1 Structural Dynamics & Vibration Control Lab., KAIST 사장교의 면진 성능 향상을 위한 납고무 받침의 설계 기준 제안 Guidelines of Designing L.R.B. for a Cable-Stayed Bridge to Reduce Seismic Responses 이 성진 : 한국과학기술원 건설 및 환경공학과 석사과정 박 규식 : 한국과학기술원 건설 및 환경공학과 박사과정 이 종헌 : 경일대학교 토목공학과 교수 이 인원 : 한국과학기술원 건설 및 환경공학과 교수 (Oct. 24. ~ 25., 2003) 2003 년도

2 Structural Dynamics & Vibration Control Lab., KAIST Backgrounds Introduction  Lead Rubber Bearing (LRB) for base isolation system  Design of base isolation system for building and short span bridges. - Design natural period of structure or effective period of base isolator  Long span bridge such as cable-stayed bridges - Flexible : long period modes and natural seismic isolation - Small structural damping

3 Structural Dynamics & Vibration Control Lab., KAIST Objective  it is difficult to apply this procedure and guidelines of isolation system directly to cable-stayed bridges.  Suggest the design procedure and guidelines of LRB for seismically excited cable-stayed bridge.

4 Structural Dynamics & Vibration Control Lab., KAIST, : elastic & plastic stiffness : effective stiffness : characteristic shear strength, : yield and ultimate strength, : yield and ultimate displacement Fig. 1 Behavior and design parameters of LRB  Determine the,, to minimize the earthquake forces and displacements. Design Procedure of LRB Design Parameters of LRB

5 Structural Dynamics & Vibration Control Lab., KAIST  The design parameters of LRB - design index (DI) is minimized or unchanged (less than 1% of maximum DI) for variation of design parameters. Proposed Design Procedure  i = 1 ~ 5 - Five important responses of cable-stayed bridge : base shear and moment at towers : shear and moment at deck level at towers : deck displacement (longitudinal direction)

6 Structural Dynamics & Vibration Control Lab., KAIST  Design procedure - Step 1 : design earthquake (history or artificial earthquake) - Step 2 : appropriate is selected for variation of. : and are assumed. - Step 3 : appropriate is selected for variation of. : use selected and assume. - Step 4 : appropriate is selected for variation of. - Step 5 : iterate step 2 ~ 4 until parameters remain unchanged.

7 Structural Dynamics & Vibration Control Lab., KAIST Numerical Examples Bridge Model Fig. 2 Bill Emerson Memorial Bridge (Benchmark cable-stayed bridge model)  Benchmark cable-stayed bridges (Dyke et al. 2003) m350.6 m m

8 Structural Dynamics & Vibration Control Lab., KAIST Design Earthquakes  Scaled El Centro earthquake (1940) g’s ( design PGA ) Fig. 3 Design Earthquake (Scaled El Centro)  Artificial earthquake ( Stationary Kanai-Tajimi filter ) - = 37.3 rad/s, = 0.3 (Spencer et al.)

9 Structural Dynamics & Vibration Control Lab., KAIST Properties of Designed LRB DI ** LRB I (Scaled El Centro)1.4W * (tf/m)0.13W (tf) LRB II (Kanai – Tajimi)1.5W (tf/m)0.12W (tf) Table 1. Properties of Designed LRB * : Pier 1, (tf), Pier 2, (tf) ** : Max. of DI =5  Need the stiffer rubber and bigger lead core size than general buildings and short-span bridges.  The plastic behavior of lead core of LRB is important to reduce the seismic response for cable-stayed bridge.

10 Structural Dynamics & Vibration Control Lab., KAIST Performance of Designed LRB  Evaluation Criteria for Benchmark Cable-stayed Bridge Max. base shear at towers Max. shear at deck level Max. base moment at towers Max. moment at deck level Max. cable deviation Max. deck displacement at abutment Normed base shear at towers Normed shear at deck level Normed base moment at towers Normed moment at deck level Normed cable deviation Max control force Max device stroke Table 2. Evaluation criteria

11 Structural Dynamics & Vibration Control Lab., KAIST  El Centro : 1940, Imperial Valley, g’s LRB I : Scaled El Centro LRB II : Kana-Tajimi Artificial Earthquake Park et al. : “ 납고무 받침의 비선형성을 고려한 벤치마크 사장교의 복합제어 ”, 한국지진공학회논문집, Vol. 3, No. 4, pp N-K : Naeim-Kelly Method ( T eff = 1.5 sec )

12 Structural Dynamics & Vibration Control Lab., KAIST  Mexico City : 1985, Galeta de Campos, g’s

13 Structural Dynamics & Vibration Control Lab., KAIST  Gebze : 1999, Turkey Gebze, g’s

14 Structural Dynamics & Vibration Control Lab., KAIST Design Properties of LRB for Earthquake Frequency  The behavior of structure is affected by not only PGA, but also the dominant frequency of earthquake.  The PGA of earthquakes : 0.36g’s Fig. 7 Power Spectral Density of input earthquakes

15 Structural Dynamics & Vibration Control Lab., KAIST  Properties of LRB Frequency Scaled Mexico City0.5 Hz0.9W (tf/m)0.15W (tf)10 Scaled El Centro1.5 Hz1.4W (tf/m)0.13W (tf)11 Scaled Gebze2.0 Hz1.5W (tf/m)0.16W (tf)9 Table 3. Properties of LRB for earthquake frequency - and of LRB : affected by dominant frequency of earthquake. - Low frequency : Need the more flexible LRB. - and of LRB : not related to dominant frequency of earthquake.

16 Structural Dynamics & Vibration Control Lab., KAIST Conclusions The guidelines and procedure of designing LRB for seismically excited cable-stayed bridge are researched. The stiffer rubber and bigger lead core size is needed for cable -stayed bridge than general structures. The plastic behavior of lead core of LRB is important to reduce the seismic response of cable-stayed bridge. The performance of designed LRB is good for several historical earthquakes. As the dominant frequency of earthquake is low, the flexible LRB is needed.

17 Structural Dynamics & Vibration Control Lab., KAIST Thank you for your attention!! Acknowledgments This research is supported by the National Research Lab. Grant (No.: 2000-N-NL-01-C-251) in Korea.