Experimental study on duplex assembled I-shaped steel panel dampers strengthened by CFRP sheets

Abstract

The shear steel panel damper (SPD) is gradually used in the seismic design owing to the stable energy dissipation capacity. To date, most shear panels in the conventional SPD are welded with stiffeners against excessive local buckling. In this study, a duplex assembled I-shaped steel panel damper strengthened by CFRP sheets (C-DAISPD) is proposed to avoid the failure owing to undesired cracks in the web plate. A hot-rolled H-beam is processed to an energy dissipation unit with the web strengthened by the carbon fiber reinforced polymer (CFRP) sheets and stiffeners welded to the flanges. Then, two units are assembled back-to-back to form a damper. The C-DAISPD is developed to enhance the effect of buckling restraint, the ductility, and the sustainable stable energy absorption. Quasi-static tests of three specimens and numerical models were conducted to investigate the strengthening effect on the damper. The results indicated that the CFRP sheets benefited the hysteretic performance and the ductility of the C-DAISPD. The bearing capacity and the energy dissipation capacity could be significantly improved with the four-edge weld connection and the increase in the width of the web.

Keywords

buckling restraint CFRP sheet duplex assembled I-shape finite element shear panel damper

Introduction

The shear steel panels damper (SPD) has considerable application advantages under shear loading, e.g., a controllable yield displacement and stable energy dissipation capacity (De Matteis et al., 2012; Nakashima et al., 1994). Therefore, the SPD is gradually applied to the lateral resisting system to reduce or prevent damage to the primary structures (Ge et al., 2012). However, previous studies indicate that the failure usually appears at the weld connection between the different plate members in the SPD owing to the stress concentration (Zhang et al., 2013). Besides, the deficiency in the buckling restraint causes the serious pinching effect (Xu et al., 2016).

To solve such problems, two methods are proposed as follows: (a) to optimize the configuration of the shear panels; (b) to add the strengthening layer to improve the performance. For the first aspect, both partial and complete restraints are proposed to improve the hysteretic performance and the energy dissipation capacity (Brando, 2013; Shahab et al., 2011). To optimize the cross-section, several weakening methods are explored on the uniform stress distribution in the shear panels (Aminzadeh et al., 2020; Deng et al., 2014). In terms of the additional strengthening layer, fiber reinforced polymers (FRP) are widely used. As proposed by Teng et al. (2007, 2012), the FRP composites can effectively enhance the seismic resistance of steel structures. Attempts on the steel shear plates were made by Petkune et al. (2016, 2018), and the results indicated that the carbon fiber reinforced polymer (CFRP) could significantly improve the deformability and energy absorption of the plates with less loss in the stiffness.

Currently, most shear panels strengthened by the FRP are adopted in the steel plate shear wall, while few are used in the SPD. Note that the conventional SPD consists of only one shear panel, and the plate is separated into several small sub-plates on both sides of the surface owing to the weld connection of the stiffeners. As the fatigue life of the FRP-strengthened steel plate significantly depends on the effective bonding length (Liu et al., 2009), the interface in the conventional SPD can hardly ensure the adequate bonding length and hence enough interfacial stress.

However, in some recent studies on the SPD, the shear panels are proposed to be restrained by some indirect stiffeners (Deng et al., 2015; Lin et al., 2020a). The buckling restraint mode is similar to that adopted in the buckling restrained braces (Guan et al., 2020). Therefore, there is enough space over the web plate to bond the FRP effectively. Besides, as the shapes of the optimized cross-section are usually not regular, the FRP is more suitable to strengthen the shear panels than other materials (e.g., metal) owing to the excellent shape flexibility (Teng et al., 2012).

Previously, the authors proposed a duplex assembled I-shaped steel shear panel damper (Lin et al., 2020a). As shown in Figure 1(a), the configuration permitted the development of the tension field and inhibited the excessive out-of-plane deformation. However, as shown in Figure 1(b) and (c), two issues causing the loss in the performance were observed in the previous tests: (a) a delay in the buckling restraint owing to the partial constraint mode; (b) unsatisfactory deformation capacity owing to the fatal cracks in the web.

Figure 1.

Problems of the previously proposed damper: (a) configuration, (b) partial constraint mode of the stiffeners, and (c) fatal cracks in the web plate.

In this study, a duplex assembled I-shaped steel shear panel damper strengthened by the CFRP sheets (C-DAISPD) was proposed to enhance the effect of the buckling restraint and avoid the undesired fatal cracks. Two stiffeners were used to constrain the buckling without any direct connection to the web plate. Meanwhile, the CFRP sheets were bonded over the web panel to prevent the aforementioned fatal cracks. Quasi-static tests and numerical analysis were conducted to verify the design concept. The experimental hysteretic behaviors, critical parameters, and energy dissipation capacity were discussed. Finally, the influences of the boundary condition and the width of the web were analyzed.

