Cantilever truss bridge
|Function / usage:||
Motorway bridge / freeway bridge
Pasco, Franklin County, Washington, USA
Kennewick, Benton County, Washington, USA
Cable Bridge (1978)
|main span||131.8 m|
|length of side spans||2 x 71.4 m|
The roadway bridge across the Columbia River between the cities of Pasco and Kennewick, WA replaces a steel truss built in 1921. The river is 732 m wide and up to 21 m deep. The flow velocity and the change in water level are small because the river is regulated by a system of dams. The required navigational clearance was 15 m. The soil comprises very hard consolidated layers of clay with a thickness of 25–30 m, which are covered by sand and gravel. Below the clay, bedrock in the form of solid basalt is present. The fan arrangement of the stay cables requires a minimum of cable steel, produces a high compression in the beam, which is favorable for concrete, and reduces the bending in the towers. Parallel wire cables of high-strength steel permit high stresses and, in combination with their high modulus of elasticity, provide a high stiffness, which creates favorable live load moments in the beam. A small distance of cable anchorages at the beam reduces the cable sizes, simplifies their anchorages, reduces the beam moments from permanent loads, simplifies the construction and improves the aerodynamic stability. Continuity of the bridge beam over the full length of the bridge, including the approaches, prevents kinks in the beam under live load and reduces the number of roadway joints, which improves the driving comfort. Even at the towers the beam is elastically supported by the cables in order to avoid the large negative moments which would be created by rigid supports at the towers. By using two cable planes anchored at the outside of the bridge beam a torsionally weak open cross-section without bottom slab can be used, which simplifies beam fabrication and construction. With this cable arrangement the roadway slab acts as the top flange of a simply supported girder in the transverse direction and thus receives only compression from the dead load and live loads. The beam depth is primarily determined by the cross girders, and can be small. Consequently, the wind area of attack and the gradient of the approaches is reduced. By choosing suitable span lengths for the approach bridges the beam depth and shape can be kept constant over the total bridge length. Strong edge girders distribute the cable forces uniformly in the longitudinal direction and permit the same shape for the main and secondary cross girders.
The roadway slab spans in the longitudinal direction between the closely spaced cross girders so that the overall high compression forces from the cables are superimposed onto the local tensile stresses from wheel loads. The fabrication of the precast elements of the bridge beam permits good quality control and rapid erection. The high compression at the cable anchorages acts on completely cured concrete from mature precast elements. The remaining shrinkage and creep is small. In addition to these technical considerations the desire to create an aesthetically pleasing bridge was equally important. For this purpose, it is especially important to have balanced proportions between all bridge members.The high slenderness of the bridge beam, 1:140, is visually increased by the fascia with a slenderness of 1:421, behind which the full beam depth is reduced by the inclined outer outside slabs. The large number of thin white cables has the tendency to blur against the sky and creates the impression of a veil.
The bridge comprises two approaches and the inner three-span symmetrical cable-stayed bridge with a beam supported by 144 cables in two planes. The cables converge closely in steel tower heads. The beam is continuous with a constant shape over the full length of the bridge. It is fixed in the longitudinal direction at abutment 1. In axes 1, 3, 4, 6 and 9 transversely fixed bearings are located. The uplift forces from the backstays are transmitted by pendulums into the foundations.
The beam cross-section comprises two outer triangular boxes and the inner roadway slab supported by cross girders. The shape of the boxes was confirmed in the wind tunnel tests. The beam of the approach bridges has the same outer shape but a bottom slab and two additional inner longitudinal girders, underneath which the bearings are located in order to reduce the transverse widths of the piers. There are only cross girders over the piers and in mid span, so that the roadway slab carries in the transverse direction. At the hold-down piers the beam is solid over a length of 9.45 m, in order to reduce the uplift forces and to carry the high bending moments in the longitudinal and transverse directions created by the three concentrated backstay cables.
The precast elements, which are 8.23 m long – equal to the cable anchorage distance – comprise the whole cross-section with a width of 24.3 m. In order to achieve the required perfect fit of the joints, the elements were match-cast against one another. Four conical steel dowels, with 51 mm diameters, protruding into steel plates were placed into the forms in order to facilitate the joining of the precast elements and the temporary shear during erection.The upper roadway reinforcement was welded for sustainability. This was costly and has not been repeated. Some additional post-tensioning is more economic.
