A NEW PROPOSED SEISMIC ISOLATION SYSTEM: DOUBLE ISOLATION SURFACES SYSTEM WITH TUNED MASS DAMPER (DISTM) Part (II): MODELING, NUMERICAL ANALYSIS, AND COMPARISON WITH CONVENTIONAL SEISMIC ISOLATION SYSTEMS
Dr. Seleemah, Ayman A. Dr. El-Khoriby, Saher R. Assoc. Prof. of Structural Engineering Assoc. Professor of Structural Engineering Benha University Tanta University Dr. Kassem, Mohamed A. Str. Eng. Ezz El-Arab, Islam M. Professor of Structural Engineering Assistant lecture of Structural Eng. Tanta University Tanta University Abstract In Part I of these two companion papers, the experimental verification of the ability of tuned mass of the new component to dissipate a substantial amount of energy was presented. In this part (Part II), the mathematical model of the new proposed system [DISTM] will be introduced. This mathematical model will be used in the analysis of three isolated R.C. bridges when subjected to three bidirectional earthquakes to evaluate the efficiency of the new [DISTM] as compared to existing seismic isolation systems and nonisolated R.C. bridge conditions. Results demonstrated superior performance of all DISTMs as compared to existing conventional seismic isolation systems.
الملخص باللغة العربية في الجزء الول من هذا البحث تم استعراض الجزء العملي والتصنيعي للمكون الجديد TMD وإثبات مدى نجاحه وكفائتة في توليد القدر المرجو من نسبة الخمول الملئمة لنظم العزل بهدف زيادة معدلت تشتيت الطاقة وتحسين أداء النظم التقليدية للعزل الزلزالى للكبارى. أما في هذا الجزء الجديد من البحث فقد تم استعراض النموذج الرياضي لنظام العزل الجديد الذي أطلق عليه النظام ذو سطحى العزل المزدوجين والمزود بمشتت الطاقة ذو الكتلة المتوالفة أو المتناغمة [Double Isolation Surfaces System with Tuned Mass Damper] وأختصارها هى DISTM وشرح فلسفة وأسلوب عمله. وقد تم تقديم تمثيل رياضى (يعتمد على برنامج (3D-BASIS-ME لنموذجين من الكبارى تم أختيارهم من البحاث السابقة، أحدهما تم إختباره سابقآ نظريآ فقط والخر أختبر نظريآ ومعمليآ بمعرفة المركز القومى لبحاث هندسة الزلزل ببفالو بالوليات المتحدة المريكية، وذلك لمقارنة نتائج الباحثيين السابقين للتأكد من دقة النتائج التى تم الحصول عليها من التحليل والتمثيل الرياضى للنموذجين اللذين تم أختيارهم، وقد أظهرت نتائج المقارنة دقة التمثيل والتحليل الرياضى للنموذجين. وعليه تم إستعراض النموذج الرياضي الكامل للكوبري النموذج الول مع وجود النظام الجديد للعزل أوأنظمة العزل التقليدية مع عمل دراسة عددية لتلك النظمة تحت تأثير مجموعه من الزلزل المختلفة في الشدة مع دراسة تأثير جساءه الركائز وكذلك العديد من المتغيرات الهامة والمؤثرة على أداء نظم العزل الزلزالى كالزمن الدوري ونسبة الضمحلل فى كل من الكوبرى وأنظمة العزل الزلزالى ومعاملت الحتكاك بأنظمة العزل المنزلقة ومدى تأثير ذلك على قيم قوى القص عند الساسات والزاحة والعجلة المتولدة عند مستوى بلطة الكوبرى بهدف توضيح تأثيرها علي النتائج سواء كان الكوبرى معزول بالنظام الجديد أو بنظم العزل التقليدية لتحديد مدى كفاءة نظام العزل الجديد وتحسينه لسلوك الكبارى مقارنة بنظم العزل التقليدية. ولقد توصلت الدراسة إلى أثبات نجاح وكفاءة هذا النظام الجديد في تقليل قوى القص عند الساسات والزاحة والعجلة المتولدة عند مستوى بلطة الكوبرى بنسب تتراوح بين 20-75% مقارنة بنظم العزل التقليدية و بنسب تتراوح بين -60 95% مقارنة بالكبارى الغير معزولة زلزاليا. كما أن هذا النظام الجديد والمبتكر فى هذا البحث يصلح للتطبيق عمليآ فى جميع أنواع المنشأت المراد عزلها زلزاليآ وبكفاءة عالية.