Duplex assembled I-shaped steel panel damper strengthened by CFRP sheets

The C-DAISPD (Figure 2) consists of two channel-like energy dissipation units, which are manufactured from the hot-rolled H-beam. The flanges and the web in an H-beam can serve as the connection plate to the structure and the shear panel to dissipate energy, respectively. Owing to the integrity between the flanges and the web after the hot-roll procedure, the amount of the connecting weld can be decreased to avoid the common failure resulting from the tearing in the welded seam between different plate members.

Figure 2.

Configuration of the C-DAISPD.

Firstly, both top and bottom flanges at the same side of the web are cut off, with the web weakened along both vertical edges. For the purpose of connection, several bolt holes are drilled into the remaining side of the flanges. The whole cut-off part is shown in the bright color in Figure 2. An H-beam is then processed to a channel-like energy dissipation unit. Subsequently, to limit the excessive local buckling of the web, two stiffeners are installed to the left and right quadrants of the diagonal lines, respectively. The stiffeners are welded only with both top and bottom flanges, simultaneously, with a 1-mm gap to the web. As the CFRP sheets benefit the uniform stress distribution over the strengthened material, the composite layers are used to prevent the undesired cracks in the web plates. Finally, two units are installed back-to-back in the structure to form a C-DAISPD.

Test program

Material properties

All energy dissipation units and stiffeners were made of Q235B, of which the nominal yield strength is 235 MPa. Details of different materials are listed in Table 1. The elastic and shear modulus of the epoxy adhesive were 28,000 MPa and 14,000 MPa, respectively. The nominal thickness of the CFRP sheet and the epoxy adhesive was 0.167 mm and 0.500 mm, respectively.

Table 1.

Material properties.

Member	Yield strength (MPa)	Ultimate strength (MPa)	Elastic modulus (MPa)
Hot-rolled H-beam	299.15	443.51	202,000
Stiffener	293.51	436.33	202,000
Fiber (longitudinal)	–	3500	251,000
Fiber (orthogonal)	–	30	25,000

Specimen design

The energy dissipation units were made of the Q235B hot-rolled H-beam, $HN 350 \times 350 \times 7 \times 11$ . The units for three specimens were identical, and the details of the dimensions are given in Figure 3. The height h of both the web plates and the stiffeners was 328 mm. The length L of the energy dissipation unit was 125 mm. Besides, the width of the weakened webs b_w, the thickness of the weakened webs t_w, the width of the stiffeners b_s, and the thickness of the stiffeners t_s were 85 mm, 7 mm, 60 mm, and 8 mm, respectively.

Figure 3.

C-DAISPD specimens: (a) energy dissipation unit (unit: mm), (b) details of the assembled units. (unit: mm), and (c) different patterns used for strengthening the plates.

Three specimens were designated as S1F00, S2F11, and S3F21. In the nomenclature, S plus the following number represents the testing sequence of the specimens, and F plus the following numbers represents the number of the CFRP sheets. The first number following the letter F represents the number of the sheets, of which the longitudinal direction is parallel to the height, and the second one means the number of those with the orthogonal direction. The details of the sheet pattern for S2F11 and S3F21 are given in Figure 3(c). The total thickness of the web plates in S1F00, S2F11, and S3F21 was 7.000 mm, 7.834 mm, and 8.001 mm, respectively. S1F00 served as a reference specimen. S2F11 and S3F21 were tested to explore the strengthening effect of the CFRP sheets.

Before the tests, the CFRP sheets were used to strengthen the outer surfaces of the web plates by the epoxy adhesive. Firstly, the bonding areas of the steel surface were sand-blasted. Subsequently, the surfaces were cleaned with acetone immediately to remove grease as well as dust. Then, the fresh chemically-active surface benefited an effective mechanical interlocking. The epoxy adhesive was applied by a brush, so that the adhesive could be dispersed uniformly over the surfaces and entirely saturate the fibers. Finally, the specimens were cured under the indoor temperature condition for 2 weeks until the adhesive achieved the full strength.

Test setup

The loading equipment, which consisted of a loading frame and an actuator, was designed to rebuild the actual working conditions of the C-DAISPD in a frame structure. As shown in Figure 4(a), a 100-t MTS actuator was installed between the reaction wall and the end of the top loading beam. The connection base was used to connect the specimen with the loading equipment. Considering the 125-mm-long flanges of the specimens, they were not long enough to drill adequate holes to ensure no slide between the specimens and the loading equipment. To detect the shear displacement precisely, each specimen was firstly welded to the connection plates. Considering that the direct welding tended to damage the bonding at the end of the CFRP sheets, different patterns of the welded seam were adopted in the three specimens (Figure 4(c) and (d)). Finally, the specimen was installed with the loading equipment using friction high-strength bolts with an adequate bolt pre-tightening force.

Figure 4.

