Modeling parameters and acceptable plastic chord rotations for diagonally reinforced concrete coupling beams
Introduction
Coupled shear walls have been commonly used in building construction, particularly in tall buildings, due to their effective seismic force resistance and architectural demands for door and window openings [[1], [2], [3], [4], [5]]. Coupling beams connect individual shear walls and play an important role in the seismic performance of coupled wall systems.
Since coupling beams withstand substantial inelastic deformation demands during earthquakes, they should be equipped with adequate reinforcement details to provide sufficient ductility and energy dissipation capacities [6].
To sustain large deformation demands during earthquakes, Paulay and Binney [7] developed diagonally reinforced concrete coupling beams (DRCBs). Past studies reported that DRCBs had superior deformation and energy dissipation capacities compared to coupling beams with conventional beam reinforcement [[8], [9], [10]]. Thus, DRCBs act as seismic fuse elements that dissipate most of the seismic input energy. When designing coupled shear wall systems and evaluating their seismic performance, it is important to use accurate modeling parameters and acceptance criteria for DRCBs.
In Table 10–19 of ASCE 41-13 [11] and ASCE 41-17 [12], the modeling parameter values for DRCBs are specified to define the force-deformation relationship. In this table, acceptable plastic chord rotations are also provided as acceptance criteria for DRCBs. However, Han et al. [13] revealed that the modeling parameter values specified in ASCE 41-17 for DRCBs are generally conservative when compared with test data of the DRCBs. Naish et al. [14,15] also reported that code compliant DRCBs could withstand a chord rotation larger than 8%, which is much greater than 5%, a limiting value specified in ASCE 41-17.
Past studies reported that modeling parameters could vary according to design parameters such as dimensions, material properties, aspect ratios, and amount of reinforcement [[16], [17], [18], [19], [20]]. The shear strength and maximum chord rotation of DRCBs could vary significantly according to the aspect ratio [21]. Han et al. [22] reported that the shear strength of DRCBs with the same amount of diagonal reinforcement varied by 76% according to the amount of transverse reinforcement. However, in ASCE 41-17, the values of modeling parameters are specified irrespective of the design parameters.
In this study, empirical equations calculating modeling parameters were proposed as a function of statistically influential design parameters based on the measured modeling parameter values of DRCBs. For this purpose, test data were collected for forty-two DRCB specimens from 18 different experimental studies. Acceptable plastic chord rotations were proposed to achieve target exceedance probabilities for immediate occupancy (IO), life safety (LS), and collapse prevention (CP) performance levels.
Section snippets
Summary of ASCE 41-17 modeling parameters
ASCE 41-17 standard includes provisions applicable for seismic evaluation and retrofit of buildings. Three tiered procedures are provided for seismic evaluation: Tier 1, screening; Tier 2, deficiency-based evaluation; and Tier 3, systematic evaluation. Particularly in Tier 3 procedure, nonlinear analyses can be used to accurately estimate seismic demands on components in buildings. Fig. 1a shows the force ()-chord rotation () relations for the concrete coupling beams specified in ASCE 41-17.
Test data of DRCB specimens
Modeling parameters and acceptance criteria were proposed to be used in seismic performance assessment of a structure and updated [11,12,[25], [26], [27]] based on accumulated experimental evidence and empirical models [16]. ASCE 41-17 is the most recent version of the ASCE 41 series, which includes the most updated modeling parameter values and acceptance criteria.
In this study, test data of 42 DRCBs are collected from past 18 experimental studies [1,[7], [8], [9], [10],14,21,22,[28], [29],
Estimation of modeling parameter values from test data of DRCB specimens
The accuracy of the values of DRCB modeling parameters , and assigned in ASCE 41-06 [27] was evaluated with test data of seven DRCB specimens by Naish et al. [14] and PEER [40]. Discrepancies were reported between measured modeling parameter values and those specified in ASCE 41-06. Modeling parameter values and acceptance criteria have been updated based on collected test data of DRCBs (ASCE 41-13; ASCE 41-17).
In ASCE 41-17, three types of force-deformation curves are provided: Types 1,
Empirical equations for modeling parameters
Fig. 6 shows the values of parameters and according to selected design parameters , (=), and where is the spacing of transverse reinforcement. As seen in Fig. 6, parameters and vary according to the design parameters. This indicates that parameters and need to be proposed to account for the contribution of important design parameters (variables). It is noted that in ASCE 41-17, constant values are specified for the modeling parameters of DRCBs irrespective
Acceptance criteria for plastic chord rotation parameters and
Acceptance criteria should be closely related to the amount of damage and failure that are acceptable for corresponding performance objectives. In ASCE 41-17, the IO performance level is defined as the post-earthquake damage state in which a structure remains safe to occupy and essentially retains its pre-earthquake strength and stiffness. The LS performance level is the post-earthquake damage state in which a structure remains a structure has damaged components but retains a margin of safety
Summary and conclusions
In this study, empirical equations to calculate the values of modeling parameters for DRCBs were proposed by conducting stepwise nonlinear regression analyses. Accurate modeling parameters need to be developed to obtain reliable seismic demands of a structure using nonlinear analyses. For this purpose, test data of 42 DRCB specimens were collected from 18 different experimental studies. The following equations were proposed for modeling parameters and , residual strength and maximum
Author statement
Prof. Han, S. W. developed idea, supervised the project and wrote the manuscript. Dr. Lee, C. S. and Cho, E.S. conducted calculations and supported completing the manuscript.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The research was supported by grants from the Ministry of Land, Infrastructure and Transport of Korea (21CTAP-C152179-03). Constructive comments of three anonymous reviewers are greatly appreciated.
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Behaviour and detailing of coupling beams with high-strength materials
2022, Journal of Building EngineeringCitation Excerpt :Hung and Lu [4] addressed the shortcomings of force-based design by proposing a performance-based design approach for coupled wall structures. Besides, tremendous research efforts have been dedicated to developing advanced numerical and analytical modeling techniques, which can produce predictable seismic performance and led to a more efficient coupling beam design [31–35]. The potential benefits to the use of HSS in coupling beams resisting earthquake effects mainly include cost savings, reduced reinforcement congestion, and improved constructability.