Hysteresis Behavior of Hybrid Rocking Walls: An Analytical Method
Publication: Practice Periodical on Structural Design and Construction
Volume 28, Issue 1
Abstract
This study proposed an analytical method to predict the hysteresis behavior of hybrid rocking walls (HRWs) in the two limit states of decompression and geometric nonlinearity. The flag-shaped curve of a HRW under a given cyclic load was described using the parameters of initial stiffness, post-yield stiffness, and the energy dissipated by the wall energy dissipaters. In this method, the hysteresis loops of the wall were determined assuming no tendon yielding and concrete crushing at the wall toes. The results of the proposed analytical method were validated via experiments on two HRWs under cyclic loads and previously validated finite element models. Comparing the results of the analytical method with those of the tests and numerical models showed that the proposed method can provide acceptable predictions for the yield point, ultimate point, initial and post-yield stiffnesses, energy dissipation level in each loading cycle, as well as the hysteresis behavior of hybrid walls. This showed the efficiency and accuracy of the proposed analytical method. Moreover, despite the simplifying assumptions, the good agreement between the analytical approach and experimental hysteresis loops indicated that the role of plastic deformation in energy dissipation at the bottom of HRWs is negligible.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
References
Aaleti, S., and S. Sritharan. 2009. “A simplified analysis method for characterizing unbonded post-tensioned precast wall systems.” Eng. Struct. 31 (12): 2966–2975. https://doi.org/10.1016/j.engstruct.2009.07.024.
Abbasi, N., H. Akbarzadeh Bengar, A. Jafari, and M. Nazari. 2021. “Numerical modeling of seismic response and damage estimation of concrete rocking walls under seismic loading.” Sharif J. Civ. Eng. 37 (2.2): 35–45. https://doi.org/10.24200/J30.2020.55368.2728.
Ajrab, J. J., G. Pekcan, and J. B. Mander. 2004. “Rocking wall–frame structures with supplemental tendon systems.” J. Struct. Eng. 130 (6): 895–903. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:6(895).
Akbarzadeh Bengar, H., A. Jafari, and M. Beheshti. 2019. “A proposed numerical model for nonlinear cyclic analysis of steel and concrete coupling beams in RC coupled shear walls system.” Sharif J. Civ. Eng. 34 (4.2): 53–64. https://doi.org/10.24200/J30.2019.1440.
ASCE. 2007. Seismic rehabilitation of existing buildings. ASCE/SEI 41-06. Reston, VA: ASCE.
Avgenakis, E., and I. N. Psycharis. 2020. “Modeling of inelastic rocking bodies under cyclic loading.” J. Eng. Mech. 146 (4): 04020020. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001751.
Christopoulos, C., A. Filiatrault, and B. Folz. 2002. “Seismic response of self-centering hysteretic SDOF systems.” Earthquake Eng. Struct. Dyn. 31 (5): 1131–1150. https://doi.org/10.1002/eqe.152.
CSI (Computers and Structures Inc). 2011. PERFORM components and elements for PERFORM-3D and PERFORMCOLLAPSE. Berkeley, CA: CSI.
Dodd, L., and J. Restrepo-Posada. 1995. “Model for predicting cyclic behavior of reinforcing steel.” J. Struct. Eng. 121 (3): 433–445. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:3(433).
Erkmen, B., and A. E. Schultz. 2009. “Self-centering behavior of unbonded, post-tensioned precast concrete shear walls.” J. Earthquake Eng. 13 (7): 1047–1064. https://doi.org/10.1080/13632460902859136.
Guo, T., G. Zhang, and C. Chen. 2014. “Experimental study on self-centering concrete wall with distributed friction devices.” J. Earthquake Eng. 18 (2): 214–230. https://doi.org/10.1080/13632469.2013.844211.
Hassani, B., and A. Jafari. 2012. “An investigation on the seismic performance of reinforced concrete panel structures.” Asian J. Civ. Eng. 13 (2): 181–193.
Hassanli, R., M. A. ElGawady, and J. E. Mills. 2016. “Force–displacement behavior of unbonded post-tensioned concrete walls.” Eng. Struct. 106 (Jan): 495–505. https://doi.org/10.1016/j.engstruct.2015.10.035.
Holden, T., J. Restrepo, and J. B. Mander. 2003. “Seismic performance of precast reinforced and prestressed concrete walls.” J. Struct. Eng. 129 (3): 286–296. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:3(286).
Jafari, A., H. Akbarzadeh Bengar, R. Hassanli, M. Nazari, and R. Dugnani. 2021a. “The response of self-centering concrete walls under quasi-static loading.” Bull. Earthquake Eng. 19 (7): 2893–2917. https://doi.org/10.1007/s10518-021-01100-5.
Jafari, A., M. R. Ghasemi, H. Akbarzadeh Bengar, and B. Hassani. 2016. “Modeling of dynamic behavior and estimation of damage incurred by self-centering rocking walls.” J. Rehabil. Civ. Eng. 4 (2): 93–108. https://doi.org/10.22075/jrce.2017.10565.1169.
