An Innovative Curved Cable-Stayed Bridge
Structural and Seismic Design*
Abolhassan Astaneh-Asl, Ph.D., P.E. (Principal Investigator)
Sung-Wook Cho and Mahmoud Hachem,
Formerly Graduate Students

Department of Civil and Environmental Engineering
University of California, Berkeley
(* The architectural design of this proposed bridge was done
by R. Gary Black, Professor of Architecture, UC-Berkel

Please send your comments to A. Astaneh-Asl at



By Abolhassan Astaneh-Asl, (Professor of Civil Engineering) and
R. Gary Black, (Assoc. professor of Architecture)

University of California, Berkeley

The innovative bridge design discussed herein is a long span curved cable stayed bridge with a single canted tower and curved deck. The superstructure of the bridge consists of a multi-cell steel box girder with composite concrete-steel deck. The single tower of the bridge is a malt- cell steel box with the core cell dedicated to the service elevator and stairs. The outer cells of the single tower are filled with high strength concrete to provide strength and stiffness in a composite action. The foundation of the main single tower is a solid footing embedded in the rock. Inelastic time history analyses were conducted to complete the seismic design and establish expected seismic performance. After description of architectural design, seismological, geotechnical and structural design aspects are discussed and a summary of seismic design and expected seismic response of the curved cable-stayed bridge concept are presented.



By Abolhassan Astaneh-Asl, (Professor of Civil Engineering) and
R. Gary Black, (Assoc. professor of Architecture)

University of California, Berkeley

The 1989 Loma Prieta earthquake caused widespread damage to transportation and other civil engineering facilities in Northern California. The quake caused collapse of a 17m (50ft) long segment of the San Francisco Oakland Bay Bridge deck and closure of the bridge for one month for repair and restoration. In the aftermath of the quake, a team of researchers from the University of California, Berkeley, led by A. Astaneh-Asl, conducted a seismic study of the East Bay Crossing of the San Francisco Oakland Bay Bridge (SFOBB) (Astaneh-Asl, 1992). The East Bay and West Bay Crossings of the San Francisco-Oakland Bay ridge are shown in Fig. 1.
The study identified areas of seismic vulnerability and suggested seismic retrofit strategies. Later, the California Department of Transportation conducted an in-house design of seismic retrofit of the East Bay Crossing. Early in 1997, the State of California, which owns and operates the bridge, announced that seismic retrofit of the east spans of the Bay Bridge is estimated to cost about $900 millions. The State also announced plans for a replacement bridge which was estimated to cost about $1.0 billion. The replacement bridge consisted of a typical reinforced concrete box girder viaduct supported on reinforced concrete Tee bents.

To review the issues related to a retrofit or replacement bridge, and to make recommendations to the State on the type of replacement bridge, a Bay Bridge Design Task Force was formed. The members of the Task Force were primarily local elected officials and transportation policy makers. The Task Force then formed an Engineering and Design Advisory Panel (EDAP) to assist the Task Force in recommending a preferred design for a new eastern span of the Bay Bridge. The EDAP developed and issued a Design Criteria to be used in design of new replacement for the East Bay Crossing. The bridge discussed in this paper was one of the designs proposed and is shown in Figures 2,3 and 4. The photomontages are digital graphics.

The Existing East Bay Crossing is about 9000 ft long connecting the Yerba Beuna Island to the east shore of the San Francisco Bay. The geotechnical, seismological and environmental aspects of the site are discussed in the following sections.

Figure 1. Existing Cantilever Span of the Bay bridge


The single tower, cable-stayed bridge is meant to be consistent with, and pay homage to, the Golden Gate Bridge and the West Bay Crossing of the San Francisco-Oakland Bay Bridge, by being a tower and cable bridge. At the same time, it is a visually memorable landmark and acts as a gateway to Oakland and other cities of the East Bay. In this respect it must be different from these bridges -- being to the turn of the millennium what the Golden Gate Bridge and the West Bay Crossing of the Bay Bridge are to the first part of the Twentieth Century.
The curved deck is suspended by cable stays from a tower which is raked to balance the forces -- both structurally and visually -- of the weight of the deck and the traffic. The bridge takes the concept of the suspended decks of the Golden Gate Bridge and West Bay Crossing of the Bay Bridge and extends it to another dimension. In these existing bridges the cables work in two dimensions to pull the forces up and over to the foundations and land masses so that they can be transferred to the earth. In the curved bridge, the forces pull the cables in three dimensions -- upward, over to the tower and back -- acting as a rein on the bridge deck. The architecture of the bridge expresses exactly what is occurring structurally.
The bridge deck includes a bicycle path and pedestrian walkway. Guardrails and handrails are designed to provide transparency to a moving vehicle.

