Research Article  Open Access
Yinghui Li, Huanjun Jiang, T. Y. Yang, "Damage Deformation of FlexureYielding SteelReinforced Concrete Coupling Beams: Experimental and Numerical Investigation", Advances in Civil Engineering, vol. 2019, Article ID 7071243, 15 pages, 2019. https://doi.org/10.1155/2019/7071243
Damage Deformation of FlexureYielding SteelReinforced Concrete Coupling Beams: Experimental and Numerical Investigation
Abstract
SRC coupling beams offer many significant advantages, including the reduction in section depth, reduced congestion at the wall boundary region, improved degree of coupling for a given beam depth, and improved deformation capacity. In this paper, 7 halfscale flexureyielding SRC coupling beams designed according to Chinese approach have been tested under cyclic loads. Detailed parameters such as aspect ratios, steel reinforcement ratios, and steel flangeweb ratios were systematically studied, and the damage behavior of SRC coupling beams were presented in this paper. The test results show that the aspect ratio, steel ratio, and steel flangeweb ratio have great influence on the damage behavior of SRC coupling beams. Threedimensional nonlinear finite element models were constructed and benchmarked through comparison with test results for both global and local damage deformation behavior. Based on the material damage and strength degradation, four performance levels were defined and corresponding chord rotation limits were obtained through the verified numerical analysis.
1. Introduction
Reinforced concrete shear wall (RCSW) with the coupling beam is one of the most prevalent seismic force resisting systems used for medium and highrise constructions worldwide [1]. In this structural system, seismic forces are resisted through a combination of flexural action of the shear walls and frame action between the shear walls and coupling beams. Under such frame action, the coupling beams should be properly designed to transfer adequate forces between adjacent walls. In addition, coupling beams are expected to be used as primary fuses to dissipate earthquake energy as they undergo inelastic deformation [2]. Therefore, the deformation capacity and energy dissipation capacity are also important for coupling beams.
Conventionally reinforced concrete coupling beam design typically results in diagonally reinforced deep beam to satisfy the stiffness, strength, and energy dissipation demands while creates constructability challenges and increases construction time and cost. Steelreinforced concrete (SRC) coupling beams provide an attractive alternative, thanks to its more attractive behavior. SRC coupling beams offer potential advantages of reduced section depth, reduced congestion at the wall boundary region, improved degree of coupling for a given beam depth, and improved deformation capacity [3]. Therefore, reinforced concrete shear wall (RCSW) with steelreinforced concrete (SRC) coupling beams is one of the new innovations in the composite seismic force resisting systems and has been widely used in Asia and North America.
Gong and Shahrooz [4] tested four onethirdscale shearyielding SRC coupling beams and found that reinforced encasement around the steel enhanced the strength and stiffness. Based on an equation developed and calibrated to test results by Gong and Shahrooz [5], the 2010 AISC Seismic Provisions [Eq. (H53)] recommend computing the expected shear strength, V_{ne}, of an SRC coupling beam aswhere is the nominal compressive strength of the concrete, is the beam section width, is the beam section effective depth, is the area of transverse reinforcement, is the nominal yield strength of transverse reinforcement, s is the spacing of transverse reinforcement, is the ratio of the expected to nominal yield strength of structural steel, is the nominal yield strength of structural steel, is the web thickness of encased steel, is the crosssectional height of encased steel, and is the flange thickness of encased steel. Su and Lam [6] tested eight halfscale steel platereinforced concrete coupling beams of short and mediumlength spans and proposed a unified design approach. Motter et al. [3] tested four onehalf scale flexureyielding SRC coupling beams embedded into reinforced concrete structural walls for realistic loading conditions and found that with adequate encased steel embedment and wall reinforcement, the performance of flexureyielding SRC coupling beams can meet or exceed that of conventionally or diagonally reinforced concrete coupling beams. Motter et al. [7] modified equation (1) to calculate nominal shear strength of SRC coupling beams as follows:
Although a number of SRC coupling beams have been tested [4–8], those results generally showed that SRC coupling beams can provide good seismic behavior; stirrups, longitudinal rebars, and embedment of encased steel have a significant impact on the failure modes of SRC coupling beams. However, those researches paid little attention to SRC coupling beam damage development during the whole loading process, which is an important reference in assessing the seismic performance of structures or structural components [9, 10]. In addition, there are two main types of encased steel used in composite coupling beams, which are Hshaped steel [3–5, 7, 8] and steel plate without flange [6]. However, the comparison research between these two types of encased steel on seismic performance of coupling beams is limited.