Test setup: (a) loading equipment, (b) displacement and strain gauges, (c) weld connection (S1F00), and (d) weld connection (S2F11 and S3F21).

In the test, the loading force was measured through the actuator cell. Two linear variable differential transformers (LVDTs), that is, D1 and D2, were used to detect the relative lateral displacement of the top and bottom flanges. And a rosette strain gauge S1 was bonded to the intersection of the two diagonal lines at the outer surface of the web plate. The details of the layout are illustrated in Figure 4(b).

Loading scheme

The quasi-static reversed cyclic loading was adopted in the tests. To obtain the initial stiffness of the three specimens, the force-controlled mode was firstly adopted at an amplitude of 5 kN, 10 kN, and 20 kN, respectively, with one cycle for each step. Subsequently, the displacement-controlled mode specified by JGJ/T 101-2015 code (Chinese Ministry of Housing and Urban Rural Development, 2015: 15) was adopted for the following loading. The minimum amplitude of the loading scheme was 3.28 mm, which was close to the yield displacement of the shear component. According to JGJ 3-2010 code (Chinese Ministry of housing and urban rural development, 2010: 19), the damper should not fail at a shear displacement of less than 2% of the height of the floor. Therefore, the maximum amplitude was selected as 65.6 mm, which was slightly larger than the requirement for a 3-meter-high floor. The shear displacements for each displacement-controlled step were 3.28 mm, 6.56 mm, 13.12 mm, 19.68 mm, 26.24 mm, 32.80 mm, 39.36 mm, 45.92 mm, 52.48 mm, 59.04 mm, and 65.6 mm. Each step was repeated twice. u and γ (equals to u/h) denote the shear displacement and the shear angle, respectively. When the actuator pushed the top beam forward, the loading direction was regarded to be positive. Otherwise, the loading direction was considered to be negative. The direction of the cut-off area in the front web was the same as the positive loading direction. During the tests, the loading was terminated when the lateral force decreased to 80% of the maximum value, or when a fatal crack appeared.

Test results

Hysteretic performance

As shown in Figure 5(a), the hysteresis curves of S1F00 was stable and plump before the first cycle at an amplitude of 6.56 mm. A slight pinching effect could be observed on the curve for this loading cycle. Then, the hysteresis loop was gradually developed from a spindle shape to a bow one. The lateral loading force for S1F00 reached the ultimate value 116.29 kN at an amplitude of 17.33 mm and dropped suddenly. The decrease mainly resulted from the tearing of the welded seam between the top flange and the connection plate. With the increase in the shear displacement, the hysteresis loop gradually changed to a reversed S shape in the final loading steps. This result was induced by the development of the tearing and the loss in the buckling restraint at a relatively large shear displacement. Finally, the lateral force decreased to 80% of the peak value at a shear displacement of 46.76 mm.

Figure 5.

Hysteresis curves: (a) S1F00, (b) S2F11, and (c) S3F21.

Compared with the hysteresis curve of S1F00, those of S2F11 and S3F21 were less plump. The phenomena were caused by the extra width of the gap between the two web plates owing to the additional composite layers. Besides, the marked pinching effect partially resulted from the decreased length of the weld connection, which will be further discussed in detail in Section Influence of the boundary condition. At a shear displacement of 32.8 mm, the shear forces of both S2F11and S3F21 began to decrease owing to the extended tearing between the flange and the connection plate. With respect to the final loading cycle, the amplitudes of S2F11 and S3F21 were 60.03 mm and 66.71 mm, respectively, which demonstrated the strengthening effect on the deformation capacity.

Deformation behavior

As the two energy dissipation units were assembled anti-symmetrically to each other, the deformation behaviors were similar in either positive or negative direction. Therefore, only the deformation behavior in the positive direction is discussed in this section. For the shear strain shown in Figure 6(a) to (c), all specimens reached the plastic stage at a shear angle of 0.01 rad. The results demonstrated that the yield displacement was small enough to enable the specimens to dissipate earthquake energy. The evolutionary progression was nearly identical until 0.02 rad. Then, the difference grew dramatically at a shear angle of 0.04 rad, which resulted from the buckling. Further, the principal strain direction could be obtained as follows:

\tan 2 θ = | \frac{γ_{xy}}{ε_{x} - ε_{y}} | = | \frac{2 ε_{45^{°}} - ε_{0^{°}} - ε_{90^{°}}}{ε_{0^{°}} - ε_{90^{°}}} |,

(1)

Figure 6.

Principal strain: (a) S1F00, (b) S2F11, (c) S3F21, and (d) principal strain direction.

Figure 6(d) plots the measured direction of the principal strain on the web plate, where θ denotes the angle between the principal tensile strain and the lateral direction. The direction of the principal strain of S1F00 kept near 45° until the shear angle reached 0.10 rad. As proposed by Timler et al. (1983), the inclination was conducive to the form of the most effective tension field. Then, a marked variation in the shear strain and principal strain angle could be observed in S1F00. The phenomena mainly resulted from the development of the existing tearing.

