Multi-drum rocking columns (MDRC) with dry joints can rock and self-center under gravity, but negative post-rocking stiffness can produce larger displacements during strong earthquakes. This study proposes a simple stiffening system that combines a spring and a prestressed cable to tune post-rocking stiffness and pretension. Theoretical formulae are derived for the initial stiffness and the post-rocking stiffness, then validated with experiments and numerical simulations. Both free-rocking and controlled MDRC configurations are examined to compare dynamic performance. Results show that the controlled system reduces peak displacement and improves self-centering properties. Parametric analyses indicate that higher spring stiffness and greater initial pretension limit multi-drum rocking and improve self-centering. Additionally, this study introduces dimensionless measure for stiffness and pretension to provide practical selection guidance which improves seismic resistance, while keeping all devices concealed to preserve architectural appearance.
Al-SubaihawiSPessikiS (2019) Static pushover response of spring anchored unbonded post-tensioned rocking systems. Engineering Structures200: 109582.
2.
Al-SubaihawiSPessikiS (2022) Seismic behaviour of spring anchored unbonded post-tensioned rocking systems. Journal of Earthquake Engineering26(12): 6428–6445.
3.
ArabpanahanMMirghaderiSHosseiniA, et al. (2021) Dynamic rocking response of SDOF-embedded foundation systems using shake table experiments. Soil Dynamics and Earthquake Engineering140: 106431.
4.
AutieroFDe MartinoGDi LudovicoM, et al. (2020) Multidrum stone columns at the Pompeii archaeological site: analysis of geometrical properties and state of preservation. Heritage3(4): 1069–1082.
5.
BitweLHabteB (2024) Numerical investigation of structural models equipped with tuned liquid damper. Journal of Vibration and Control30(13–14): 2971–2980.
6.
ContentoADi EgidioAPagliaroS (2022) Dynamic and seismic protection of rigid-block-like structures with combined dynamic mass absorbers. Engineering Structures272: 114999.
7.
CuiLGuoALiH (2011) Investigation of the parameters of Hertz impact model for the pounding analysis of highway bridge. Procedia Engineering14: 2773–2778.
8.
Di EgidioAContentoA (2024) Seimic performance of two rigid blocks coupled through a Maxwell visco-elastic device. Engineering Structures301: 117319.
9.
Di EgidioAContentoAOlivieriC, et al. (2020) Protection from overturning of rigid block‐like objects with linear quadratic regulator active control. Structural Control and Health Monitoring27(10): e2598.
10.
Di EgidioAOlivieriCContentoA, et al. (2023) Improving the dynamic and seismic behaviour of rigid block-like elements through active mass dampers. Engineering Structures275: 115312.
11.
DrososVAnastaspoulosI (2014) Shaking table test of multidrum columns and portals. Earthquake Engineering and Structural Dynamics43: 1703–1723.
12.
FroozanfarMMoradiSKianoushR, et al. (2024) Review of self-centering rocking systems for earthquake-resistant building structures: state of the art. Journal of Building Engineering84: 108607.
13.
GattiGSveltoC (2023) Performance of a vibration isolator with sigmoidal force-deflection curve. Journal of Vibration and Control29(23–24): 5713–5724.
14.
GB50011-2010 (2010) Code for Seismic Design of Building. China Architecture & Building Press.
15.
GiouvanidisADimitrakopoulosE (2017) Nonsmooth dynamic analysis of sticking impacts in rocking structures. Bulletin of Earthquake Engineering15(5): 2273–2304.
16.
HarouniPAhmad AttariNRofooeiF (2023) Vibration control through the robust nonlinear absorber with negative stiffness and internal resonance creation. Journal of Vibration and Control29(5–6): 1254–1267.
17.
HousnerG (1963) The behavior of inverted pendulum structures during earthquake. Bulletin of the Seismological Society of America53(2): 403–417.
18.
HuSHuRYangM, et al. (2024) Numerical and experimental study on the damping performance of the fluid viscous damper considering the gap effect. Journal of Vibration and Control30(21–22): 4946–4963.
19.
JiaLFanKXiangP, et al. (2022) Shaking table test on single‐story rocking‐column steel frame under excitations along strong axis. Structural Control and Health Monitoring29(12): e3125.
20.
KounadisAPapadopoulosG (2016) On the rocking instability of a three-rigid block system under ground excitation. Archive of Applied Mechanics86(5): 957–977.
21.
LaiZChenQHuangL (2021) A semianalytical Hertzian frictional contact model in 2D. Applied Mathematical Modelling92: 546–564.
22.
LamFHeMYaoC (2008) Example of traditional tall timber buildings in China – the Yingxian pagoda. Structural Engineering International18(2): 126–129.
23.
MakrisN (2014) A half-century of rocking isolation. Earthquakes and Structures7(6): 1187–1221.
24.
MakrisNVassiliouM (2015) Dynamics of the rocking frame with vertical restrainers. Journal of Structural Engineering141(10): 04014245.
25.
ManzoNVassiliouM (2022) Cyclic tests of a precast restrained rocking system for sustainable and resilient seismic design of bridges. Engineering Structures252: 113620.
26.
MichaltsosGRaftoyiannisI (2016) Dynamic behavior of ancient frames consisting of classical columns with architrave. Archive of Applied Mechanics86(12): 2033–2052.
27.
MuthukumarSDesRochesR (2006) A Hertz contact model with non-linear damping for pounding simulation. Earthquake Engineering & Structural Dynamics35(7): 811–828.
28.