In this paper, the cyclic test of 7 halfscale flexureyielding SRC coupling beams designed according to Chinese code JGJ1382016 [11] is presented and damage development was recorded throughout the whole loading process. The main design parameters studied are aspect ratio (spantodepth ratio), steel ratio (ratio of encased steel section area to beam section area), and steel flangeweb ratio (ratio of flange steel section area to web steel section area of encased steel). In order to develop further insight into the observed experimental behavior, this paper also presents the development and benchmarking of detailed 3D nonlinear finite element models for predicting the damage behavior of the tested SRC coupling beams. The models explicitly account for material inelasticity including concrete cracking and interaction behavior between rebar, encased steel, and concrete and are benchmarked using results from the experimental program. Based on the damage characters and strength degradation, four performance levels were defined and corresponding chord rotation limits were obtained through the verified numerical analysis.
2. Test Program
2.1. Test Specimens
Seven halfscale SRC coupling beams with various span lengths and steel configurations were tested. To ensure the SRC coupling beams are well connected to the concrete pedestal, an embedment length of encased steel welded with shear studs and longitudinal bars in the pedestal is selected as 700 mm, which is more than sufficient to be treated as a fixed boundary condition. The calculation for the embedment length of encased steel will be discussed at the end of this section. Since this study just focuses on the damage deformation of SRC coupling beams, the damage deformation of wall piers that are connected to SRC coupling beams is expected to be zero. Therefore, the pedestal is constructed not to simulate a shear wall but just to serve as a rigid block to fix the SRC coupling beams, and the rebar in pedestal is designed more than enough to resist shear and moment from the coupling beam end. In addition, as the SRC coupling beams are designed as flexureyielding which behavior is expected to be governed by flexure, only half of the SRC coupling beam instead of the whole span is tested in the laboratory, which is similar to other researches [3–5,7]. The beam specimens are free to elongate in this test since the axial load from restrained adjacent coupled walls is approximately 4–7% of axial load capacity of coupling beams [12], which is relatively small and is negligible in this research. To ensure the bonding between the encased steel and concrete, 10 mm diameter shear studs spaced at a distance of 100 mm were welded on the flange and web of encased steel according to Chinese code JGJ1382016 [11].
The cross sections of specimens are identical that the height is 500 mm and width is 300 mm, and the longitudinal and transverse reinforcements of specimens are also identical. Figure 1 shows the dimensions of the specimens, the steel reinforcement and encased steel details, and the perspective view of the specimens. The detailed design parameters especially the beam length and encased steel configuration of specimens are shown in Table 1. Specimens Beam1, Beam2, and Beam3 have all the parameters same except the aspect ratio (spantodepth ratio is equal to 2L/500). Specimens Beam1, Beam4, and Beam5 have all the parameters same except the steel flangeweb ratio (area ratio of flange steel to web steel of encased steel is equal to 2t_{f}B_{s}/(H_{s} − 2t_{f})/t_{w}). Specimens Beam2, Beam6, and Beam7 have all the parameters same except the steel ratio (steel ratio is equal to (H_{s}t_{w} + 2(B_{s} − t_{w})t_{f})/150000). The tensile test results of the steel plate and steel bar are listed in Table 2. The concrete cubic compressive strength f_{cu} is 57.8 MPa.
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Notes: H_{s} represents the cross sectional height; B_{s} represents the flange width; t_{w} represents the web thickness; t_{f} represents the flange thickness. 