With respect to S2F11, the decline in the principal strain angle appeared at an amplitude of 0.04 rad. Meanwhile, the compressive strain, which should be a minus, was detected to be positive. The result was caused by the fact that the out-of-plane deformation where the gauge located developed to the web of the adjacent unit. Therefore, the tensile and compressive strains were transformed from the in-plane stress condition to the triaxial one. The dramatical variation of the strains resulted from the appearance of the direct contact between two webs. Then, the principal strain angle kept less than 30° at the shear angle from 0.06 rad to 0.14 rad until both the tensile and compressive strains decreased below zero at the shear angle of 0.16 rad, which indicated that the curvature of the buckling changed to the opposite direction. As there was no stiffener to limit the buckling in the middle part of the web, a pure shear condition formed again with the principal strain angle close to 45°. For S3F21, as the angle stabilized around 40°, it was indicated that the web plate was in a nearly pure shear condition during the whole loading. The final principal strain angle of S3F21 was slightly less than that in S2F11. Considering that there was one more composite layer with the longitudinal direction in S3F21, the phenomenon indicated that the CFRP sheets slightly changed the direction of the principal strain.

Failure mode

All specimens remained elastic when the shear angles were less than 0.01 rad. Subsequently, the webs began to yield and entered the hardening stage. Meanwhile, the slight out-of-plane deformation was immediately limited by the stiffeners. As mentioned in Section Hysteretic performance, a marked tearing, which resulted in a sudden drop in the restoring force, appeared at the shear angle of 0.06 rad. Similar phenomena, including yielding, buckling, buckling restraint, and tearing in the weld connection, could be observed in all specimens, except for the debonding of the CFRP sheets only in the two strengthened specimens. Note that the tearing between the flange and the connection plates did not lead to a drop in the restoring force in S2F11 and S3F21. Figure 7 plots the debonding of the CFRP sheets near the top flange at the shear angle of 0.06 rad. However, there was no obvious phenomenon (e.g., the sudden drop of the shear force and the stiffness degradation) observed in the hysteresis curves of S2F11 and S3F21. Considering the high temperature during the welding process, the bonding of the composite layers was indirectly affected and tended to be of low quality near the flange and the end of the web before the tests. As there was little development of the debonding in the following loading steps, the remaining bonding could be regarded to be effective in the tests.

Figure 7.

Debonding of the CFRP sheets: (a) S2F11 and (b) S3F21.

With respect to the final failure, the corresponding ultimate shear angles were 0.14 rad, 0.18 rad, and 0.20 rad for S1F00, S2F11, and S3F21, respectively. Similar cracks, which resulted from the tearing between the flange and the connection plates, could be observed in all specimens. The cracks extended along the direction of the length of the flanges with the increase in the shear displacement. Subsequently, a fatal crack in the web appeared in S1F00 (Figure 8(a)), which directly caused the drop of the restoring force to less than 80% of the maximum value. However, no fatal crack appeared in the web plates of S2F11 and S3F21 as opposed to S1F00. The results indicated that the CFRP sheets mitigated the stress concentration and formed a homogeneous stress distribution. The failure of S2F11 and S3F21 was caused by the development of the cracks between the flange and the connection. As the extension of the cracks lasted for nearly half of the whole loading step, the failure modes of S2F11 and S3F21 could be regarded as the ductile failure. Therefore, it could be demonstrated that the presence of the CFRP sheets could lead to the ductile failure as opposed to the brittle one in S1F00.

Figure 8.

Failure mode: (a) S1F00, (b) S2F11, and (c) S3F21.

Discussion and analysis

Skeleton curve

The skeleton curves were obtained by connecting the peak points of the first cycle loops under each loading step. As shown in Figure 9, little difference among the three specimens could be observed in the force-controlled loading cycles. However, the lateral force of S1F00 was repeatedly larger than those of both S2F11 and S3F21 at the shear angle from 0.01 rad to 0.04 rad. The ultimate lateral forces of S1F00, S2F11, and S3F21 reached 112.11 kN, 104.69 kN, and 113.83 kN with the corresponding shear angle of 0.04 rad, 0.08 rad, and 0.08 rad, respectively. Then, the lateral force of S1F00 gradually decreased with the increase in the shear angle until the force dropped to less than 80% of the peak force at the shear angle of 0.14 rad. With respect to the other two specimens, the lateral forces kept steady around the ultimate forces at the shear angle from 0.08 rad to 0.14 rad (S2F11), and from 0.08 rad to 0.20 rad (S3F21), respectively. The plateau in the two skeleton curves resulted from the uniform stress distribution owing to the CFRP sheets. Besides, as a larger ultimate force and a larger corresponding shear angle could be observed in S3F21 than those in S2F11, it was indicated that the increase in the number of the composite layers was conducive to the improvement of both the bearing capacity and the ductility.

