Seismic performance assessment of eccentrically braced steel frames with variable-cross-section horizontal shear links

Abstract

Based on the principle of web weakening, two types of variable-cross-section shear links for horizontal eccentrically braced steel frames (H-EBFs) were analyzed in this study. In the first design, an I-section link (L2) was designed with a lower web and wider flange than that of an ordinary shear link (L1), and in the second design, an I-section link composed of two small I-section beams (L3) was designed. To study the seismic behavior of the two types of H-EBFs, cyclic loading tests were performed on three scaled specimens, L2 (H-EBF-L2), L3 (H-EBF-L3), and a traditional link (H-EBF-L1). The results showed that most of the inelastic actions of the three specimens were concentrated in the shear links and that the failure modes were similar. Compared with specimen H-EBF-L1, the links of specimens H-EBF-L2 and H-EBF-L3 had better deformability, and the bearing capacity of the frames also improved simultaneously; thus, the energy-dissipation mechanism of H-EBF improved. The material costs of specimens H-EBF-L2 and H-EBF-L3 were reduced to a certain extent, realizing economic benefits. Additionally, the numerical models of the three specimens were established. The modeling results were in good agreement with the test results, and it was verified that the model could accurately simulate the loading process of the tests.

Keywords

Eccentrically braced steel frame variable-cross-section link quasi-static test numerical simulation seismic performance

Introduction

Eccentrically braced frames (EBFs), which are commonly used seismic lateral load resisting systems, combine the advantages of moment-resisting steel frames and concentrically braced steel frames (Azad & Topkaya, 2017; Bouwkamp et al., 2016; Vetr et al., 2017; Vetr and Ghamari, 2019), which have high elastic stiffness and good energy-dissipation ability during earthquakes (Bosco and Rossi, 2009; Lian et al., 2015). The design concept of an eccentric brace is that the development of plastic deformation of the structure is concentrated on the energy-dissipation link, whereas other structural members maintain an elastic working state and rely on the plastic deformation of the energy-dissipation link to dissipate seismic energy (Li et al., 2021). The seismic performance of EBFs is restricted to the inelastic rotation of active links (Tapia-Hernández and García-Carrera, 2019), and EBFs with shear yield links result in stiffer structures and more stable hysteresis performance (Dubina et al., 2008; Engelhardt and Popov, 1989). Therefore, a majority of the existing research mainly focused on EBFs with shear links (Lian and Su, 2017a; Ziane et al., 2019).

Many studies, which mainly focused on experimental and theoretical research, have been conducted on EBFs with shear links. Tian et al. (2018) designed and manufactured a scaled three-story K-shaped EBF (KEBF) and subjected it to a shaking table test. The results showed that the shear deformation of the energy-dissipation links under an earthquake could effectively absorb more seismic energy. Okazaki and Engelhardt (2007) and Okazaki et al. (2009) proposed two types of flange connection energy-dissipation beams, performed an experimental research, and summarized the law of the flange slenderness limit of energy-dissipation beams. Lian and Su (2017a, 2017b) designed and manufactured an EBF with a vertical shear link and a Y-shaped link and studied the deformation ability. Simultaneously, some scholars proposed the replaceable energy-dissipation beam of EBFs and studied the ductility, stiffness, bearing capacity, and energy-dissipation capacity of the replaceable energy -dissipation beam (Bozkurt and Topkaya, 2017, 2018; Ioan et al., 2016; Özkılıç and Topkaya, 2021; Yin et al., 2019). With respect to theoretical research, Bosco and Rossi (2009), and Rossi and Lombardo (2007) proposed the damage distribution capacity factor, evaluated the seismic performance of an EBF system, and defined the analytical relationship between the overstrength factor of links, damage distribution capacity factor, and plastic rotation of links. Gulec et al. (2011) used link plastic rotation as the demand parameter, proposed a method for identifying damage states and corresponding repairs, and provided an ordered sequence of the fragility function of EBF link beams. Li et al. (2021) designed four groups of KEBF structures with different number of stories, studied the distribution of story shear force under rare earthquakes via numerical simulation, and proposed a lateral force distribution model with higher accuracy. Additionally, the optimization method of the energy-dissipation beam was also studied, for example, web openings and stiffener arrangements of energy-dissipation beams (Ohsaki and Nakajima, 2012; Prinz and Richards, 2009).