Figure 2. Aerial View of Proposed Bridge
(Digital Photo Montage by C. Peri, UC-Berkeley)

Figure 3. View of the Proposed Design from Northwest

Figure 4. View of the Proposed Design From West




At the site of the bridge, the top of bed rock is estimated to be more than 400 ft below water surface. On top of the bedrock, there is a 300 to 400 ft layer of alluvial soil. A layer of Bay Mud rests on top of the soil. The depth of Bay Mud varies considerably throughout the site.


The site of the new bridge, as shown in Fig. 5, is located between the two most active faults of northern California; the Hayward and San Andreas faults. In the aftermath of the Loma Prieta earthquake, a comprehensive study of seismic vulnerabilities of the existing East Bay Crossing was conducted by A. Astaneh-Asl et al. (1992). As part of these studies, seismic aspects of the site as well as activities of the Hayward and San Andreas faults were studied by Bolt and Gregor (1993). The studies resulted in development of synthesized ground motions for the site. Fig. 6 shows the acceleration response spectra used to generate acceleration time-histories used in the the design and inelastic analysis of the proposed bridge.

The amplification of ground motion at the Yerba Beuna Island occurs only for very short period range of up to 0.5 seconds. This is due to the fact that Yerba Beuna Island is a rock outcropping. As a result, to minimize the seismic amplification in the proposed bridge design, Yerba Beuna Island was chosen as the location of the main tower of the bridge. Also, it was decided that there will be only one tower founded on the Yerba Beuna Island since there is no other location in the entire length of the East Bay Crossing where the bedrock can be reached at economical depth for foundations to be still economical.

Figure 5. Bay Area and Major Faults

Figure 6. Spectra Used to Generate Acceleration Time Histories

Various alignments were studies for the bridge. A straight bridge alignment would place the main span almost right on an underwater mud-channel formed by mud filling the pre-ice age river bed. The river currently is Temescal Creek in the East Bay.
One of the reasons for curved alignment of the proposed bridge was to skirt the Temescal Young Bay Mud channel and support the bridge on stronger and firmer soil strata. There were several other advantages in using a curved deck such as aesthetic and structural stability and making the length of the bridge shorter as well as having less environmental impact. Figure 7 shows the alignment of the existing bridge, the alignment proposed by Caltrans for the replacement and the alignment for the proposed curved cable-stayed bridge. Figure 8 shows the proposed bridge at the right side tip of Yerba Beuna Island.

Figure 7. Yerba Beuna Island and the Bridge

Figure 8. Alignments



The location of the proposed bridge, as well as the existing suspension part of the Bay bridge is shown in Figure 2. The proposed bridge, shown in Figures 3, 4, 9 and 10, consists of two parts: (i) an 1,800 feet long steel single tower, curved cable stayed bridge with its single tower on the Yerba Beuna Island and (ii) an approximately 8,500 feet long causeway connecting the cable stayed bridge to the Toll Plaza on the Oakland shore.
By choosing steel as the primary material for the design, the following advantages are achieved:

· The flexibility of steel enables a graceful curved design and sloped tower for an elegant appearance and a reliable structural and seismic performance.
· The curved design results in a shorter bridge length saving in cost of construction, maintenance and the gas and time spent by drivers through the 150 years design life of the bridge. The shorter length also reduces the environmental disturbance of the Bay.
· The light weight of the proposed bridge, 50% less than comparable concrete designs, results in considerable savings in the cost of construction as well as reducing the seismic forces.
· High-performance weathering steel, used in our proposed bridge, provides protection against corrosion and eliminates the need for painting. Any painting of outside surfaces for aesthetic reasons will last for at least forty years and possibly longer in the East Bay environment.

