RESPONSE ANALYSIS STUDY OF A BASE-ISOLATED BUILDING BASED

Transcription

1 4th International Conference on Earthquake Engineering Taipei, Taiwan October 12-13, 2006 Paper No. 224 RESPONSE ANALYSIS STUDY OF A BASE-ISOLATED BUILDING BASED ON SEISMIC CODES WORLDWIDE Demin Feng 1, Tian-Chyuan Chan 2, and Shuguang Wang 3, Hsi-Yun Chen 4 and Yaw-Nan Chang 5 ABSTRACT The procedures to do response analysis of a seismically isolated building are summarized based on the building codes of Japan, China, the USA, Italy and Taiwan. While a dynamic response analysis method is recommended in all five building codes, a simplified design procedure based on equivalent linear analysis is also permitted under limited conditions. Subsequently, a typical 14-story reinforced concrete building, isolated with lead-rubber bearings is analyzed using each of the five building codes. The average response values are taken as design values to compare with the results by the equivalent linear analysis method. The deformation of the isolation level and the base shear force coefficient of the superstructure are compared. Finally, the response reduction factor defined in the Japanese code is applied to the other four building codes to improve the accuracy of equivalent linear analysis results. Keywords: Building code, Seismically isolated building, Dynamic response analysis, Equivalent linear analysis INTRODUCTION After the 1994 Northridge earthquake in the USA, the 1995 Hyogoken-Nanbu earthquake in Japan and the 1999 Chi-Chi earthquake in Taiwan, the number of seismically isolated buildings has increased rapidly. Over the same period, building codes have been revised and updated to include requirements for design of seismically isolated buildings. In this paper, a comparative analysis on a seismically isolated building is presented in order to understand and illustrate the differences in the isolation provisions of the building design codes of Japan, China, the USA, Italy and Taiwan. Both equivalent linear analysis and time history analysis methods are summarized. While a dynamic response analysis method is recommended in all five building codes, a simplified design procedure based on equivalent linear analysis is also permitted under limited conditions. Since several safety factors have to be considered beyond the results of the equivalent linear analysis, the dynamic response analysis usually results in more economical designs. Subsequently, a typical 14-story reinforced concrete building, isolated with lead-rubber bearings (s), is analyzed using each of the five building codes. The building s characteristics such as weight, height, hysteresis properties and soil condition are same in all cases. The properties of the isolation devices are also kept constant, with a total yield force for the isolation system of four percent of the total weight, so that the following discussion will restrict to buildings with hysteretic type dampers. The deformation of the isolation level and the base shear force coefficient of the superstructure are compared. 1 Senior Engineer, Fujita Corporation, Tokyo, Japan, feng@fujita.co.jp 2 Associate Professor, China University of Technology, Taipei, China, wowchan@ms32.hinet.net 3 Professor, Nanjing University of Technology, Nanjing, China, @vip.sina.com 4 General Manager, Taiwan Seismic Isolation Technologic Co., Ltd., Taipei, China, tsit@url.com.tw 5 General Manager, Ko Jen Structural Engineer Official, Taipei, China, kj2888@ms64.hinet.net 1

2 DESIGN METHODS A simplified design procedure based on equivalent linear analysis permitted in limited cases and a dynamic response analysis method are summarized in this section. It should be noted that to compare the results of these two analysis methods, the various parameters defined in the different codes may not be defined or applied in exactly the same way in all cases. Equivalent Linear Analysis Method () An equivalent linear analysis based on a single-degree-of-freedom (SDOF) system is defined in all five codes. All of the codes define limitations on the applicability of the method, and these are summarized in Table 1. Table 1. Applicability of the equivalent linear analysis method in the five different codes Code Structure Japan China USA Italy Taiwan Limitation on site seismicity S 1 < 0.6g Limitation on soil class 1,2 I,II,III A,B,C,D 1,2 Maximum plan dimension 50m Maximum height of superstructure 60m 40m 19.8m 20m Maximum number of stories T f 1s 4 5 Location of devices Base only Base only Maximum mass-stiffness centers eccentricity 3% 3% K v /K e 800 Tension in isolator Not allowed Not allowed Allowed Not allowed Yield strength > 0.03W Period range of T e T 2 > 2.5s 3T f ~3.0s 3T f ~3.0s 2.5s Maximum value of Tv < 0.1s Where T f is the natural period of fixed-base superstructure, T 2 is the period of the isolation system considering only the stiffness of rubber bearings, T e is the equivalent period of the isolation system, and T V is the period of the isolation system in vertical direction. The main limitations are summarized as follows: 1. The construction site class is limited to hard soil condition, except in the Italian code. 2. The maximum height of the superstructure is limited, except in the Taiwanese code. In the Japanese and Chinese codes, the limitation on the height of the target building is more relaxed. Thus, the target buildings capable to adopt isolation technologies extend widely. 3. The location of the isolation devices is limited to the base of structure in the Japanese and Chinese codes. 4. No tension is allowed in the isolation devices, except in the USA code. 5. There are limitations on the period of the isolated structure, except the Chinese code. It is very interesting that in the Japanese code there is a low limitation on the period. On the contrary, in the Italian, USA and Taiwanese codes, there is an upper limitation of the period. In generally, the base shear force is obtained from the spectral acceleration and weight as shown in Equation (1). 2

