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RECENT DEVELOPMENT IN DESIGN OF STRESS RIBBON BRIDGES

Jiri Strasky, PhD, PE, Consulting Engineer, Greenbrae, CA ABSTACT

Recent applications of stress ribbon pedestrian bridges built in the USA and UK are described in terms of their architectural and structural solution, the process of construction and the influence of the structural arrangement on the static and dynamic analysis. The bridges have a very slender deck assembled from precast members formed by two edge girders stiffened by transverse ribs. The main advantage of these structures is that they have a minimal environmental impact because they use very little material and can be erected independently from the existing terrain. Since they do not need bearings or expansion joints they need only minimal long-term maintenance. Recent developments in which the stress ribbon is combined with arches or external cables are also presented.

Keywords: Stress ribbon, Precast segment, Composite slab, High-strength concrete, Prestressing, External tendon, Nonlinear analysis.

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INTRODUCTION

Fig.1 Bridge at Nymburk, CR Fig.2 Bridge at Redding, CA Stress-ribbon bridges is the term that has been coined to describe structures formed by a very slender concrete deck with the shape of a catenary - see Figs.1 and 2. They can be designed with one or more spans and are characterized by successive and complementary smooth curves. The curves blend into the rural environment and their forms, the most simple and basic of structural solutions, clearly articulate the flow of internal forces. Their fine dimensions also correspond to a human scale. Such structures can be either cast in-situ or formed of precast units. In the case of precast structures the deck is assembled from precast segments that are suspended on bearing cables and shifted along them to their final position – see Fig.3. Prestressing is applied after casting the joints between the segments to ensure sufficient rigidity of the structures. The main advantage of these structures is that they have a minimal environmental impact because they use very little material and can be erected independently from the existing terrain. Since they do not need bearings or expansion joints they need only minimal long-term maintenance. A characteristic feature of stress ribbon structures, in addition to their very slender concrete decks, is that the stiffness and stability comes from their geometric stiffness. They are able to resist not only uniformly distributed load (see Fig.5) but also large concentrated loads created by the wheels of heavy trucks (see Fig.4). Extremely large flood that accrued in summer 2002 in the Czech Republic also confirmed that they are able to resist a large ultimate load. Although the stress ribbon structures have low natural frequencies, our experience confirmed that the excited speed of motion of the deck created by walking is within acceptable limits. Also our detailed dynamic test confirmed that vandals cannot damage these structures. According to the author’s design seven stress-ribbon bridges have been built in the Czech Republic (CR) [1]. He also participated in the design of the first stress-ribbon structure of a span of 127.00 m that was built across the river Sacramento in Redding, California [2]. Recently the author also participated in the design of five stress ribbon bridges that were built both in the United States and United Kingdom. This paper summarizes the experience gained with the design and presents new developments.

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Fig.3 Bridge at Redding, CA - erection Fig.4 Bridge in Prague-Troja, CR – load test

Fig.5 Bridge in Prague-Troja, CR – load test STRUCTURAL SOLUTION – STATIC AND DYNAMIC ANALYSIS The structural arrangement of a typical two span structure is shown in Fig.6b. The deck is in a variable slope corresponding to the shape of the catenary. The maximum slope of the deck close supports is 8%. The stress ribbon is fixed at the end abutments transferring the tension from the stress ribbon into the soil. A slender pier with a concrete saddle forms the intermediate support. The structural arrangement of the stress ribbon bridges is determined by their static function and by their process of construction. During the erection the structure acts as a perfectly flexible cable (see Fig.6a), during the service as a stress ribbon that is stressed not only by normal forces but also bending moments (see Fig.6b). However, the shape and the stress of the structure at the end of the erection determine the stresses that originate in the structure when in use. The stress ribbon is stressed mainly by normal forces. Significant bending moments originate only at the supports. Bending moments due to the point load that represent loading by maintenance cars are relatively very low. Since the deck is always post-tensioned, the negative bending moments at the supports are very low. But positive bending moments are very large and have a significant influence on the arrangement of the stress-ribbon structure at the supports.