Figure 9. Analysis Model of the Proposed Bridge

Figure 10. Analytical Model of the proposed Bridge


By placing the main tower on the solid rock of the Yerba Beuna Island, we have reduced the foundation to a bare minimum. In addition, the seismic forces transmitted to the structure through the main tower are reduced significantly compared to forces in an offshore caisson or a pile-supported foundation. The foundation at this conceptual stage is tentatively considered to be excavated within the solid rock and after placing the tower base the grillage is filled with concrete with possible local reinforcements. The grillage consists of a steel multi- cell box with wall reinforced openings for concrete embedment. The steel grillage is extended upward from the top of the foundation to become the base of the tower. The first jacket units of the tower will be connected to this base extension and the erection of the other tower jackets will continue.

The Sloped Tower

The tower, at this conceptual stage, is considered to be a steel composite section. The cross section of tower consists of a steel shell outside and concrete inside with a circular utility and elevator shaft at C.G. of cross section. The tension side of tower is narrower and has more steel while the compression side is wider to take advantage of compressive strength of concrete.

The Bents Used at the End Piers of the Main Cable-Stayed Bridge

The bents at the location of end piers of main cable-stayed bridge are tentatively considered to be U-shaped bents.

The Support Articulations

The end supports consist of an expansion bearing free to move in longitudinal (tangential) direction and restrained in transverse (radial direction). The bearing allows bending rotations to take place both in vertical and horizontal planes. In addition, two tie downs one on each side of the bearing connect the superstructure to top of the pier. The main purpose of the tie downs is to restrain torsional movements at the end supports. If further analyses and design mandates the use of dampers, such devices will be placed at the end locations to dampen the longitudinal movements.
The support at the location of main tower consists of a fixed bearing that restrains movement in both longitudinal and transverse directions but allows bending rotations to take place in both vertical and horizontal planes. Similar to end supports, two tie down arms are used here to restrain torsional movements at the location of the support.

The Superstructure of the Bridge

The superstructure of the proposed bridge is mainly a curved multi-cell steel box girder supported by the cable stays and a single sloped tower as shown in Figures 5 and 6. The roadway is a lightweight reinforced concrete slab supported on stringers and floor beams. In the mid-portion of the box, the top flange consists of steel plate supporting the lightweight concrete slab and acting as composite with the slab. Outside this area, the top flange of the box is only lightweight concrete slab acting as composite with the webs and bottom flange of the steel box. The superstructure of the bridge is supported on three articulated supports; one at the location of tower and two at the location of the end piers. The details of these supports were discussed in the previous section.

The Expansion Joints

The expansion joints are located at the end supports of the main cable stayed bridge. For the causeway section, depending on the final design of the superstructure, necessary expansion joints will be provided.

The Cable-Stays

The cables of the bridge will be 0.6" diameter galvanized wires with co-extruded HDPE pipe on it. To control dynamic wind response of the cables, viscous or rubber based dampers will be installed at the deck anchorage areas, if necessary. No cable ties, which usually does not enhance the appearance will be needed.


The steel used for the bridge will be high-performance weathering steel. Weathering steel has been used successfully since 1960's throughout the US including California. This type of steel does not need painting. However, if the outside surface is painted for aesthetic reasons, the cost of painting the bridge every 40 years or so will be considered in the final cost estimate. The high-performance weathering steel has a higher strength than the regular steel and more importantly it has increased ductility. The higher strength results in cost efficiency and the increased ductility leads to an excellent seismic performance of the bridge.


The bridge was designed to resist the effects of dead load, live load, temperature change and seismic event due to a magnitude 7.3 rupture of the nearby Hayward fault. The load combinations considered in design were: (a) dead load plus live load of traffic as per AASHTO-LRFD (1994), and; (b) Dead load, live load and seismic ground motions of Hayward fault rupture.
The wind load was not considered in design load combinations. This was because of proximity of the site of bridge to two major faults, seismic effects were governing at global level. However, wind effects on the geometry of the deck as well as on possible vibration of stay cables were considered at the local level. The authors believe that for final wind design of a bridge of this size, especially with innovative architecture and structural configurations, wind tunnel tests need to be conducted.
Static and dynamic analyses conducted indicate that the behavior of the curved cable-stayed structure under gravity, wind, earthquakes and the combined effects of these loads are stable and desirable. The flutter and vortex shedding effects due to wind are expected to be insignificant. This is primarily due to the use of the streamlined cross section of the steel box, Figure 6, and the tripod nature of the curved structure supported at three corners of a triangle.