3 M B(ξ, Te ) S a ( Te ) K e DD DD = ; DM = α γ DD ; s = (1) K e RI where D D is the design displacement of the isolation system, M is the total weight of the building, B(ξ,T e ) is the response reduction factor, ξ is the effective damping, S a (T e )is the site response acceleration considering site soil conditions, K e is the effective stiffness of the isolation system, D M is the maximum design displacement used to determine the clearance, α is the coefficient related to the eccentricity of the isolation system, γ is the safety factor (>1.2) related to variation of properties, s is the shear force in the base of the superstructure, and R I is the reduction factor related to the ductility of the superstructure. In Table 3, the details of the equivalent linear method are given and the main points can be summarized as follows: 1. The coefficient related to the eccentricity of the isolation system is considered in all codes. A fixed value of 1.1 is defined in the Japanese code, while the other codes give same equations for calculation. 2. A reduction factor considering the ductility of the superstructure is included in all of the codes except that of Japan. In the Chinese code, the effective weight which is usually 85% of the actual weight is used for this effect. 3. The Chinese, USA and Taiwanese codes use the same formula to calculate the shear force distribution in the superstructure over the height. 4. In the Chinese code, a more simplified method is also proposed to be consistent with conventional seismic design methods. A horizontal reduction factor based on the ratio of the base shear force between iso (shear force after isolation) and fix (shear force for fixed-base condition) is shown in Table 2. This factor is used to link with the conventional Seismic Intensity design method which is popularly used by structural engineers. For example, if the iso / fix is calculated as 0.26~0.35, then a reduction coefficient of 0.5 is obtained from the table, such that the superstructure of a seismically isolated building in Seismic Intensity area 8 may be designed as if it were a fixed-base building in the area 7. Table 2. Horizontal reduction factor determined by the ratio of base shear force (China) iso / fix reduction coefficient The convergence procedure of the equivalent linear analysis method is shown in Figure 1. The procedure is summarized as follows: 1. Assume a displacement D D0 of the isolation system. 2. Calculate the effective stiffness K e and effective damping ξ e of the isolation system, assuming a bi-linear model for the isolation system. 3. Calculate the equivalent period T e of the isolation system. 4. Calculate the corresponding response reduction factor B(ξ e,t e ) and the spectral acceleration S a (T e ). 5. Calculate a new isolation system displacement D D using Equation (1). 6. Repeat the above steps until D D converges. K 2nd K 1st K 3rd ISO ξ 1st Hysteresis loop ξ ξ 2nd 3rd D D D D0 Figure 1. Illustration of the convergence procedure for the equivalent linear analysis method D 3

4 Table 3. Summary of the equivalent linear method in the five different building codes Structure Symbol Japan China USA Italy Taiwan D D M Fh ( ξ ) Z Gs S0( Te ) K e ISO / K e S g D1 2 4π B T D D M S ( T, ξ ) a K e e, min e g 2 4π SaDT 2 B ed Isolation system 12e 12e 12e 12e D TD 1.1 (1 + y i ) (1 + y ) 2 2 i (1 + y ) 2 2 i (1 + y 2 2 i ) 2 2 b + d b + d b + d b + d ISO D D K e S a (T e ) β M K e max DD, K e max DD, K e D D D M γ D TD λ S DTD D M 1.5 D TD Super-structure s ISO ISO ISO / RI ISO / RI ISO / RI j γ ( A iξ + e ) S MiHi M jh n j= 1 j M H S i i n j= 1 M H j j M j S a ( Te, ξ e ) S MiHi M jh n j= 1 j Sub-structure b γ ISO ISO K e max DD, ISO KeDD / 0. 8RI Isolation system period T e 2π M / Ke 2π 2π M / Ke, min M / K e 2π M / K e 2π M / K e Where D D is the design displacement, M is the total weight of the building, B(ξ,T e ) is the response reduction factor, ξ is the effective damping, S a (T e ) is the site response acceleration considering site class, K e is the effective stiffness, D M is the maximum design displacement used to determine isolation system clearance, α is the coefficient related to eccentricity of the isolation system, γ: is the safety factor, s is the shear force at the base of the superstructure, and R I is the reduction factor considering the ductility of the superstructure. 4