Figure 9.

Skeleton curves.

Critical mechanical parameters

The critical mechanical parameters for the specimens are summarized in Table 2, including the initial stiffness K_initial, the yield force F_y, the yield displacement u_y, the ultimate force F_ult, and the ultimate displacement u_ult. The initial stiffness was obtained by dividing the lateral force by the corresponding displacement in the first force-controlled loading cycle. The yield force and the yield displacement were determined by the initial stiffness and the ultimate force as recommended by Feng et al. (2017). By comparison, it was found that S1F00 possessed the smallest initial stiffness among all specimens, although the difference was rather small. Thus, it was indicated that the CFRP sheets could slightly enhance the initial stiffness of the damper. However, the yield force of S1F00 was repeatedly larger than those of both S2F11 and S3F21, while the yield displacement was nearly 20% smaller than those of the other specimens. The results indicated that most parts of the strengthened web plates yielded at a relatively large shear displacement owing to the uniform stress distribution. However, as little difference was observed with respect to the ultimate force, it was indicated that the CFRP sheets did not significantly improve the ultimate bearing capacity of the strengthened specimen as expected. As the conclusion is rather different from that proposed by Petkune et al. (2016, 2018), the potential cause will be further investigated in Section Influence of the boundary condition.

Table 2.

Critical mechanical parameters for specimens.

Specimens	K_initial/(kN mm⁻¹)	F_y (kN)	u_y (mm)	F_ult (kN)	u_ult (mm)	u_ul /u_y
S1F00	55.81	82.11	3.83	112.11	46.76	12.21
S2F11	55.93	72.15	4.43	104.69	60.03	13.55
S3F21	56.32	77.71	4.51	113.83	66.71	14.79

The ductility coefficient (equals to u_ult/u_y) is an important parameter to represent the displacement ductility and deformation capacity of the damper. As listed in Table 2, it could be found that the coefficient values of S2F11 and S3F21 were 11.0% and 21.2% larger than that of S1F00, respectively, although the yield displacement of S1F00 was the smallest among the three specimens. The results indicated that the CFRP sheets were beneficial to the ductility and deformation capacity of the C-DAISPD. Specifically, as the value of S3F21 increased by 9.2% to that of S2F11, the strengthening effect could be improved with the increase in the number of the composite layers.

Stiffness degradation

The secant stiffness K_sec is adopted to represent the stiffness degradation, which is defined as the slope of the straight line connecting the peak points in the first cycle loop. As shown in Figure 10, except for the initial stiffness, the stiffness in the two strengthened specimens was smaller than that of S1F00 until the shear angle reached 0.06 rad. The result was different from the data obtained by Petkune et al. (2016, 2018), which demonstrated the effectiveness of the CFRP sheets in the improvement of the stiffness in the shear panels throughout the loading tests. The difference in the stiffness degradation mainly resulted from the weld connection between the flange and the connection plate, which will be further discussed in Section Influence of the boundary condition. Compared with S2F11, the secant stiffness of S3F21 was repeatedly larger, concluding that the increase in the number of the CFRP sheets was beneficial to a slowdown in the stiffness degradation.

Figure 10.

Stiffness degradation.

Energy dissipation capacity

As the C-DAISPD mainly absorbs earthquake energy through plastic shear deformation, two parameters, that is, E_s and E_c, are used to represent the energy dissipation capacity. E_s denotes the energy dissipated in the first cycle at each loading level, while E_c represents the cumulative energy absorbed in the whole loading steps. As shown in Figure 11(a), the energy dissipated by the three specimens was close to each other until the web plate buckled at a shear angle of 0.04 rad. Subsequently, S1F00 absorbed a larger amount of energy than the other two specimens at the shear angle from 0.04 rad to 0.10 rad owing to a larger secant stiffness and less pinching effect. The ultimate energy dissipation capacity of S2F11 and S3F21 was achieved at the shear angle of 0.14 rad and 0.12 rad, respectively. However, S1F00 and S2F11 soon failed to work due to the extended crack after the peak energy dissipation capacity was achieved, while S3F21 kept absorbing a steady amount of energy at the shear angle from 0.12 rad to 0.20 rad. Therefore, it was indicated that the sustainable energy dissipation capacity benefited from an increasing number of the composite layers. Similar conclusions could also be drawn from Figure 11(b) with the amount of the cumulative dissipated energy sorted in the same sequence.

Figure 11.

Energy dissipation capacity: (a) dissipated energy in per cycle and (b) cumulative dissipated energy.

