	0.573	0.585	0.598	0.610
2.0	0.557	0.569	0.581	0.594	0.607

. The concrete strength in the compression zone of the embedded area was improved by depositing stirrups at the top and bottom of the embedded area, and the steel-beam flange width was less than the wall thickness. Consequently, the theoretical shear strength of the joint was lower than the experimental value. To modify the theoretical model and derive the strength of the constrained concrete in the compression zone, V_u/f_b = V_n(theory)/(0.85 f_c) was used to obtain Equation (13), as follows:

$$f_{\mathrm{b}}/f_{\mathrm{c}}=0.85V_{\mathrm{u}}/V_{\mathrm{n}\left(\mathrm{theory}\right)}$$

(13)

where f_b represents the concrete bearing stress.

Based on the research findings of Kriz [19], an inextricable connection exists between the strength of the confining concrete and f_b, f_c, and b/t. To illustrate this relationship, Figure 15, which contains four sets of data, depicts the correlation between b/t and f_b/f_c. In addition to the ratios of the experimental test values to the results of the calculation with the theoretical model for JF-S1, JF-S2, and JF-S3, the assumption of f_b/f_c = 0.85 was proposed when b and t were equal. Using these four sets of data, the relationship between b/t and f_b/f_c was successfully fitted, as shown in Equation (14).

$$f_{\mathrm{b}}=0.88f_{\mathrm{c}}{(b/t)}^{-0.7}$$

(14)

By replacing 0.85 f_c in Equation (13) with f_b in Equation (14), Equation (15) can be obtained. The calculation results, as listed in Table 7, were in good agreement with the test results.

$$V_{\mathrm{n}\left(\mathrm{calc}.\right)}=V_{\mathrm{n}}={\displaystyle \frac{0.59{\beta }_1{l}_{\mathrm{e}}b{f}_{\mathrm{b}}\left(1+b_i/b\right)\left(0.84-0.29{\beta }_1\right)}{0.84+a/l_e}}$$

(15)

Equation (15) expresses the shear strength expression derived when c/l_e = 0.589, which is a unique solution for the shear strength. Based on the c/l_e values at various compressive strengths with reference to the Building Code Requirements for Reinforced Concrete (ACI 318-14) [20], Table 8 lists the calculated values of c/l_e for combinations of a/l_e from 0.2 to 2.0 and f_c from 27.6 MPa (4000 psi) to 55.2 MPa (8000 psi). The calculation results indicated the following: (1) As the compressive strength, f_c, increased, c/l_e decreased with an increase in a/l_e, and the rate of decrease gradually decreased. (2) When a/l_e remained constant, c/l_e increased as f_c increased. (3) The variation in c/l_e was insignificant when considering various combinations of a/l_e and f_c. To ensure accuracy and convenience, the calculations were divided into two groups based on the ratios of a/l_e. When a/l_e ranged from 0.2 to 0.8, the mean value of c/l_e was 0.643, with a ratio of the range to mean value of only 8.9%. However, when a/l_e ranged from 1.0 to 2.0, the mean value of c/l_e was 0.594, with a ratio of the range to mean of only 6.5%.

Using these two sets of c/l_e values, Equation (11) can be solved for V_n. Notably, the thickness of the steel protective layer did not effectively limit the embedded area of the steel beam when subjected to an ultimate load. Consequently, the effective embedded length of the steel beam should be taken into account, which was (l_e − c_s) and (a + c_s), instead of l_e and a, respectively. Thus, it can be rewritten in the form of Equation (12), as follows. When $0<(a+c_{\mathrm{s}})/(l_{\mathrm{e}}-c_{\mathrm{s}})\le 0.8$ and $c/(l_{\mathrm{e}}-c_{\mathrm{s}})=0.643$, the following is true:

$$V_{\mathrm{n}\left(\mathrm{proposed}\right)}={\displaystyle \frac{0.64f_{\mathrm{b}}{\beta }_{1}b\left(l_{\mathrm{e}}-c_{\mathrm{s}}\right)\left(1+b_i/b\right)\left(0.87-0.32{\beta }_1\right)}{0.87+\left(a+c_{\mathrm{s}}\right)/\left(l_{\mathrm{e}}-c_{\mathrm{s}}\right)}}$$

(16)

When $0.8<(a+c_{\mathrm{s}})/(l_{\mathrm{e}}-c_{\mathrm{s}})\le 2.0$ and $c/(l_{\mathrm{e}}-c_{\mathrm{s}})=0.594$, the following is true:

$$V_{\mathrm{n}\left(\mathrm{proposed}\right)}={\displaystyle \frac{0.59f_{\mathrm{b}}{\beta }_{1}b\left(l_{\mathrm{e}}-c_{\mathrm{s}}\right)\left(1+b_i/b\right)\left(0.85-0.30{\beta }_1\right)}{0.85+\left(a+c_{\mathrm{s}}\right)/\left(l_{\mathrm{e}}-c_{\mathrm{s}}\right)}}$$

(17)

$$f_{\mathrm{b}}=5\sqrt{f_{\mathrm{c}}}{(t/b)}^{0.7}$$

(18)

where c_s is the concrete cover thickness.