Presently, research on H-EBFs needs to be improved. To analyze the seismic behavior of H-EBFs in detail and to simplify the design process of replaceable links, two shear yield links with different web weakening forms were proposed. The structures of L2 and L3 are shown in Figure 1. The traditional link L1 has the same cross-section details as the adjacent beams; link L2 has a lower web section and wider flanges than those of the beam, which has a transition area connected between link L2 and the beams; link L3 consists of two smaller I-sections, which have the same flanges as those of the adjacent beam sections. To evaluate the seismic performance of H-EBF with links L2 (H-EBF-L2) and L3 (H-EBF-L3), three one-bay and one-story 1/2.6 scaled frames were designed and tested under static-quasi-cyclic loading. Moreover, numerical analyses were conducted using the software ABAQUS (Tong et al., 2018).

Figure 1.

Link details: (a) L1, (b) L2, and (c) L3.

Methodology

Description of prototype structures

Three 10-story office buildings were designed using H-EBF-L1, H-EBF-L2, and H-EBF-L3, respectively. The buildings were assumed to be located in a region corresponding to site class III and seismic design group II specifications with a peak ground acceleration of 0.2 g with a 10% probability of exceedance in a 50-year period, as per the Chinese code (GB50011-2010, 2016). For design purposes, the loads were composed of representative gravity loads, including dead loads, 50% live loads, and horizontal seismic loads. The unfactored dead and live loads were 8.5 kN/m² and 3.0 kN/m², respectively. The nominal seismic loads were calculated by following the provisions in the Chinese code (GB50011-2010, 2016). The steel members were designed according to the specification requirements (GB50017-2017, 2017; JGJ99-2015, 2015).

The plan and elevation views of the buildings are shown in Figure 2. To simplify the design and analysis, only a plane model in the X-direction was selected for analysis, as shown in Figure 2(b). The height and span of each story was 3.9 m and 7.8 m, respectively, and the length of the links in each story was 1.0 m. According to the codes (AISC341-16, 2016; GB50011-2010, 2016), the link was short (or shear yield) in design, and the net length of the link should not be greater than 1.6 times the ratio of the full plastic flexural capacity of the link to the shear capacity of the link (AISC341-16, 2016; GB50011-2010, 2016). A welded I-section made of Q235B steel (f_y = 235 MPa) was used for all the structural members. After numerous design iterations, the design stress ratios were approximately 0.8, 0.8–0.9, and 0.7 for links, columns and beams, and braces, respectively. Through calculation and analysis, the maximum story drift ratios under the design seismic loading for the three buildings were located on the eighth story. According to the aforementioned results, H-EBFs on the eighth story were selected as the prototype models, as shown in Figure 2(c).

Figure 2.

Prototype structures (unit: mm): (a) Plan view, (b) elevation view, and (c) prototype frame.

Specimen descriptions

According to laboratory conditions, three single-story and single-span H-EBFs were designed and manufactured, with the ratio of 1: 2.6. The main difference among the three specimens is that the links of L1, L2, and L3 are used, respectively, and the other components have the same size, as shown in Table 1 and Figure 3. The masses of specimens H-EBF-L1, H-EBF-L2 and H-EBF-L3 were 261 kg, 231 kg, and 242 kg, respectively. The masses of specimens H-EBF-L2 and H-EBF-L3 were 11.4% and 7.3% less than that of specimen H-EBF-L1, respectively. To reduce the stress concentration, circular arc transition was adopted in fillet welds of the specimens. In addition, in order to obtain the material characteristics of plates with different thicknesses in the specimens, the steel tensile specimens were made from the processed base metal of the frame specimens, and the standard tensile tests were carried out. Table 2 shows the average values of the material characteristics of steel plates with different thicknesses.

Table 1.

Dimensions of the members (unit: mm).

Members	Section size (h×b_f×t_w×t_f)
Members	H-EBF-L1	H-EBF-L2	H-EBF-L3
Column	H150 × 130 × 6 × 8	H150 × 130 × 6 × 8	H150 × 130 × 6 × 8
Beam	H150 × 130 × 6 × 8	H150 × 90 × 6 × 8	H150 × 130 × 6 × 8
Link	H150 × 130 × 6 × 8	H120 × 130 × 6 × 8	H50 × 130 × 6 × 8
Brace	H80 × 80 × 6 × 6	H80 × 80 × 6 × 6	H80 × 80 × 6 × 6

h is the section height, b_f is the flange width, t_w is the web thickness, and t_f is the flange thickness. The link of specimen H-EBF-L3 is divided into two identical small links. Only one small link cross-section is considered in Table 1.