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Fig.6 Static function of the stress ribbon: a) erection, b) service The deck of the stress ribbon can be formed by a very slender solid section that can be further reduced by waffles that create a coffered soffit. The area of the deck is determined by a compression capacity of concrete that has to be post-tensioned in such a way, that after the loading of the structure there are no tension stresses in the deck. Since the bending moments due to the point load are low, the depth of the deck is only determined by the sufficient cover requirements of the prestressing steel. The deck of stress ribbon structures can be cast in a formwork that is suspended on the bearing cables or can be assembled from precast segments. In our first structures the segments were hung on bearing cables situated in the troughs, after the erection the deck was post-tensioned by the second group of cables situated in the ducts within the segments or in the troughs – see Fig.3. The bearing cables were protected by cast-in-place concrete that was cast simultaneously with the joints between the segments. The longitudinal joint between the cast-in-place and precast concrete, where shrinkage cracks may have occurred, was covered by a waterproof overlay. In our latest designs precast segments with a composite slab (see Figs.11 and 16) form the deck. The segments are suspended on bearing cables and serve as a false-work and formwork for casting of the composite slab that is cast simultaneously with the joints between the segments. Both the precast segments and the composite slab are post tensioned by prestressing cables that are situated together with the bearing cables within the cast-in-place slab. A continuous deck slab without any joints provides excellent protection to prestressing steel and requires minimum maintenance. A typical section of the stress-ribbon is not able to resist the bending moments that originate at the supports. There are two options how to solve this problem.

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The deck can be supported by saddles (pier tables) from which it can rise after its post-tensioning or when temperature drops – see Figs.12 and 14. If the deck is assembled from precast segments it is necessary to post-tension the deck by short cables. Short cast-in-place haunches can also reduce the bending stresses at the stress ribbon – see Figs.17 and 18. Although the bending moments are larger than in the structure of the constant depth, the resulting stresses are smaller. The haunches that are designed as partially post-tensioned members have to be sufficiently reinforced by rebars situated close to their bottom fibers. Modern programs for non-linear analysis allow expression of the static function of the stress-ribbon structures. The deck can be modeled by mutually connected parallel members that can express the function of the bearing and prestressing cables, precast deck and cast-in-place concrete – see Fig.7b. In the initial stage the forces in bearing cables are in equilibrium with the self-weight of the deck.

Fig.7 Modeling of the stress ribbon Due to creep and shrinkage of concrete the sag of the structure reduces in time. Therefore the tension forces in the deck increase – see Fig.7a. Also, due to the redistribution of forces between the cables and concrete (losses of post-tensioning) tension forces in the deck increase in time. Since the ratio of the area of the prestressing steel to the concrete area is larger than in conventional prestressed concrete structures these losses have greater value and have to be carefully analyzed. For analysis of the redistribution of stresses a special procedure that uses standard programs has been developed [3]. A very detailed analysis has confirmed that positive bending moments close to the supports do not change significantly in time.

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The stress-ribbon structures have low natural frequencies and damping. Therefore it is necessary to carefully check their response to pedestrian and wind loading [4]. In contrast to the ‘Guide Specification for Design of Pedestrian Bridges’ published by the AASHTO, in which the first bending frequency is checked, the analysis of the stress ribbon bridges is based on the checking of the speed and acceleration of the motion of the deck. In accordance with [4] the pedestrian loading is represented by a pulsating point load F=180 kN moving along the main span.