NakaharaKHisatokuTNagaseT, et al. (2000) Earthquake response of ancient five-story pagoda structure of Horyu-ji temple in Japan. In: 12th World Conference on Earthquake Engineering, 2000. https://www.iitk.ac.in/nicee/wcee/article/1229.pdf
29.
PengY (2024) Seismic mitigation analysis of base-isolated structure with sliding magnetic bearings considering local-site conditions. Journal of Building Engineering91(March): 109662.
30.
PitilakisKTsinidisGKarafagkaS (2017) Analysis of the seismic behavior of classical multi-drum and monolithic columns. Bulletin of Earthquake Engineering15(12): 5281–5307.
31.
PsycharisILemosJPapastamatiouD, et al. (2003) Numerical study of the seismic behaviour of a part of the Parthenon Pronaos. Earthquake Engineering & Structural Dynamics32(13): 2063–2084.
32.
PulatsuBSarhosisVBretasE, et al. (2017) Non-linear static behaviour of ancient free-standing stone columns. Proceedings of the Institution of Civil Engineers - Structures and Buildings170(6): 406–418.
33.
RahgozarNPouraminianMRahgozarN (2023) Structural optimization of vertical isolated rocking core-moment frames. Journal of Vibration and Control29(15–16): 3451–3460.
34.
Ríos-GarcíaGBenavent-ClimentA (2020) New rocking column with control of negative stiffness displacement range and its application to RC frames. Engineering Structures206: 110133.
35.
RohHReinhornA (2010) Nonlinear static analysis of structures with rocking columns. Journal of Structural Engineering136(5): 532–542.
36.
SalehiMSiderisPLielA (2017) Numerical simulation of hybrid sliding-rocking columns subjected to earthquake excitation. Journal of Structural Engineering143(11): 04017149.
37.
SalehiMSiderisPLielA (2021) Experimental testing of hybrid sliding‐rocking bridge columns under torsional and biaxial lateral loading. Earthquake Engineering & Structural Dynamics50(10): 2817–2837.
38.
SarhosisVBaraldiDLemosJ, et al. (2019) Dynamic behaviour of ancient freestanding multi-drum and monolithic columns subjected to horizontal and vertical excitations. Soil Dynamics and Earthquake Engineering120: 39–57.
39.
ShaBXieLYongX, et al. (2021) An experimental study of the combined hysteretic behavior of dougong and upper frame in Yingxian wood pagoda. Construction and Building Materials305: 124723.
40.
ShenYSuiP (2024) Dynamics analysis and parameter optimization of a vibration absorber with geometrically nonlinear inerters. Journal of Vibration and Control30(21--22): 5031–5046.
StirosS (2020) Monumental articulated ancient Greek and Roman columns and temples and earthquakes: archaeological, historical, and engineering approaches. Journal of Seismology24(4): 853–881.
43.
SunZXiangPJiaL, et al. (2022) Seismic response and kinematic mechanisms of single-story pavilion-type timber frame based on shaking table test. Structures45: 1701–1716.
44.
TavakoliHNaghaviFGoltabarA (2014) Dynamic responses of the base-fixed and isolated building frames under far-and near-fault earthquakes. Arabian Journal for Science and Engineering39(4): 2573–2585.
45.
Thiers‐MoggiaRMálaga‐ChuquitaypeC (2019) Seismic protection of rocking structures with inerters. Earthquake Engineering & Structural Dynamics48(5): 528–547.
46.
UstaP (2021) Investigation of a base-isolator system’s effects on the seismic behavior of a historical structure. Buildings11(5): 217.
47.
WangJZhouW (2023) Experimental and numerical response of unbonded post-tensioned rocking wall under lateral cyclic loading. Journal of Building Engineering66: 105827.
48.
WuLWangK (2024) Optimization design and stability analysis for a new class of inerter-based dynamic vibration absorbers with a spring of negative stiffness. Journal of Vibration and Control30(3–4): 822–836.
49.
WuYLiuTOehlersD (2006) Fundamental principles that govern retrofitting of reinforced concrete columns by steel and FRP jacketing. Advances in Structural Engineering9(4): 507–532.
50.
XiangPXieRLiZ, et al. (2020) Seismic performance of a single-story articulated steel structure system. Journal of Engineering Mechanics146(10): 04020108.
51.
XiangPSongGFanK, et al. (2022) Shaking table test on a low-damage controlled multiple-rocking-column steel frame. Engineering Structures254: 113896.
52.
XiaoweiYYanfengW (2021) Study on seismic and shock absorption performance of Yi Ci Hui stone pillar. IOP Conference Series: Earth and Environmental Science676(1): 012033.
53.
XieRLiZXiangP, et al. (2021) Dynamic behaviors of steel multiple-rocking-column structural system with rocking stoppers. Engineering Structures243: 112649.
54.
YimCChopraAPenzienJ (1980) Rocking response of rigid blocks to earthquakes. Earthquake Engineering & Structural Dynamics8(6): 565–587.
55.
ZhangRYanZLiuJ, et al. (2023a) Seismic performance of a low-damage rocking column base joint along weak axis. Journal of Building Engineering67: 106056.
56.
ZhangXCaoDLiuM, et al. (2023b) Vibration isolation performance of simply supported beam installed with a negative stiffness device. Journal of Vibration and Control29(7–8): 1726–1737.
57.
ZhangH-TZhangRSunZ, et al. (2024) Dynamic behaviors of steel multiple-rocking-column system with varying post-rocking stiffness. International Journal of Mechanical Sciences277: 109422.
58.
ZhaoFCaoSLuoQ, et al. (2023) Enhanced design of the quasi-zero stiffness vibration isolator with three pairs of oblique springs: theory and experiment. Journal of Vibration and Control29(9–10): 2049–2063.