Figure 3.

Details of test specimens (unit: mm): (a) Specimen H-EBF-L1, (b) specimen H-EBF-L2, (c) specimen H-EBF-L3, (d) details of link L1 and beam for specimen H-EBF-L1, (e) details of link L2 and beam for specimen H-EBF-L2, and (f) details of link L3 and beam for specimen H-EBF-L3.

Table 2.

Material properties of steel.

Nominal thickness (mm)	Yield strength (N/mm²)	Ultimate strength (N/mm²)	Yield strain	Elastic modulus (×10⁵ N/mm²)	Elongation (%)
6	308	426	0.0015	2.01	21.7
8	270	433	0.0014	2.03	19.8

Quasi-static test

According to the principle of performance-based design, the columns in eccentrically braced frame should be kept within the elastic range when subjected to force. At the same time, it is difficult to apply vertical load to the columns because the top of the column will have a certain horizontal displacement under horizontal loading. Therefore, in these tests, only the horizontal cyclic load was applied, which was applied by the hydraulic actuator with the maximum load stroke of 1000 kN.

As for the horizontal load applied in the specimens, if applied at the intersection of beam–column joints, the link will bear larger axial force, and the plastic deformation of the link will lead to the uneven transfer of the horizontal load to the two columns, which is inconsistent with the actual situation that the axial force at the link is close to zero under earthquake action. To reduce the axial force in the link, two loading columns and one loading beam were added to the upper part of each specimen, as shown in Figure 4. The horizontal load was applied to the top of the loading column and transmitted through the hinged loading beam, so that the horizontal displacement on both sides of the specimen was synchronized. The loading column refers to extending the frame column up to 600 mm, with the top hinged with the loading end of the actuator. The loading beam adopts a square section with a side length of 200 mm and a thickness of 30 mm, which has high rigidity and can ensure the elastic deformation state during the tests.

Figure 4.

Test setup and loading protocol: (a) Test setup (unit: mm) and (b) loading protocol.

To prevent large out-of-plane deformation of specimens during the test, a lateral restraint system was designed and manufactured in this paper, which was mainly composed of welded channel steel frames at the front and rear sides of the specimens and a plurality of connecting channels, as shown in Figure 5. The function of connecting channel steel was to connect the welded channel steel frame and reaction column into a whole through high-strength bolts. Because the friction between the lateral restraint system and the specimen has certain influence on the test results, in order to reduce the influence of friction, roller wheels were set at the intersection of beam–column joints and at both ends of the link.

Figure 5.

Lateral bracing system: (a) 3D view and (b) vertical view.

In the quasi-static test, according to the suggestions in the Chinese code JGJ/T101-2015, 2015 (a) before yielding, the specimen was loaded by load control, and each stage was cycled once; (b) after yielding, the specimen was loaded by displacement control. The yield displacement was the displacement increment of each cycle, which was twice per cycle. The loading rate of the actuator was 0.05 mm/s until the specimen was damaged.

Test measurements

Linear variable displacement transducers (LVDTs) were installed in the test models, as shown in Figure 6(a). Two vertical LVDTs (DL1 and DL2) were installed at the link ends to measure the link rotation. Two horizontal LVDTs (DL3 and DL4) were installed at the two ends of the beam-to-column connection to measure the horizontal displacement of the structure. A horizontal LVDT (DL5) was installed at the bottom end of the ground beam to measure the horizontal displacement during the loading process.

Figure 6.

Experimental setup to obtain various measurements: (a) Arrangement of measurements and (b) L3 link strain gauge.

Strain gauges and strain rosettes were installed at the structural members of specimens H-EBF-L1 and H-EBF-L2 to assess the stress states at critical positions, as shown in Figure 6. Strain gauges C, B, G, and Br represent the strain gauges installed at the columns, beams, link, and braces, respectively. Additionally, strain rosettes (R1–R6) were installed on the web of the link. With respect to the link of specimen H-EBF-L3, it was difficult to attach the strain rosettes to the small link web. Hence, strain gauges (G1–G8) were used, as shown in Figure 6(b).

