Integrating of Nonlinear Shear Models into Fiber Element for Modeling Seismic Behavior of Reinforced Concrete Coupling Beams, Wall Piers, and Overall Coupled Wall Systems
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Abstract
Reinforced concrete (RC) coupled wall systems, compared with RC shear wall without opening, have more complex nonlinear behavior under the extreme earthquake loads due to the existence of coupling beams. The behavior characteristics induced by nonlinear shear deformation such as shear–flexure interaction, pinching effect, strength and stiffness deterioration are clearly observed in numerous cyclic tests of RC coupling beams and shear walls. To develop an analytical model capable of accurately and efficiently assessing the expected seismic performance of RC coupled wall systems, it is critical to define the appropriate key components models (i.e., nonlinear models of RC wall piers/shear walls and coupling beams). Classic fiber beam element based on the theory of Euler–Bernoulli beam is frequently adopted to simulate the nonlinear responses of slender RC wall piers and coupling beams in the literature because it is able to accurately model the response characters from interaction of axial–bending moment at the section level. However, classic fiber beam element cannot capture the nonlinear behaviors of non-slender structures mainly controlled by nonlinear shear deformation. To overcome this shortcoming, a modified force-based fiber element (MFBFE) including shear effect is introduced and used as the analysis element of non-slender RC coupling beams and shear walls. At the section level, a novel shear model for RC coupling beams and an existed shear model for RC shear walls are respectively added to this fiber element to simulate nonlinear responses of these two key components. The analytical model for RC coupled walls hence is formed through integrating the proposed models of these two key components. The validations with different experimental results of cyclic tests including key components and structural system reported in the literature using these proposed models are performed. Good agreements are achieved for all of these proposed models via comparisons between predicted results and experimental data.
Keywords
reinforced concrete coupled wall systems fiber element including shear effect reversed-cyclic loading nonlinear analysis shear model1 Introduction
Reinforced concrete (RC) coupled wall systems consisting of RC wall piers and coupling beams are efficiently lateral forces resisting systems and can provide enough lateral stiffness for mid- to high-rise buildings to withstand earthquake-type loads. Recent earthquake investigations have demonstrated that this structural type is a reliable and robust design scheme to resist earthquake excitations. Compared to global collapse failure of RC frame structures subjected to strong ground motions, RC coupled walls are generally able to avoid complete collapse yet expose to local fractures in the key components such as shear failure of RC coupling beams and flexural failure at the bottom of wall piers. Shear brittle failure is sudden and unexpected, and occurs with no any symptoms, leading to serious risk for people’s lives and property. As such, engineers and researchers all dedicate to developing effective and reliable strategies to forbid occurrence of such danger failure modes. ACI building code (ACI-318-11 2011) indicates that RC coupling beams with aspect ratio less than 2 and shear stress demand greater than 0.33 \(\sqrt {f_{c}^{'} }\) MPa (4 \(\sqrt {f_{c}^{'} }\) psi) need to be arranged a special diagonal reinforcement layout to prevent the occurrence of shear failure, where \(f_{c}^{'}\) is the compressive strength of concrete.
Wall piers behavior is generally classified according to wall aspect ratio (AR), as either shear-controlled (AR less than 1.0–1.5) or flexure-controlled (AR greater than 2.5–3.0). For walls between these aspect ratios (referred to as moderate aspect ratio walls), nonlinear responses associated with both axial/bending and shear behavior. Recently, a large number of experimental investigations have shown that flexural and shear yielding of moderate aspect ratio walls occur near-simultaneously, even this interaction has been observed on slender RC walls with aspect ratios greater than 2.0 (Wang et al. 1975; Vallenas et al. 1979; Hines et al. 1995, 2002; Sayre 2003; Thomsen and Wallace 2004; Massone et al. 2004; Dazio et al. 2009; Lowes et al. 2012). This interaction between nonlinear flexural and shear behavior, commonly referred to as shear–flexure interaction. Coupling beam behavior is commonly judged according to span–depth ratio. The results obtained from the test conducted by Paulay (1971) on conventionally reinforced coupling beams presented dominant shear behavior with span–depth ratios of 1.02 and 1.29. Failure mechanisms such as diagonal tension or sliding shear were encountered during the tests. Jun et al. (2018) pointed that coupling beams with a span–depth ratio of no more than 2.5 tend to fail in shear-dominant rather than in flexure. Fisher et al. (2018) presents the results from a recent experiment on a coupling beam at the University of Toronto. The results show that a flexure-only analysis would account for only 53% of the total predicted deformation. Addition of the effect of curvature resulting from shear (but not shear strain) increases the predicted percentage to 57%, while, inclusion of shear strains increases the percentage to 100%. To improve the ductility of concrete coupling beams and to suppress the shear failure mode, many studies have been carried out through last decades (Paulay 1974; Tassios et al. 1996; Galano and Vignoli 2000; Lequesne et al. 2012; Han et al. 2015). These experimental studies revealed that coupling beams, when they are diagonally reinforced with enough confinement, can provide adequate stability and excellent ductility.