Jafari, A., M. R. Ghasemi, H. Akbarzadeh Bengar, and B. Hassani. 2018a. “Seismic performance and damage incurred by monolithic concrete self-centering rocking walls under the effect of axial stress ratio.” Bull. Earthquake Eng. 16 (2): 831–858. https://doi.org/10.1007/s10518-017-0227-2.
Jafari, A., M. R. Ghasemi, H. A. Bengar, and B. Hassani. 2018b. “A novel method for quantifying damage to cast-in-place self-centering concrete stepping walls.” Struct. Concr. 19 (6): 1713–1726. https://doi.org/10.1002/suco.201700247.
Jafari, A., M. Preti, M. Beheshti, and R. Dugnani. 2021b. “Self-centering walls strengthening by high-performance concrete: A feasibility study.” Mater. Struct. 54 (3): 1–20. https://doi.org/10.1617/s11527-021-01710-0.
Kam, W. Y., S. Pampanin, A. Palermo, and A. J. Carr. 2010. “Self-centering structural systems with combination of hysteretic and viscous energy dissipations.” Earthquake Eng. Struct. Dyn. 39 (10): 1083–1108. https://doi.org/10.1002/eqe.983.
Kang, L., H. Qian, Y. Guo, Z. Li, S. Zhang, and G. Song. 2021. “Seismic performance of SMA/ECC concrete shear wall with self-centering and self-repairing.” In Proc., Earth and Space 2021, 331–336. Reston, VA: ASCE.
Kurama, Y., S. Pessiki, R. Sause, and L.-W. Lu. 1999. “Seismic behavior and design of unbonded post-tensioned precast concrete walls.” PCI J. 44 (3): 72–89. https://doi.org/10.15554/pcij.05011999.72.89.
Kurama, Y. C. 2002. “Hybrid post-tensioned precast concrete walls for use in seismic regions.” PCI J. 47 (5): 36–59. https://doi.org/10.15554/pcij.09012002.36.59.
Kurama, Y. C. 2005. “Seismic design of partially post-tensioned precast concrete walls.” PCI J. 50 (4): 100. https://doi.org/10.15554/pcij.07012005.100.125.
Li, Y., J. Li, Y. Shen, and W. Xu. 2020. “Cyclic behavior and simplified design method of hybrid rocking columns with external energy-dissipators.” J. Earthquake Tsunami 14 (6): 2050026. https://doi.org/10.1142/S1793431120500268.
Lu, X., and H. Wu. 2017. “Study on seismic performance of prestressed precast concrete walls through cyclic lateral loading test.” Mag. Concr. Res. 69 (17): 878–891. https://doi.org/10.1680/jmacr.16.00363.
Mander, J. B., M. J. Priestley, and R. Park. 1988. “Theoretical stress-strain model for confined concrete.” J. Struct. Eng. 114 (8): 1804–1826. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1804).
Marriott, D., S. Pampanin, D. Bull, and A. Palermo. 2008. “Dynamic testing of precast, post-tensioned rocking wall systems with alternative dissipating solutions.” Bull. N.Z. Soc. Earthquake Eng. 41 (2): 90–103. https://doi.org/10.5459/bnzsee.41.2.90-103.
Ou, Y.-C., M. Chiewanichakorn, A. J. Aref, and G. C. Lee. 2007. “Seismic performance of segmental precast unbonded posttensioned concrete bridge columns.” J. Struct. Eng. 133 (11): 1636. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:11(1636).
Perez, F. J., and O. Mauricio. 2018. “Verification of a simple model for the lateral-load analysis and design of unbonded post-tensioned precast concrete walls.” PCI J. 63 (5): 51–70. https://doi.org/10.15554/pcij63.5-01.
Perez, F. J., S. Pessiki, and R. Sause. 2013. “Experimental lateral load response of unbonded post-tensioned precast concrete walls.” ACI Struct. J. 110 (6): 1045–1055.
Perez, F. J., R. Sause, and S. Pessiki. 2007. “Analytical and experimental lateral load behavior of unbonded posttensioned precast concrete walls.” J. Struct. Eng. 133 (11): 1531–1540. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:11(1531).
Preti, M., and A. Meda. 2015. “RC structural wall with unbonded tendons strengthened with high-performance fiber-reinforced concrete.” Mater. Struct. 48 (1–2): 249–260. https://doi.org/10.1617/s11527-013-0180-8.
Rahmzadeh, A., M. S. Alam, and R. Tremblay. 2018. “Analytical prediction and finite-element simulation of the lateral response of rocking steel bridge piers with energy-dissipating steel bars.” J. Struct. Eng. 144 (11): 04018210. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002216.
Restrepo, J. I., and A. Rahman. 2007. “Seismic performance of self-centering structural walls incorporating energy dissipators.” J. Struct. Eng. 133 (11): 1560–1570. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:11(1560).
