CC BY
34
DOI: 10.23968/2500-0055-2023-8-1 -37-43
STRUCTURAL AND PARAMETRIC ANALYSIS OF LEAD RUBBER BEARINGS AND EFFECT OF THEIR CHARACTERISTICS ON THE RESPONSE SPECTRUM ANALYSIS
Faqiri Amanollah, Nadezhda Ostrovskaya*, Yuriy Rutman
Saint Petersburg State University of Architecture and Civil Engineering Saint Petersburg, Russia
Corresponding author's e-mail: ostrovskaya.nv@yandex.ru Abstract
Introduction: Earthquakes are one of the most frequent and potentially disruptive natural disasters. Up to this day, numerous methods have been tested and applied to prevent damage to buildings and structures as a result of earthquakes. Currently, one of the widely used methods is to provide seismic isolation between the building and the ground. Its main purpose is to reduce the interaction between the building and the ground as well as the impact of soil movement on the building. For our study, we chose a system of lead rubber bearings as isolators used to improve the seismic resistance of buildings. Purpose of the study: We aimed to expand the tool kit for the analysis of seismic isolation based on rubber bearings and demonstrate the effectiveness of ETABS software. Methods: The paper investigates the behavior of an isolation system with lead rubber bearings for various earthquake records with the use of ETABS software according to UBC-97 standards and software developed specifically for this study in Excel. Results: Based on the developed software, we analyzed how changes in properties of base isolators affect the behavior of structures exposed to earthquakes.
Keywords: seismic isolation, seismic bearing, rubber bearing, seismic isolation effectiveness.
Introduction
One of the important challenges of structural engineers is to find a suitable solution to reinforce structures so that they could withstand earthquakes. In traditional design methods, the seismic resistance of buildings is provided by the combination of stiffness, plasticity, and energy losses in the main components of the structure. In modern design methods, seismic isolation systems are utilized to ensure the safety and resistance of structural components to earthquakes as well as to reduce material consumption for structural components. Currently, seismic isolation systems are widely used to prevent structural vibrations from earthquakes, which allows structural components to remain in the elastic deformation range and makes it possible to prevent their significant damage and destruction (Tamim Tanwer et al., 2019).
There are many damping devices, including rubber bearings (with/without a lead core), friction and kinematic dampers. In recent decades, they have been used in practical seismic design of structures and are still being developed (Buckle and Mayes, 1990; Rutman and Ostrovskaya, 2019; Tyapin, 2020; Uzdin et al., 2012).
Fig. 1 shows an example of a lead rubber bearing (LRB) widely used all over the world (Jangid, 2007; Tyler and Robinson, 1984). The LRB is made of alternating layers of rubber and steel plates with one or several lead cores inside. The core is deformed, ensures the hysteresis operation of the structure as
well as sufficient stiffness, strength and resistance to low lateral loads, light winds, and minor earthquakes (Bhandari et al., 2018).
The LRB force/displacement relationship is nonlinear, and the correct prediction for the behavior of isolated base structures under seismic effects depends heavily on the mathematical model chosen to describe the system. For instance, there are several hysteresis models to describe the dynamic behavior of the LRB: linear, polynomial, and curvilinear (Wen, 1980). A suitable model for the dynamic behavior of the system is usually based on the characteristics of pulse energy, obtained as a result of dynamic or static experiments. In recent decades, much effort has been made to develop methods to identify non-linear hysteresis systems. These methods include least squares estimation in the time domain (Kilar et al., 2011; Lin et al., 2001; Wenbin, 2000; Yang and Lin, 2004). Thus, the task of determining the parameters of seismic bearings and simulating the behavior of the structure / seismic isolation system is quite relevant.
Subject, tasks, and methods
Fig. 2 shows a design scheme and main design parameters of the LRB (Sharbatdar et al., 2011). To determine the isolator parameters, Uniform Building Code UBC-97, corresponding to the regulations, was used (ICBO, 1997). The target period of the building and material properties were determined based on the following considerations: the values from 2 to 3 seconds are the desired values of the
Fig. 1. Schematic diagram of the LRB (Smirnov and Bubis, 2014):
1 — support plates fastened to the non-seismically isolated and seismically isolated parts of the structure;
2 — flanged steel plates; 3 — steel plates located between rubber plates; 4 — rubber plates; 5 — a rubber cover protecting the inner layers of rubber and metal; 6 — holes for anchor bolts required to fasten the bearing to the non-seismically isolated and seismically isolated parts of the structure; 7 — key holes; 8 — a lead core.
isolation system oscillation period. The modulus of elasticity E, the shear modulus G, and the maximum shear strain Ymax differ depending on the type of the LRB selected.