Numerical analysis has been developed to simulate the seismic behavior of coupled wall systems by many researchers (Takayanagi and Schnobrich 1979; Saatcioglu et al. 1983; Hung and El-Tawil 2011; Hung 2012; Eljadei and Harries 2014; Fox et al. 2014; Harries et al. 2004; Vuran and Aydinoglu 2016; Kim 2016; Kim and Choi 2017). In the reference (Takayanagi and Schnobrich 1979), researchers developed a model used for nonlinear static and dynamic analyses of a 10-story coupled wall structure, in which wall piers and coupling beams were simulated with line elements, and the two ends of every line element defined zero-length springs with assigning the corresponding inelastic materials that was used for modeling the plastic hinges. Saatcioglu et al. (1983) performed nonlinear dynamic analysis of a 20-story coupled wall structure with the scheme that each structural member was idealized as a line element and inelastic behavior was simulated through defining plasticity hinges at member ends; each hinge was designated a hysteretic model that incorporates effects of axial force-moment interaction, shear yielding, strength degradation, pinching, reloading and unloading branches of hysteresis loops. Hung (2012) implemented the hybrid simulation strategy of a 12-story composite coupled wall system in which the displacement-based beam column element was employed to simulate RC shear walls and steel coupling beams respectively; the shear wall cross section was modeled using fiber sections and the steel coupling beams were modeled with considering nonlinear shear and flexural behaviors through the tactic that the moment of inertia of the full cross section was used for bending and the full web area was used for shear; however, the shear behavior of wall was not taken into account in this scheme. Eljadei and Harries (2014) conducted nonlinear static (pushover) and dynamic analyses of a 12-story prototype coupled wall structure; the wall piers were modeled using a general quadratic beam-column model, and the Giberson one-component beams were used for representing the coupling beams. Fox et al. (2014) proposed a simplified capacity design method, with which nonlinear time-history analyses of a set of 15 coupled walls were performed; the flexural and axial responses of coupled walls were simulated by distributed plasticity fiber beam elements with defining the nonlinearity materials at the section level, and additional transverse springs between wall elements were chosen to model shear response of coupling beams; nevertheless, these transverse springs just exhibit linear shear behaviors.
By reviewing the existed coupled wall models above (Takayanagi and Schnobrich 1979; Saatcioglu et al. 1983; Hung and El-Tawil 2011; Hung 2012; Eljadei and Harries 2014; Fox et al. 2014; Harries et al. 2004; Vuran and Aydinoglu 2016), they can be classified as two categories, that is, lumped plasticity models and distributed nonlinearity models. It has been validated that the distributed plasticity models (e.g., classic fiber beam elements) can not only reflect the real plasticity development but produce the accurate response results of RC structures under both static and dynamic loads (Spacone et al. 1996). Classic fiber beam elements (i.e., displacement-based and force-based fiber elements) based on the cross-sectional discretization in a series of fibers have been developed to simulate nonlinear responses of RC structures governed by flexural deformation. With assigning the corresponding uniaxial constitutive models at the section level, the section behavior under axial and bending forces is captured through integrating fiber stresses over the whole cross-section. However, classic fiber beam elements are not capable of considering shear stresses, and thus shear behavior at the section level cannot be directly acquired. To eliminate this limitation, many researchers carried out various studies by introducing the Timoshenko beam theory into the force-based fiber element (FBFE) due to its simplicity, efficiency, and robustness to account for the shear effects of RC structures (Petrangeli et al. 1999; Marini and Spacone 2006). Petrangeli et al. (1999) successfully conducted a fiber section model that can allow for shear stresses, deformations, and stiffness at the section level using a new concrete law based on micro-plane theory. But this model demands extra computation cost at the section level because the additional equilibrium is imposed. A two-dimensional (2D) modified force-based fiber beam element (MFBFE) allowing for uniaxial bending and shear effect based on the Timoshenko beam theory is introduced by (Marini and Spacone 2006), in which the axial and bending responses follow the traditional fiber section model, and shear effect is simulated by a nonlinear V-γ constitutive law at the section level. The shear deformation is decoupled from axial and bending effects in the section stiffness. The shear and flexural forces, nonetheless, are coupled at the element level because of enforced equilibrium along the element. It is noteworthy that this strategy has an unrivaled advantage in simulating shear-critical components, because the element bending moments are constrained by the element shear forces if shear failure at the section level occurs before flexural failure. A large number of numerical analyses of RC structures have been conducted considering flexure-shear interaction using modified force-based fiber beam element (Ferreira et al. 2014; Correia et al. 2015; Almeida et al. 2015; Lucchini et al. 2017; Zimos et al. 2018; Feng and Xu 2018; Bitar et al. 2018). However, these models were developed for RC beams and columns, not suit for coupled walls.