The spans of the approach bridges were post-tensioned with 24 con- tinuous draped tendons for 2.5 MN each. The precast elements were provided with straight bar tendons of at least 26 mm and 32 mm diameters which were coupled at each joint. The epoxy resin in the joint required a minimum compression of 0.5 MN/m2 during curing so that a minimum construction post-tensioning of 2.6 MN was selected. At the bridge center the number of longitudinal bars increases strongly because the normal force from the stay cables gradually tapers down to zero and the live load bending moments increase. The cast-in-place joints at the bridge center and at the tips of the approach bridges are post-tensioned with over- lapping tendons. Each cross girder of the main bridge is post-tensioned transversely with a 2.25 MN tendon. The stiff triangular edge boxes distribute the cable forces in the longitudinal direction so that at the cable anchorages only three short 1.0 MN tendons are additionally required in order to tie back the vertical cable components to the inner edge of the inclined slab.
Stay cables and anchor heads
The tensile forces in the stay cables are carried by parallel wires with 6.35 mm (1⁄4") diameter steel St1450/1650 (fy/GUTS) in accordance with ASTM A421. The wire bundles are surrounded by a 3⁄8 inch strand helix which keeps the wire in order and guarantees a minimum distance to the surrounding PE pipe. The black PE pipes are wrapped with white UV-resistant PVF tapes for coloring. The wires terminate in steel anchor heads with strengths of 380/580 N/mm2 where they are anchored in a retainer plate with button heads. The main anchorage force between the wires and the anchor head is created by the clamping effect of the so-called HiAm anchorage which uses small steel balls to fill the interstices between the wires and the inner cone. The steel balls are secured in place by epoxy resin filled with zinc dust.
Stay cable anchorages
At the superstructure the stay cables are anchored into the outer edge beams. Part of the cable force flows directly via the contact area into the concrete, the remainder running into the steel pipe and from there via the welded shear rings into the concrete. The distribution depends on the support area and the stiffness ratio between concrete and steel which is subject to change. In the concrete, the horizontal component of the inclined cable force spreads as normal force over the complete beam cross-section, whereas the vertical component is carried in the inclined transverse tendons. At the upper end of the steel pipe a neoprene ring centers the stay cable against the steel pipe. Outside the tip of the steel pipe a neoprene boot seals the steel pipe against the intrusion of water. The boot is connected to the steel pipe and the stay cable with stainless steel straps. At the tower head the stay cables are individually anchored in the steel tower heads. The large cable forces required thick steel plates, each steel tower head weighing 63 t.
In order to prove the required characteristics of the cable anchorages two tests with 2.54 m long specimens with 83 wires each were executed.
The towers are designed as frames with vertical legs and struts, fixed to the foundations.The legs consist of reinforced concrete, the struts are post-tensioned. The box cross-section of the legs has constant wall thickness and tapers upwards in both directions with vertical inclines. The steel tower heads rest on the tower legs. In addition, at their out-sides concrete „ears“ carry shear from different cable forces in the main span and the side span plus moments from transverse wind into the tower legs.
The US neopot bearings which carry the horizontal and vertical loads are roughly similar to those fabricated worldwide. For the safety of the bridge against possible moderate earthquakes it was not strengthened, but the beam was permitted to remain at rest against the horizontal oscillations of the soil and in this way to avoid inertia forces from earthquake accelerations. For this purpose the longitudinal bearing at the abutment and the transverse bearings at the towers were provided with the desired failure joints. The relative movements between beam and piers are limited to 25 cm in all directions.
At the hold-down piers uplift forces occur, together with longitudinal movements of the superstructure, for which tension pendulums from parallel wire cables with 157 wires each are arranged. In order to prevent a kink in the wires at the entrance into the anchor heads. Since even the moment from the friction in the spherical surface would create too high additional bending stresses in the wires due to non-linear effects from tension – a strong steel pipe with a longitudinal hinge at its center ensures the rotation of the anchor heads. In order to avoid the strong increase of compression forces in the bearings, the steel pipes are provided with a longitudinal joint in the central point of counter-flexion. The very limited depth in the anchorage region of the superstructure requires the cable anchor heads to be anchored with support nuts.