Fig.8 Typical natural modes Maximum acceleration is limited to 0.5 f0

1/2 [m/s2]. All our bridges comply with this requirement and users do not complain about the feeling of discomfort when walking or standing on the bridge. Our dynamic load tests have also confirmed that the bridges cannot be damaged by excessive vibration caused by vandals. Also the ratio r of the pure torsion to bending frequency (mode D/mode B) is always higher than value rcr = 2.5 that is considered as a critical for the aerodynamic stability of structures. Since the stress-ribbon bridges are usually situated in recreation areas, observation platforms situated at mid-spans are also required. Therefore a study of these structures was also carried out. The structures with observation platforms of different widths were tested in the wind tunnel. The results of the tests have confirmed that these structures have a sufficient aerodynamic stability too. Since the stress-ribbon structures are very light (the tension force due to a live load has approximately the same value as due to a dead load), the stresses from the longitudinal and transverse seismic forces are also within acceptable limits. RECENT TYPICAL APPLICATIONS BRIDGE ACROSS THE ROUGH RIVER, GRANTS PASS, OREGON Rogue River Bridge built in 2000 in Grants Pass, Oregon connects a major park on one side of the Rogue River to the County Fairgrounds on the other side of the river [6] – see Fig.9.

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Fig.9 Grants Pass Bridge The bridge is form by a stress ribbon of three spans is 73.15 + 84.73 + 42.67 3 m for an overall length of 200.55 m. The corresponding sags at mid-spans are 1.10, 1.55 and 0.31 m. The bridge of the width of 4.7 m provides a 4.3 m wide multi-use path. Observation areas located on widened deck segments at mid-span above the river (see Fig.10) and wetland offer users a location to stop and enjoy the river. The bridge also provides for vital emergency vehicle access and

Fig.10 Observation platform carries city water and sanitary sewer pipelines across the Rogue River. The

horizontal force from the stress ribbon is resisted by inclined steel piles and tie backs. At the abutments and above the intermediate supports the stress ribbon is supported by concrete saddles (see Figs.12 and 13) that allow passing of the pipelines though them. The bridge deck is formed from precast concrete segments with a coffered soffit that are composite with a cast-in-place deck slab – see Fig.11. The segments are suspended on bearing tendons, the composite deck is post-tensioned by prestressing tendons.

Fig.11 Deck Both bearing and prestressing tendons are situated within the deck slab. Above the saddles the segments are 1.00 m long and have a solid cross section. Before the erection of bearing tendons these segments were post-tensioned by short internal tendons.

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Fig.12 Intermediate support – during erection Fig.13 Intermediate support The arrangement of the structure was developed on the basis of very detailed static and dynamic analyses. To reduce the dynamic response of the structure to seismic load, the transverse stiffness of piers was reduced as much as possible. Dynamic analysis has confirmed that the excited speed of motion and acceleration are within acceptable limits.

Construction of the bridge was commenced by construction of the end abutments and piers. Then the solid abutment and pier segments were erected – see Fig.12. After casting of the joints between them the segments were post-tensioned by short tendons. Then the bearing tendons were pulled across the river and post-tensioned to the design stress. Subsequently the segments were suspended on bearing tendons and shifted along them into the design position At first the segments of the side spans were erected, then the segments of the main span. After that the formwork of the observation platforms was suspended on the mid-span segments, and the prestressing tendons and reinforcement of the deck slab were placed. Then the observation platforms together with the composite slab were cast and subsequently post-tensioned.

Fig.14 Intermediate support The bridge was designed by OBEC, Consulting Engineers, and Jiri Strasky, Consulting Engineer; the contractor was Holm II, Inc.

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KENT MESSENGER MILLENNIUM BRIDGE, MAIDSTONE, UK The pedestrian bridge forms part of river park project along Medway in Maidstone, United Kingdom. The deck of the bridge is formed by a two span stress ribbon that was - for the first time - designed with a cranked alignment - see Fig.15. The length of the bridge is 101.50 m, the span length of the main span bridging the river is 49.5 m, and the span length of the side span is 37.5 m. The angle plan between the spans is 25 degree.