Keywords: Isolated bridges; Base isolation; Seismic response; Bearing period Energy dissipation; [DISTM]; Bearing damping, Earthquake.
1. Introduction Structural engineers, in their attempt to reduce earthquake hazards on essential facilities, are always seeking for new concepts and new technologies for protection against earthquakes. Several approaches were explored such as seismic isolation, seismic energy dissipation, and active control. Seismic isolation attempts to uncouple the structure, in the horizontal direction, from its basis through an isolation surface. Seismic energy dissipation depends on introducing energy dissipation components into the structural system. Many types of energy dissipation devices have been used. Among these are the friction, yielding steel, viscoelastic, viscous fluid, tuned liquid, and tuned mass dampers. The main characteristic of these devices is their ability to dissipate a substantial amount of earthquake induced energy and hence enhance the response of the structure during earthquakes. Some researchers explored the combination of seismic isolation and seismic energy dissipation technologies for protection of bridge structures. For example, Tsopelas et. al. [1] and Constantinou et al. [2] studied a system consisting of sliding bearings, rubber restoring force devices and fluid dampers. Moreover, Tsopelas and Constantinou [3,4] studied a system consisting of sliding bearings and fluid restoring force and damping devices and another system consisting of lubricated PTFE sliding bearings and mild steel dampers, respectively. It was found that such combinations are useful, at various levels, in enhancing the behavior of the isolation systems. An innovate combination and rearrangement of seismic isolation and energy dissipation techniques have been explored in this study. These resulted in a new seismic isolation system which was called Double Isolation Surfaces system with Tuned Mass damper [DISTM]. The main idea of the new proposed system is to filter the seismic motion through two levels of isolation; and to increase the total damping of the whole seismic isolation system. The main objectives of this study were; (1) to introduce the new proposed component for seismic isolation of important structures like bridges; (2) to develop a successful mathematical model of the new component; (3) to experimentally assess the capability of the tuned mass damper of the new system to dissipate a substantial amount of energy; (4) to evaluate the optimum and most economic tuned mass ratio; (5) to study different bridges' response to different earthquake excitations when isolated by the new component; (6) to compare the response of bridges isolated via the new component with those non- isolated and those isolated by conventional seismic isolation systems; and (7) to investigate the effect of different parameters of seismic isolation systems on the isolators' performance. The selected parameters are the bearing period of elastomeric and sliding bearings, and friction coefficient of sliding bearings. To cover objective No.(3) presented above, an experimental schedule was planned and shaking table experimental tests were conducted on different configurations of the tuned mass damper component. Detailed information regarding this phase of the research was presented in part I of these two companion papers.
2. Description of the New Proposed System [DISTM] The main idea of the new proposed system is to filter the seismic motion through two levels of isolation; and to increase the total damping of the whole seismic isolation system. Fig.(1) shows a schematic presentation of the new proposed system. As shown in the figure, the new system consists of three components mounted between the bridge pier and deck. The lower component can be any known seismic isolation system. For example, it can be elastomeric bearing (either LRB or NZ system), or sliding type of bearing like FPS system. The middle component is a tuned mass damper that is tuned to have the same frequency of the isolated bridge and to have an optimum damping as described earlier in part I of these two companion papers. The upper component is an elastomeric bearing (Laminated Rubber Bearing LRB), with weak stiffness. In case of a seismic event, the tuned mass of the TMD is expected to move out of phase of the whole system, which consequently will increase the damping of the system. Most of the seismic energy is expected to be dissipated at the upper and lower seismic isolation systems and a considerable part of the rest of the energy is expected to be dissipated by the tuned mass damper component. Different configurations of the new proposed component are shown in Fig. (1). It should be pointed out that, the system will be denoted as DISTM- type (1, 2, or 3) according to the lower seismic isolation component (LRB, NZ, or FPS), respectively.