For the various static and dynamic calculations a modified STRUDL- program was used. The action forces for the final stage were determined at a plane frame with 111 nodes and 180 members. All stay cables received a slightly reduced effective modulus of elasticity of 2 • 105 N/mm2. The concrete stiffness of the beam and the towers was calculated for uncracked sections, taking into account the reinforcement. The local beam moments were calculated with a girder grid by using the forces from the overall systems. The edge box girders were replaced by stiff members located in the shear centers. The towers were investigated in a 3D-system, for which the cable forces and longitudinal deflections of the overall system were introduced with the exception of those loadings which cause torsion in the tower legs. Special local problems such as the introduction of the cable forces into the longitudinal steel plates of the tower heads were treated by means of finite elements.
The longitudinal oscillation period of the completed bridge comes to about 0.5 sec. As soon as earthquake forces shear off the desired failure joints, the period increases to about 12 sec, which renders the system nearly insensitive to the rapid movements of an earthquake.
Static wind loads
The design wind speed for the unloaded bridge in accordance with AASHO was assumed as 160 km/h. For the determination of the static drag factors, wind tunnel tests were performed on a section model at a scale of 1:38.4 and length of 1.8 m. Five different edge configurations were investigated but they did not give significantly different results. For larger wind angles of attack the wind speed decreases more strongly than the drag factors increase. The drag factor for the stay cables was taken as 0.7 and that for the bluff tower legs with 2.0.
Since the bridge is located in the vicinity of the infamous Tacoma Narrows Bridge, the aerodynamic stability was investigated in depth. With the same section model used for the static wind tests the dynamic characteristics were investigated in the wind tunnel. It was found that wind oscillations of any kind only occur outside the assumed wind spectrum.
The construction engineering was performed backwards by dismantling the final bridge.
Desired shape in the final stage after shrinkage and creep
Beam: The shop form of the precast elements was determined from the following considerations:
- all precast elements are fabricated 3 mm longer than their final lengths in order to take into account one half of their later shortenings due to elastic and shrinkage and creep deformations –all cast-in-place joints are cast in their final shape
- the gradient after shrinkage and creep must reach the theoretical value.
For the determination of the coordinates of the cable anchor points the following influences were taken into account:
- the change of the fixed points for the intermediate construction stages due to elasticity, shrinkage and creep determined the location of four characteristic points,
- the changes in the lengths of all precast elements due to elasticity, shrinkage and creep
- the thickness of all final joints between elements, taking into account sandblasting, comes to 3 mm (the actual thickness was finally measured at only 0.6 mm)
- the temperature during construction was assumed to be 13°C, and the temperature during casting of the elements was estimated and considered in the bridge geometry.
The lengths of the precast elements were not influenced by the ambient temperature during casting because the steel forms expand similarly to the concrete.
Towers: The towers were built in such a way that the locations of the cable anchor points at the tower heads are those in the final stage after shrinkage and creep. For this purpose, the tower heads were cast 44 mm higher for the first tower and 4 mm higher for the second tower. Their pier settlement was assumed to be 13 mm. The tower heads were built in and rotated by 0.066° (0.046°) in the direction of the side spans, in order to compensate for the different cable forces under permanent load in the main and side spans.
Cable lengths: The fabrication lengths of the stay cables were calculated between the coordinates of the cable anchor points at the beam and towers plus the following corrections:
- distance between the theoretical and actual distance (shims plus bearing plates)
- elastic elongations
- slip in both anchor heads, assumed 5 mm
- required overlength during construction
- difference between the construction temperature (13°C) and the calibration temperature of the measuring tapes (20°C).