Fig.15 – Maidstone Bridge The stress ribbon is formed by precast segments with a composite deck slab – see Fig.16. The segments are suspended on bearing cables and serve as a false-work and formwork for casting of the composite slab that was cast simultaneously with the joints between the segments. The stress ribbon is fixed into the abutments’ anchor blocks and it is frame

connected with the intermediate support. At all supports cast-in-place haunches are designed – see Fig.16 and 17. The precast segment of the length of 3.00 m are formed by 80 mm thick slab that gives a form of the soffit and edges of the deck. In longitudinal axis of the each segment a rectangular opening covered by stainless grid is designed. The opening serves for drainage of the deck and lighting of the underneath ground. Between the openings airport runway lights are

Fig.16 Deck situated.

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Fig.17 Intermediate support – during erection Fig.18 Intermediate support Both the precast segments and the composite slab are post tensioned by prestressing tendons that are situated together with the bearing cables within the cast-in-place slab – see Fig.16. The bearing cables and prestressing tendons are formed by 7 and 12 monostrands grouted in Polyethylene ducts. Arrangement of cables and tendons and their anchoring comply with special UK requirements for post-tensioned structures. The intermediate support that is situated in the axis of the angle break resists the resultant horizontal force from the adjacent spans into the foundation by a system formed by a compression strut and a tension tie – see Fig.17 and 18. The compression strut is formed by stairs, the tension tie is formed by a stainless steel tube. Since the value of the horizontal force depends on the position of the live load, for several loading cases the tube acts as a compression member too. Large tension force from the stress ribbon is transferred into the soil formed by weald clay by a combination of vertical drilled shafts and inclined micro-piles. The structure was designed on the basis of a very detailed static and dynamic analysis. The structure was modeled by a 3D frame flexibly fixed into the soil. The stress ribbon was modeled by mutually connected parallel members that can express the function of the bearing and prestressing cables, precast deck, and cast-in-place concrete. The analysis was performed by a program system ANSYS as a geometrically non linear structure. In the initial stage, bearing-cable forces are in equilibrium with the self-weight of the deck. The change of direction in the bridge deck plan creates transverse and torsional forces for which the structure was carefully checked. Similar to the all stress ribbon structures significant bending stresses originate close to the supports. These stresses were reduced by designing of cast-in-place haunches that were checked as partially prestressed members. In a dynamic analysis natural frequencies and modes were determined first. Then the speed and acceleration of the deck motion was checked. The response of the structure for a pulsating point moving along the deck, that represents the pedestrian loading, was checked.

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Fig.19 Erection of a segment Fig.20 Casting of the deck slab Before the erection of the deck the abutments and the intermediate support including the haunches were cast (see Fig.17). Till the tensioning of the bearing cables, the stability of the intermediate support was guaranteed by temporary supports. The bearing cables were erected as stay cables. At first, erection strands were pulled across the river and left bank, then the PE duct were suspended and moved into the design position. After that the monostrands were pushed through the ducts. After the tensioning of the bearing cables the segments were erected by a mobile crane. At first the erected segment was placed on ‘C’ frame, then transported into the design position under the bearing cables, lifted and suspended on the bearing cables (see Fig.19). All segments were erected in one day. After the erection of the segments the tension force in the cables was corrected, the prestressing tendons and reinforcing steel of the composite slab were placed and the joints between the segments, closure and slab were cast. The slab was cast simultaneously in both spans symmetrically from the mid-spans to the closures. To guarantee that concrete remain plastic until the entire deck was cast a retarder was used (see Fig.20).

After two days the bearing and prestressing tendons were grouted. When the cement mortar reached a sufficient strength the prestressing tendons were post-tensioned to 15 % of the final prestressing force. When the concrete reached the sufficient strength the structure was post-tensioned to the full design level. The function of the bridge was also verified by a dynamic test that proved that the users do not have feeling of discomfort when walking or standing on the bridge – see Fig.21.