The flexural capacity and shear capacity of specimens were calculated based on the tested material strength, and the corresponding resistance capacity of specimens is shown in Table 3. The flexural capacity was calculated using equations in Chinese code JGJ1382016 [11] and fiber section analysis, respectively. The shear capacity was calculated by using equations in Chinese code JGJ1382016 and equation (2) proposed by Motter et al. [7], respectively. The flexural capacity and shear capacity equations of SRC coupling beam with a symmetrical rebar and symmetrical encased steel in Chinese code JGJ1382016 are shown as follows:where is the coefficient modifying the compression stress of concrete compression zone, is the effective depth of concrete compression zone, is the nominal yield strength of longitudinal reinforcement, is the area of longitudinal reinforcement, is the distance from center of compression rebar to the edge of compression zone, is the area of encased steel flange, is the distance from center of compression encased steel flange to the edge of compression zone, is the distance from upper edge of encased steel web to the edge of compression zone, is the distance from lower edge of encased steel web to the edge of compression zone, and is the nominal tensile strength of the concrete. A similar result for moment capacity and shear capacity was obtained using different equations or methods, which proves the accuracy of the equations or methods. In addition, the lateral load resistance capacity calculated by M_{n}/L is smaller than that calculated by V_{n}, which testifies the flexureyielding design intention.
The minimum required embedment length of encased steel is determined using Equation H42 in the 2010 AISC Seismic Provisions by taking equal to M_{n}/L, which equation is modified considering the effect of concrete cover [3] and is shown as follows:where is the shear capacity of the embedded steel, t_{wall} is the thickness of the shear wall connected to SRC coupling beams and is taken as 860 mm in this study which is the width of the pedestal, is the depth factor, relating the depth of the Whitney stress block to the neutral axis depth, and c is the concrete cover thickness of the pedestal. The maximum required embedment length of seven SRC coupling beam specimens calculated using equation (5) is 435 mm. Considering the connection between lateral hydraulic actuator and reaction wall in the laboratory, the embedment length (the height of the pedestal) is determined to be 700 mm, which is more than sufficient to fix the SRC coupling beam specimens.
2.2. Test Setup
The test setup that is illustrated in Figure 2 was used in this study, which consists of a rigid floor, a reaction wall, a hydraulic actuator, instrumentations, and data acquisition systems. The specimens were tested under reversed cyclic lateral load using the servocontrolled hydraulic actuator. Before the specimen reaching the yielding point which was monitored by the outmost strain gauges attached to the encased steel, the lateral load was controlled by force and just one reversed cycle was loaded during each loading level. Then after that, the lateral load was controlled by displacement and three reversed cycles were loaded during each loading level. The lateral loading protocol of specimen Beam1 is shown in Figure 3, and each reversed loading cycle was finished in 2 minutes.
Linear variable displacement transducers (LVDTs) were installed to the specimens to measure the lateral displacements and the curvatures in the critical regions. Strain gauges were attached to measure the strain of steel plates and steel bars at plastic hinge zones. The values of the lateral load, the global and local displacements, and the strains were recorded automatically through the data acquisition system throughout the whole loading process. Typical damage states including crack evolution, concrete crushing and spalling, and rebar buckling and fracture were recorded through observation and photographs during the loading process. During the first cycle of each loading level, the maximum crack width was measured at largest lateral load or largest displacement and the corresponding maximum residual crack width was measured at zero loads. The crack width was measured using the crack comparison card, which has a measurement range of 0.02–5 mm.
3. Test Results
3.1. Damage Behavior
The sequence of observed typical damage states is similar for all specimens, and the typical damage states of specimen Beam1 at different loading levels are illustrated in Figure 4, which is a representative for all specimens. In general, the damage started by forming horizontal cracks at the bottom of the specimen at the tension side, as shown in Figure 4(a). Then, the oblique cracks started to appear when the lateral load reaches 500 kN, as shown in Figure 4(b). Tensile yielding of the steel flange was detected using strain gauges with the increase of loading levels. At this instant, the force control loading protocol was switched to the displacement control mode. Afterwards, the initial concrete crushing of compressive side at the bottom of the specimen was observed when lateral displacement reaches 10 mm, as shown in Figure 4(c). Under the following load cycles, the large cracks concentrated at the interface, as shown in Figure 4(d). Then, the spalling of concrete cover appeared when the lateral displacement reaches 22.5 mm, as shown in Figure 4(e). At this loading level, the lateral load carrying capacity of specimen started to fall off. After concrete cover of the specimen completely spalled off, the longitudinal bars and hoops outcropped and then the longitudinal bars buckled during the following cycles when the lateral displacement reaches 27.5 mm, as shown in Figure 4(f), and the fracture of the longitudinal bars was observed at subsequent larger lateral displacement which is 32.5 mm, as shown in Figure 4(g). The test continued with the lateral displacement increased gradually until the global instability appeared when the lateral displacement reaches 42.5 mm. After the test, the concrete was removed and the fracture of encased steel was observed, as shown in Figure 4(h), and no encased steel buckling was found.