3. Mathematical Model and Equations of Motion of the DISTM The bridge including the DISTM system adopted in the analysis is shown in Fig. (2). The bridge deck is considerably stiffer than the isolation bearings, which are used for the seismic isolation of the superstructure, and the piers are assumed to be fixed at the foundation level. The span lengths are quite short so that the whole bridge is experiencing the same vibration. Further, the mass md of bridge deck, the mass mp of the piers, and the mass mt of the tuned mass in the new proposed seismic isolation system are considered as lumped masses. Seismic ground motion acting along the longitudinal and transversal axes of the bridge excites the system. It should be noted that the scope of this study is limited to regular bridges. The height of the pier is denoted as h. The pier is characterized by an elastic stiffness, kp, and viscous damping coeffcient, cp. The lower isolation bearing under the tuned mass is characterised by an effective stiffness kl , and equivalent viscous damping coefficient, cl. The upper isolation bearing located above the tuned mass and under the deck of the bridge is characterized by an effective stiffness, ku, and equivalent viscous damping coefficient, cu. Moreover, the tuned mass damper has an equivalent viscous damping coefficient, ct. In order to simplify the analysis all piers are considered identical in size and stiffness. Further simplification considers a rigid deck and elimination of the rotational degrees-of-freedom.Under these assumptions, the isolated regular bridge can be modelled as a three degree-of-freedom system in both directions as shown in Fig. (2). The total displacement amplitudes are expressed as: u u u t p l ...... …...... (1) ud ut uu
Where u p , ut , and ud are the total displacement amplitudes of the top of the pier, the tuned mass damper, and the bridge deck, respectively, as depicted in Fig. (2).
The system corresponds to the three degrees-of-freedom u p ,ut and ud . The .. structure motion results from horizontal ground acceleration, u g t , the equation of motion of the bridge system can be cast in matrix form as follows: .. . u d u d md 0 0 cu cu 0 .. . 0 mt 0 u t cu cu cl ct cl u t .. . 0 0 mp u p 0 cl cl c p u p . u d ku ku 0 md 0 0 1 . .. ku ku kl kl u t ug 0 mt 0 1 ……………………..… (2) . 0 kl k p kl u p 0 0 m p 1 This equation of motion is solved numerically utilizing program 3D-BASIS-ME. It should be pointed out that the upper and lower stiffness were obtained utilizing the specific equations of each type of bearing. For detailed information regarding that, the reader is referred to Tsopelas et al. [5].
4. Modeling and Analysis Objectives The principal objective of modeling and analysis tools is to obtain the seismic response of bridges in terms of structural displacements and member forces and deformations. This quantification is required for the seismic assessment and/or design of bridges isolated via the new component. In this study, two bridge models were used in the numerical analysis. These two bridge models were carefully selected after a comprehensive review of most of the previous studies in this area of research. The first model [Model-I] was studied analytically by Ghobarah and Ali [6], Wang et al. [7], Jangied [8] and Jangied et al. [9]. This model has an advantage with its real practical dimensions. The second model [model-II] was thoroughly studied both analytically and experimentally at the National Center for Earthquake Engineering Research (NCEER), (1992 to 2005). The description of these two models are presented below,
4.1 Bridge Model-I This is a continuous, cast-in-place concrete box girder bridge. It is presumed (without any checks) that the original bridge design is sufficient to sustain the loads and displacement demands when seismically isolated as described herein. The bridge consists of three-span continuous deck supported by isolation bearings as shown in Fig. (3), and with properties listed in Table 1. The substructure of the bridge consists of rigid abutments and reinforced concrete piers. The isolation bearings are provided between superstructure and substructure at abutment and pier locations.
