398 / JOURNAL OF BRIDGE ENGINEERING / NOVEMBER/DECEMBER 2001R ELIABILITY -B ASED A SSESSMENT OF S USPENSION B RIDGES :A PPLICATION TO THE I NNOSHIMA B RIDGEBy Kiyohiro Imai 1 and Dan M. Frangopol, 2 Fellow, ASCEA BSTRACT : Many suspension and cable-stayed bridges were designed and constructed between Honshu Islandand Shikoku Island in Japan. All these bridges were designed according to the allowable stress design method.In the allowable stress design method, it is not possible to quantify the reliabilities of both bridge componentsand the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgentneed to assess the safety of suspension bridges from a probabilistic viewpoint. To develop cost-effective designand maintenance strategies, it is necessary to assess the condition of suspension bridges using a reliability-basedapproach. This is accomplished by a probabilistic f i nite-element geometrically nonlinear analysis. This studydescribes an investigation into the reliability assessment of suspension bridges. The combination of reliabilityanalysis and geometrically nonlinear elastic analysis allows the determination of reliabilities of suspensionbridges. A probabilistic f i nite-element geometrically nonlinear elastic code, created by interfacing a systemreliability analysis program with a f i nite-element program, is used for reliability assessment of suspensionbridges. An existing suspension bridge in Japan, the Innoshima Bridge, is assessed using the proposed code.The assessment is based on static load effects. Reliabilities of the bridge are obtained by using 2D and 3Dgeometrically nonlinear models. Furthermore, damage scenarios are considered to assess the effects of failureof various 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 cable-stayed bridges, including the world’slongest 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 Honshu Is-land and Shikoku Island in Japan. These bridges lie on threeroutes which connect these two main islands. All these bridgeswere designed according to the allowable stress designmethod. In the allowable stress design method, it is not pos-sible to quantify the reliabilities of both bridge componentsand the entire bridge system. Therefore, in light of currentreliability-based design philosophy, there is an urgent need toassess the safety of suspension bridges from a probabilisticviewpoint. Optimum maintenance strategies need to be devel-oped for these bridges by balancing their lifetime reliabilityand expected life-cycle maintenance costs. 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 f i nite-elementmethod. The geometrically nonlinear analysis is explained indetail in Bathe (1982), Crisf i eld (1991), Zienkiewicz and Tay-lor (1991), and Felippa (1998). In this study, the f i nite-elementformulation for geometrically nonlinear elastic structures(GNS) is used for the analysis.The determination of the reliability index is an optimizationproblem in the standard normal space (Shinozuka 1983; Angand Tang 1984). There are two basic methods to estimate thestructural reliability: the f i rst-order reliability method (FORM)and the second-order reliability method (SORM). FORM ap-proximates the failure surface by a hyperplane, and SORMapproximates the failure surface by a paraboloid. If the failuresurface is nonlinear, SORM will provide more exact results.However, if the failure surface is nearly f l at, the reliabilities1 Deputy Mgr., Economic Div., Honshu Shikoku Bridge Authority, Ur-ban Ace Sannomiya Build., Chuo-ko, Kobe 651-6591, Japan.2 Prof., 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 dateone month, a written request must be f i led with the ASCE Manager ofJournals. The manuscript for this paper was submitted for review andpossible publication on June 15, 2001; revised June 28, 2001. This paperis part of the Journal of Bridge Engineering, Vol. 6, No. 6, November/December, 2001. qASCE, ISSN 1084-0702/01/0006-0398–0411/$8.001 $.50 per page. Paper No. 22602.associated with both methods are nearly the same. Since thedetermination of the reliability index is an optimization prob-lem, it is necessary to evaluate the response gradient. If thestructural response can be described by an analytical solution,the response gradient can be evaluated without the aid of thef i nite-element method. However, if the structure is complex,it is virtually impossible to get the response gradient withoutthe aid of the f i nite-element method. For this reason, the f i nite-element reliability analysis has been developed. The f i nite-el-ement reliability method for the geometrically nonlinear struc-tures has been developed by Liu and Der Kiureghian (1989,1991).Based on their pioneering work, an interface was createdbetween the system reliability analysis code RELSYS devel-oped by Estes and Frangopol (1998) and the deterministic non-linear f i nite-element analysis code FEAP developed by Taylor(1996). In this study, the reliability assessment of an existingsuspension bridge, the Innoshima Bridge (Fig. 3), for live andwind loads is conducted by using 2D and 3D geometricallynonlinear models, respectively. The assessment is based onstatic load effects. Damage scenarios are also considered toassess the effects of failure of various elements on the relia-bility of undamaged elements and on the reliability of theoverall bridge. Finally, sensitivity information is obtained toevaluate the dominant factors that affect bridge reliability.DESIGN OF INNOSHIMA BRIDGEBridge DescriptionThe Innoshima bridge [Figs. 3 (photo), 4 (location), and 5(general view)] was constructed by the Honshu-ShikokuBridge Authority (HSBA) in 1983. This bridge is located onthe Onomichi-Imabari route (Fig. 4). The center span of theInnoshima Bridge is 770 m with two side spans of 250 m.The roadway is 20 m from safety fence to safety fence andaccommodates four lanes of traff i c. The suspended structureconsists of two stiffening trusses spaced 26 m apart. Lateraltrusses, spaced 10 m apart, connect the two stiffening trusses.The lateral trusses are braced by upper and lower diagonalmembers. Plate girders are supported on the upper chords ofthe lateral trusses. A pedestrian way is supported on the lowerchords of the lateral trusses. The height of towers is 135.85m. Each tower consists of two shafts connected by two hori-zontal struts and cross bracing. Since the Honshu-Shikoku