The main stages of the calculation were as follows: first, a building with rigid fixing was modeled, and vertical loads in the interior, exterior and corner columns were determined. After that, the design parameters of the LRB were calculated using an Excel spreadsheet. Then those parameters were used to determine the LRB parameters in ETABS. As a result, the following design parameters were obtained for three different types of the LRB (Table 1).
Description of the design solutions adopted with the use of the LRB. To test the model, we considered a standard 10-story reinforced concrete building located in the earthquake-prone area V, with an open floor, as shown in Figs. 3 and 4. The dimensions of the building in plan view are 30 and 24 m in the x and y directions, respectively (Ferraioli and Mandara, 2017). The height of the first floor is 3.6 m, and the height of the rest floors is 3 m. Thus, the total height
of the building is 30.6 m. The slab thickness is 0.150 m. The design static loads are taken to be equal to 3.4 kPa for the partitions and 1.5 kPa for the floors and the roof. Table 2 shows other characteristics of concrete and reinforcement. The axial load for the interior, exterior and corner columns is 5332.06 kN, 4529.19 kN, and 3911.39 kN, respectively. The design was performed as per American standard ASCE07 and UBC-97 (ICBO, 1997). In the calculations, concrete of grade M35 was used, and high yield strength deformed (HYSD) bars with a minimum yield strength of 415 MPa were utilized as both longitudinal and transverse reinforcement.
Modeling and design of a building with an LRB. ETABS software was used for the calculation. Fig. 5 shows a design scheme in the form of a spatial frame. It should be noted that in ETABS (and in some foreign design programs), static non-linear pushover analysis is implemented by introducing plastic hinges into the sections of the design scheme components where, from the point of view of the program user, inelastic deformations should
Fig. 2. Design scheme and main design parameters of the LRB
Table 1. Design parameters of the LRB for ETABS
Final input data for ETABS Exterior columns Interior columns Corner columns
Rotational inertia (kN/m) 0.0146 0.0207 0.0107
U1 Effective stiffness (kN/m) 721.991 849.977 623.510
U2 & U3 Effective stiffness (kN/m) 2913 3430 2516
U2 & U3 Effective damping 0.1 0.1 0.1
U2 & U3 Distance from the end — J (m) 0.0058 0.0058 0.0058
U2 & U3 Stiffness (kN/m) 24.559 28.913 21.209
U2 & U3 Yield strength (kN) 142.2 167.4 122.8
Bearing diameter, DLRB (m) 0.789 0.856 0.75
Total height of the LRB, h (m) 0.34 0.35 0.34
develop. This significantly increases the error probability since it is almost impossible to define an appropriate mechanism for the destruction of a complex structure and criteria for the transition of its components into plastic condition.
The use of the response spectrum function in accordance with the standards is a more unified procedure, which does not require additional user control over the structure operation, and that creates
Table 2. Initial data for structural modeling
No. Parameter Value
1 First floor height (m) 3.6
2 Floor height (m) 3
3 Building height (m) 30.6
4 Column size (m) 0.6^0.6 or 0.5^0.5
5 Number of floors 10
6 Beam size (m) 0.4x0.5
7 Floor slab thickness (m) 0.150
8 Modulus of elasticity of concrete Ec (GPa) 25
9 Design strength of concrete Fck (MPa) 30
10 Reinforcement yield strength (MPa) 415
11 Poisson's ratio 0.2
12 Dead load on the slab (kN/m2) 4.5
13 Load on the floor with partitions (kN/m2) 3.4
14 Load on the roof (kN/m2) 1.5
15 Load on the walls (kN/m) 7.5
16 Specific weight of reinforced concrete (kN/m3) 25.00
17 Material Concrete M35 and reinforcement Fe-415 (HYSD, compliant with IS-2002)
18 Reinforcement High strength deformed steel compliant with IS-2002. Modulus of elasticity — 200 kN/mm2
the advantage of using the response spectrum analysis method compared with the calculation according to the plastic mechanism. Results and discussion The spectral analysis of the structure isolated with the use of the LRB and the non-isolated structure yielded the following results presented in Figs. 6-10.