4.2 Bridge Model-II This model of bridge was thoroughly studied both experimentally and analytically at NCEER (National Center for Earthquake Engineering Research), (1992 to 2005). At quarter length scale, the bridge model is shown in Fig. (4). It has a clear span of 4.8 m (15.7 feet), height of 2.53 m (8.3 feet) and total weight of 157.8 kN (35.5 kips). The deck consists of two AISC W14*90 sections which are transversely connected by beams. Additional steel and lead weights are added to reach the model deck weight of 143 KN (32.1 kips), as determined by the similitude requirements. Each pier consists of two AISC TS6*6*5/16 columns with a top made of channel section which was detailed to have sufficient torsional rigidity. The tubular columns are connected to beams which are bolted to the shaking table. The bridge model was designed to have flexible piers so that under non-isolated conditions the fundamental time period in the longitudinal direction is 0.25 sec. (or 0.5 sec. in prototype scale). Damping in the model was estimated to be 0.02 of critical in its non-isolated condition.
5. Verification of Numerical Simulation An important stage is to verify that the analytical simulation model results are accepted and, to a good extent, compatible with results published in the references for analytical simulations and also for real shaking table tests. For this, both bridge models were utilized. That is, the three bridges of model-I with different pier shapes and bridge model-II. The dynamic responses of the three bridges of model-I as calculated by program 3D-BASIS-ME when subjected to three different earthquake ground motions for the cases of non-isolated bridge and isolated bridge utilizing LRB and NZ systems is compared with the results presented in Jangid [8]. The comparison is tabulated in Table (2). As shown in the table, comparison was conducted for maximum response of deck acceleration and displacements in both orthogonal directions. Also, these tables presented the percentage of the difference between the results obtained in this study and those presented by Jangid, [8,9]. As shown in these tables, the results are very close with a maximum difference of about 5%. Fig.(5) shows another comparison in which the dynamic response of bridge model-II as recorded both experimentally in a real shaking table test and analytically as calculated by Tsopelas et al.,[10] are compared to the numerical simulation of the present study. It should be mentioned that, the comparison is conducted for both bearing displacement time history and loops of bearing displacement versus pier base shear over weight of the bridge. The top graphs of Fig.(5) presents the results given in Tsopelas et al., [10] while the lower graphs present the results obtained in this study utilizing program 3D-BASIS-ME. Moreover, these results were obtained when the bridge was subjected to 200% of El-Centro, 1940 earthquake. As shown in the figure, the comparisons are very satisfactory and show very good agreement with experimental results in both time history of displacement and bearing displacement-base shear loops, respectively.
6. Evaluation of Optimum Tuned Mass Ratio To obtain the best seismic performance of the bridge system isolated by the new proposed component, it is essential to know the optimum mass of the tuned mass component. For this, a numerical study of bridge-1 of model-I when isolated by DISTM-3 and with different tuned mass ratios was conducted. The tuned mass ratios were changed from 0.5% to 3.0% with constant interval of 0.5%; while all other parameters were fixed to obtain optimum tuned mass ratio which reduces the dynamic responses of RC bridge isolated by DISTM. The maximum deck displacement, deck acceleration, and base shear of the bridge system utilizing DISTM-3 with different tuned mass ratios are shown in Fig. (6). It is observed from the figure that the ratio of the tuned mass has negligible effect on the key response parameters of the bridge. Thus, using the minimum tuned mass ratio (0.5%) would be more beneficial from both an economic and industrial points of view. Therefore, this ratio is recommended for bridge applications and will be used henceforth in this study.