The value of a/l_e for the JF series of specimens was 1.11; thus, Equation (14) was used to calculate the shear strength of the connections. The calculated results, as listed in Table 8, indicated that the test results, V_u/V_n(proposed), for specimens JF-S1, JF-S2, JF-S3, and JFS3-NU were 0.99, 1.05, 1.02, and 1.02, respectively, thus indicating that the calculated results were well correlated with the experimental results.

6. Design Proposals

To achieve the design concept of “weak connections and strong components”, the strength capacities of joint designs (V_d and V_l) are required to meet the following formula requirements:

$$V_{\mathrm{d}}=V_{\mathrm{n}\left(\mathrm{proposed}\right)}/\varphi \ge 1.1R_{\mathrm{y}}{V}_l$$

(19)

where ϕ represents the ratio of V_y to V_u, and R_y represents the ratio of the expected yield stress to the specified minimum yield stress.

The calculated shear strength, V_n(proposed), of the connection was obtained by considering the ultimate shear strength from the test results. To ensure that the steel beam entered the elastic–plastic stage and the connection remained in the basic elastic stage, factors ϕ and R_y were introduced into Equation (19). The ratio V_y/V_u for each specimen in Table 6 was relatively constant; therefore, a value of 0.85 was considered. The value of R_y was obtained from AISC341-16 and ranged from 1.1 to 1.5.

Vertical reinforcement in the embedded area satisfied the requirements of El-Tawil S (2010) and AISC341-16. Based on the test results and recommendations by ASCE [21], the horizontal reinforcement in the embedded area and its upper and lower areas should satisfy the following requirements.

Regarding the horizontal stirrups in the embedded area, the following two requirements should be considered: (1) the spacing between the horizontal reinforcing bars should not be greater than 100 mm and should not be less than two layers, and (2) the horizontal reinforcement should be connected reliably with the longitudinal reinforcement of the wall and the steel beam, or it should pass through the web of the steel beam with the longitudinal reinforcement.

The horizontal stirrups in the upper and lower areas of the embedded area should satisfy the following three requirements: (1) the volume stirrup ratio should not be less than the volume stirrup ratio of the edge constraint member area, (2) the spacing between the horizontal stirrups should not be greater than 100 mm and should not be less than two layers, and (3) the distance between the stirrups adjacent to the steel beam should not be greater than 50 mm from the flange of the steel beam.

7. Conclusions

The test results for the four full-scale specimens were used to analyze the force-transmission mechanism of the steel coupling beam and shear wall. Based on the reported study, the following conclusions were drawn:

(1) The shear strength of the connection was significantly enhanced by incorporating horizontal stirrups into the embedded area and upper and lower areas. The test results for the JF series specimens surpassed the shear strength calculated by Mattock and Gaafar by a factor greater than two.

(2) An equal stress distribution in the inner and outer compression zones of the beam section was achieved through the constraints of the flanges, webs, compression stiffeners, end stiffeners, and horizontal reinforcement. A simplified rectangular stress distribution was employed in the front zone of the connection, whereas a parabolic stress distribution was applied to the back area.

(3) The installation of inverted U-shaped bars did not significantly enhance the yield and ultimate bearing capacities of the joint but effectively reduced the damage to the connection. Consequently, we recommended incorporating inverted U-shaped bars into construction while disregarding their impact on the capacity of the connection.

(4) Various combinations of the a/l_e ratios and concrete compressive strengths were used to calculate the corresponding c/l_e. The calculated bearing capacities of the developed connection (Equation (15)) were highly consistent with the experimental results.

(5) Equations (16)–(18) were employed to calculate the connection shear strength and formulate the shear strength to yield ratio coefficient and steel coupling beam strength coefficient as expressions for design objectives. This approach was adopted to satisfy the design standards for strong connections and weak components.

(6) The horizontal stirrups in the embedded area and its adjacent regions should satisfy the minimum structural standards to ensure that the concrete in the connection is held in place effectively, as specified in Section 6.

These conclusions were clearly based on a relatively limited number of tests and analytical studies. Additional test data from more complete subassemblies and more detailed analytical studies are recommended to supplement the results reported herein. The research team will persist in refining the research methodology by incorporating additional influencing factors, such as the contribution of floor slabs to the initial stiffness of steel coupling beams, long-term performance, durability, and environmental impact, to further enhance the theoretical system.