Numerical study

Numerical model

As there were many complex factors affecting the performance of C-DAISPD, a meticulous finite element (FE) model was established using the Abaqus/Explicit software to supplement the analysis. The C3D8R, S4R, and COH3D8 elements were adopted for the simulation of the energy dissipation unit (i.e. the stiffeners, the flanges, and the web plates), the CFRP sheet, and the epoxy adhesive, respectively (Figure 12). Considering the debonding of the composite layers near the weld connection in the tests, the corresponding elements were only established over the area of the web plate. The kinematic hardening model was used to represent the properties of steel, which is given by:

α = \sum_{i}^{n} α_{i},

(2)

α_{i} = \frac{C_{i}}{γ_{i}} (1 - e^{- γ_{i} ε_{p}}),

(3)

where α is the total backstress tensor; n is the total number of backstress; α _i is the i-th backstress tensor; C_i is the kinematic hardening model parameter related to the i-th backstress; γ_i is the kinematic hardening model parameter related to the recovery item of the i-th backstress; ε_p is the plastic strain. C₁, γ₁, C₂, and γ₂ were taken as 1200, 9, 200, and 0, respectively. The material properties listed in Section Material properties were adopted for the three types of materials. The quads damage criterion (Kabir et al., 2016) was used to characterize the mechanical behavior of the epoxy adhesive between the CFRP sheets and the web. Therefore, once the interfacial shear failures in two interfacial directions or the peeling failure in the normal direction appeared, the corresponding COH3D8 elements would stop functioning to represent the debonding in the epoxy adhesive.

Figure 12.

Numerical model.

As there was no failure in the connection area between the stiffeners and the inner sides of the flanges in the experiments, these two plate members were established as an integrity. The epoxy adhesive was tied to the outer surfaces of the web plates, and the CFRP sheets were attached to the adhesive. To precisely characterize the buckling restraint to the web plate, the hard contact was adopted to represent the extrusion when the 1-mm-wide gap was achieved (Deng et al., 2015). The Coulomb friction was used to simulate the contact behavior between the two surfaces, which was taken as 0.15 (Genna et al., 2012). Besides, the first buckling mode was adopted to represent the initial imperfection at the amplitude of H/250 as suggested in GB 50017-2017 code (Chinese Ministry of Housing and Urban Rural Development, 2017: 30).

The boundary conditions for the models with and without the CFRP sheets were slightly different according to the welding connection forms of the three specimens. As shown in Figure 12, the three edges of the flanges and the bolt hole (the red lines) were welded to the connection plates in all specimens, while the partial area in the rest edges of the flanges (the blue lines) was only welded in S1F00. The circular contour of the holes was simplified as a rectangular while considering the shape of the element. The welded areas of the bottom and top flanges were slaved to RP-1 and RP-2, respectively.

Validation of the FE model

With the same loading scheme as that of the experiments, the numerical models of the three specimens were loaded until the amplitude reached 19.68 mm, where the sudden drop was observed in the experiment. Note that the boundary condition of S1F00 was identical to the initial form until the shear displacement reached 17.44 mm. Then, it was transformed into the degraded one (Figure 12). Figure 13 plots the comparison between the FE model and the test. By comparison, the numerical curves were in good accordance with both the experimental hysteresis curves and skeleton curves. The main difference was that the pinching effect was more obvious in the experimental results, which resulted from the continuous development of the tearing in the flange and the welded seam. As this was not the controlling factor in the early loading stage, the simplification was regarded to be acceptable. The verifying results indicated that the proposed numerical models were appropriate to represent the hysteretic behavior of the specimens.

Figure 13.

Numerical results of specimens: (a) S1F00, (b) S2F11, and (c) S3F21.

Influence of the boundary condition

As there was additional half an edge welded in the initial boundary condition of S1F00 than those in the other specimens, the stiffness of the former specimen was repeatedly larger. The phenomenon explained why the experimental results were different from the conclusion proposed by Petkune et al. (2016, 2018), where the shear panel was effectively constrained along all the edges. Similar to the experimental results, the transformation in the weld connection caused the sudden drop of the restoring force in S1F00, while the same phenomena were not observed in other specimens. The results indicated that the performance of the C-DAISPD significantly depended on the connection between the flanges and the structure.

With respect to the boundary condition, the tested weld connection pattern (including the transformation in S1F00) and the extended one were adopted in the following numerical analysis, respectively. The boundary condition of the latter group of models (S1F00E, S2F11E, and S3F21E) was kept identical to the initial pattern of S1F00. For simplicity, the initial and degraded patterns are defined as the four-edge type and the three-edge edge type in the following description, respectively. As shown in Figure 14, when the weld connection was similar to the four-edge type, the strengthened models were repeatedly larger in both restoring force and energy dissipation capacity than those without the composite layer. However, the result was contrary when the model was with the three-edge weld connection. The phenomena indicated that the CFRP sheets could improve the bearing capacity and energy dissipation capacity only when the four-edge type was permitted. The transformation in the boundary condition caused a significant decrease in the restoring force and energy absorption, which explained why the improvement on the specimens could only be observed at a large shear displacement. Nevertheless, further experiments are planned to explore the potential improvement with respect to the connection.

