Seismic Capacity Design and Retrofit of Reinforced Concrete Staggered Wall Structures
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Abstract
This study investigates the seismic performance of a staggered wall structure designed with conventional strength based design, and compares it with the performance of the structure designed by capacity design procedure which ensures strong column-weak beam concept. Then the seismic reinforcement schemes such as addition of interior columns or insertion of rotational friction dampers at the ends of connecting beams are validated by comparing their seismic performances with those of the standard model structure. Fragility analysis shows that the probability to reach the dynamic instability is highest in the strength designed structure and is lowest in the structure with friction dampers. It is also observed that, at least for the specific model structures considered in this study, R factor of 5.0 can be used in the seismic design of staggered wall structures with proposed retrofit schemes, while R factor of 3.0 may be reasonable for standard staggered wall structures.
Keywords
staggered wall structures seismic performance capacity design friction dampers1 Introduction
Reinforced concrete (RC) buildings having vertical shear walls both as partition walls and as load resisting systems have advantage in economic use of structural materials and ease of construction using slip forms. The seismic performance of RC shear wall structures have been widely investigated by many researchers (Wallace 2012; Kim 2016). The shear walls are also effective in preventing spread of fire (Kang et al. 2016). However the buildings with shear partition walls are not preferred these days mainly because the plan layouts fixed by the shear walls fail to meet the demand of people who prefer spatial variability. A staggered wall structure has story-high walls placed at alternate levels, which makes the system easier to remodel and consequently more sustainable while the economy and constructability of shear wall structures still maintained. Fintel (1968) proposed a staggered system for RC buildings in which staggered walls with attached slabs resist the gravity as well as the lateral loads as H-shaped story-high deep beams, and observed that the staggered wall systems would be more economical. Mee et al. (1975) investigated the structural performance of staggered wall systems by carrying out shaking table tests of 1/15 scaled models. Lee and Kim (2013) investigated the seismic performance of staggered wall structures with middle corridor; Kim and Baek (2013) conducted seismic risk assessment of staggered wall system structures; and Kim and Lee (2014) proposed a formula for fundamental natural period of staggered wall structures. Recently seismic behavior factors of the system were investigated based on the procedure recommended in the FEMA P 695 (2009) (Lee and Kim 2013, 2015), and ATC 19 (1995) (Kim et al. 2016). The seismic performance of a similar structure system in steel, the staggered truss system, has already been investigated (Kim et al. 2015; Kim and Kim 2017), and the system has been applied in many real building projects.
The staggered wall systems, however, have not been widely applied in practice due mainly to the lack of knowledge in the structural performance of the system. This study investigates the seismic performance of a staggered wall structure designed with conventional strength based design, and compares it with the performance of the structure design by capacity procedure which intends to ensure strong column-weak beam behavior. Then the seismic reinforcement schemes such as addition of interior columns or insertion of rotational friction dampers at the ends of connecting beams are implemented using the capacity design procedure. Their effects on enhancing seismic load-resisting capacity are validated by comparing their seismic performances with those of the standard model structure.
