Seismic Behavior of Nonductile RC Frame Slotted with Corrugated Steel Plate Shear Walls

Two specimens of nonductile reinforced concrete (RC) frame (ND-1) and nonductile RC frame retroﬁtted by corrugated steel plate shear walls slotted with columns (ND-2) are established by ﬁnite element. These specimens have same dimensions and steel skeletons. Finite element models had been veriﬁed by the existing experimental results. The hysteresis curves, skeleton curves, ductility, and stiﬀness curves of Specimen ND-1 and Specimen ND-2 are compared. The results show that the reinforcement eﬀect is signiﬁcant. Twenty-four models are built to study the seismic behavior on diﬀerent inﬂuence parameters. The parameters are slit width, thickness of corrugated steel plate shear walls, concrete strength of nonductile RC frame, and boundary conditions of corrugated steel plate shear walls at slotted parts. The results indicate that the strength is declined with the increase of slit width. With the increase of thickness and concrete strength, the strength and stiﬀness are enhanced. The strength is larger with the boundary than without. Slit width and thickness have an important impact on the stiﬀness. Concrete strength and boundary conditions have little impact on stiﬀness. The strengthened nonductile RC frames have enough ductility.


Introduction
In earthquake zones of China, there were number of older, low-rise concrete buildings which have not been retrofitted for earthquake safety. ese two-storey to five-storey structures may meet the old building-code standards. However, new building codes reflected later earthquake engineering research and incorporated structural elements that allowed concrete buildings to bend and stretch a bit during earthquakes. Older designs were short of those details. ere were hundreds of thousands of buildings that have not been retrofitted. ose brittle buildings were called "nonductile RC" buildings. "Ductile" meant flexible, while "reinforced concrete" refers to concrete embedded with material such as steel mesh and rebar. From an earthquake point of view, nonductile RC frames were lack of ductility and energy dissipation. Some scholars [1][2][3][4][5][6][7][8][9] have studied the seismic performance of nonductile frame structures and corrugated steel plate shear walls. Wu et al. [10] developed a multiscale model of nonductile frame. e hysteresis curves and skeleton curves of nonductile frame were analyzed by the developed model. e results showed that the multiscale model can simulate the boundary conditions of concrete components. Sae-Long et al. [11] proposed a fiber frame element for nonductile RC columns. e results revealed the essence of inclusion of shear response and shear flexure interaction. Shoraka et al. [12] introduced advanced analytical models to simulate the nonlinear dynamic response of nonductile RC structures. It estimated the expected losses of existing nonductile concrete buildings considering their vulnerability to collapse. e results showed that collapse did not occur in low earthquake shaking intensities and losses were dominated by nonstructural damage. It was effective to use the method of earthquake vulnerability.
On the basic of the researches, it was necessary to reinforce nonductile RC frame structures. At present, there were two main forms of reinforcements. One was steel bracing, and another one was carbon fiber reinforced plastic (CFRP). Song et al. [13] proposed shape memory alloy (SMA) braces. e nonlinear dynamic analyses and hysteresis performance of the SMA braces were studied. e results indicated that SMA braces strengthening nonductile concrete structures dissipated earthquake energy effectively. Khampanit [14] researched bucklingrestrained braces reinforcing nonductile RC frames. An experiment and numbers of dynamic analyses were carried to verify the effectiveness of buckling-restrained braces.
e researchers showed that this kind of braces enhanced stiffness, lateral force capacity, and energy dissipation of nonductile RC frames. Sarno and Manfredi [15] studied buckling-restrained braces (BRBs) to reinforce nonductile RC frames. Seven code-compliant natural earthquake records were selected and employed to perform inelastic response history analyses at serviceability.
e results of analysis indicated that more than 60% of input seismic energy was dissipated by the BRBs at ultimate limit states. Chen et al. [16] conducted a study on a 1/2 scale two-span and two-storey specimen. e experiment was to research CFRP reinforced nonductile RC frames. e results showed that the average displacement ductility factor of retrofitted RC frame is 2.81. ere was a large safety stock space when the maximum storey drift ratio reaches 1/50. Lv et al. [17] considered three reinforcement schemes about fiber reinforced polymer (FRP) rehabilitation. It compared seismic collapse fragilities between nonductile RC frames and reinforced specimens. e results showed that FRP rehabilitation scheme strengthening the entire structure promoted the seismic collapse resistance effectively. e objective of this research is to study the reinforcement effect of corrugated steel plate shear walls slotted with columns. e paper changed parameter types (such as slit width, thickness, concrete strength, and boundary conditions) and compared seismic performance at different conditions. e significance of this research is to propose corrugated steel plate shear walls reinforcing nonductile RC frames, which were separated with columns. e corrugated steel plate shear walls generate large oblique tension after buckling. is force extends to the surrounding RC beam and column members. e columns will bear the resulting transverse tension. As a result, the corresponding additional bending stress was generated in RC columns. To avoid the negative effect of steel plate tension belt on the RC frame columns, the corrugated steel plate shear was slotted with columns and connected with beams only.