Fig.21 Opening of the bridge

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The bridge was designed by Cezary M Bednarski, Studio Bednarski, London, UK and by Strasky Husty and Partners, Consulting Engineers, Ltd., Brno, Czech Republic. UK liaison & checking was done by Flint & Neill Partnership, London, UK. The bridge was built by Balfour Beatty Construction Ltd., Surrey, UK. RECENT DESIGNS AND DEVELOPMENT BRIDGE ACROSS THE FREEWAY R3508 NEAR OLOMOUC, CZECH REPUBLIC

Fig.22 Olomouc Bridge The one disadvantage of the classical stress-ribbon type structure is the need to resist very large horizontal forces at the abutments, which determines the economy of that solution in many cases. For that reason, we have developed a self anchored structural system where the

Fig.23 Olomouc bridge: a) cross section, b) elevation

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horizontal forces from the stress ribbon is balanced by horizontal force from arch. This structural system is utilized in a design of the bridge crossing a freeway R3508 that is being built near a city of Olomouc, Czech Republic (see Fig.22). The bridge is formed by a stress ribbon of two spans that is supported by an arch. The prestressed band of the length of the 79.2 m is assembled of precast segments supported and post-tensioned by external tendons – see Fig.23 and 24.

The geometry of the structure, load and level of the post-tensioning is designed is such a way that horizontal force in the stress ribbon and in the arch have the same magnitude. Since the arch footings and stress ribbon anchor blocks are connected by compression struts, the bridge functions as a self anchored structure that loaded the footing by vertical reactions only.

Fig.24 Structural arrangement The precast segments are designed from high-strength concrete of the characteristic strength of 80 MPa, the cast-in-place arch from a high-strength concrete of strength of 70 MPa. The external cables are anchored at the end abutments and are deviated on saddles formed by the arch crown and short spandrel walls. At the abutments the tendons are supported by short saddles formed by cantilevers protruded from the anchor blocks. The stress ribbon and arch is mutually connected at the central of the bridge. The arch footings are founded on drill shafts, the anchor blocks on micro-piles. The structural solution was developed on the basis of the tests done at the Brno Technical University and on the basis very detailed static and dynamic analysis. Great attention was also devoted to analysis of the buckling of the arch. The bridge was designed by author’s design firm Strasky, Husty and Partners, Ltd., Brno, Czech Republic. JOHNSON CREEK BRIDGE, OREGON The proposed bridge across the Johnson Creek is situated on the Springwater trail, in Milwaukee, Oregon. The bridge is formed by a partially self anchored suspension structure of span of 60.80 m – see Figs.25 and 26. The deck is in variable longitudinal slope with maximum slope at abutments 5%. The proposal tries to solve a problem of the erection of the

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self anchored structures which decks are usually cast or assembled on falsework before the suspension cables are installed and tensioned.

Fig.25 Johnson Creek Bridge Fig.26 Deck The deck is formed by precast segments and composite deck slab. The segments are identical to the segments that were used in the construction of the Grants Pass Pedestrian Bridge across the Rough River in Oregon (see Fig.11). Each third segment is connected with triangular steel struts that transfer the radial forces from the external cables into the deck. The deck is fixed into end abutments that are founded on battered steel piles. The external cables are also anchored into the end abutments. The piles are economically designed for resisting the erection horizontal force only.

Fig.27 Construction sequences

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The erection procedure was developed from the erection of the stress ribbon structures. The erection bearing cables that are situated within a composite portion of the deck are erected and tensioned at first. The cables are anchored into the end abutments that resist a horizontal force corresponding to the weight of segments and relatively large erection sag. Then the segments are suspended on the bearing cables and shifted along them into the design position – see Fig.27a. The segments are erected with steel struts. The segments are mutually connected by two types of steel members that guarantee their fix or pin connection. Then the external cables are erected and tension – see Fig.27b. By tensioning of the cables the structure moves into the design position. After that the joints between the segments and between the abutments are cast. In this way a self anchored structure is created - see Fig.27c. STUDY OF LONG SPAN STRESS RIBBON STRUCTURE A study of the stress ribbon structure of the span of 198 m (650 ft) has been done for the four arrangements of the cross section (see Fig.28 through 31):