To develop simple, accurate, and efficient models capable of capturing the cyclic behaviors of key components (i.e., diagonally reinforced coupling beams and RC wall piers) and overall coupled wall systems, new modified force-based beam element (MFBBE) and wall element (MFBWE) composed of MFBFE and shear models were developed in MATLAB (2014). This paper presents the formulations of MFBBE and MFBWE, and also the nonlinear force–deformation constitutive laws of concrete, reinforcement bars, and shear models used in these formulations. To examine the efficiency, stability, and accuracy of MFBBE and MFBWE, comparisons with the existed test data of the key components (Lequesne et al. 2012; Han et al. 2015; Gulec and Whittaker 2009) are performed. As confinement effect of the stirrups can improve the plasticity deformation capacity of RC structures, appropriate confined concrete models (Mander et al. 1988; Legeron and Paultre 2003) for the nonlinear cyclic simulation are thus discussed and summarized. At last, a comprehensive structural system model named CWE for RC coupled wall, integrating MFBBE and MFBWE, is proposed and validated through comparison with the experimental data of cyclic tests of two RC coupled wall specimens.
2 Formulation of the MFBFE
3 Fomulation and Validation of the MFBBE
The MFBBE is formulated by integrating a MFBFE and a shear model for diagonally reinforced coupling beams. The MFBFE has been introduced in the previous section. The shear model will be introduced in this section. The shear response of diagonally reinforced coupling beams is simulated using a nonlinear V-γ constitutive law. Considering the specified behavior characteristics of diagonally reinforced coupling beams (e.g., stiffness and strength degradation, and pinching effect induced by nonlinear shear deformations), the hysteretic model needs to be reasonably developed to represent its shear response. For diagonally reinforced coupling beams, the four nonlinear phases corresponding to concrete cracking, longitudinal bars yielded, maximum shear capacity, and ultimate shear failure are experienced during the loading history. The backbone curve of the hysteretic model, therefore, should be determined using four control points in a single load direction so as to describe the nonlinear behavior characters of diagonally reinforced coupling beams, and the hysteretic rules should exhibit the effect of pinching, strength and stiffness deterioration.
3.1 Determination of the Shear Model for Diagonally Reinforced Coupling Beams
3.2 Determination of Shear Force at the Cracking Point
When the cross-section cracks, the edge strain of concrete at the tensile side is equal to the limit tensile strain of concrete, that is, \(\varepsilon_{cx} = \varepsilon_{tu}\). The section curvature keeps constant under the condition of cross-sections remain plan and normal to the deformed longitudinal axis. According to the compatible condition, the strains of longitudinal and diagonal bars can be calculated by the following equations.
3.3 Determination of Shear Displacement at the Cracking Point
3.4 Determination of Shear Force at the Yielding Point
3.5 Determination of Shear Displacement at the Yielding Point
3.6 Determination of Shear Force at the Maximum Point
3.7 Determination of Shear Displacement at the Maximum Point
3.8 Determination of Failure Point
3.9 Determination of Hysteretic Rules
Figure 5 shows a typical reversed shear cycle. The loading starts in the positive load direction and follows the backbone curve for the unload-reload paths described in the previous section when the crack shear force is not reached. Once the crack shear force is exceeded, at point A the load direction is reversed. Unloading from point A follows a straight line shooting for point B whose coordinates are (0.85 δ_{A}, 0) according to the reference (Said et al. 2005). As loading continues in the negative direction, a significant reduction in the tangent stiffness occurs and this allows for the pinching effect experienced by non-slender RC structures under reversed-cyclic loading. Loading in the negative direction proceeds until point C (0.85 δ_{D}, V_{cr}) is reached and the loading path is changed and leads the response to point D, at which loading in the negative direction follows the negative backbone curve. As the loading is re-reversed at point E, the unloading stiffness to point F (0.85 δ_{E}, 0) is calculated in the same way as for the positive direction. After point F, positive loading continues with a reduced stiffness calculated based on the coordinates of point H until the positive reloading branch is reached at point G (0.85 δ_{H}, V_{cr}). Reloading then follows that of the previous reloading branch until the positive backbone curve is reached.
3.10 Model Evaluation and Validation
Design parameters.