Experimental results and analysis

Test phenomena

The yielding load (P_y) and corresponding yielding displacement (Δ_y) for the three tested specimens are shown in Table 3. The failure processes of the tests involving H-EBF-L1, H-EBF-L2, and H-EBF-L3 are shown in Figures 7 –9. The structural behaviors of specimen H-EBF-L1 are shown in Figure 7. Overall, (1) the link showed visible shear deformation at 2 Δ_y (P = −318 kN, Δ=−9 mm); (2) the link web buckled locally with the paint falling off at 3 Δ_y (P=−358 kN, Δ=−14 mm); (3) the weld at the brace-to-beam connection slightly cracked at 5 Δ_y (P=−396 kN, Δ=−25 mm), and the crack length was approximately 2/3rd times the brace web depth at 6 Δ_y (P=−395 kN, Δ=−30 mm). Then, the test was stopped.

Table 3.

Yielding load and corresponding yielding displacement.

Specimens	P_y (kN)	Δ_y (mm)
H-EBF-L1	302	4.67
H-EBF-L2	295	4.17
H-EBF-L3	262	5.93

Figure 7.

Failure states of specimen H-EBF-L1.

Figure 8.

Failure process of specimen H-EBF-L2.

Figure 9.

Failure process of specimen H-EBF-L3.

For the specimen H-EBF-L2 shown in Figure 8, (1) the link showed slight shear deformation at 3 Δ_y (P=−367 kN, Δ=12 mm); (2) the link web buckled locally with paint falling off at 5 Δ_y (P=−411 kN, Δ=−20 mm); (3) the left brace experienced local buckling at 7 Δ_y (P=−460 kN, Δ=−27 mm), and the buckling developed rapidly until 8 Δ_y (P=−485 kN, Δ=−31 mm). Then, the test was stopped.

Figure 9 shows the structural damage evolution of H-EBF-L3. The test process can be described as follows: (1) at the displacement level of 2 Δ_y (P=401 kN, Δ=12 mm), the link showed visible shear deformation; (2) at the displacement level of 4 Δ_y (P=−453 kN, Δ=−24 mm), local buckling occurred at the flange of the link; (3) at the displacement level of 5 Δ_y (P=−468 kN, Δ=−29 mm), partial buckling of the link flange developed further; (4) at the displacement level of 7 Δ_y (P=−506 kN, Δ=−41 mm), the weld fractured at the web-to-flange connection of the link, thereby terminating the test.

In conclusion, the plastic deformation of the three specimens was mostly isolated to the links by the shearing yield, whereas the other non–energy-dissipating members were in the elastic range or experienced slightly inelastic deformation (e.g., the brace-to-column connection and brace). At the end of the test, the weld of the brace-to-beam connection was fractured in specimen H-EBF-L1, as shown in Figure 7. Out-of-plane deformation occurred in the brace of specimen H-EBF-L2, as shown in Figure 8. The link weld of the web-to-flange connection was torn in specimen H-EBF-L3, as shown in Figure 9. However, the monitored bearing capacity of all three specimens did not decrease significantly, indicating that the remaining load-bearing capacities of the EBFs were high.

Hysteretic performance

The hysteretic curves of the test results are shown in Figure 10, and the yield point, limit point, and ductility coefficient of the three specimens are listed in Table 4. Overall, the hysteretic curves were all spindle-shaped and full without a pinned phenomenon. This indicates that all three specimens had good energy-dissipation capacity. In the force-controlled loading stage, the hysteretic curve almost coincided with a straight line, indicating that the structure was in the elastic working range. With an increase in displacement, the envelope area of the hysteretic loop increased gradually. As shown in Table 3, when the test was stopped, the maximum inter-story displacement ratios of specimens H-EBF-L1, H-EBF-L2, and H-EBF-L3 were 1/49.8, 1/48.2, and 1/36.2, respectively, all of which met the requirement of 1/50 in the Chinese code (GB50011-2010, 2016). Furthermore, compared with specimen H-EBF-L1, the yield load, ultimate load, and ductility of H-EBF-L2 and H-EBF-L3 improved significantly. This was related to the weak link section.

Figure 10.

Hysteretic curves of specimens: (a) H-EBF-L1, (b) H-EBF-L2, and (c) H-EBF-L3.

Table 4.

Analysis of hysteretic curves.

