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1、398 / JOURNAL OF BRIDGE ENGINEERING / NOVEMBER/DECEMBER 2001RELIABILITY-BASED ASSESSMENT OF SUSPENSION BRIDGES: APPLICATION TO THE INNOSHIMA BRIDGEBy Kiyohiro Imai1 and Dan M. Frangopol,2 Fellow, ASCEABSTRACT: Many suspe

2、nsion and cable-stayed bridges were designed and constructed between Honshu Island and Shikoku Island in Japan. All these bridges were designed according to the allowable stress design method. In the allowable stress des

3、ign method, it is not possible to quantify the reliabilities of both bridge components and the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgent need to assess t

4、he safety of suspension bridges from a probabilistic viewpoint. To develop cost-effective design and maintenance strategies, it is necessary to assess the condition of suspension bridges using a reliability-based approac

5、h. This is accomplished by a probabilistic finite-element geometrically nonlinear analysis. This study describes an investigation into the reliability assessment of suspension bridges. The combination of reliability anal

6、ysis and geometrically nonlinear elastic analysis allows the determination of reliabilities of suspension bridges. A probabilistic finite-element geometrically nonlinear elastic code, created by interfacing a system reli

7、ability analysis program with a finite-element program, is used for reliability assessment of suspension bridges. An existing suspension bridge in Japan, the Innoshima Bridge, is assessed using the proposed code. The ass

8、essment is based on static load effects. Reliabilities of the bridge are obtained by using 2D and 3D geometrically nonlinear models. Furthermore, damage scenarios are considered to assess the effects of failure of variou

9、s elements on the reliability of undamaged components and on the reliability of the bridge. Finally, sensitivity information is obtained to evaluate the dominant effects on bridge reliability.INTRODUCTIONSuspension and c

10、able-stayed bridges, including the world’s longest suspension bridge [the Akashi Kaikyo Bridge (Fig. 1)] and the world’s longest cable-stayed bridge [the Tatara Bridge (Fig. 2)], were designed and constructed between Hon

11、shu Is- land and Shikoku Island in Japan. These bridges lie on three routes which connect these two main islands. All these bridges were designed according to the allowable stress design method. In the allowable stress d

12、esign method, it is not pos- sible to quantify the reliabilities of both bridge components and the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgent need to asse

13、ss the safety of suspension bridges from a probabilistic viewpoint. Optimum maintenance strategies need to be devel- oped for these bridges by balancing their lifetime reliability and expected life-cycle maintenance cost

14、s. Therefore, it is nec- essary to evaluate the reliability of suspension bridges. The analysis of suspension bridges is conducted as a geo- metrically nonlinear elastic analysis using the finite-element method. The geom

15、etrically nonlinear analysis is explained in detail in Bathe (1982), Crisfield (1991), Zienkiewicz and Tay- lor (1991), and Felippa (1998). In this study, the finite-element formulation for geometrically nonlinear elasti

16、c structures (GNS) is used for the analysis. The determination of the reliability index is an optimization problem in the standard normal space (Shinozuka 1983; Ang and Tang 1984). There are two basic methods to estimate

17、 the structural reliability: the first-order reliability method (FORM) and the second-order reliability method (SORM). FORM ap- proximates the failure surface by a hyperplane, and SORM approximates the failure surface by

18、 a paraboloid. If the failure surface is nonlinear, SORM will provide more exact results. However, if the failure surface is nearly flat, the reliabilities1Deputy Mgr., Economic Div., Honshu Shikoku Bridge Authority, Ur-

19、 ban Ace Sannomiya Build., Chuo-ko, Kobe 651-6591, Japan. 2Prof., Dept. of Civ., Envir., and Arch. Engrg., Univ. of Colorado, Boulder, CO 80309-0428. Note. Discussion open until May 1, 2002. To extend the closing date on

20、e month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on June 15, 2001; revised June 28, 2001. This paper is part of t

21、he Journal of Bridge Engineering, Vol. 6, No. 6, November/ December, 2001. ?ASCE, ISSN 1084-0702/01/0006-0398–0411/$8.00 ? $.50 per page. Paper No. 22602.associated with both methods are nearly the same. Since the determ

22、ination of the reliability index is an optimization prob- lem, it is necessary to evaluate the response gradient. If the structural response can be described by an analytical solution, the response gradient can be evalua

23、ted without the aid of the finite-element method. However, if the structure is complex, it is virtually impossible to get the response gradient without the aid of the finite-element method. For this reason, the finite- e

24、lement reliability analysis has been developed. The finite-el- ement reliability method for the geometrically nonlinear struc- tures has been developed by Liu and Der Kiureghian (1989, 1991). Based on their pioneering wo

25、rk, an interface was created between the system reliability analysis code RELSYS devel- oped by Estes and Frangopol (1998) and the deterministic non- linear finite-element analysis code FEAP developed by Taylor (1996). I

26、n this study, the reliability assessment of an existing suspension bridge, the Innoshima Bridge (Fig. 3), for live and wind loads is conducted by using 2D and 3D geometrically nonlinear models, respectively. The assessme

27、nt is based on static load effects. Damage scenarios are also considered to assess the effects of failure of various elements on the relia- bility of undamaged elements and on the reliability of the overall bridge. Final

28、ly, sensitivity information is obtained to evaluate the dominant factors that affect bridge reliability.DESIGN OF INNOSHIMA BRIDGEBridge DescriptionThe Innoshima bridge [Figs. 3 (photo), 4 (location), and 5 (general view

29、)] was constructed by the Honshu-Shikoku Bridge Authority (HSBA) in 1983. This bridge is located on the Onomichi-Imabari route (Fig. 4). The center span of the Innoshima Bridge is 770 m with two side spans of 250 m. The

30、roadway is 20 m from safety fence to safety fence and accommodates four lanes of traffic. The suspended structure consists of two stiffening trusses spaced 26 m apart. Lateral trusses, spaced 10 m apart, connect the two

31、stiffening trusses. The lateral trusses are braced by upper and lower diagonal members. Plate girders are supported on the upper chords of the lateral trusses. A pedestrian way is supported on the lower chords of the lat

32、eral trusses. The height of towers is 135.85 m. Each tower consists of two shafts connected by two hori- zontal struts and cross bracing. Since the Honshu-Shikoku400 / JOURNAL OF BRIDGE ENGINEERING / NOVEMBER/DECEMBER 20

33、01FIG. 3. Photo of Innoshima Bridge (HSBA)FIG. 4. Nishi-Seto Highway as of Year 2001wind tunnel tests are required. In the design process, the cross sections that are required by the static analyses are tested and verifi

34、ed by the wind tunnel tests. The wind load used for the static design is estimated by a basic wind velocity, correction factors, aerodynamic coeffi- cients, and projection areas of structures. The basic wind ve- locity f

35、or the Innoshima Bridge is V10 = 37 m/s, where V10 = expected value of 10-min mean wind velocity for a 150-year return period at an elevation of 10 m above sea level. Based on the basic wind velocity, the design wind vel

36、ocity is cor-rected according to elevation, length, and height of the struc- tures. The wind load for the main cable and stiffening girder is given for the static design in the HSBA standard (1976) as1 2 P = ?C ? (? ? V

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