Specimen | Lequesne et al. (2012) | Han et al. (2015) | ||
---|---|---|---|---|
CB-1 | CB-2 | SD-2.0 | BD-2.0 | |
\(f_{c}^{'}\), MPa | 41 | 41 | 40 | 40 |
\(f_{y}\) (longitudinal reinforcement), Mpa | 430 | 440 | 506 | 506 |
\(f_{y}\) (ties), Mpa | 525 | 475 | 506 | 506 |
\(f_{y}\) (diagonal reinforcement), Mpa | 430 | 430 | 438 | 438 |
\(f_{u}\) (diagonal reinforcement), Mpa | 680 | 680 | 587 | 587 |
b (beam width), mm | 150 | 150 | 250 | 250 |
h (beam height), mm | 600 | 600 | 525 | 525 |
L (beam length), mm | 1050 | 1050 | 1050 | 1050 |
\(\rho_{d}\) (diagonal bars ratio), % | 1.11 | 1.11 | 2.35 | 2.35 |
\(\rho_{s}\) (stirrup ratio), % | 1.24 | 1.43 | 2.84 | 2.43 |
\(\rho_{l}\) (longitudinal bars ratio), % | 1.9 | 1.9 | 1.42 | 1.42 |
α, degree | 24.6 | 24.6 | 20.4 | 22.1 |
Span–depth ratio, L/h | 1.75 | 1.75 | 2.0 | 2.0 |
4 Fomulation and Validation of the MFBWE
The formulation of the MFBWE is formally identical to that of the MFBBE, but the only thing that is different from the MFBBE is the shear model. For RC shear walls, the three stages regarding reinforcement yielded, maximum shear capacity, and ultimate shear failure are considered as the primary nonlinear behavior. Therefore, the most suitable shear model for RC shear walls should have a backbone curve capable of defining three control points and hysteretic rules that can describe the pinching, strength and stiffness deterioration. The Ibarra-Krawinkle Pinching (IKP) material model (Ibarra et al. 2005) that incorporates energy-controlled stiffness and strength deterioration herein is utilized as the shear model of RC shear walls.
The maximum shear-resistant formula is mainly related to the shape of shear wall section, which can be found in the literature (Gulec and Whittaker 2009).
The residual shear strength for the skeleton curve could be difficult to be either estimated in an empirical formula or calibration in experimental data, because the most of quasi-static cyclic tests were terminated in general before the walls shear strength dropped significantly. For the post-capping stiffness \(K_{c}\), it can be estimated through fitting the experimental data.
Properties of concrete.
Concrete type | f_{cu, 150 mm} (MPa) | f_{c, 150 mm} (MPa) |
---|---|---|
C30 | 20.7 | 19.7 |
C40 | 37.7 | 30.8 |
Properties of reinforcing bars.
Reinforcement type | Φ4 | Φ6 | Φ8 | Φ10 | Φ10 | Φ12 |
---|---|---|---|---|---|---|
Diameter (mm) | 3.91 | 6.54 | 8.05 | 9.41 | 9.74 | 12.55 |
Yielding strength (MPa) | 348 | 392 | 343 | 352 | 379 | 325 |
Ultimate strength (MPa) | 409 | 479 | 447 | 493 | 554 | 195 |
Elastic modulus (MPa) | 198,800 | 200,600 | 206,800 | 202,700 | 181,200 | 169,000 |
Details parameter of specimens.
Specimen | Section dimension (mm) (span × depth × width) | Aspect ratio | Concrete strength | Axial compression ratio | Longitudinal bar | Stirrup |
---|---|---|---|---|---|---|
SW1-1 | 2000 × 1000 × 125 | 2.0 | C30 | 0.1 | 6Φ10 | Φ6@80 |
SW1-2 | 2000 × 1000 × 125 | 2.0 | C30 | 0.2 | 6Φ10 | Φ6@80 |
SW1-3 | 2000 × 1000 × 125 | 2.0 | C30 | 0.3 | 6Φ10 | Φ6@80 |
SW2-1 | 1000 × 1000 × 125 | 1.0 | C40 | 0.3 | 6Φ10 | Φ6@80 |
SW2-2 | 1500 × 1000 × 125 | 1.5 | C40 | 0.3 | 6Φ10 | Φ6@80 |
SW2-3 | 2000 × 1000 × 125 | 2.0 | C40 | 0.3 | 6Φ10 | Φ6@80 |
SW3-1 | 2000 × 1000 × 125 | 2.0 | C30 | 0.2 | 6Φ10 | Φ6@80 |
SW3-2 | 2000 × 1000 × 125 | 2.0 | C40 | 0.3 | 6Φ10 | Φ6@80 |
SW4-1 | 2000 × 1000 × 125 | 2.0 | C40 | 0.3 | 6Φ8 | Φ6@80 |
SW4-2 | 2000 × 1000 × 125 | 2.0 | C40 | 0.3 | 6Φ10 | Φ6@80 |
SW5-1 | 2000 × 1000 × 125 | 2.0 | C40 | 0.3 | 6Φ10 | Φ6@80 |
SW5-2 | 2000 × 1000 × 125 | 2.0 | C40 | 0.3 | 6Φ10 | Φ6@80 |
SW6-1 | 2000 × 1000 × 125 | 2.0 | C40 | 0.3 | 6Φ10 | Φ4@80 |
SW6-2 | 2000 × 1000 × 125 | 2.0 | C40 | 0.3 | 6Φ10 | Φ6@80 |
5 Fomulation and Validation of the Cwe
The comparisons of selected indicators from CWE and test ones.