Specimens	Loading direction	K₀ (kN/mm)	Yield point		Ultimate point		Ductility (Δ_u/Δ_y)
Specimens	Loading direction	K₀ (kN/mm)	P_y (kN)	Δ_y (mm)	P_u (kN)	Δ_u (mm)	μ	Δ_u/H
H-EBF-L1	Push (−)	86.6	237	4.87	395	30.1	6.18	1/49.8
	Pull (+)	88.7	232	4.67	396	30.1	6.44	1/49.8
	Average	87.7	235	4.77	396	30.1	6.31	1/49.8
H-EBF-L2	Push (−)	83.9	295	4.17	485	31.1	7.45	1/48.2
	Pull (+)	86.6	278	4.17	482	32	7.67	1/46.8
	Average	85.3	287	4.17	484	31.6	7.56	1/47.5
H-EBF-L3	Push (−)	84.8	298	5.51	506	41.4	7.47	1/36.2
	Pull (+)	88.6	262	5.93	508	41.7	7.03	1/35.9
	Average	86.7	280	5.72	507	41.6	7.25	1/36.1

K₀ is the initial stiffness, H is the frame height, μ is the ductility coefficient.

The backbone curves of the three specimens are shown in Figure 11(a). The backbone curves consisted of linear elastic and elastic–plastic parts, and the displacement at the turning point (specimen yield) was approximately 5 mm. The decreasing order of bearing capacity of the three specimens under the same displacement was H-EBF-L3 > H-EBF-L2 > H-EBF-L1. The stiffness degradation curves of the three specimens are shown in Figure 11(b). H-EBF-L1 had the maximum initial stiffness, followed by specimens H-EBF-L3 and H-EBF-L2, respectively. With an increase in the load, the stiffness decreased rapidly in the early stage and tended to be flat in the later stage. Generally, the stiffness degradation trends of the three specimens were similar.

Figure 11.

Backbone curves and stiffness degradation curves: (a) Backbone curves and (b) stiffness degradation curves.

The energy dissipation of the specimens was obtained by calculating the hysteretic loop area of each cycle. The equivalent viscous damping coefficient is generally used as an evaluation index to evaluate the energy-dissipation capacity of the specimens (JGJ/T101-2015, 2015). In the load control stage, all three specimens were in an elastic state, and the dissipated energy remained at a low level. Therefore, in this study, we analyzed the loading stage of the displacement control, as shown in Figure 12. It can be observed that with the gradual increase in the inter-story displacement angle, the dissipation energy of the three specimens increased gradually, and the dissipation energy of specimen H-EBF-L3 was the largest, followed by that of the specimens H-EBF-L2 and H-EBF-L1, respectively, as shown in Figure 12(a). Moreover, under the same inter-story displacement angle, the equivalent damping coefficients of specimens H-EBF-L2 and H-EBF-L3 were significantly higher than those of specimen H-EBF-L1. This indicates that specimens H-EBF-L2 and H-EBF-L3 have better energy-dissipation capacity, as shown in Figure 12(b).

Figure 12.

Energy-dissipation curves: (a) Dissipated energy and (b) equivalent viscous damping coefficient.

Damage mechanism

The EBFs had a good energy-dissipation capacity. This was mainly related to the inelastic response of the link. To prove this conclusion, the following results were focused on the link rotations, inter-story drifts, shear capacity, and strain of non–energy-dissipation segments.

The inter-story drift angle (θ) of the frame and link rotation angle (α) under loading are shown in Figure 13. In the initial force-controlled loading stage, the inter-story drift angle and link rotation angle of specimens H-EBF-L1, H-EBF-L2, and H-EBF-L3 were very small initially and increased rapidly with the increase in horizontal displacement after yielding. The increase in the inter-story drift angle and link rotation angle of specimen H-EBF-L3 was the fastest. When the test was stopped, the link rotation angles of specimens H-EBF-L1, H-EBF-L2, and H-EBF-L3 were 0.083, 0.10, and 0.11 radians, respectively. These values are substantially greater than the inter-story drift angle under the same load and meet the requirements of the code (AISC341-16, 2016). The results showed that a larger vertical deformation of the link can effectively reduce the overall deformation of the frame and reduce the damage degree of important members.

Figure 13.

Angle of inter-story drifts and link rotations.