Establishment of Nonductile RC Frame
2.1. Specimens Design. Two specimens of nonductile RC frame (ND-1, N is present non; D is present ductile) and nonductile RC frame retrofitted by corrugated steel plate shear walls slotted with columns (ND-2) were designed with the same dimensions and steel skeletons as shown in Figure 1. e reduced scale was 1/2. e clear span was 2.7 m, storey height was 1.8 m, and the total height was 2.65 m. e cross sections of column and beams were 180 × 200 mm, 150 × 250 mm, and 400 × 400 mm, respectively. e specimens were designed as nonductile frames. One of the standards about nonductile frame was insufficient transversal ties. Hence, it did not consider the joint area with dense transversal ties reinforcement.
Specimen ND-2 was reinforced by corrugated steel plate shear walls. e layout of corrugated steel plate shear walls is shown in Figure 2. e selected slit width was 10 mm. Corrugated steel plate shear walls were arranged on both sides of the frame. Corrugated steel plate shear walls were connected with beams using angle steel and tapping screws. e slabs of two pieces of corrugated steel plate shear walls were distributed as the shape of "X". As the reason of the limitation of plate width, rivets were adopted to connect two corrugated steel plate shear walls. e connection method of corrugated steel plate shear walls and beams meets the demand of practical engineering. To research the influence of various factors of slotting with columns, the study of corrugated steel plate shear walls reinforced method is at the stage of finite element analysis at present.  Figure 3. e properties of concrete, longitudinal bars, transversal ties, and corrugated steel plate are summarized in Table 1.

Loading Program and Boundary Conditions.
e vertical load applied to the two columns was 51.48 kN. Axial compression ratio was N/f c A � 0.1. Low cyclic loads were applied at the end of the beam and the loading program can be seen in Figure 4. e loading program was as per Qiu [18]. It indicated that one of the load rules was displacement-controlled loading. is load rule was also suitable for simulation. Considering the convergence of models, each load step had one cycle at a time. e bottom of two columns was rigid coupling. Vertical loads were applied as the form of area loads. e beam end was coupled for cycle loading.
e element of reinforced concrete is SOLID 65. e steel bars are dispersed in the concrete. e element of corrugated steel plate shear wall is SHEEL 181. e contact between elements is via the common nodes by cutting. e model is 3D. e boundary conditions at the base of the corrugated plates are solid joint.

Constitutive Model.
On the basis of existing research, our team had published [19] about the material modes including concrete model, steel bar model, and corrugated steel plate model. e concrete model had an ascending part and descending part, which are shown in Figure 5. e steel bar and steel plate model was divided into two straight lines. In other words, the stress was close to ideal plasticity in a large deformation after reaching the yield strength. Steel bar and corrugated steel plate model are shown in Figure 6.