ft B B' C D D
5 X 6m=30m
-6.00m — —6.00m- — 6.00m-
= 1 J t-
E 3 E <0 ; H C C : c c
i 3 -t
-6.00m- 3
Fig. 3. Standard floor plan
11J J {1 ' I
y
I'l Vr'l
rLTLT
1 1 1 1 jl |i jiH|
6.00r nx5=30 .OOrn
Fig. 4. Scheme of the transverse frame of the reinforced concrete building structure
Table 3. Seismic characteristics of the construction facility as per UBC-97
No. Parameter Value Remark
1 Seismic zone factor (Z) 0.36 (UBC 97, Table 16-I)
2 Seismic load As per ASCE07
3 Seismic source type B (UBC 97, Table 16-S)
4 Distance to a known source 5 (UBC 97, Table 16-S)
5 Soil profile type SD (UBC 97, Table 16-J)
6 Near-source factor (Na) 1.2 (UBC 97, Table 16-S)
7 Near-source factor (Nv) 1.6 (UBC 97, Table 16-T)
8 Seismic coefficient (Ca) 0.36 (UBC 97, Table 16-Q)
9 Seismic coefficient (Cv) 0.56 (UBC 97, Table 16-R)
10 Design period TD, s 2.5
11 Behavior coefficient 1.25
12 Effective damping (pd or pm) 0.05
13 Damping coefficient (pd or pm) 1
The following designations are used in these figures: FB — a system without seismic isolation; LRB — a system with seismic isolation using the LRB. The results are given for the effects of an operating basis earthquake as well as for the system response spectrum analysis.
A comparison of the values of the maximum displacement for story drift and the shear force for each story, obtained based on the response spectrum analysis, makes it possible to note that displacement, drift, and shear forces decrease by 30% or more when the LRB is used. In the assessment of the maximum displacement of the LRB system, which is one of the main parameters in the design of seismic
Fig. 5. Scheme of the spatial frame of the reinforced concrete building structure with the LRB
isolation, as well as the maximum displacement of the base section of the structure and the building as a whole, the spectrum analysis method proved to be a simple and effective method.
In conclusion, it should be noted that it is important to choose the right parameters of seismic isolators. The system response spectrum analysis is one of the easiest and effective tools to determine the required properties of isolators, taking into account the complex movement of the structure. The proposed method for determining the LRB parameters using Excel in accordance with UBC-97 has acceptable accuracy in terms of assessing the design parameters of the LRB. Considering the behavior of the isolated structure and the fact that the bearings have non-linear characteristics, it is possible to choose the most effective model for the seismic bearing and structure by analyzing the response spectrum of the system.
Fig. 6. Drift in the X and Y directions (earthquake)
Fig. 7. Drift in the X and Y directions (spectrum analysis)
Fig. 8. Displacement in the X and Y directions (earthquake)
Fig. 9. Displacement in the X and Y directions (spectrum analysis)
References
Bhandari, M., Bharti, S. D., Shrimali, M. K. and Datta, T. K. (2018). Assessment of proposed lateral load patterns in pushover analysis for base-isolated frames. Engineering Structures, Vol. 175, pp. 531-548. DOI: 10.1016/j.engstruct.2018.08.080.
Buckle, I. G. and Mayes, R. L. (1990). Seismic isolation: history, application, and performance — a world view. Earthquake Spectra, Vol. 6, Issue 2, pp. 161-201. DOI: 10.1193/1.1585564.
Ferraioli, M. and Mandara A. (2017). Base isolation for seismic retrofitting of a multiple building structure: design, construction, and assessment. Mathematical Problems in Engineering, Vol. 2017, 4645834. DOI: 10.1155/2017/4645834.
ICBO (1997). Uniform Building Code (UBC-97). Vol. 2. Structural Engineering Design Provisions. Whittier, California: International Conference of Building Officials, 492 p.
Jangid, R. S. (2007). Optimum lead-rubber isolation bearings for near-fault motions. Engineering Structures, Vol. 29, Issue 10, pp. 2503-2513. DOI: 10.1016/j.engstruct.2006.12.010.
Kilar, V., Petrovcic, S., Koren, D., and Silih, S. (2011). Seismic analysis of an asymmetric fixed base and base-isolated high-rack steel structure. Engineering Structures, Vol. 33, Issue 12, pp. 3471-3482. DOI: 10.1016/j.engstruct.2011.07.010.
Lin, J.-W., Betti, R., Smyth, A. W., and Longman, R. W. (2001). On-line identification of non-linear hysteretic structural systems using a variable trace approach. Earthquake Engineering & Structural Dynamics, Vol. 30, Issue 9, pp. 1279-1303. DOI: 10.1002/eqe.63.