2 Application of Energy Dissipation Devices in Shear Wall Structures
Even though there is no known example of a staggered wall structure with energy dissipation devices, many researchers have been investigating the possibility of mitigating seismic response of structures with shear walls using dampers. Madsen et al. (2003) investigated the seismic performance of viscoelastic damping systems placed between shear walls at the coupling beam locations. Finite element methods were used to analyze the effects of dampers in these structural systems under different earthquakes records. The results of the analysis of the 20-storey structure with dampers in all levels illustrated that dampers could be used to improve the mitigation of seismic forces. Chung et al. (2009) proposed a friction damper that was applied between coupled shear walls in order to reduce the deformation of the structure induced by earthquake loads. It was found that the control performance of the proposed friction damper was superior to that of a coupled wall with a rigid beam. Mao et al. (2012) proposed a shape memory alloy (SMA) damper to be located in the middle of a coupling beam in a coupled shear wall building. In this study it was intended that, after earthquakes, deformation of the dampers can recover automatically because of the pseudoelasticity of austenite SMA material. Nonlinear time history analysis was conducted for an 18-story frame-shear wall structure with such SMA dampers to verify seismic response control effect of this damper. MacKay-Lyons (2013) developed the viscoelastic coupling damper (VCD) for RC coupled wall high-rise buildings. These dampers were introduced in place of coupling beams to provide distributed supplemental damping in all lateral modes of vibration. A parametric study has been conducted to determine the optimal number and placement of the dampers to achieve enhanced seismic performance. Results highlight the improved performance of VCDs over RC coupling beams at all levels of seismic hazard. Pant et al. (2015) developed viscoelastic coupling dampers to be located at coupling beams between two shear walls and at outrigger beams. They applied the system to a 40-story RC structure and found that the viscoelastic coupling dampers can be effective in reducing both structural and nonstructural damage under MCE level seismic events. The research results presented above confirm the effectiveness of energy dissipation devices in the design of shear wall structures.
3 Seismic Performance of Staggered Wall Structures
3.1 Configuration and Design of Staggered Wall Structures
Member size and rebars of the first story exterior columns.
Model | Frame | Size (mm) | Main rebars |
---|---|---|---|
SD | A | 560 × 560 | 8-D25 |
B | 660 × 660 | 8-D29 | |
CD | A | 580 × 580 | 8-D29 |
B | 680 × 680 | 8-D32 | |
CD_IC | A | 540 × 540 | 8-D29 |
B | 640 × 640 | 8-D29 | |
CD_FD | A | 580 × 580 | 8-D29 |
B | 680 × 680 | 8-D32 |
3.2 Analysis Modeling of the Structure
3.3 Seismic Performance of the Strength-Designed Structure
4 Capacity Design Procedure
It is observed in the previous section that structural damage is concentrated in the exterior columns rather than in the connecting beams in the staggered wall structure designed following the code-based approach. In this section a capacity design procedure is applied to achieve the strong column-weak beam design of the model structure so that the damage in columns and the brittle failure mode observed in the conventional design are prevented. To this end the model structure is designed in such a way that the plastic hinges are concentrated at the connecting beams while the other members remain elastic. Similar approach has been successfully applied to the design of special truss moment frames by Chao and Goel (2006), who designed the special segment in the truss girders using the plastic design procedure. The design process was adopted to the AISC Seismic Provisions (2010).
5 Seismic Retrofit Schemes for Staggered Wall Structures
5.1 Addition of Interior Columns
Also the required balancing lateral forces, obtained similarly to Eqs. (4) and (5) considering the plastic moments of the added connecting beams, are applied to the design of the interior as well as the exterior columns. The member sizes of the model structure with interior columns are presented in Table 1, where it can be observed that both the column size and the beam rebars decrease as a result of the addition of interior columns. The fundamental natural period along the transverse direction is reduced to 0.31 s due to the increased stiffness.
5.2 Addition of Rotational Friction Dampers
Member size and rebars of the second story coupling beams in the frame A.
Model | Longitudinal bar | |
---|---|---|
Top | Bottom | |
SD | 5-D22 | 5-D22 |
CD, CD_FD | 5-D13 | 5-D13 |
CD_IC | 2-D19 | 2-D19 |
For model structures with rotational friction dampers at the ends of connecting beams, the same capacity design procedure is applied to lead the formation of plastic hinges in the connecting beams where the friction dampers are installed. The slip forces of the dampers are determined in such a way that their moment capacities are equal to the maximum moment of the connecting beams. To ensure yielding of dampers prior to other structural elements when the model structure is subjected to design seismic load, the structures are designed in such a way that the plastic hinges are concentrated at the connecting beams and the other members remain elastic. The failure point of the friction dampers at which the friction force is lost is conservatively assumed to be 0.3 rad based on the experimental results of rotational friction dampers (Chung et al. 2009).