Verification of Finite Element Models.
Our team [19] had verified the finite element model through comparing the hysteretic curves and skeleton curves of experimental and finite element results. e deviation of peak loads was 0.88% and 1.92%, respectively.

Finite Element Modeling of Nonductile RC Frame.
Based on the verification of finite element models, the paper established the seismic behavior of nonductile RC frame retrofitted by corrugated steel plate shear walls slotted with columns only. e nonductile RC frame (ND-1) and the reinforced frame (ND-2) are shown in Figures 7(a) and 7(b). Slit width of Specimen ND-2 was 10 mm.

Strength and Ductility.
e hysteretic curves and skeleton curves of Specimen ND-1 and Specimen ND-2 are shown in Figures 8 and 9. e yield load, ultimate load, displacements, and ductility can be seen in Table 2. It indicated that the strength had been improved 100.76% when the nonductile RC frame was strengthened with corrugated steel plate shear walls. e ductility was improved from 2.86 to 3.67.

Stiffness.
e stiffness curves of Specimen ND-1 and Specimen ND-2 are shown in Figure 10. e initial stiffness and ultimate stiffness can be seen in Table 3. It showed that the initial stiffness and ultimate stiffness had been enhanced by 63.85% and 38.26%. e stiffness had been improved greatly.

Energy Dissipating Capacity.
e accumulated energy dissipation curves of Specimen ND-1 and Specimen ND-2 are shown in Figure 11. It showed that the accumulated energy dissipation of Specimen ND-1 and Specimen ND-2 was 1602.26 kN mm and 10138.14 kN mm. e energy dissipation improved by 84.20%.

Parameters Analysis
e paper discussed 24 specimens (ND-1-ND-24) in different influence parameters. e influence parameters are listed in Table 4. It can be seen from the table that the slit width was composed of 5 mm, 10 mm, 20 mm, 30 mm, 40 mm, 60 mm, 100 mm, 200 mm, 300 mm, and 400 mm. e selected slit width was on the basis of Zhao [20] team research. e thickness of corrugated steel plate shear walls was divided into 0.4 mm, 0.6 mm, and 0.8 mm. e selected thickness was in the light of experiments and finite element analysis [19,21]. e concrete compressive strength of nonductile RC frame was 30 MPa, 40 MPa, 50 MPa, and 60 MPa, respectively. Boundary conditions of corrugated steel plate shear walls at slotted parts were divided into two parts: Z-direction constraint and without constraint.

Discussion
Hysteretic curves, skeleton curves, ductility, and stiffness are discussed in this section. e influence parameters are slit width, thickness, concrete strength, and boundary conditions. As can be seen in Table 4    Advances in Civil Engineering finite element analysis [19,21]. e reason for selecting big difference slit width was to contrastively analyze the mechanical property under the big difference slit width from Section 5.1 to Section 5.4. It can be seen from the figures that the hysteretic curves were not full while the slit width was larger. In the other words, the plump degree declined with the increase of corrugated steel plate width. It manifested that corrugated steel plate shear walls slotted with columns could achieve good dissipation capacity. When the slit width was within the scope of 200 mm, the energy dissipating could gain good performance.

Skeleton Curves.
e skeleton curves of different slit width are shown in Figure 13. Loads, displacement, and ductility of different slit width are listed in Table 5. e skeleton curves had the same trend. Because of the convergence of finite element models, the paper compared different strength under the displacement of about 50 mm. e skeleton curves derived from the maximum load and displacement of each hysteretic loop and the yield loads and ultimate loads are listed in Table 3        Advances in Civil Engineering were 10 mm, 100 mm, 200 mm, and 400 mm, respectively. e strength declined witg the increase of the slit width.

Ductility.
e ductility of different slit width can be seen in Table 5. e ductility was 3.67, 3.28, 3.26, and 3.18, respectively. e value of ductility was above 3.0, which indicated that nonductile RC frame retrofitted by corrugated steel plate shear walls slotted with columns gained enough ductility.

