Phase II Benchmark Control Problem for Seismic Response of Cable-Stayed Bridges

Juan Martin Caicedo Shirley J. DykeGrad. Res. Asst. & Doc. Candidate ProfessorDepartment of Civil Engineering Department of Civil & Mechanical EngineeringWashington University, Box 1130 Purdue University,

St. Louis, MO 63130 West Lafayette, IN 47907jc11@cive.wustl.edu sdyke@purdue.eduph: (314) 935-4436 ph: (314) 935-5695fax: (314) 935-4338 fax: (314) 935-4338

Seok Jun Moon Lawrence BergmanSenior Researcher Professor

Korea Institute of Machinery & Materials Department of Aero/Astro EngineeringP.O. Box 101, Yusung University of IllinoisTaejon, 305-600 Korea Urbana, IL 61801

sjmoon@kimm.re.kr lbergman@uiuc.eduph: +82-42-868-7428 ph: (217) 333-4970fax: +82-42-868-7418 fax: (217) 244-0720

Gursoy Turan Steven HagueAssistant Professor HNTB Corporation

Department of Civil Engineering 715 Kirk Drive Izmir Institute of Technology Kansas City, Missouri, 64105

Izmir, Turkey shague@hntb.comgturan@likya.iyte.edu.trph: +90 (232) 498 6278

Keywords:

Benchmark problems, structural control, cable-stayed bridges, protective systems, earth-

quake engineering, smart systems

2000, 2002; also see: <http://wusceel.cive.wustl.edu/>). Based on detailed drawings of the Emer-son bridge, a three-dimensional evaluation model was developed to represent the complex behav-ior of the full scale benchmark bridge. A linear evaluation model, using the equations of motiongenerated around the deformed equilibrium position, was deemed appropriate. Because the struc-ture is attached to bedrock, the effects of soil–structure interaction were neglected. To simplify theproblem for phase I, two assumptions were made regarding the excitation. This problem focusedon a one dimensional ground acceleration applied in the longitudinal direction and uniformly andsimultaneously applied at all supports. Researchers reported their Phase I results during a themesession devoted to this problem held at the Third World Conference on Structural Control in April2002 in Como, Italy (Agrawal, et al., 2002; Turan et al., 2002; Moon et al., 2002a; Bakule, et al.,2002).

Although a significant amount of expertise was accumulated during phase I, the assump-tions made regarding the excitation (longitudinal and simultaneously acting) limited the extent towhich this problem modeled a realistic situation. A structure’s response to an earthquake is basedon the simultaneous action of three translational components of ground motion: two in the hori-zontal plane, and one in the vertical direction. Structures are typically analyzed for the two hori-zontal components of ground motion. The structural response depends on the incidence angle (theangle between the ground motion components and the structural axes). Additionally, the excita-tion is expected to vary at each of the supports due to the length of these structures. A phase IIproblem was developed to extend the problem to consider these issues.

This paper presents the second generation of benchmark control problems for cable-stayedbridges. In this problem the ground acceleration may be applied in any arbitrary direction usingthe two horizontal components of the historical earthquake with a specified incidence angle.Multi-support excitation is also considered in this phase of the study. Here the prescribed groundmotion is assumed to be identical at each support, although it is not applied simultaneously. Weassume that bent 1 undergoes a specified ground motion, and the motion at the other three sup-ports is identical to this motion but delayed based on the distance between adjacent supports andthe speed of the L-wave of a typical earthquake (3 km/sec). The total response of the structure isobtained by superposition of the response due to each independent support input (Chopra, 2001;Clough and Penzien, 1993).

This problem has been prepared to provide a testbed for the development of effective strate-gies for the control of long-span bridges. This second generation problem considers the control ofmore complex motions of the bridge as compared to the first generation problem. To evaluate theproposed control strategies in terms that are meaningful for cable-stayed bridges, appropriateevaluation criteria and control design constraints are specified within the problem statement.Additionally, an alternate model of the bridge is developed for evaluating the robustness of thedesigns. This model includes the effects of snow loads on the bridge deck. Designers/researchersparticipating in this benchmark study will define all devices, sensors and control algorithms used,evaluate them in the context of their proposed control strategies, and report the results. Thesestrategies may be passive, active, semi-active or a combination thereof. The phase II problem willbe made available for downloading on the benchmark web site in the form of a set of MATLAB®

equations <http://wusceel.cive.wustl.edu/quake/>. A sample control design is included.

November 5, 2002 2 Caicedo, et al.

Benchmark Cable-Stayed Bridge The cable-stayed bridge used for this benchmark study is the Bill Emerson Memorial

Bridge spanning the Mississippi River (on Missouri 74–Illinois 146) near Cape Girardeau, Mis-souri, designed by the HNTB Corporation (Hague, 1997). The bridge is currently under construc-tion and is to be completed in 2003. Instrumentation is being installed in the Emerson bridge andsurrounding soil during the construction process to evaluate structural behavior and seismic risk(Çelebi, 1998).

Seismic considerations were strongly considered in the design of this bridge due to the loca-tion of the bridge (in the New Madrid seismic zone) and its critical role as a principal crossing ofthe Mississippi River. In early stages of the design process, the loading case governing the designwas determined to be due to seismic effects. Earthquake load combinations in accordance withAmerican Association of State Highway and Transportation Officials (AASHTO) division I-Aspecifications were used in the design. Various designs were considered, including full longitudi-nal restraint at the tower piers, no longitudinal restraint, and passive isolation. When temperatureeffects were considered, it was found that fully restraining the deck in the longitudinal directionwould result in unacceptably large stresses. Based on examination of the various designs, it wasdetermined that incorporating force transfer devices would provide the most efficient solution.

Sixteen 6.67 MN (1,500 kip) shock transmission devices are employed in the connectionbetween the tower and the deck. These devices are installed in the longitudinal direction to allowfor expansion of the deck due to temperature changes. Under dynamic loads these devices areextremely stiff and are assumed to behave as rigid links. Additionally, in the transverse directionearthquake restrainers are employed at the connection between the tower and the deck and thedeck is constrained in the vertical direction at the towers. The bearings at bent 1 and pier 4 aredesigned to permit longitudinal displacement and rotation about the transverse and vertical axis.Soil-structure interaction is not expected to be an issue with this bridge as the foundations of thecable-stayed portion is attached to bedrock.

As shown in Fig. 1, the bridge is composed of two towers, 128 cables, and 12 additionalpiers in the approach bridge from the Illinois side. It has a total length of 1205.8 m (3956 ft). Themain span is 350.6 m (1150 ft) in length, the side spans are 142.7 m (468 ft) in length, and theapproach on the Illinois side is 570 m (1870 ft). A cross section of the deck is shown in Fig. 2.The bridge has four lanes plus two narrower bicycle lanes, for a total width of 29.3 m (96 ft). Thedeck is composed of steel beams and prestressed concrete slabs. Steel ASTM A709 grade 50W isused, with an of 344 MPa (50 ksi). The concrete slabs are made of prestressed concrete with a

Bent 1

(1150’) (468’) (1870’)

Pier 2 Pier 3 Pier 4

(468’)

Figure 1: Drawing of the Cape Girardeau Bridge.

Illinois approach

x··g

33321 64

1 Cable Number

142.7m 350.6m 142.7m 570.0m

fy

November 5, 2002 3 Caicedo, et al.

http://www.eng.uci.edu/~anil/benchmark.html