7. Numerical Analysis of the Bridges Isolated by the New System [DISTM] The equations of motion are utilized to study the behavior of the new system in much detail. This will bring in perspective the advantages and disadvantages of the new system as compared with other existing seismic isolation systems. To make sure that the results are general, the three different bridge systems used by Jangid [8] were studied to represent different cases of bridge flexibility. Moreover, three different earthquake ground motions were used to represent a general case of loading that the system may exhibit. These earthquakes are the famous El-Centro, 1940, and Kobe, 1995 earthquakes representing moderate and severe seismic events, respectively, and the Northridge, 1994 earthquake which represents a near fault type of excitation that the system may be subjected to. During each of these excitations, one component of each earthquake was applied in the longitudinal direction of the bridge, while the other orthogonal component was applied in the transversal direction. Depending on the type of isolation utilized at the lower surface of isolation of the DISTM, specific parameters were studied for the elastomeric bearing system and another set of parameters were studied for the sliding bearing systems. For the elastomeric bearing systems, the main parameter was the time period of the isolation devices (Tb). This time period was varied from 1.5 to 4 sec. at an interval of 0.5 sec., to cover a wide range of natural periods that exist in practice. For the sliding bearing systems, the studied parameters include: (i) bearing period Tb which was also varied from 1.5 to 4.0 sec at an interval of 0.5 sec; and (ii) friction coefficient of the isolation system, max , which was varied from 0.03 to 0.15 to represent typical levels of friction. It is worthwhile to note that the same range of the above mentioned parameters were also covered for analysis of bridges when isolated by conventional seismic isolation systems to have a clear comparison between the new proposed system and conventional seismic isolation systems. Absolute peak response parameters of the three bridge models are summarized in Tables 3 to 5 along with the responses of the same bridges when isolated by conventional isolation systems only. To get a clear vision of the response of each of the new proposed systems as compared to its corresponding conventional seismic isolation system, a reduction factor, [R] was calculated as follows:
R = (Rconventional - RDISTM)/ Rconventional Where: Rconventional is the absolute peak response of bridge isolated by conventional seismic isolation system; RDISTM is absolute peak response of the same bridge isolated by the corresponding new seismic isolation system [DISTM]. Values of R are listed in Tables 3 to 5. It should be mentioned that an increase in the reduction factor [R] means better performance of bridge isolated by the new proposed system [DISTM]. To eliminate the dependency of the reduction factor, R on the bridge model, ground excitation type and direction and to make the results more general, the average value of R for all bridge types and ground excitations in both directions, was calculated and the results are presented in Fig. (7). It is clear that the values of R are always positive and lie in the range of 27% to 43% for the displacement; 27% to 37% for deck acceleration; and 25% to 30% for base shear, respectively. DISTM-1 caused the best reduction of 43% and 29% for the displacement and base shear, respectively, followed by DISTM-3, which caused displacement reduction of 40% and base shear reduction of 25%. DISTM-2 caused the least level of reduction with values of 27% and 30% for the reduction in displacement and base shear, respectively. While all new systems caused comparable level of reduction of the base shear (about 28%), DISTM-1 and DISTM-3 caused the best displacement reduction of about 41%, and DISTM-2 caused the lowest displacement reduction of 27%. Generally speaking, the practical significance of such results is that changing a specific seismic isolation system to its corresponding DISTM would enhance the behavior of the bridge and reduce its response by say 30% over that obtained utilizing conventional seismic isolation systems. This level of reduction of the response is extremely beneficial since it means a very low level of base shear that will assure that the bridge piers response will essentially be within its elastic capacity. Moreover, the reduction of the displacement response will reduce the size of the seismic gap significantly. Reduction in acceleration response will benefit infra-structural systems that would be attached to the bridge.
7.1 Effect of bearing period
The effect of the bearing period (Tb) on the peak response of bridge-1 isolated either by the new systems [DISTM-1,-2,-3] or by conventional seismic isolation systems, when subjected to three different bidirectional ground excitations are shown in Figs (8 to 10), respectively. For the case of isolation using DISTM, the damping in bearings is considered to be a combination of the bearing damping itself and the additional damping provided by the tuned mass damper. This additional damping was considered to be the optimum level of damping described earlier in the previous paper (Part-I). In each of these figures, the absolute response of the bridge when isolated by DISTM and the corresponding response of the bridge when isolated by the corresponding conventional seismic isolation system are plotted to illustrate the difference. It is observed that in general, the response of the bridge when isolated by DISTM is identically similar to that of the bridge when isolated by corresponding conventional seismic isolation system. However, the response when isolated by DISTM is always less than that when isolated by the corresponding ordinary seismic isolation system. This is partially attributed to the increased damping resulting from the tuned mass damper system and partially due to the existence of two isolation surfaces in the DISTM. Another observation is that, while increasing the bearing period has no specific influence on deck displacement, it causes both the deck acceleration and pier base shear to decrease. This holds true for all systems and for all ground excitations.