The shear capacities of the three specimens, which can be calculated using equations (1) and (2), are shown in Table 5. The actual shear capacity of the three specimens exceeded the design values, and the overstrength factors were 1.3, 2.1, and 2.7, respectively. Compared with H-EBF-L1, the overstrength factors of H-EBF-L2 and H-EBF-L3 were improved. The maximum internal force design increasing coefficient of different components of EBFs given in the code was 1.4 (GB50011-2010, 2016), and appropriate adjustments should be made accordingly

V_{l, a} = \frac{F_{actuator} H}{L}

(1)

V_{l, d} = 0.58 A_{w} f_{y}

(2)

Table 5.

Shear capacity of links.

Specimens	V_l,a (kN)	V_l,d (kN)	Overstrength factors
H-EBF-L1	191.3	143.6	1.3
H-EBF-L2	233.8	111.5	2.1
H-EBF-L3	244.9	90.0	2.7

where V_l,a is the actual value of the shear bearing capacity of the link, V_1,d is the design value of the shear bearing capacity of the link, A_w is the area of the web section of the link, F_y is the yield strength of steel, F_actuator is the actuator load, H is the story height of the frame, and L is the single-span length of the frame.

The link flange and web strains of specimens H-EBF-L1, H-EBF-L2, and H-EBF-L3 are shown in Figure 14. The web strain was obtained by calculating the main strain from the strain rosettes. The web size of the link in specimen H-EBF-L3 was extremely small to stick strain rosettes. Hence, only the strains of the upper and lower flanges were recorded. As shown in Figure 14(a) and (b), the link web strain was much larger than the link flange strain under the same force for specimens H-EBF-L1 and H-EBF-L2. The link web attained the yield state earlier than the flanges. This corresponded to the shear yield failure of specimens H-EBF-L1 and H-EBF-L2, as shown in Figures 7 and 8. As shown in Figure 14(c), under the same force, the upper flange strain of specimen H-EBF-L3 was much larger than that of the lower flange strain. When the frame was close to failure, the upper flange strain of specimen H-EBF-L3 increased suddenly. This corresponded to the local buckling deformation and failure of the flange of specimen H-EBF-L3, as shown in Figure 9. This also explains the rapid increase in the link rotation angle as shown in Figure 13.

Figure 14.

Strain analysis of the link: (a) H-EBF-L1, (b) H-EBF-L2, and (c) H-EBF-L3.

The strain responses of the non–energy-dissipation segments are shown in Figure 15. It can be observed that the non–energy-dissipation segments of the three specimens were in the elastic stage. At the end of the test, the beams and columns of specimens H-EBF-L1 and H-EBF-L3 were plastically deformed at strain values of approximately 1.5 ε_y and 1.2 ε_y, respectively, and the brace of specimen H-EBF-L2 was locally buckled at a strain value of 2.5 ε_y. The analysis showed that the structural components of the three specimens were basically in a safe state during loading, while specimen H-EBF-L3 can better ensure that the deformation of structural components is at a small level. Additionally, when the structure is about to fail, a small plastic deformation may occur in the non–energy-dissipation segments.

Figure 15.

Strain responses: (a) H-EBF-L1, (b) H-EBF-L2, and (c) H-EBF-L3.

In summary, by reducing the effective web area of specimen H-EBF-L2, it can be observed that under the applied loading, the web stress was greater than that of the flange, the link was prone to shear yield deformation, and the stress of non–energy-dissipating members was adjusted. The deformation capacity and energy consumption capacity of specimen H-EBF-L2 were significantly improved compared with those of specimen H-EBF-L1. In specimen H-EBF-L3, a double-layer beam with a hole in the link web was adopted, and the upper flange of the link end was prone to large buckling deformation, which could lead to significant energy dissipation.

Numerical analysis

Numerical model

In this study, ABAQUS was used for numerical analysis, in which geometric and material nonlinearities were considered. A linear kinematic hardening material law was selected for the analysis. The mechanical properties of the steel used in this study are listed in Table 2. The geometric dimensions of all three specimens were used, as described in the above sections. All members adopted 4-node shell elements (S4R in the ABAQUS element library) with plasticity, large deflection, and large strain capability, as shown in Figure 16. To ensure the calculation efficiency and accuracy, the mesh size of the links and bracings, beams, and columns were 20 mm, approximately 20–150 mm, and approximately 50 mm, respectively. Two reference points were assigned at the bottom of the columns in the model, as shown in Figure 16. Six degrees of freedom were restrained to simulate the fixed-end conditions. Moreover, the out-of-plane constraint (U_x=0) of the model was applied to the same position of the roller wheel to simulate the out-of-plane constraint of the test. The numerical models of specimens H-EBF-L2 and H-EBF-L3 were similar to the model of specimen H-EBF-L1.