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The typical damage development was roughly the same for the seven specimens. All specimens exhibited flexureyielding behavior since steel web yielding occurred later than steel flange yielding, and no hoop rebar of specimens was found yielding before longitudinal rebar buckling or fracture. The typical damage development was as follows: horizontal cracking on the tensile side of the specimen, tensile yielding of the steel plate and rebar, principle tensile yielding of steel web, concrete crushing and spalling on the compressive side of the specimen, and rebar buckling and fracture.
The crack distribution of specimens Beam 1, Beam 2, and Beam 3 with different aspect ratios before concrete spalling is shown in Figure 5. With the increase of aspect ratio, the cracking region is enlarged, and more flexural cracks and less diagonal cracks occurred. The flangeweb area ratio and steel ratio have little influence on the crack distribution.
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3.2. Force and Deformation Characteristics
Lateral load versus chord rotation (lateral displacement divided by specimen length) hysteretic curves of specimens and corresponding skeleton curves with typical damage states marked on it are shown in Figure 6. The hysteretic curves of specimens show SRC coupling beams exhibited little pinching effect and small degradation behavior until the longitudinal rebars were fractured, which shows SRC coupling beams have excellent energy dissipation capability. By comparing specimens Beam1, Beam2, and Beam3, the hysteresis behavior is similar among these three specimens. In general, the specimen with higher aspect ratio results in smaller hysteresis loops since the lateral load resistance capacity is lower at same lateral chord rotation. By comparing specimens Beam1, Beam4, and Beam5, increase flangeweb area ratio results in fuller (smaller pinching) and more stable (smaller strength degradation) hysteresis loops, since flange steel contributes to SRC coupling beam flexural behavior more than web steel. By comparing specimens Beam2, Beam6, and Beam7, increased steel ratio also results in fuller and more stable hysteresis loops, as larger steel ratio leads to more flange steel and more web steel.
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Table 4 lists the mean values of chord rotation at the damage characteristic points in the specimens’ skeleton curves in two opposite loading directions. Experimental results show that although the longitudinal bars were placed outside the encased steel, encased steel still yielded before the longitudinal bars since the yielding strain of the longitudinal bars is 75% larger than the encased steel (as shown in Table 2). After the longitudinal bars fractured, the specimens can still experience larger displacement with small lateral load carrying capacity degradation because the encased steel plate possessing much larger deformation capacity than the steel bar was still effective to resist the lateral load.
 
Note: θ_{c}, θ_{sty}, θ_{rty}, θ_{swy}, θ_{cc}, θ_{cs}, θ_{rb}, and θ_{rf} represent the chord rotation of specimens at damage states of concrete cracking, steel tensile yielding, rebar tensile yielding, steel web principle tensile yielding, concrete crushing, concrete spalling, rebar buckling, and rebar fracture, respectively. For Beam5, rebar tensile yielding and steel web principle tensile yielding occurred at the same time. For Beam6, steel tensile yielding and rebar tensile yielding occurred at the same time. 