Figure 11 shows gravity load stresses in the upper flange of the steel box. In designing the deck, a number of alternate positions for live load were considered. Since this bridge has very heavy traffic on it, more than 280,000 vehicles per day, there are various scenarios for traffic jams on various lanes. Therefore it was deemed necessary to analyze the bridge with full dead load but partial live load placed in a way that it can create maximum bending and torsional effects. The studies indicated that when the live load was placed on all five westbound lanes (the upper half of the curve) and no live load on the five eastbound lanes (the lower half of the curve) the forces in the superstructure were the largest. The stresses shown in Figure 11 are for this condition of loading. The combined stresses did not exceed the yield stress of the steel used in the superstructure, which is 480 MPa (70 ksi) high performance steel.

Figure 11. Stresses in the Upper Flange of Box Girder Due to Gravity

Figure 12. First Four Modes of Vibration

The same dead load and live load combination as discussed in above section was considered in seismic analyses. Seismic analyses were conducted by building an elastic model of the main span as well as a 3-span segment of the causeway and subjecting the models to three components of base excitations. In the analytical model the box girder of the deck was modeled using shell elements for the steel plates and concrete slab and beam-column elements for the rolled members used as stiffeners for the shells. The foundation, embedded in the rock was modeled as fixed support. However, for final design, and after obtaining bore-hole data on the static and dynamic properties of the supporting rock, especially for the location of the main tower, rigorous soil-structure- interaction studies should be conducted and proper stiffness and damping matrices be assigned to the base of the tower. The 3-span segment of causeway was the segment immediately to the east of the main cable-stayed span.
Figure 12 shows first four modes of vibration of curved cable stayed bridge. The first significant mode with a relatively large mass participation was mode 3, which is essentially a longitudinal mode. Mode 4 was the second significant mode with a mass participation of about 32%. This mode was essentially the transverse mode of the vibration (radial direction of the curve). One interesting observation is that for this curved cable stayed bridge the cumulative mass participation is about 72% just after only 3 modes.
Figure 13 shows movements of top of the tower in horizontal x and y directions. The x and y directions are longitudinal and transverse directions of the bridge respectively. Maximum drift ratio (horizontal displacement/ height) at top of tower was about 1.45%. Figure 14 shows horizontal force at the abutment support.

Figure 13. Orbit Displacements of Base and Top of Tower

Figure 14. Time History of Force at the Abutment


One of the major considerations in design of long span bridges is construction sequence. The construction sequence for the curved cable-stayed bridge is shown in Figure 15. After excavation in the rock island of Yerba Beuna, the base of tower will be placed in the excavated area and after adding nominal reinforcements, the concrete foundation will be cast. The next step is to add prefabricated segments of the tower. The segments that are steel box sections are field-bolted to each other. As the tower rises above the cable attachment level, the prefabricated deck segments will be added on both sides of the tower. These deck segments will be connected to the tower by their corresponding stay cables. As the tower rises further, more deck segments are added. In essence, the rising of tower and extension of the deck on both sides of the tower are synchronized such that after adding the top segment of the tower, the last segments of the deck will be added. As the construction of steel tower and steel segments of deck continues, the concrete deck is cast starting from the tower base and moving out in both directions. In the meantime, the concrete will be pumped inside the outer cells of the tower. Finally, the last cable adjustments will be made to have the bridge deck at exact position for dead load.

Figure 15. Sequence of Construction


The curved cable-stayed bridge designed by the authors and presented herein had the following structural and seismic characteristics:
1. The main span of the proposed bridge is a curved cable stayed bridge supported on single canted tower located at the apex of the arch. The slope of the canted tower and radius of the deck is designed to ensure that under the gravity load, the center of gravity of the entire main span passes through the center of the foundation of the main tower, providing a "stable-equilibrium" for the bridge.
2. The canted tower acts as a balancing mass bringing the center of gravity of the entire bridge to location of the foundation of main tower. As a result, under gravity load, the bridge is in state of stable equilibrium.
3. Because of curved deck, the dominant mode shapes were quite different from the mode shapes expected of straight bridges. The torsional modes were not dominant in this curved cable stayed bridge. The reason is related to the fact that the curved deck is a three dimensional structure supported at three locations: the main tower and end priers. This results in the superstructure acting as a "tripod" under dynamic effects and being quite stable against torsion modes.
4. The response of bridge to the artificial magnitude 7.3 earthquake was essentially elastic. The ground motions used in the analysis were generated to represent the Maximum Credible Earthquakes emanating from the nearby Hayward Fault when it ruptures.
5. A construction sequence for the bridge was developed and proposed. Following the proposed sequence, after construction of the foundation of the main tower, the superstructure of the bridge can be constructed "growing" from the foundation without any need to disturb the delicate environment of the Yerba Beuna Island where the main tower is located.