Specimen | Type | Lower actuator maximum shear/kN | Upper actuator maximum shear/kN | Base maximum shear/kN | Energy dissipation/J | |||
---|---|---|---|---|---|---|---|---|
Positive | Negative | Positive | Negative | Positive | Negative | |||
CW-1 | Test | 423 | − 423 | 987 | − 973 | 1410 | − 1396 | 443,108 |
CWE | 436 | − 436 | 992 | − 977 | 1428 | − 1413 | 475,195 | |
Fiber Model | 458 | − 449 | 1063 | − 1051 | 1521 | − 1500 | 558,292 | |
CW-2 | Test | 596 | − 646 | 1014 | − 1064 | 1610 | − 1710 | 562,755 |
CWE | 579 | − 579 | 1003 | − 987 | 1582 | − 1566 | 595,810 | |
Fiber Model | 637 | − 612 | 1051 | − 1031 | 1688 | − 1643 | 676,166 |
The error comparisons of the selected indicators.
Specimen | Type | Errors in lower actuator maximum shear | Errors in upper actuator maximum shear | Errors in base maximum shear | Errors in energy dissipation | |||
---|---|---|---|---|---|---|---|---|
Positive | Negative | Positive | Negative | Positive | Negative | |||
CW-1 | Test | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
CWE | 3.07% | 3.07% | 0.51% | 0.41% | 1.28% | 1.22% | 7.24% | |
Fiber model | 8.27% | 6.15% | 7.70% | 8.02% | 7.87% | 7.45% | 25.99% | |
CW-2 | Test | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
CWE | − 2.85% | − 10.37% | − 1.08% | − 7.23% | − 1.74% | − 8.42% | 5.87% | |
Fiber model | 6.88% | − 5.26% | 2.64% | − 3.10% | 4.20% | − 3.92% | 20.15% |
6 Discussion of the Models
The modified force-based fiber element (MFBFE) takes into account the element shear deformation, which enables this element to handle a coupled axial–shear–bending response at the element level. At the section level, a novel shear model for RC coupling beams (MFBBE) and an existed shear model for RC shear walls (MFBWE) are respectively added to MFBFE to simulate nonlinear responses of these two key components. The analytical model for RC coupled walls (CWE) is developed through integrating the proposed models of these two key components. The proposed models are validated against coupling beams, shear walls and coupled walls specimens under cyclic loading, compared to the very limited experimental data. It is found that the models can provide a more precise prediction on the response compared with the traditional fiber element, in regards to the initial stiffness, peak shear strength, strength and stiffness degradation, and especially pinching effects.
However, the proposed models have several limitations. First, curvature and shear distortion are uncoupled at the section level and sectional analysis under flexure assumes plane-sections-remain plane in these models. This approach, although practical and sufficient for many cases, will not represent the actual mechanical behavior of coupling beams with diagonal cracking and “real” shear failure (diagonal tension or compression), and cannot be considered as generalized approach to represent the physical behavior of coupling beams. Wall piers in coupled walls will undergo significant fluctuations in axial loads during seismic responses, and uncoupling their nonlinear shear behavior from their axial/flexural response at the section level is also not a generalized approach for characterization of their shear behavior. Second, the Menegotto–Pinto reinforcement model is employed for the cyclic behavior. Although the model can effectively reproduce the Bauschinger effect, bar buckling, and bar fracture because of high tensile strain, it fails to account for fracture because of fatigue. Furthermore, modeling approaches have not been sufficiently validated against local deformation characteristics (rotations, curvatures, strains) because of a lack of detailed experimental data. In addition, the proposed models are validated only under cyclic loading in this study, the validation of nonlinear dynamic analysis should be further studied.
7 Conclusions
A novel analytical model for nonlinear simulation of RC coupled wall systems under reversed cyclic loading is proposed in this paper. The model incorporates two key components, which are analytical models of RC shear wall and diagonally reinforced coupling beams. The critical issues associated with the numerical modeling schemes for these two key components are discussed in detail and depth through comparisons using the observed experimental data and analytical results. To validate accuracy and accuracy of the proposed analytical model for diagonally reinforced coupling beams, four experimental specimens are used as analytical examples, one of which is analyzed by different modeling strategies to find out the optimum modeling method including definition of four control points in the backbone curve, utilization of Mander and Legeron confined concrete models, and effect of sectional shear deformation, and other specimens are thus simulated by the selected optimum modeling scheme. Good agreements are achieved for all of these four specimens through comparisons of hysteretic curves analyzed from analytical means and observed by experimental tests. This outcome confirms that the proposed analytical model is able to capture the nonlinear behavior observed in the tests including strength and stiffness deterioration, maximum shear force, and pinching characteristic.
For the nonlinear simulation of RC shear wall, the modeling method similar to the diagonally reinforced coupling beams is adopted to simulate two 1/2 scale RC shear wall specimens. Validation of accuracy and efficiency via comparisons between the experimental data and the simulated results is received. This illustrates the reasonability of the proposed RC shear wall model in modeling nonlinear response of RC shear wall, and further demonstrates that the validated modeling method is appropriate to the simulation of RC shear wall.
Using the validated modeling strategy, an overall RC coupled wall system model, integrating the proposed analytical models of diagonally reinforced coupling beams and RC shear wall is presented to simulate two large-scaled RC coupled wall specimens. The predicted results including degradation of stiffness and strength, moderate pinching behavior, hysteretic energy dissipation as well as maximum shear force compared to corresponding test findings show a good level of agreement, verifying that the proposed RC coupled wall model is capable of describing the nonlinear behavior observed from test.