5 Time History Analysis Method (THA) Even though all of the codes include provisions for dynamic response analysis, the details required to undertake such an analysis for a seismically isolated structure are not clearly available in any of the codes. In most of the codes, two dynamic response analysis methods are defined: response spectrum analysis and time history analysis. For a seismically isolated building, the time history analysis method is the most accurate and is widely used. Thus following discussions will focus on the time history analysis. In the time history analysis method, synthetic input motions that have been spectrally-matched with the design response spectrum or real earthquake records appropriately scaled or modified should be used for the dynamic response analyses. Since results from the dynamic response analyses are strongly dependent on the selected input motions, several input motions are recommended. In the Japanese code, based on more than three (usually six) input motions, the maximum response values are taken as design values. In the Chinese code, based on three input motions, the average response values are taken as design values. In the USA and Italian codes, a minimum of three time history pairs must be used for the analyses. If three time history pairs are used, the design must be based on the maximum response quantities obtained, however, if seven (or more) time history pairs are used the design may be based on the average values of the calculated responses. Since the time history analysis method usually results in smaller response values, in the USA and Taiwan codes the results of the time history analyses are limited by the results from the equivalent linear method. For example, in the USA code, the total design displacement of the isolation system shall not be taken as less than 90% of the result due to the equivalent linear method. On the other hand, there is no limitation in the Japanese and Italian codes In this paper, the superstructure is modelled as a non-linear shear type multiple-degree-of-freedom system, where the shear elements are usually derived from a static non-linear push-over analysis. The isolation level is modelled as a shear-rocking system, where a bilinear model is used for the shear component. The elastic rocking component is calculated from the vertical stiffness of the bearings. Input motions are applied directly at the base. Building Model ANALYSIS MODEL AND RESULTS A typical 14-story reinforced concrete building isolated with lead-rubber bearings (s) is used in this Paper. The building s weight, height, hysteresis properties and soil condition are same for all five codes. The building has plan dimensions of 64.25m 16.25m and is 45.20m in height. The superstructure is designed as frame system in X direction and shear wall system in Y direction. The fundamental periods of the fixed-base model are T x =0.894s and T y =0.447s. It is noted that, as indicated in Table 1, the height of this building exceeds the equivalent linear analysis method s limitations of the USA and Italian codes. R F 10 F Nonlinear shear model 5 F 1 F Sway spring Rocking spring Figure 2. Elevation view and shear building lumped-mass model of 14-story building For dynamic response analysis, the superstructure is modeled as a nonlinear shear type multipledegree-of-freedom system, as shown in Figure 2, where a degrading tri-linear model is used for the 5

6 shear elements. The base isolation system is modeled as a shear-rocking system, with a modified bilinear Ramberg-Osgood model used for the shear component. The varying-stiffness proportional type damping is assumed, where the ratio is 3% for the superstructure (fixed-base model), 0% for shear and 1% for rocking. Isolation System The isolation system consists of 19 lead rubber bearings and 4 natural rubber bearings. The isolation system s yield strength is 4% of the total building weight. The plan of the isolation system is shown in Figure 3 and the properties are shown in Table 4. RB RB RB RB Figure 3. Plan of the isolation layer Table 4. Properties of the isolation system Dir. d K d W Rocking spring Rotational inertia (kn) (KN/m) (kn) d /W (kn cm/rad) (kn cm 2 ) X 4.21E E Y 4.07E E+08 Analysis Results Equivalent linear analysis is carried out and the calculation converges quickly for all five codes. Time history analysis results are obtained as the average value of those from the ten input motions. All of the analysis results are shown in Figure 5. In addition to the superstructure base shear coefficient α S and the isolation system design displacement D D obtained using the equivalent linear method (), the inter-story drift obtained from the time history analysis (THA) is shown. Only X direction is shown, in which the superstructure is a reinforced concrete frame system. The average THA results for the ten input motions are compared with the results of the. The response results are summarized in Table 5 and summarized as follows: 1. The building studied here is much taller than the maximum height of 20m allowed by the USA and Italian codes for the (Table1). Thus, the results of the should be treated with caution. 2. For, both the eccentricity coefficient α and the safety factor γ shown in Equation (1) are not considered in the response results. 3. The design displacements from the are generally larger than those from THA. 4. For THA, DD is a somewhat larger in Y direction. This is a result of the larger lateral stiffness and thus shorter period of the shear wall system in the direction. 5. In the Japanese code, the vertical distribution of shear force seems worse than the conventional Ai distribution used in the aseismic design, thus resulted in under-estimation of the shear force in the super-structure. 6