7.2 Effect of coefficient of friction The effect of variation of friction coefficient of the new system DISTM-3 and FPS system are plotted in Fig. (11) for bridge-1 when subjected to different ground motions. For plotting these spectra, max is varied from 0.03 to 0.15; and the values of the parameters held constant are 0.0 ( difference between friction coefficient at initial and maximum sliding velocity) and Tb=2 sec. In general, for both systems, it is observed that the increase in friction coefficient decreases the displacement of the bridge but increases pier base shear as well as deck accelerations. Moreover, the reduction of dynamic responses of the bridge isolated by the new system under Kobe excitation are more than those associated with El-Centro or Northridge ground motions. This is attributed to the classification of these excitation types.
8. Overall Evaluation of DISTM-1, -2 and -3. To evaluate the performance of the new system as compared to the cases with non-isolation and the corresponding conventional seismic isolation systems, the reduction percent were calculated for the average responses of the three bridges of model-I with bearing period increased from 1.5 sec to 4.0 sec at an interval of 0.5 sec. Results are presented in Figs (12 and 13). As shown in Fig. (12), compared to the case of non-isolation, existence of DISTM caused significant reduction in all response quantities. The reduction is observed in both longitudinal and transversal directions with comparable level of reduction. The range of reduction lies between 60% and 95%. No specific trend of the reduction is observed with respect to earthquakes characteristics. Fig (12) clearly demonstrates the effectiveness of the new system as a successful technique in protection of bridges. Moreover, at small bearing period; the rate of the reduction in both acceleration and pier base shear responses is high and lies in the range of 85% and 80%, respectively. These reductions are higher than those observed for conventional seismic isolation systems in which the reduction rates ranged from 50% to 80% (not shown here). This clearly demonstrates the effectiveness of the DISTM as compared to conventional seismic isolation systems. The bearing period has minor effect on the reduction values with highest reductions associated with least bearing period of 1.5 sec. This will not only lead to highest level of reduction, but also will lead to minimum deck displacement, while keeping the reduction in deck acceleration and pier base shear within the range of 85% and 80%, respectively, compared to the non- isolated case. To get a clear vision on the improvement of the response obtained using DISTM systems as compared to corresponding conventional seismic isolation systems, the reductions of key structural responses are calculated and averaged for the three bridges and the results are shown in Fig (13) for all systems and all excitations. Clearly there is an improvement in the performance of the bridges for all the three DISTMs as compared to the corresponding conventional seismic isolation systems with displacement reduction of 20% to 75%, acceleration reduction of 30% to 60%, and the pier base shear reduction of 20% to 50%, respectively. The rates of the reduction do not take regular trend with the change in bearing period. However, they are earthquake dependent with least reductions observed with Kobe earthquake for DISTM-2 and 3. Figure (13) confirms that using DISTM will give superior performance over that when using conventional seismic isolation systems. This improvement occurred in all response quantities with rates in the range of say 20% to 75% over that caused when using conventional systems. Again, since the reductions are independent of bearing period, it might be recommended to use the minimum bearing period, which seems to give acceptable level of reductions in all responses values, and for different earthquakes.