In order for indicating that the influence of nonlinear shear deformations from diagonally reinforced coupling beams and RC wall piers on the nonlinear response of overall RC coupled wall systems is apparent, another modeling scheme in terms of classical fiber model is adopted to simulate these two RC coupled walls. Note that all of the material models as well as various parameters are identical other than the adoption of the shear models for diagonally reinforced coupling beams and RC shear wall. Comparisons between experimental data and simulation results show that the predicted nonlinear behavior characteristics including hysteresis energy dissipation, maximum shear force, and strength and stiffness deterioration have obvious discrepancy with the corresponding experimental findings. This further proves that the nonlinear shear deformations of coupling beams and wall piers in a coupled wall system are not able to be ignored.
Notes
Authors’ contributions
KD, HL, and JB contributed to methodology, software, formal analysis and writing original draft. JS contributed to the supervision and discussion. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
Please contact author for data requests.
Funding
The authors would like to acknowledge the financial support funded from the National Key Research and Development Program of China (2017YFC1500605), the National Natural Science Foundation of China (No. 51878631), and Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2017jcyjAX0147 and cstc2018jcyjAX0331).
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- ACI 318-11. (2011). Building code requirements for structural concrete and commentary. ACI Committee 318, Farmington Hills.Google Scholar
- Almeida, J. P., Correia, A. A., & Pinho, R. (2015). Force-based higher-order beam element with flexural–shear–torsional interaction in 3D frames. Part II: Applications. Engineering Structures, 89, 218–235.CrossRefGoogle Scholar
- Bitar, I., Grange, S., Kotronis, P., & Benkemoun, N. (2018). A comparison of displacement-based Timoshenko multi-fiber beams finite element formulations and elasto-plastic applications. European Journal of Environmental and Civil Engineering, 22(4), 464–490.CrossRefGoogle Scholar
- Correia, A. A., Almeida, J. P., & Pinho, R. (2015). Force-based higher-order beam element with flexural–shear–torsional interaction in 3D frames. Part I: Theory. Engineering Structures, 89, 204–217.CrossRefGoogle Scholar
- Dazio, A., Beyer, K., & Bachmann, H. (2009). Quasi-static cyclic tests and plastic hinge analysis of RC structural walls. Engineering Structures, 31(7), 1556–1571.CrossRefGoogle Scholar
- Eljadei, A. A., & Harries, K. A. (2014). Design of coupled wall structures as evolving structural systems. Engineering Structures, 73(73), 100–113.CrossRefGoogle Scholar
- Feng, D. C., & Xu, J. (2018). An efficient fiber beam-column element considering flexure-shear interaction and anchorage bond-slip effect for cyclic analysis of RC structures. Bulletin of Earthquake Engineering, 16(11), 5425–5452.CrossRefGoogle Scholar
- Ferreira, D., Bairán, J. M., Mari, A. R., & Faria, R. (2014). Nonlinear analysis of RC beams using a hybrid shear–flexural fibre beam model. Engineering Computations, 31(7), 1444–1483.CrossRefGoogle Scholar
- Fisher, A. W., Collins, M. P., & Bentz, E. C. (2018). Influence of shear on deformations of coupling beams (pp. 1156–1163). High Tech Concrete: Where Technology and Engineering Meet.Google Scholar
- Fox, M. J., Sullivan, T. J., & Beyer, K. (2014). Capacity design of coupled RC walls. Journal of Earthquake Engineering, 18(5), 735–758.CrossRefGoogle Scholar
- Galano, L., & Vignoli, A. (2000). Seismic behavior of short coupling beams with different reinforcement layouts. ACI Structural Journal, 97(6), 876–885.Google Scholar
- Gerin, M., Adebar, P. (2004). Accounting for shear in seismic analysis of concrete structures. In: Proc., 13th World Conf. on Earthquake Engineering.Google Scholar
- Gong, B., & Fang, E. (1988a). Behavior of reinforced concrete coupling beams between shear walls under cyclic loading. Journal of Building Structure, 9(1), 34–40. (in Chinese).Google Scholar
- Gong, B., & Fang, E. (1988b). Experimental investigation and full-range analysis of reinforced concrete coupling beams between shear walls. Building Science, 4(4), 41–45. (in Chinese).Google Scholar
- Gulec, C. K., Whittaker, A. S. (2009). Performance-based assessment and design of squat reinforced concrete shear walls. Technical Report MCEER-09-0010.Google Scholar
- Han, S. W., Lee, C. S., Shin, M., et al. (2015). Cyclic performance of precast coupling beams with bundled diagonal reinforcement. Engineering Structures, 93, 142–151.CrossRefGoogle Scholar