For specimens Beam1, Beam2, and Beam3 with different aspect ratios, specimen Beam1 with the aspect ratio of 2 has the largest lateral load carrying capacity, which is 1148.7 kN and is 2.46 times that of specimen Beam3 and 1.53 times that of specimen Beam2, which means that the lateral load carrying capacity changes in inverse proportion with the aspect ratio, and all specimens reached its flexural strength. In general, the larger aspect ratio specimen tends to have smaller lateral load carrying capacity at the individual damage characteristic point. Considering displacements of the individual damage state, the initial damage states (concrete cracking, steel tensile yielding, and rebar tensile yielding) of specimen Beam3 with a aspect ratio of 5 tend to occur later than those of specimen Beam1 with a aspect ratio of 2, which is consistent with the elastic chord rotation equation of the Timoshenko cantilever beam, which is as follows:where M is the fixed end section moment of the cantilever beam, L is the length of the cantilever beam, E is the elastic modulus, I is the section moment inertia, G is the shear modulus, and A is the effective shear section area. When L is larger than (h is the beam section height), chord rotation increases with the increase of the beam length under the same fixed end moment. The damage states such as steel web principle yielding, concrete crushing, concrete spalling, rebar buckling, and rebar fracture of specimen Beam3 tend to occur earlier than those of specimen Beam1 because specimen Beam3 has a relatively smaller moment gradient at the plastic zone, which causes flexural damages of Beam3 to occur easily, and smaller shear force in Beam3 leads to smaller shear deformation also.
For specimens Beam1, Beam4, and Beam5 with different flangeweb area ratios of encased steel, specimen Beam4 with a flangeweb ratio of 0.5 has the largest lateral load carrying capacity, which is 1186.6 kN and is 3.3% larger than that of specimen Beam1 and 22.5% larger than that of specimen Beam5, which means that the specimen without the flange of encased steel has a significant smaller lateral load carrying capacity. The reason that specimen Beam4 with a smaller flangeweb ratio has slightly larger lateral load capacity than specimen Beam1 is that the encased steel consists of steel plates with different thicknesses and different yielding strengths, and the average yielding strength of encased steel of specimen Beam4 is slightly larger than that of specimen Beam1. The calculated lateral load capacity (M_{n}/L) for specimens Beam4 and Beam1 shown in Table 3 verified this explanation. Considering the displacements of individual damage states, except the damage states like steel tensile yielding and rebar tensile yielding, the other damage states of specimen Beam1 with a flangeweb ratio of 1 tend to occur later than those of specimen Beam5 with a flangeweb ratio of 0. This is because the flange steel enhances the compression behavior of the concrete and delays the concrete crushing and spalling. In addition, shear deformation of specimen Beam1 with smaller web steel is larger than that of specimen Beam5 at the same damage state.
For specimens Beam2, Beam6, and Beam7, with the increase of steel ratio from 5% to 8.3%, the lateral load carrying capacity increases from 750.3 kN to 968.8 kN by 29.2%, which means that the lateral load carrying capacity of SRC coupling beam was influenced largely by the steel ratio. Except initial damage states like concrete cracking, rebar tensile yielding, and steel web principle tensile yielding, the other damage states of specimen Beam6 with a steel ratio of 6.7% tend to occur later than those of specimen Beam2 with a steel ratio of 5% and Beam7 with a steel ratio of 8.3%.
Concrete cover cracking influences the encased steel corrosion initiation and the crack width influences the corrosion propagation; thus, both influence the performance of structures [13]. The maximum residual crack width of all specimens, represented by W_{m,res}, was measured during the test cycles before concrete cover crashed or spalled. The variation of maximum residual crack width with the chord rotation is shown in Figure 7. Generally, the maximum residual crack width rises up with the increase of the chord rotation. The maximum residual crack width of the specimen at the same rotation tends to be smaller with the increase of the aspect ratio or steel ratio for the average value of that for both directions. For specimens Beam1, Beam4, and Beam5 with different flangeweb area ratios of encased steel, Beam4 has the smallest maximum residual crack width while Beam1 has the largest maximum residual crack width at the same rotation.
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4. Numerical Analysis and Verification
4.1. Modeling
Threedimensional nonlinear finite element models were developed to simulate the inelastic behavior of tested SRC coupling beam specimens using Abaqus [14]. Not only the global forcerotation behavior but also the local material damage behavior during the test process including concrete (cracking, crushing, and spalling), steel yielding, and rebar (yielding, buckling, and fracture) was predicted through finite element analysis. It has been reported [15–17] that material damage states, i.e., spalling and yielding, are not dependent on the history of loading but are rather closely related to the maximum displacement that the structure has experienced. Therefore, a monotonic analysis was sufficient for predicting damage deformation of flexureyielding SRC coupling beams.