Figure 14.

Comparison on different boundary condition: (a) numerical skeleton curve and (b) numerical dissipated energy in per cycle.

Influence of the width of the web

As proposed by Deng et al. (2014), little stress flows near the two free vertical edges of the steel shear panel. To investigate the bonding effect on the utilization of the area with little stress, FE models with different web widths were established on the basis of the four-edge connection. For each type of the model (i.e. with or without the CFRP sheets), various web widths b_FE were selected as 1.00b_w,test, 1.25b_w,test, 1.50b_w,test, 1.75b_w,test, and 2.00b_w,test, where b_w,test is the tested width of the web. The models were loaded with the same loading scheme adopted in Section Influence of the boundary condition.

According to Corte et al. (2013), the ultimate force of an SPD is close to the shear force corresponding to the shear angle of 0.08 rad. Therefore, the shear force corresponding to the shear angle of 0.08 rad was considered as the ultimate force in this section. As shown in Figure 15, comparisons were conducted on the yield force, the ultimate force, and the energy dissipation capacity. F_Frp and E_s,Frp are the shear force and dissipated energy of the models with the CFRP sheets, respectively, while F_NF and E_s,NF are the parameters for those without the composite layers. As proposed by Lin et al. (2020b), the shear panel with two clamped and two free edges mainly resisted the shear force through the partial tension field (PTF) action after the yielding. As the larger enhancement was obtained in the ultimate force than in the yield force, the phenomenon indicated that the bonding of the composite layer benefited the function of the PTF action. In addition, with the width increasing, both ratios of the three indexes were improved, indicating that the composite layers could function better in a web with a larger width.

Figure 15.

Comparison on different aspect ratios: (a) shear force and (b) dissipated energy (0.08 rad).

With respect to the seismic design, the additional damping ratio ξ_d of a damper to the structure is specified in JGJ297-2013 code (Chinese Ministry of Housing and Urban Rural Development, 2013: 37) as follows:

ζ_{d} = \frac{E_{damper}}{4 π (E_{structure} + E_{damper})},

(4)

where E_damper is the energy dissipated by the pure steel damper in a hysteresis cycle at a certain shear displacement, and E_structure is that dissipated by the primary structure. As the introduction of the CFRP sheets has little influence on the energy absorption of the structure, E_structure is regarded to be constant in the composite system. An enhancement coefficient η is obtained as 1.28 according to the comparison shown in Figure 15(b), so that the additional damping ratio ξ_d,CFRP can be calculated as follows:

ζ_{d, CFRP} = \frac{η E_{damper}}{4 π (E_{structure} + η E_{damper})},

(5)

By substituting equation (4) into equation (5), the value of ξ_d,CFRP is obtained as follows:

ζ_{d, CFRP} = \frac{η ζ_{d}}{4 π ζ_{d} (η - 1) + 1},

(6)

Therefore, considering that the damper is strengthened with the CFRP sheets, equation (6) can be used as a simplified conservative estimation for the damping ratio in the seismic design.

Conclusion

This paper proposes a duplex assembled I-shaped steel panel damper strengthened by the CFRP sheets. Quasi-static tests and numerical analyses were carried out to investigate the performance of the C-DAISPD. The major conclusions are made as follows:

The C-DAISPD achieves the stable and plump hysteretic performance owing to the presence of the CFRP sheets and the buckling restraint of the indirect adjacent web and stiffeners. The ductility and the energy dissipation capacity of the damper are significantly improved as well. Besides, the increase in the number of the CFRP sheets can effectively benefit such a phenomenon.

The bonding of the CFRP sheets can uniform the stress distribution over the shear panel. Although the layout of the CFRP sheets slightly changes the principal strain angle, the composite layers can mitigate the stress concentration of the web plates and inhibit the undesired fatal crack. With a better deformation capacity, the failure pattern of the strengthened shear plate can be transformed from the brittle mode to the ductile one.

The bearing capacity of the C-DAISPD significantly depends on the boundary condition. A four-edge weld connection can permit both the bearing capacity and the energy dissipation capacity to be improved at any amplitude of the shear displacement. However, an inadequate connection tends to delay the appearance of the enhancement until a large shear displacement is achieved.

The bonding of the CFRP sheets benefits the partial tension field action of the shear panel, so that a larger ultimate force can be achieved. The improvement to the damper owing to the composite layer can be increasingly enhanced with the increase in the width of the web. Besides, a simplified conservative estimation for the additional damping ratio is proposed while considering the introduction of the composite layers.

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: The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51678136, 51808109), China Scholarship Council (Grant No. 201906090096), and the Natural Science Foundation of Jiangsu (Grant No. BK20180385).