Sadeghi, M., F. Jandaghi Alaee, H. Akbarzadeh Bengar, and A. Jafari. 2022. “Evaluating the efficiency of supplementary rebar system in improving hysteretic damping of self-centering rocking walls.” Bull. Earthquake Eng. 20 (11): 6075–6107. https://doi.org/10.1007/s10518-022-01421-z.
Shahmansouri, A. A., H. Akbarzadeh Bengar, and A. Jafari. 2020. “Modeling the lateral behavior of concrete rocking walls using multi-objective neural network.” J. Concr. Struct. Mater. 5 (2): 110–128. https://doi.org/10.30478/jcsm.2021.272480.1192.
Smith, B. J., Y. C. Kurama, and M. J. McGinnis. 2011. “Design and measured behavior of a hybrid precast concrete wall specimen for seismic regions.” J. Struct. Eng. 137 (10): 1052–1062. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000327.
Smith, B. J., Y. C. Kurama, and M. J. McGinnis. 2013. “Behavior of precast concrete shear walls for seismic regions: Comparison of hybrid and emulative specimens.” J. Struct. Eng. 139 (11): 1917–1927. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000755.
Sritharan, S., S. Aaleti, R. S. Henry, K. Y. Liu, and K. C. Tsai. 2015. “Precast concrete wall with end columns (PreWEC) for earthquake resistant design.” Earthquake Eng. Struct. Dyn. 44 (12): 2075–2092. https://doi.org/10.1002/eqe.2576.
Twigden, K. M., and R. S. Henry. 2019. “Shake table testing of unbonded post-tensioned concrete walls with and without additional energy dissipation.” Soil Dyn. Earthquake Eng. 119 (Apr): 375–389. https://doi.org/10.1016/j.soildyn.2018.05.007.
Twigden, K. M., S. Sritharan, and R. S. Henry. 2017. “Cyclic testing of unbonded post-tensioned concrete wall systems with and without supplemental damping.” Eng. Struct. 140 (Jun): 406–420. https://doi.org/10.1016/j.engstruct.2017.02.008.
Wang, B., S. Zhu, J. Zhao, and H. Jiang. 2019. “Earthquake resilient RC walls using shape memory alloy bars and replaceable energy dissipating devices.” Smart Mater. Struct. 28 (6): 065021. https://doi.org/10.1088/1361-665X/ab1974.
Wang, Z., J. Wang, G. Zhao, and J. Zhang. 2020. “Modeling seismic behavior of precast segmental UHPC bridge columns in a simplified method.” Bull. Earthquake Eng. 18 (7): 3317–3349. https://doi.org/10.1007/s10518-020-00817-z.
Wang, Z., J.-Q. Wang, T.-X. Liu, and J. Zhang. 2018. “An explicit analytical model for seismic performance of an unbonded post-tensioned precast segmental rocking hollow pier.” Eng. Struct. 161 (Apr): 176–191. https://doi.org/10.1016/j.engstruct.2018.02.025.
Xiao, S. J., L. H. Xu, and Z. X. Li. 2020. “Design and experimental verification of disc spring devices in self-centering reinforced concrete shear walls.” Struct. Control Health Monit. 27 (7): e2549. https://doi.org/10.1002/stc.2549.
Xu, L., S. Xiao, and Z. Li. 2018. “Hysteretic behavior and parametric studies of a self-centering RC wall with disc spring devices.” Soil Dyn. Earthquake Eng. 115 (Dec): 476–488. https://doi.org/10.1016/j.soildyn.2018.09.017.
Xu, L., S. Xiao, and Z. Li. 2020. “Behaviors and modeling of new self-centering RC wall with improved disc spring devices.” J. Eng. Mech. 146 (9): 04020102. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001838.
Yooprasertchai, E., I. J. Hadiwijaya, and P. Warnitchai. 2016. “Seismic performance of precast concrete rocking walls with buckling restrained braces.” Mag. Concr. Res. 68 (9): 462–476. https://doi.org/10.1680/jmacr.15.00237.
Information & Authors
Information
Published In
Practice Periodical on Structural Design and Construction
Volume 28 • Issue 1 • February 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jul 28, 2022
Accepted: Sep 1, 2022
Published online: Nov 21, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 21, 2023
ASCE Technical Topics:
- Continuum mechanics
- Cyclic loads
- Dynamic loads
- Dynamics (solid mechanics)
- Energy dissipation
- Engineering fundamentals
- Engineering mechanics
- Finite element method
- Hybrid methods
- Hysteresis
- Material mechanics
- Material properties
- Materials characterization
- Materials engineering
- Methodology (by type)
- Numerical methods
- Rheology
- Solid mechanics
- Stiffening
- Structural behavior
- Structural dynamics
- Structural engineering
- Structural members
- Structural systems
- Thermodynamics
- Walls
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