7 6. For THA, all inter-story drifts are less than 1/ Both α S and D D agree well for the Japanese code. Based on the results of the THA, the response reduction factor appears to be well formulated. 8. The largest variations in α S and D D for the and THA are seen for the Chinese code. The small response reduction factor and slowly decreasing response spectrum in the long period may account for this. 9. In the Italian code, the response accelerations in the superstructure are assumed constant in the. Thus the shear force coefficient over the height is constant. Since the building is much taller than the Italian code limit of 20m for, the shear force coefficient over the height of the building is not constant. 10. In the USA, Italian and Taiwanese codes, some superstructure ductility is considered when calculating the shear force in the superstructure. Both α ISO, directly obtained from the displacement D D, and α S, considering the superstructure ductility factor R I, are shown in Table 5. R I =1.125, 1.5 and 1.5 respectively, are defined by the three codes, and the Taiwanese code gives better agreement for the shear force coefficient over the height. Table 5. Comparison of analysis results THA (average) X Direction Y Direction D D (cm) α ISO α S D D (cm) α S D D (cm) α S Japan China USA Italy Taiwan α ISO = ISO /ΣW ; α S = S /ΣW considering the superstructure ductility factor R I Japan China SHEAR FORCE COEFFICIENT DRIFT ANGLE STORY DEFLECTION (cm) Figure 5. Results from equivalent linear method and time history analysis (continued on next page) 7

8 USA Italy Taiwan SHEAR FORCE COEFFICIENT DRIFT ANGLE STORY DEFLECTION (cm) Figure 5. (continued) Results from the equivalent linear method and time history analysis. DISCUSSIONS Equivalent linear analysis () and time history analysis (THA) are both carried out to obtain the earthquake responses of the isolated building by using all of the five codes. The average THA results for the ten input motions are compared with the results of the. As shown in Table 5, the design displacements and shear force coefficient from the are generally great larger than those from THA except by using the Japanese code. Normally, the THA will get the more accuracy results than the, and it will be very difficult for the designers to use the widely. The results of are considered to be dependent on the response reduction factor by damping strongly. Since the two analysis methods get the closest agreement by using the Japanese code, the response reduction factor F h defined in the Japanese code is applied to the other four building codes to improve the accuracy of results. The response reduction factors defined in the other four codes are 8~16% larger than that in the Japanese code at a critical damping of 20% (Feng, 2006a). 8

9 F 1.5 h = ; F ( h ) h v h (2) d where h v and h d are the viscous damping and the hysteretic damping of the base isolated system. By using this equation, the new analysis results of the four design codes are summarized in Table 6. It is clear that the results get great improvements. Table 6. Comparison of response displacement results of the isolated building (Unit: cm) THA (average) (Before adjust) (After adjust) (X+Y)/2 Japan China USA Italy Taiwan CONCLUSIONS The paper has compared the seismic isolation codes of Japan, China, USA, Italy and Taiwan. Response analyses of a 14-story reinforced concrete building isolated with lead-rubber bearings were performed following the requirements of the five different codes. The main findings of the study are summarized as follows: 1. The building codes vary widely in their definitions of seismic hazard for design. Design earthquake return period and story drift limits of the different codes have been summarized. 2. For the five different assumed building site locations, the 5% damping response spectra in the Taipei basin has the largest amplitude in the long period range. For the 20% damping response spectra, the Chinese code gives the largest amplitude when periods longer than 3.2s. 3. All of the codes include a response reduction factor to account for the variation of response as a result of damping. Amongst all the codes, the Japanese code has the largest response reduction factor. 4. The 14-story building with a lead-rubber bearing isolation system is analyzed using equivalent linear analysis and time history analysis methods. The results of the two different methods varied considerably for the five different codes, with the closest agreement given by the Japanese code and the widest variation by the Chinese code. 5. The response reduction factor by damping defined in the Japanese code can also be used in the other four design codes and can get great improvements for the results. REFERENCES ASCE, 2003, Minimum Design Loads for Buildings and Other Structures, SEI/ASCE 7-02, (Reston, VA: American Society of Civil Engineers). Dolce, M., 2004, Italian regulations for the design of seismic isolated buildings. Dolce, M. and G. Santarsiero, 2004, Development of regulations for seismic isolation and passive energy dissipation in Italy and Europe, Proceedings of Passive Control Symposium 2004, Tokyo Institute of Technology, European Standard, Dec. 2003, Eurocode 8: Design of structures for earthquake resistance (FINAL DRAFT). Feng, D., etc., 2006a, A comparative study of seismic isolation codes worldwide, 1stECEES, Papers no. 63, 66 ICC, 2002, 2003 International Building Code, (Falls Church, VA: International Code Council). Ministry of Construction, P.R.China, 2001, Code for seismic design of buildings, GB (in Chinese). Ministry of the Interior, Taiwan, 2005, Seismic Design Code for Buildings (in Chinese). MRIT, etc., 2000, The Notification and Commentary on the Structural Calculation Procedures for Building with Seismic Isolation