ORCID iDs

Yu Lin

Dongzhi Guan

References

Aminzadeh

Kazemi

Tavakkoli

(2020) A numerical study on optimum shape of steel slit dampers. Advances in Structural Engineering 23(14): 2967–2981.

Brando

Agostino

De Matteis

(2013) Experimental tests of a new hysteretic damper made of buckling inhibited shear panels. Materials and Structures 46: 2121–2133.

Chinese Ministry of Housing and Urban Rural Development (2010) Technical Specification for Concrete Structures of Tall Building JGJ 3-2010. Beijing: China Architecture and Building Press, p.19.

Chinese Ministry of Housing and Urban Rural Development (2013) Technical Specification Seismic Energy Dissipation of Buildings JGJ 297-2013. Beijing: China Architecture and Building Press, p.37.

Chinese Ministry of Housing and Urban Rural Development (2015) Specification for Seismic Test of Buildings JGJ/T 101-2015. Beijing: China Architecture and Building Press, p.15.

Chinese Ministry of Housing and Urban Rural Development (2017) Code for Design of Steel Structures GB 50017-2017. Beijing: China Architecture and Building Press, p.30.

Corte

D’Aniello

Landolfo

(2013) Analytical and numerical study of plastic overstrength of shear links. Journal of Constructional Steel Research 82: 19–32.

De Matteis

Brando

Mazzolani

(2012) Pure aluminium: An innovative material for structural applications in seismic engineering. Construction and Building Materials 26: 677–686.

Deng

Pan

Sun

, et al. (2014) Shape optimization design of steel shear panel dampers. Journal of Constructional Steel Research 99: 187–193.

10.

Deng

Pan

, et al. (2015) Development of a buckling restrained shear panel damper. Journal of Constructional Steel Research 106: 311–321.

11.

Feng

Qiang

(2017) Discussion and definition on yield points of materials, members and structures. Engineering Mechanics 34(3): 36–46.

12.

Chen

Kang

(2012) Demand on stiffened steel shear panel dampers in a rigid-framed bridge pier under repeated seismic ground motions. Advances in Structural Engineering 15(3): 525–546.

13.

Genna

Gelfi

(2012) Analysis of the lateral thrust in bolted steel buckling-restrained braces. II: Engineering analytical estimates. Journal of Structural Engineering 138(10): 1244–1254.

14.

Guan

Yang

Liu

, et al. (2020) Concept and behaviour of all-steel miniature bar-typed structural fuses with torsional effect. Journal of Constructional Steel Research 164: 105795.

15.

Kabir

Fawzia

Chan

, et al. (2016) Numerical studies on CFRP strengthened steel circular members under marine environment. Materials and Structures 49: 4201–4216.

16.

Lin

Yang

Guo

, et al. (2020a) Development of duplex assembled I-shaped steel panel dampers. Journal of Constructional Steel Research 174: 106267.

17.

Lin

Yang

Guan

, et al. (2020b) Modified strip model for indirect buckling restrained shear panels dampers. Journal of Constructional Steel Research 175: 106371.

18.

Liu

Xiao

Zhao

(2009) Experimental study of fatigue crack growth behavior in adhesively reinforced steel structures. Composite Structures 90: 12–20.

19.

Nakashima

Iwai

Iwata

, et al. (1994) Energy dissipation behaviour of shear panels made of low yield steel. Earthquake Engineering & Structural Dynamics 23(12): 1299–1313.

20.

Petkune

Donchev

Hadavinia

, et al. (2016) Performance of pristine and retrofitted hybrid steel/fibre reinforced polymer composite shear wall. Construction and Building Materials 117: 198–208.

21.

Petkune

Donchev

Hadavinia

, et al. (2018) Comparison of the behavior of steel, pure FRP and hybrid shear walls under cyclic seismic loading in aspect of stiffness degradation and energy absorption. Construction and Building Materials 165: 621–630.

22.

Teng

(2007) Behaviour of FRP-jacketed circular steel tubes and cylindrical shells under axial compression. Construction and Building Materials 21: 827–838.

23.

Teng

Fernando

(2012) Strengthening of steel structures with fiber-reinforced polymer composites. Journal of Constructional Steel Research 78: 131–143.

24.

Timler

Kulak

(1983) Experimental Study of Steel Plate Shear Walls. Structural Engineering Report No. 114. Alberta: University of Alberta Edmonton, pp. 89–98.

25.

Shahab

Mirtaheri

Mirzaeifar

, et al. (2011) Modifying the shear buckling loads of metal shear walls for improving their energy absorption capacity. Advances in Structural Engineering 14(6): 1247–1257.

26.

Nie

Fan

(2016) Cyclic behaviour of low-yield-point steel shear panel dampers. Engineering Structures 126: 391–404.

27.

Zhang

Aoki

Zhang

, et al. (2013) Experimental investigation on the low-yield-strength steel shear panel damper under different loading. Journal of Constructional Steel Research. 84: 105–113.