Rutman, Yu. L. and Ostrovskaya, N. V. (2019). Dynamics of structures: earthquake resistance, seismic protection, wind loads. Saint Petersburg: Publishing House of the Saint Petersburg State University of Architecture and Civil Engineering, 253 p.
Sharbatdar, M. K., Hoseini Vaez, S. R., Amiri, G.G., and Naderpour, H. (2011). Seismic response of base-isolated structures with LRB and FPS under near fault ground motions. Procedia Engineering, Vol. 14, pp. 3245-3251. DOI: 10.1016/j. proeng.2011.07.410.
Smirnov, V. I. and Bubis, A. A. (2014). Discussion of the draft national standard: "Anti-seismic and seismically isolated construction design code. Design rules". Earthquake Engineering. Constructions Safety, No. 3, pp. 22-33.
Tamim Tanwer, M., Kazi, T. A., and Desai, M. (2019). A study on different types of base isolation system over fixed based. In: Satapathy, S. and Joshi, A. (eds.). Information and Communication Technology for Intelligent Systems. Smart Innovation, Systems and Technologies, Vol. 106. Singapore: Springer, pp. 725-734. DOI: 10.1007/978-981-13-1742-2_71.
Tyapin, A. G. (2020). Equation of planar vibrations of rigid structure on kinematic supports after A.M. Kurzanov. Earthquake Engineering. Constructions Safety, No. 5, pp. 19-31.
Tyler, R. G. and Robinson, W. H. (1984). High-strain tests on lead-rubber bearings for earthquake loadings. Bulletin of the New Zealand Society for Earthquake Engineering, Vol. 17, No. 2, pp. 90-105. DOI: 10.5459/bnzsee.17.2.90-105.
Uzdin, A. M., Yelizarov, S. V., and Belash, T. A. (2012). Earthquake-resistant constructions of transport buildings and structures. Moscow: Rail Transport Training Center, 501 p.
Wen, Y. K. (1980). Equivalent linearization for hysteretic systems under random excitation. Journal of Applied Mechanics, Vol. 47, Issue 1, pp. 150-154. DOI: 10.1115/1.3153594.
Wenbin, Q. J. L. (2000). Static Pushover Analysis-an analytical tool for performance/displacement-based seismic design. Building Structure, Vol. 30, No. 6, pp. 23-26.
Yang, J. N. and Lin, S. (2004). On-line identification of non-linear hysteretic structures using an adaptive tracking technique. International Journal of Non-Linear Mechanics, Vol. 39, Issue 9, pp. 1481-1491. DOI: 10.1016/j.ijnonlinmec.2004.02.010.
КОНСТРУКТИВНЫЙ И ПАРАМЕТРИЧЕСКИЙ АНАЛИЗ СВИНЦОВЫХ РЕЗИНОМЕТАЛЛИЧЕСКИХ ОПОР И ВЛИЯНИЕ ИХ ХАРАКТЕРИСТИК
НА АНАЛИЗ СПЕКТРА ОТКЛИКА
Факири Амоналлах, Надежда Владимировна Островская*, Юрий Лазаревич Рутман
Санкт-Петербургский государственный архитектурно-строительный университет Санкт-Петербург, Россия
*E-mail: ostrovskaya.nv@yandex.ru Аннотация
Введение: Землетрясения являются одним из часто наблюдаемых стихийных бедствий, которые могут иметь весьма разрушительные последствия. До сегодняшнего дня было опробовано и применено множество различных методов для предотвращения повреждений сооружений и конструкций, которые могут возникнуть в результате землетрясений. Одним из широко используемых в настоящее время методов является применение сейсмоизоляции между зданием и грунтом, основной целью которого является уменьшение взаимодействия между ними и уменьшение влияния движения грунта на здание. В качестве изоляторов, применяемых в сейсмостойких зданиях, была выбрана система резинометаллических опор со свинцовым сердечником. Цель исследования: настоящая статья ставит целью расширить инструментарий средств расчета сейсмоизоляции на базе резинометаллических опор и показать эффективность применения программного комплекса ETABS. Методы: в статье проводится исследование поведения системы изоляции с применением резинометаллических опор со свинцовым сердечником для различных записей землетрясений с использованием программного комплекса ETABS согласно нормам UBS-97 и программного обеспечения, разработанного специально для этого исследования в Exel. Результаты: с помощью разработанного программного обеспечения анализировалось влияние изменения различных свойств изоляторов основания на поведение конструкции под действием землетрясений.
Ключевые слова: сейсмоизоляция, сейсмоопора, резинометаллическая опора, эффективность сейсмоизоляции.