- Harries, K. A., Moulton, J. D., & Clemson, R. L. (2004). Parametric study of coupled wall behavior—implications for the design of coupling Beams. Journal of Structural Engineering, 130(3), 480–488.CrossRefGoogle Scholar
- Hindi, R. A., & Hassan, M. A. (2004). Shear capacity of diagonally reinforced coupling beams. Engineering Structures, 26(10), 1437–1446.CrossRefGoogle Scholar
- Hines E. M., Dazio A., & Seible F. (2002). Seismic performance of hollow rectangular reinforced concrete piers with highly-confined boundary elements phase III: Web crushing tests. Rep. No. SSRP-2001/27; Univ. of California, San Diego, p 239.Google Scholar
- Hines E. M., Seible F., & Priestley, M. J. N. (1995). Cyclic tests of structural walls with highly-confined boundary elements. Rep. No. SSRP-99/15; Univ. of California, San Diego, p 266.Google Scholar
- Hirosawa, M. (1975). Past experimental results on reinforced concrete shear walls and analysis on them. Kenchiku Kenkyu Shiryo, No. 6, Building Research Institute, Ministry of Construction (in Japanese).Google Scholar
- Hung, C. C. (2012). Modified full operator hybrid simulation algorithm and its application to the seismic response simulation of a composite coupled wall system. Journal of Earthquake Engineering, 16(6), 2575.CrossRefGoogle Scholar
- Hung, C. C., & El-Tawil, S. (2011). Seismic behavior of a coupled wall system with HPFRC materials in critical regions. Journal of Structural Engineering, 137(12), 1499–1507.CrossRefGoogle Scholar
- Ibarra, L. F., Medina, R. A., & Krawinkler, H. (2005). Hysteretic models that incorporate strength and stiffness deterioration. Earthquake Engineering and Structural Dynamics, 34(12), 1489–1511.CrossRefGoogle Scholar
- Jun, Z., Kou, L., Fuqiang, S., Xiangcheng, Z., & Chenzhe, S. (2018). An analytical approach to predict shear capacity of steel fiber reinforced concrete coupling beams with small span–depth ratio. Engineering Structures, 171, 348–361.CrossRefGoogle Scholar
- Kabeyasawa, T., Shiohara, T., Otani, S., et al. (1982). Analysis of the full-scale seven story reinforced concrete test structure: Test PSD3. In: Proc. 3rd JTCC, US-Japan Cooperative Earthquake Research Program.Google Scholar
- Kim, D. K. (2016). Seismic response analysis of reinforced concrete wall structure using macro model. International Journal of Concrete Structures & Materials, 10(1), 99–112.CrossRefGoogle Scholar
- Kim, J., & Choi, Y. (2017). Seismic capacity design and retrofit of reinforced concrete staggered wall structures. International Journal of Concrete Structures and Materials, 11(2), 285–300.CrossRefGoogle Scholar
- Kolozvari, K., Orakcal, K., & Wallace, J. W. (2015). Modeling of cyclic shear–flexure interaction in reinforced concrete structural walls. I: Theory. Journal of Structural Engineering, 141(5), 04014135.CrossRefGoogle Scholar
- Legeron, F., & Paultre, P. (2003). Uniaxial confinement model for normal- and high-strength concrete columns. Journal of Structural Engineering, 129(2), 241–252.CrossRefGoogle Scholar
- Lehman, D. E., Turgeon, J. A., Birely, A. C., et al. (2013). Seismic behavior of a modern concrete coupled wall. Journal of Structural Engineering, 139(8), 1371–1381.CrossRefGoogle Scholar
- Lequesne, R.D. (2011). Behavior and design of high-performance fiber-reinforced concrete coupling beams and coupled-wall systems. Ph.D Dissertation, Michigan: The University of Michigan.Google Scholar
- Lequesne, R. D., Parra-Montesinos, G. J., & Wight, J. K. (2012). Seismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall systems. Journal of Structural Engineering, 139(8), 1362–1370.CrossRefGoogle Scholar
- Lowes, N. L., Lehman, E. D., Birely, C. A., Kuchma, A. D., Marley, P. K., & Hart, R. C. (2012). Earthquake response of slender planar concrete walls with modern detailing. Engineering Structures, 43, 31–47.CrossRefGoogle Scholar
- Lucchini, A., Franchin, P., & Kunnath, S. (2017). Failure simulation of shear-critical RC columns with non-ductile detailing under lateral load. Earthquake Engineering and Structural Dynamics, 46(5), 855–874.CrossRefGoogle Scholar
- Mander, J. B., Priestley, M., & Park, R. (1988). Theoretical stress-strain model for confined concrete. Journal of Structural Engineering, 114(8), 1804–1826.CrossRefGoogle Scholar
- Marini, A., & Spacone, E. (2006). Analysis of reinforced concrete elements including shear effects. ACI Structural Journal, 103(5), 645–655.Google Scholar
- Massone, L. M., Orakcal, K., & Wallace, J. W. (2004). Load-deformation responses of slender reinforced concrete walls. ACI Structural Journal, 101(1), 103–113.Google Scholar