Damaged plasticity model was used to simulate the concrete inelastic behavior in SRC coupling beam specimens. This model is applicable in the situation that the concrete is at low confinement pressures (less than four to five times the largest compressive stress that can be carried by the concrete in uniaxial compression), which is suitable for SRC coupling beams. Moon et al. [18] used this model to study the confinement effect of steel tubes on the infilled concrete, and Babazadeh et al. [17] used this model to study the spalling of the concrete for RC bridge columns. The uniaxial stressstrain relationship for the concrete recommended in Chinese code GB500102010 [19] was adopted here, as shown in Figure 8(a). The compression strength of the concrete is 37.3 MPa, which is the prismatic compression strength of concrete f_{ck}, which is calculated based on the conversion formula in Chinese code 500102010 [19], and the tested cubic compression strength of concrete f_{cu} is equal to 57.8 MPa.
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Ductile damage plasticity model was used to simulate the encased steel and rebar inelastic behavior in SRC coupling beam specimens. This model offers a general capability for predicting the onset of failure and a capability for modeling progressive damage and failure of ductile metals. Zhu et al. [20] used this model to simulate the steel tearing of concretefilled steel tube columns. The strengthening stage of steel adopted a bilinear model, hardening stiffness of which is 1% of elastic stiffness, and damage initiated at tensile strain and damage evolution adopted a linear damage form. Considering the cyclic fatigue of longitudinal rebar under earthquakes, Priestley [21] suggested the tensile strain of the longitudinal rebar to be reduced by 40%. Shi et al. [22] carried out the structural steel low cycle fatigue test and proved that the tensile strain of Q345B steel was reduced by 20.3% and Q235B steel was reduced by 38.6% after cyclic loading. The fracture strain was conservatively taken as two times tensile strain refer to the former test results. The uniaxial stressstrain relationship for the 12 mm diameter rebar is shown in Figure 8(b).
Eightnode solid elements with reduced integration (C3D8R) were used for the concrete, fournode shell elements with reduced integration (S4R) were used for the encased steel, and twonode linear displacement truss elements were used for rebar. A perfect bond was assumed between the steel, rebar elements, and the concrete part; therefore, the truss elements and shell elements were embedded in the concrete instance using the ∗EMBEDDED ELEMENT option. The bottom surface of the pedestal was fixed against all degrees of freedom. A reference point was modeled on the surface of the loading plate, which was constrained with the surface of the loading plate using the ∗COUPLING option available in the ABAQUS library.
4.2. Analysis Results
The global skeleton curves of all the specimens obtained from the FEA are compared with the skeleton curves obtained from the test, and two of them are shown in Figure 9. The FEA model gave a stiffer result in the positive part and softer one in the negative part for specimen Beam1 compared to the experimental result, which may be due to the slippage of the pedestal or the gap between loading head and specimen in the test. The local material damages obtained from FEA are also compared with test results, and concrete spalling and rebar fracture are shown in Figure 10. From the qualitative comparison, good agreement is achieved between experimental and FEA results not only on the global behavior but also on the local material damage behavior.
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Concrete crushing and spalling were predicted through the compression strain of concrete. Priestley [21] suggested a value of 0.004 for cover concrete edge compressive crushing strain, and Jiang et al. [23] proposed an equation to calculate the confined concrete edge compression spalling strain, which is equal to 0.005 for test specimens. The concrete crack width was predicted through the tensile strain of rebar. Priestley [21] suggested a value of 0.01 for longitudinal rebar tensile strain to control the residual crack width within 1.0 mm. The chord rotations corresponding to different concrete damage states obtained from finite element analysis were compared with the test result, as shown in Table 5. From the quantitative comparison for concrete damage deformation, finite element analysis can only provide a statistically consistent simulation result not specifically accurate simulation result for each specimen. The mean rotation ratios between FEA and the test for the concrete residual crack width equal to 1 mm, concrete crushing, and concrete spalling are 0.99, 0.83, and 0.74, respectively. If the cover concrete edge compression crushing strain is revised to 0.005 and confined concrete edge compression spalling strain is revised to 0.0075, the mean rotation ratios between FEA and the test for concrete crushing and concrete spalling are 1.04 and 1.03, respectively.