AASHTO. (1994). "AASHTO LRFD bridge design specification". American Association of State Highway and Transportation Officials.

AASHTO. (1999). "AASHTO LRFD bridge design specification". American Association of State Highway and Transportation Officials.

Astaneh-Asl, A., Bertero, V., Bolt, B., Mahin, S., Moehle, J. and Seed, R. (1989). "Preliminary report on the seismological and engineering aspects of the October 17, 1989 Santa Cruz (Loma Prieta) earthquake', Report, UCB/EERC -89/14, Univ. of California, Berkeley.

Astaneh-Asl, A. (1990). "Damage to San Francisco Oakland Bay Bridge" Report to the Governor's Board of Inquiry on Loma Prieta Earthquake, Dept. of Civil and Env. Engrg., Univ. of California, Berkeley.

Astaneh-Asl, A. (1992a). "Seismic studies of the San Francisco-Oakland Bay Bridge." Proc., 10th World Conf. on Earthquake Engrg., Association Española de Ingeniería Sísmica, Madrid, Spain.

Astaneh-Asl, A.(1992b). "Seismic retrofit concepts for the Bay Bridge." Report to California Dept. of Transportation, Dept. of Civil and Env. Engrg., University of California, Berkeley.

Astaneh-Asl, A. (1994). "Seismic retrofit concepts for the East Bay Crossing of the San Francisco-Oakland Bay bridge." Proc.,, Fifth US National Conf. On Earthquake Engrg. Earthquake Engineering Research Institute, Chicago, Illinois.
Astaneh-Asl, A. (2001) " Seismic retrofit concepts for the east spans of the San Francisco Bay bridge", Proc. Structural Faults and Repair-2001, Commonwealth Institute, London.

Astaneh-Asl, A., McMullin, K., Wang, K., and Suharwardi, I. (1993). "Seismic condition assessment of the East Bay crossing of the San Francisco-Oakland Bay Bridge, Volume 6: Three-dimensional elastic time-history dynamic analyses." Report No. UCB/CEE- Steel- 93/08, Department of Civil and Environmental Engineering, University of California, Berkeley.

Astaneh-Asl, A. (1997). "The steel curved cable-stayed bridge designs: 1. The sloped tower design and; 2. The vertical tower design." Report No. UCB/CEE-Steel- 97/05, Department of Civil and Environmental Engineering University of California, Berkeley.

Astaneh-Asl, A. and Ravat, S. (1998). "Cyclic behavior and seismic design of steel H-piles." Report No. UCB/CEE-Steel- 98/01, Department of Civil and Environmental Engineering, University of California, Berkeley, May.

ASTM, (2000), "Standard Specification for Carbon and High-Strength Low-Alloy Structural Steel Shapes, Plates, and bars and Quenched-and-Tempered Alloy Structural Steel Plates for Bridges", Annual Book of ASTM Standards, American Society for Testing and Materials, West Conshohocken, PA.

Bolt, B. and Gregor, N., (1993) , "Synthesized strong ground motions for the seismic condition assessment of the eastern portion of the San Francisco Bay Bridge", Report No. UCB/EERC-93/12, University of California, Berkeley.

Caltrans (1999). "Caltrans seismic design criteria, Version 1.1". Technical Report, California Department of Transportation, Sacramento.

DMG. (1969), "Geologic and engineering aspects of San Francisco Bay fill", California Division of Mines and Geology, Special Report 97.

Rogers, J. D., and S. H. Figures, (1991). "Engineering geologic site characterization of the greater Oakland-Alameda area, Alameda and San Francisco counties, California", Report to the National Science Foundation, Grant No BCS-9003785.