- Massone, L. M., Orakcal, K., & Wallace, J. W. (2009). Modeling of squat structural walls controlled by shear. ACI Structural Journal, 106(5), 646–655.Google Scholar
- MATLAB User’s Guide (2014). The MathWorks Inc.Google Scholar
- Menegotto, M., & Pinto, P. E. (1973). Method of analysis for cyclically loaded RC plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending. Lisbon: International Association for Bridge and Structural Engineering.Google Scholar
- Ozselcuk A. R. (1989). Experimental and analytical studies of coupled wall structures. Ph.D. dissertation, Univ. of California, Berkeley, CA.Google Scholar
- Paulay, T. (1971). Coupling beams of reinforced concrete shear walls. Journal of Structural Engineering, ASCE, 97(3), 843–862.Google Scholar
- Paulay, T., Binney J. R. (1974). Diagonally reinforced coupling beams of shear walls. Shear in Reinforced Concrete, SP-42. Farmington Hills, MI: American Concrete Institute, p. 579–98.Google Scholar
- Petrangeli, M., Pinto, P. E., & Ciampi, V. (1999). Fiber element for cyclic bending and shear of RC structures. I: Theory. Journal of Engineering Mechanics, 125(9), 994–1001.CrossRefGoogle Scholar
- Saatcioglu, M., Derecho, A. T., & Corley, W. G. (1983). Modelling hysteretic behaviour of coupled walls for dynamic analysis. Earthquake Engineering and Structural Dynamics, 11(5), 711–726.CrossRefGoogle Scholar
- Said, A., Elmorsi, M., & Nehdi, M. (2005). Non-linear model for reinforced concrete under cyclic loading. Magazine of Concrete Research, 57(4), 211–224.CrossRefGoogle Scholar
- Santhakumar, A. R. (1974). The ductility of coupled shear walls. Ph.D. dissertation, Univ. of Canterbury, Christchurch, New Zealand.Google Scholar
- Sayre, B. (2003). Performance evaluation of steel reinforced shear walls. M.S. thesis, Univ. of California, Los Angeles.Google Scholar
- Scott, B., Park, R., & Priestley, M. (1982). Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates. ACI Journal Proceedings, 79(1), 13–27.Google Scholar
- Shiu, K. N., Aristizabal-Ochoa, J. D., Barney, G. B., Fiorato, A. E., & Corley W. G. (1981). Earthquake resistant structural walls: Coupled wall tests. Rep. to National Science Foundation; Construction Technology Laboratories, Portland Cement Association, Stokie, IL.Google Scholar
- Spacone, E., Filippou, F. C., & Taucer, F. F. (1996). Fiber beam-column model for non-linear analysis of RC frames: part i. formulation. Earthquake Engineering and Structural Dynamics, 25(7), 711–726.CrossRefGoogle Scholar
- Takayanagi, T., & Schnobrich, W. C. (1979). Non-linear analysis of coupled wall systems. Earthquake Engineering and Structural Dynamics, 7(1), 1–22.CrossRefGoogle Scholar
- Tassios, T. P., Moretti, M., & Bezas, A. (1996). On the behavior and ductility of reinforced concrete coupling beams of shear walls. ACI Structural Journal, 93(6), 711–720.Google Scholar
- Thomsen, J. H., & Wallace, J. W. (2004). Displacement-based design procedures for slender reinforced concrete structural walls—Experimental verification. Journal of Structural Engineering, 130(4), 618–630.CrossRefGoogle Scholar
- Vallenas J. M., Bertero V. V., & Popov E. P. (1979). Hysteretic behaviour of reinforced concrete structural walls. Rep. No. UBC/EERC-79/20; Univ. of California, Berkeley, CA, 234.Google Scholar
- Vulcano, A., Bertero, V. V., Colotti, V. (1988). Analytical modeling of RC structural walls. In: Proc., 9th World Conf. on Earthquake Engineering.Google Scholar
- Vuran, E., & Aydınoğlu, M. N. (2016). Capacity and ductility demand estimation procedures for preliminary design of coupled core wall systems of tall buildings. Bulletin of Earthquake Engineering, 14(3), 721–745.CrossRefGoogle Scholar
- Wallace, J. W. (2007). Modeling issues for tall reinforced concrete core wall buildings. Structural Design of Tall and Special Buildings, 16(5), 615–632.MathSciNetCrossRefGoogle Scholar
- Wang T. Y., Bertero V. V., & Popov E. P. (1975). Hysteretic behaviour of reinforced concrete framed walls. Rep. No. UBC/EERC-75/23; Univ. of California, Berkeley, CA, 367.Google Scholar
- Zhang, H., Lv, X., Lu, L., et al. (2007). Influence of boundary element on seismic behavior of reinforced concrete shear walls. Earthquake Engineering and Engineering Vibration, 27(01), 92–98. (in Chinese).Google Scholar
- Zimos, D. K., Mergos, P. E., & Kappos, A. J. (2018). Modelling of R/C members accounting for shear failure localisation: Finite element model and verification. Earthquake Engineering and Structural Dynamics, 47(7), 1631–1650.CrossRefGoogle Scholar
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