9. Conclusions Form the results presented in this paper, the following conclusions can be drawn: 1- A new innovation towards improving existing seismic isolation technology is presented by introducing the DISTM. The main idea of the new proposed system is to filter the seismic motion through two levels of isolation; and to increase the total damping of the whole seismic isolation system. In case of a seismic event, the tuned mass of the TMD is expected to move out of phase of the whole system, which consequently will increase the damping of the system. Most of the seismic energy is expected to be dissipated at the upper and lower seismic isolation systems and a considerable part of the rest of the energy is expected to be dissipated by the tuned mass damper component. 2- The DISTM systems gave superior performance over existing conventional seismic isolation systems with observed reductions in all response parameters; specifically: - Displacement reductions are of 41, 31, and 29% for DISTM-1, -2, and -3, respectively. - Acceleration reductions are of 27, 37, and 30% for DISTM-1, -2, and -3, respectively. - Base shear reductions are of 40, 27, and 25% for DISTM-1, -2, and -3, respectively. 3- Generally speaking, changing a specific seismic isolation system to its corresponding DISTM would enhance the behavior of the bridge and reduce its response by say 30% over an already reduced response in bridges isolated by conventional isolation systems. 4- Compared to the case of non-isolation, isolation utilizing DISTM caused significant reduction in all response quantities. The reduction is observed in both longitudinal and transversal directions with comparable level of reduction. Ranges of reduction lied between 60% and 95%. 5- The new system [DISTMs] follow the same trend of behavior as the corresponding traditional seismic isolation systems with bearing period, bearing damping, and friction coefficient. 6- When considering isolation using DISTM, it might be recommended to use the minimum bearing period, which seems to give acceptable level of reductions in all responses values, and for different earthquakes.
10. References: 1. Tsopelas P., Okamoto, S., and Constantinou, M. C., (1994) "NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges: Experimental and analytical study of a system consisting of sliding bearings, rubber restoring force devices and fluid dampers," Report No. NCEER-94-0002, National center of Earthquake Engineering Research, Buffalo, New York.
2. Constantinou, M.C., Kartoum, A., Reinhorn, A.M. and Bradford, P. (1992). “Sliding isolation system for bridges: Experimental study”, Earthquake Spectra, Vol. 8, 321-344.
3. Tsopelas, P., Constantinou, M.C., Kim, Y.S., and Okamoto, S. (1993) “NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges: Experimental and Analytical Study of Pendulum System (FPS)” Report No. NCEER-93-0020, National Center for Earthquake Engineering Research, Buffalo, New York.
4. Tsopelas, P., Constantinou, M.C., Kim, Y.S., and Okamoto, S. (1993) “NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges: Experimental and Analytical Study of Pendulum System (FPS)” Report No. NCEER-93-0020, National Center for Earthquake Engineering Research, Buffalo, New York.
5. Tsopelas, P. C., Constantinou, M. C., and Reinhorn, A. M., (1994c). "3D-BASIS-ME: computer program of seismically isolated single and multiple structures and liquid storage tanks," Report No. NCEER-94- 0010, National Center for Earthquake Engineering Research, Buffalo, New York.
6. Ghobarah, A. and Ali, H.M. (1988). “Seismic performance of highway bridges”, Engineering Structures, Vol. 10, 157-166.
7. Wang, Y.P., Chung, L.L., and Liao, W.H., (1998), “Seismic response analysis of bridges isolated with friction pendulum bearings,” Earthquake Engineering and Structural Dynamics, 27:1069-1093. 8. Jangid ,R. S., (2004) “Seismic response of isolated bridges” Journal of Bridge Engineering, Vol. 9, No.2.
9. Jangid, R. S. and Kunde, M. C., (2006). ”Effect of pier and deck flexibility on the seismic response of isolated bridges” Journal of Bridge Engineering, Vol. 11, No. 1.
10. Tsopelas, P., Constantinou, M.C., Kim, Y.S., and Okamoto, S. (1993) “NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges: Experimental and Analytical Study of Pendulum System (FPS)” Report No. NCEER-93-0020, National Center for Earthquake Engineering Research, Buffalo, New York.
11. Ezz El-Arab, (2007) "Comparative assessment and Development of Earthquake protective systems for RC Bridges" Ph.D in structural engineering, waiting for defense, Tanta University . ) 1.5 n i (
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