Stiffness Curves.
e stiffness curves of different slit width are presented in Figure 14. e initial stiffness and ultimate stiffness of different slit width are presented in Table 6. When the slit width was 10 mm, the structure gained greater initial stiffness. When the slit width was in the scope of 100 mm-200 mm, the stiffness was closely relatively and decreased somewhat. e initial stiffness decreased largely when the slit width changed into 400 mm.

Skeleton Curves.
e skeleton curves of slit widths 5 mm and 100 mm are shown in Figures 17 and 18. Loads, displacement, and ductility of different thickness are listed in Table 7. When the slit width was 5 mm, the ultimate loads of    Advances in Civil Engineering thickness 0.6 mm and 0.8 mm were improved by 34.15% and 53.03% compared to that of thickness 0.4 mm, respectively. When the slit width was 100 mm, the ultimate loads of thicknesses 0.6 mm and 0.8 mm were improved by 44.20% and 78.55% compared to that of thickness 0.4 mm, respectively.

Ductility.
e ductility of different thickness can be seen in Table 7. It can be seen from the table that the ductility was enhanced with the increase of thickness. When the slit width was 5 mm, the ductility was from 4.19 to 4.52. When the slit width was 100 mm, the ductility was from 3.24 to 3.34. It indicated that the space between the columns and corrugated steel plate shear walls worked and gained good ductility. e columns were protected from the additional bending moment and axial force of corrugated steel plate shear walls.

Stiffness Curves.
e stiffness curves of slit width 5 mm and 100 mm are presented in Figures 19 and 20. e initial stiffness and ultimate stiffness of different thickness are presented in Table 8. e thickness 0.8 mm obtained larger stiffness than thickness 0.6 mm and 0.4 mm. Initial stiffness of thickness 0.6 mm was improved by 35.50% and 45.73% than that of thickness 0.4 mm. Initial stiffness of thickness 0.8 mm was improved by 44.59% and 89.41% than that of thickness 0.4 mm. It showed that nonductile RC frame retrofitted by corrugated steel plate shear walls slotted

Ductility.
e ductility of different concrete strength is presented in Table 9. It can be seen from the table that the ductility was enhanced with the increase of concrete strength. When the slit width was 60 mm, the ductility was from 3.42 to 3.62. When the slit width was 200 mm, the ductility was from 3.26 to 3.65. It indicated that the strengthened non-ductility RC frame earned good seismic performance in the scope of 60 MPa.

Stiffness Curves.
e stiffness curves of slit width 60 mm and 200 mm are presented in Figures 25 and 26. e initial stiffness and ultimate stiffness of different concrete strength are presented in Table 10. e concrete strength 60 MPa had the largest initial stiffness 5.93 kN/mm and the concrete strength 30 MPa had the smallest initial stiffness 4.48 kN/mm when the slit width was 60 mm. e concrete strength 60 MPa had the largest initial stiffness 5.32 kN/mm and the concrete strength 30 MPa had the smallest initial stiffness 4.32 kN/mm when the slit width was 200 mm. e stiffness was increased by 32.37% and 23.15%, respectively. It indicated that concrete strength influenced stiffness was not as large as the thickness parameter.

Hysteretic Curves.
e paper chose slit width 20 mm, 30 mm, 40 mm and 300 mm to study the influence of boundary conditions. e boundary conditions were with and without Z-direction constraint on the edge of corrugated steel plate shear walls. e hysteretic curves of slit width 20 mm, 30 mm, 40 mm and 300 mm are shown in Figures 27(a) and 27(b)-30(a) and 30(b). ese figures indicated that the strength and energy dissipation were improved with Z-direction constraint.
e Z-direction constrain transferred the internal shear better. It made better use of materials of the edge of corrugated steel plate shear walls.