Shen, J. H. and Astaneh-Asl, A. (1993). "Hysteresis behavior and modeling of double-angle semi-rigid connections." Report No. UCB/CE-Steel-93/10. Department of Civil and Environmental Engineering, University of California, Berkeley, December.

Trask, P.D. and Rolston, J. W. (1951). "Engineering geology of San Francisco Bay, California", Bulletin of the Geological Society of America, Vol. 62, pp. 1079-1110. September.


Publications in the following list that have their title underlined, can be viewed, sent to an e-mail address or printed, free of charge, by clicking on the underlined title of the publication.
To purchase a copy of the reports in the following list (with their title NOT underlined) you can mail a cashier check ( or a check drafted in a US Bank) for $40.00 US Dollars, payable to "The Regents of the University of California" to: A. Astaneh, 781 Davis Hall, University of California, Berkeley, CA, 94720-1710, USA. Please write the title of the requested report on your check or cover letter. In 3-4 weeks an offset print, a Xerox copy or a PDF version (on CD) of the report (whichever is available) will be mailed to you. The requested report will be mailed to US addresses using airmail and to addresses outside the US using ground mail. If you like more information on obtaining the reports or would like expedited delivery, please send an e-mail to



02-Astaneh-Asl, A. and Black, R.G. (2001) "Seismic and Structural Engineering of a Curved Cable-Stayed Bridge", J. of Bridge Engineering, ASCE, Vol. 6, No.6, Nov/Dec pp. 439-450.
01-Astaneh-Asl, A. (1997). "The steel curved cable-stayed bridge designs: 1. The sloped tower design and; 2. The vertical tower design." Report No. UCB/CEE-Steel- 97/05, Department of Civil and Environmental Engineering University of California, Berkeley.


The study reported here was conducted jointly at the Department of Civil and Environmental Engineering and Department of Architecture of University of California, Berkeley.
In developing the structure as well as construction methods for the proposed bridge, the designers (authors) benefited from the advice and comments provided by the following individuals: Professor Richard Furlong, Professor Theodore Galambos, Walter Gatti, Dann Hall, Philip Malachowski, Professor Thomas V. Mc
Evilly, Jay Murphy, James Neal, Robert Nickerson, John Ratajczak, Dr. J. David Rogers, David Lee, Dr. Ivan Viest and Dr. Victor A. Zayas. The input from these individuals, each a leader in their field was very invaluable and is sincerely appreciated. However, the opinions expressed in this paper are those of the authors and do not necessarily reflect the opinions of the above-mentioned individuals, others whose name appear in this paper or the University of California at Berkeley where both authors are faculty members.
Christopher Peri of the Department of Architecture at University of California, Berkeley, produced the computer-based photomontage of the proposed bridge design. The architectural design of the bridge was done by R. G. Black. Architectural students Brandon Jorgensen and David Galbraith also participated in architectural aspects.
A. Astaneh-Asl conducted the structural and seismic design as well as analyses of the bridge with the assistance of S. W. Cho, M. Hachem and J. Liu, graduate students at the Department of Civil and Env. Engineering of the University of California, Berkeley. The computer program used to conduct the analyses was SAP2000 nonlinear, generously donated by the Computers and Structures Inc. of Berkeley to the University of California Berkeley.



The information presented here has been prepared in accordance with recognized engineering principles and is for general information only. While it is believed to be accurate, this information should not be used or relied upon for any specific application without competent professional examination and verification of its accuracy, suitability, and applicability by a licensed professional engineer, designer or architect. The publication of the material contained herein is not intended as a representation or warranty on the part of any person or agency named herein, that this information is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of this information assumes all liability arising from such use. Caution must be exercised when relying upon specifications and codes developed by others and incorporated by reference herein since such material may be modified or amended from time to time subsequent to the posting of this material. The authors bear no responsibility for such material other than to refer to it and incorporate it by reference at the time of the initial posting of this document.


( to purchase a copy of these reports, please see above note under "Publications").
Astaneh-Asl, A. (1997). "The steel curved cable-stayed bridge designs: 1. The sloped tower design and; 2. The vertical tower design." Report No. UCB/CEE-Steel- 97/05, Department of Civil and Environmental Engineering University of California, Berkeley.

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