Figure 16.

Numerical model of specimen H-EBF-L1.

Numerical results

A comparison between the numerical simulation and experimental results is shown in Figures 17 –19. It can be observed that the numerical simulation results of the three specimens were in good agreement with the experimental results, thereby indicating that the numerical model can accurately simulate the loading process of the test. Generally, the bearing capacity obtained in the test was slightly larger than that obtained in the numerical simulation, but the hysteretic curves obtained from the numerical simulation were more stable than those obtained from the test.

Figure 17.

Hysteretic curves of specimens: (a) H-EBF-L1, (b) H-EBF-L2, and (c) H-EBF-L3.

Figure 18.

Comparison of backbone curves: (a) H-EBF-L1, (b) H-EBF-L2, and (c) H-EBF-L3.

Figure 19.

Comparison of stiffness degradation curves: (a) H-EBF-L1, (b) H-EBF-L2, and (c) H-EBF-L3.

The numerical and experimental results are presented in Table 6. The initial stiffness, yield load, and ultimate load of specimens indicate a difference of 14.63%, 15%, and 7.99% between the experimental and numerical results, respectively.

Table 6.

Comparison between the numerical and experimental results.

Model		K₀ (kN/mm)	P_y (kN)	Δ_y (mm)	P_u (kN)	Δ_u (mm)
H-EBF-L1	Experiment	87.7	235	4.77	396	30.1
	Numerical analysis	76.8	245	5.01	379	30.2
	Error (%)	14.19	4.25	5.03	4.48	0.33
H-EBF-L2	Experiment	85.3	287	4.17	484	31.6
	Numerical analysis	72.4	237	4.98	431	31.8
	Error%	17.8	21.1	19.42	12.3	0.63
H-EBF-L3	Experiment	86.9	280	5.72	507	41.6
	Numerical analysis	77.6	234	5.78	473	41.8
	Error (%)	11.9	19.65	1.05	7.19	0.48

Error = (Experiment − Numerical)/Experiment.

From the abovementioned comparison, it was noted that there were some differences between the experimental and numerical results. The following reasons can be attributed for the difference in values: (1) insufficient consideration of material hardening during the numerical analysis; (2) insufficient consideration of various damping effects in the test during numerical analysis (i.e., friction between the rollers and the frame); and (3) no consideration of the instability of the hydraulic actuator in the numerical analysis. In conclusion, the overall comparisons showed that the discrepancies were acceptable. This proved the validity of the numerical models, which can be a good reference for future research.

Conclusions

In this study, cyclic loading tests were performed on three H-EBFs. Furthermore, numerical models were proposed to reproduce the experimental results using ABAQUS. The following conclusions can be drawn based on the result of this study:

A majority of the inelastic deformations, which developed sufficiently, of the three specimens were localized within the shear links. Moreover, the other non–energy-dissipation segments remained in the elastic state. The hysteretic curves of the three specimens were relatively fat without pinching, thereby demonstrating a good energy-dissipation capacity.

The inter-story displacement ratios of the three specimens met the design requirements. The bearing capacity and deformation capacity of specimen H-EBF-L3 were the highest, and the shear capacity of its energy-dissipation beam was the highest. Generally, the seismic performance of EBFs with varying cross-section links (H-EBF-L2 and H-EBF-L3) is comparable to that of the traditional H-EBF with the same cross-section link (H-EBF-L1). H-EBFs with lower effective height of the link web and the two-layer beam proposed in this study increased the strain in webs and flanges, improved the shear deformation of the link, and enhanced the energy-dissipating mechanism for higher bearing capacity and deformations. Furthermore, the material cost of specimens H-EBF-L2 and H-EBF-L3 were reduced, thus providing good economic benefits.

The numerical models established using ABAQUS showed good agreement with the experimental results. This will be helpful for future research on the seismic performance of H-EBF with varying cross-section links.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was financially supported by the Natural Science Foundation of Hebei Province (E2019208322, E2021208010), the Science and Technology Research Project of Hebei University (QN2019082), and the Hebei Province Postgraduate Innovation Funding Project (No. CXZZSS2021100).

ORCID iDs

Ruoyang Wu

Haifeng Yu

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