Skeleton curves.
e skeleton curves of slit width 20 mm, 30 mm, 40 mm and 300 mm are shown in Figures 31-34. Loads, displacement and ductility of different boundary conditions are listed in Table 11. When the slit width was 20 mm, the ultimate loads of Z-direction constrain was improved by 13.93% than that of non-constrain. When the slit width was 30 mm, the ultimate loads of Zdirection constrain was improved by 9.26% than that of nonconstrain. When the slit width was 40 mm, the ultimate loads of Z-direction constrain was improved by 11.91% than that of non-constrain. When the slit width was 300 mm, the ultimate loads of Z-direction constrain was improved by 27.71% than that of non-constrain.

Ductility.
e ductility of different boundary conditions is presented in Table 11. It can be seen from the table that the ductility was improved with Z-direction constrain. However, the enhancement was not so obvious. e improved range was 1.71%, 1.69%, 0.57% and 2.88%, respectively. It indicated that changing the boundary conditions had little effect on ductility.

Stiffness Curves.
e stiffness curves of slit width 20 mm, 30 mm, 40 mm and 300 mm are presented in Figures 35-38. e initial stiffness and ultimate stiffness of different boundary conditions are presented in Table 12. It can be seen from the table that the Z-direction constraint was improved 13.23%, 13.81%, 7.80%, 27.49% than that of non-constraint, respectively. e trend of stiffness curves were in accordance with each other. e improved amplitude was not a large increase.

Explanation of Slotted Principle.
e proposed slotted principle was based on the following principles. When shear walls adopt plain plate, the shear buckling tends to occur at lower lateral forces. en shear walls take lateral loads through oblique tension band action. e columns anchor the oblique tension band while the tension belt also causes a relatively high additional bending moment to the columns [22]. e proposed corrugated steel plate shear walls have ribs on the surface, which improves buckling strength prominently. It solves the buckling of plain plate easily. rough the analysis of each parameter in the paper, it can be seen that corrugated steel plate shear walls transmit force in the form of in-plane shear. e force form accords with the slotted principle. Strength, ductility, stiffness, and energy dissipating perform well within a reasonable slit range. e nonductile RC frame gained good seismic performance.

Conclusions
Two specimens, Specimen ND-1 and Specimen ND-2, are compared. ere were 24 models to research the seismic behavior on different influence parameters. e parameters are slit width, thickness of corrugated steel plate shear walls, concrete strength of nonductile RC frame, and boundary conditions of corrugated steel plate shear walls at slotted  parts. Hysteresis curves, skeleton curves, ductility, and stiffness curves were researched in the paper. e following conclusions can be drawn: (i) To verify the availability of the models, the simulated results were compared with experimental results. e effective model indicated that the corrugated steel plate shear walls slotted with columns played a positive role in seismic behavior. (ii) e paper selected four slit widths (10 mm, 100 mm, 200 mm, and 400 mm) to study the seismic performance of reinforced nonductile RC frame. Hysteresis curves and skeleton curves manifested that the strength was declined when the slit width was larger. Ductility had been improved in the strengthening with corrugated steel plate shear walls. Ductility was above 3.0 and the ductility was larger with the slit width being smaller. Stiffness was enhanced with the decrease of slit width. (iii) With the thickness of corrugated steel plate shear walls increasing, the strength, ductility, stiffness, and energy dissipating capacity were enhanced greatly. e reinforced nonductile RC frame had enough seismic performance. (iv) With concrete strength increasing, the strength and stiffness were enhanced gradually. e influence of concrete strength on ductility was little. (v) Boundary conditions of corrugated steel plate shear walls at slotted parts were an important influence on nonductile RC frame. With the boundary conditions, larger strength, ductility, and stiffness can be gained. However, the increase was not very significant. (vi) When the slit width was within the scope of 300 mm, the seismic behavior of nonductile RC frame slotted with corrugated steel plate shear walls could gain good performance.

Data Availability
All relevant data used in this study are within the paper and its Optional Supplementary Materials.

Conflicts of Interest
e authors declare that they have no conflicts of interest.