5.3 Seismic Performance of the Retrofitted Structures
6 Seismic Safety of the Model Structures
6.1 Collapse Margin of the Model Structures
In this section the validity of the capacity design approach and the retrofit schemes for staggered wall structures is verified by statistical seismic performance evaluation procedure proposed in the FEMA P695 (2009). In this approach nonlinear incremental dynamic analyses are conducted to establish the median collapse capacity and collapse margin ratio (CMR) for the analysis models. The adjusted collapse margin ratio (ACMR) is obtained by multiplying the collapse margin ratio (CMR), which is the ratio of the median collapse intensity (\( \widehat{{S_{CT} }} \)) and the MCE (maximum considered earthquake) intensity (S_{MT}), and the spectral shape factor. Acceptable values of adjusted collapse margin ratio are based on total system collapse uncertainty, β_{TOT}, and established values of acceptable probabilities of collapse.
Estimation of collapse margin of the model structures.
\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{S}_{CT} \) | S_{MT} | CMR | SSF | ACMR | ACMR_{20%} | Pass/fail | |
---|---|---|---|---|---|---|---|
SD | 0.7 | 0.25 | 2.8 | 1.08 | 3.1 | 1.8 | Pass |
CD | 0.8 | 0.24 | 3.3 | 1.09 | 3.5 | 1.8 | Pass |
CD_IC | 1.1 | 0.25 | 4.4 | 1.08 | 4.7 | 1.8 | Pass |
CD_FD | 1.3 | 0.24 | 5.4 | 1.14 | 6.1 | 1.8 | Pass |
6.2 Fragility Analysis
7 Response of Structures Designed with Higher R Factor
Member size and rebars of the first story exterior columns designed using R = 5.
Model | Frame | Size (mm) | Main bar |
---|---|---|---|
SD | A | 460 × 460 | 8-D25 |
B | 580 × 580 | 8-D25 | |
CD | A | 480 × 480 | 8D-29 |
B | 580 × 580 | 8D-29 | |
CD_IC | A | 480 × 480 | 8D-29 |
B | 560 × 560 | 8D-29 | |
CD_FD | A | 480 × 480 | 8D-29 |
B | 580 × 580 | 8D-29 |
Member size and rebars of the second story coupling beams in the frame A designed using R = 5.
Model | Longitudinal bar | |
---|---|---|
Top | Bottom | |
SD | 3-D19 | 3-D19 |
CD, CD_FD | 2-D19 | 2-D19 |
CD_IC | 2-D16 | 2-D16 |
8 Conclusions
This study investigated the seismic performance of a staggered wall structure designed with conventional strength based design, and compared it with the performance of the structures designed by capacity design procedure. Then the seismic reinforcement schemes such as addition of interior columns or insertion of rotational friction dampers at the ends of connecting beams were validated by comparing their seismic performances with those of the standard model structure.
According to pushover analysis, the strength-designed structure failed due mainly to failure of exterior columns, whereas in the capacity designed structures major strength drop occurred due to plastic hinge formation in beams. Fragility analysis showed that the probability to reach the dynamic instability was highest in the strength designed structure and was lowest in the structure with friction dampers. The capacity design applied in this study turned out to be most effective for large earthquakes which cause severe damage to structures. In the model with interior columns, the probabilities of reaching the Slight and the Moderate damage states were quite significant, and the probability of reaching the Extensive and the Complete damage states decreased most substantially in the structure with friction dampers. The collapse probabilities of all model structures designed with the R factor of 3.0 were smaller than 0.1, which confirmed that the seismic design variables used for the model structures were valid. However in the structures designed with the R factor of 5.0, the collapse probabilities turned out to be less than 0.1 only in the structures retrofitted with interior columns or friction dampers. Based on the analysis results of the specific analysis model structures considered in this study, it was concluded that R factor of 5.0 might be used in the seismic design of staggered wall structures with proposed retrofit schemes, while R factor of 3.0 might be reasonable for standard staggered wall structures.
Notes
Acknowledgements
This paper was supported by Sungkyun Research Fund, Sungkyunkwan University, 2016.
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