Steel flange tensile yielding and web principle tensile yielding were predicted directly through steel yielding strain recorded in Table 2. The chord rotations corresponding to different steel yielding states obtained from finite element analysis were compared with the test result, as shown in Table 6. The finite element analysis can provide a statistically consistent simulation result, and the mean rotation ratios between FEA and the test for steel flange tensile yielding and steel web principle tensile yielding are 1.23 and 1.08, respectively.

Rebar tensile yielding and rebar fracture were predicted directly through rebar yielding strain and tensile strain recorded in Table 2. Rebar buckling was predicted through confined concrete ultimate compressive strain, which is calculated using equation suggested by Priestley [21]. The chord rotations corresponding to different rebar damage states obtained from finite element analysis were compared with the test result, as shown in Table 7. The finite element analysis can provide a statistically consistent simulation result, and the mean rotation ratios between FEA and the test for rebar tensile yielding, rebar buckling, and rebar fracture are 0.74, 1.03, and 0.90, respectively.

4.3. Performance Index Limit Analysis
The seismic performance of SRC coupling beams is affected by the material damage, which is related to the material strain. On the other hand, the degradation of the load carrying capacity of SRC coupling beams affects its seismic performance also. Based on the study on the material damage strain limits [21, 23] and component strength degradation limits [24], four performance levels are defined, as shown in Table 8. Since there is a lack of test records of specimens’ deformation at damage states of concrete strain equal to 0.002 or crack width equal to 2 mm, the chord rotation of specimens at different performance levels can only be obtained through FEA. Table 9 shows the chord rotations of SRC coupling beam specimens at different performance levels, and then the mean values were adopted as the performance index limits, which were 0.005 rad, 0.014 rad, 0.024 rad, and 0.047 rad for the four performance levels.
 
Note: ε_{y} is the yielding strain of steel or rebar, ε_{su} is the tensile strain of steel or rebar, ε_{cu} is the ultimate strain of the concrete, P_{max} is the lateral load carrying capacity of specimens. 

5. Summary and Conclusions
Seven halfscale flexuralyielding SRC coupling beam specimens designed according to Chinese approach were tested under cyclic load. The influence of design parameters such as aspect ratio, flangeweb area ratio of encased steel, and steel ratio on damage development, hysteretic behavior, strength, and maximum residual crack width were discussed. Finite element analysis was conducted for specimens; both global skeleton curves and local material damage were simulated simultaneously. Through quantitative comparison, finite element analysis can provide a statistically consistent simulation result for material damages for each specimen. Some conclusions are drawn from this research:(1)All specimens failed in flexural mode. The damage development was roughly the same, and the typical damage states were recorded through the whole loading process, which can be used in assessing the seismic performance level of SRC coupling beams.(2)With the increase of aspect ratio, the lateral load carrying capacity drops down significantly and the maximum residual crack width tends to be smaller. With the increase of flangeweb area ratio of encased steel, the hysteretic curve gets fuller. The specimen with intermediate flangeweb area ratio has the largest lateral load carrying capacity but smallest maximum residual crack width. With the increase of steel ratio, the lateral load carrying capacity increases significantly while the maximum residual crack width drops down.(3)The finite element model was benchmarked through comparison with test results for both global loaddeformation curves and local material damages. Both qualitative and quantitative comparisons testify the accuracy of finite element models. The cover concrete edge compression strain and confined concrete edge compression strain were recommended to be 0.005 and 0.0075, respectively, for accurately modeling concrete crushing and spalling. Based on the damage characters and strength degradation, four performance levels were defined and corresponding chord rotation limits were obtained through the verified numerical analysis.
Data Availability
All the data in this paper are obtained from tests and numerical analysis, and no other data in the literature are used to support this study.
Conflicts of Interest
The authors declare that there are no potential conflicts of interest with respect to the research, authorship, and publication of this article.
Acknowledgments
The financial support from the Program of Shanghai Academic Research Leader (grant number 18XD1403900) and the National Key Research and Development Program of China (grant number 2017YFC1500701) is gratefully acknowledged.
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Copyright © 2019 Yinghui Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.