Fig.28 Structure A - Cross section Fig.29 Structure B - Cross section

Fig.30 Structure C - Cross section Fig.31 Structure D - Cross section

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Fig.32 Structure C - Elevation The stress ribbon decks are assembled of precast segments from strength concrete of characteristic strength of 80 MPa. The segments are supported by external bearing tendons situated at segment edges and are post-tensioned by external tendons. They are four arrangements of the external tendons: Structure A tendons are situated under the deck. The tendons follow geometry of the stress ribbon deck to which they are attached. Structure B tendons (cables) are situated on both sides of the deck. In the elevation the cables follow the shape of the stress ribbon, in the plan they have a shape of the second degree parabola with maximum sag of 5.00 m. At mid-span they are attached to the deck; along their length they are connected with the deck by stiff cross beams protruding from the segments. Structure C tendons have a shape of suspension cables. The inclined cables have a shape of the second degree parabola. They horizontal sag is 5.00 m, the vertical sags are f + 5.00 m. At mid-span the cables are attached to the deck, in all joints between the segments they are suspended on the suspension cables by inclined hangers. Structure D a tendon (a cable) is situated in the bridge axis under the deck. The cable has a shape of the second degree parabola with maximum sag of f + 5.00 m. The cable is connected with the deck by vertical struts situated at joints between the segments. In the transverse direction of the deck the struts have a triangular shape. The structures were analyzed for the effects of the dead load, live load of 4 kN/m2, and for temperature changes ∆t = +/- 200C. The analyses were done for structures that after post-tensioning of the external tendons have a maximum slope at the abutments p = 5% and p = 8%. Corresponding sags at midspan are 2.475 m and 3.960 m.

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For all structures also natural modes and frequencies were determined. The analysis proved that all structures are able to resist the design load, however the Structure C has superior behavior. Also its aesthetic impression is excellent. STUDY OF CURVED STRESS RIBBON STRUCTURE

At present we are also working on the study of the curved stress ribbon structure that is eccentrically supported by external tendons that follow the geometry of the curved structure – see Fig.33. The static analyses done so far proved that the structure is feasible. At present we are working on its dynamic analysis. Fig.33 Curved stress ribbon

CONCLUSIONS The stress ribbon structures described in this paper proved to be very efficient structural type that utilizes high-stress concrete and external prestressing. They have a minimum impact on the environment and their architecture is developed from clear structural systems. Therefore we believe that the stress ribbon structures will find future applications. REFERENCES 1. Strasky,J.: Precast stress ribbon pedestrian bridges in Czechoslovakia. PCI JOURNAL,

May-June 1987. 2. Redfield,C.-Strasky,J.: Sacramento River Pedestrian Bridge. ASCE Structural Congress,

Chicago, 1996. 3. Strasky,J.-Navratil,J.-Susky,S.: Applications of Time-Dependent Analysis of in the

Design of Hybrid Bridge Structures. PCI JOURNAL, July – August 2001. 4. Design Criteria for Footbridges. Department of Transport, UK 1988. 5. Strasky,J.: Stress-Ribbon Pedestrian Bridges. International Bridge Conference. Pittsburgh

1999. 6. Rayor, G.- Strasky,J.: Design and Construction of Rogue River (Grants Pass) Pedestrian

Bridge. Western Bridge Engineers’ Seminar, Sacramento, California, September 2001. 7. Strasky,J.: Long-Span, Slender Pedestrian Bridges. Concrete International, February

2002. 8. Redfield, C.- Strasky,J.: Blue River Ranch Bridge. IABSE Symposium Vancouver 2002.