The distance between the anchor heads determined in this way was adjusted for the wire cutting length for:
- distance between support plane and retainer plate
- additional length for button heading the wires, 12.5 mm each
- additional 10 mm to avoid too short
Geometry and action forces during construction: As mentioned earlier, the construction engineering was done backwards by dismantling the system. Onto the action forces in „final stage“ at t = ∞ shrinkage and creep were superimposed with negative sign in order to reach the stage „opening for traffic“ at t = 1. Then the superimposed dead loads were removed to reach the stage „enter joint closure“ at t = 0. To open the bridge by calculation one traveler was placed across the center joint, the post-tensioning was taken off and six cables on each side of the joint were shortened in such a way that all action forces in the nodes of both sides of the joints became zero. After that the beam was opened and each of the two bridge halves was dismantled, taking into account shrinkage and creep and the construction equipment. During dismantling, geometrical controls were applied and at the end the overriding condition was fulfilled that all action forces had become zero. After this first global run for dismantling, complete erection cycles were calculated for several typical intermediate systems and the resulting stresses investigated. It became apparent that the tensile forces at the underside of the second last joint between precast elements required special measures. In order to introduce additional compression into the critical joint during construction most stay cables were initially installed too long, thus producing a temporary negative moment at the critical joints.
Tower construction: The tower foundations were built within sheet piles in 8 m and 15 m deep water respectively. After installing the sheet piles and dredging down to the load-bearing soil the concrete base slabs were cast under water. After pumping out of the water the remainder of the foundations were built conventionally in the dry. When the intended foundation level was reached for tower 4, it became apparent that the actual load-bearing soil layer was 0.6–3.0 m deeper. Since the sheet piles could not be elongated, 316 steel piles with double-T cross-section were driven, on which the base slab was supported. The tower legs were cast with jumping forms in 4.27 m sections on a weekly cycle. The steel tower heads were fabricated in Japan. The up to 21 mm filled welds of the corbels for the cable anchorages were stressed- relieved. In order to keep the transportation weight small, each tower head was split into three compartments of 21 t weight each, which were later connected by high-strength bolts.
Fabrication of precast elements: The cast-in-place beam of the approaches was built on scaffolding extending over the full length, cast spanwise and post-tensioned as complete units. At the tips of their cantilevers over the river auxiliary piers were left in place in order to adjust the moments (and geometry to a limited extent) in the beam before closing the joints to the main bridge. The cast-in-place starter pieces at the towers were cast-in-place on scaffolding. For their bulkheads, short precast elements were used, which had served as counter-planes for match-casting the first elements on both sides of the tower. The precast elements were cast in a steel form on shore near the bridge on a weekly cycle. Match-casting was used; a release agent was sprayed onto the joints to enhance the separation of the two elements and to improve the joint surfaces.
For the forming of each individual corbel against which the stay cables are later anchored, a special three-dimensional adjustable form was used. The completed element was very carefully aligned against the form because the correct run of geometry and action forces depended on the precise fit between the precast elements. Shortly before installation the transverse tendons were post-tensioned. From then onwards the precast elements had to be supported at their edge girders in the axis of the stay cables, whereas before they rested underneath the inner longitudinal girders.
Beam installation: Large precast elements were selected because, amongst other reasons, the complete stayed beam is located above sufficiently deep water for floating-in the 270 t elements. Initially it was planned to lift the two elements symmetrical to a tower simultaneously. In order to prevent progressive collapse in the case of one element crashing down it was necessary to stay the tower heads to both sides. The final backstays were used for temporarily staying the towers, and as forestay an auxiliary cable was anchored at a tower head between the location of the flattest final forward cable and at the foundation of the other tower. After a certain learning curve a construction progress of 12 elements equal to about 100 m per month was achieved. The large horizontal compression forces in the beam from the weight of each unbalanced element in the main span was supported by transversely post-tensioned corbels in the tower axis. The precast elements were transported to site on a pontoon and lifted with the help of a traveler to the already erected beam. Before closing, the joints were troweled with a two-component epoxy resin. The uniformly distributed stress bars were threaded into their ducts and coupled with threaded sleeves. Some reinforcement bars cross the joint, welded to the short rebars protruding into the pockets on both sides of the joint. (This welding of rebars proved to be tedious and was not repeated for later bridges. Instead, the number of stressed bars was increased.) After shifting the new precast element against the already installed ones the stress bars were post-tensioned, so that a uniform pressure of 0.5 N/mm2 ensured a tight fit of the joint and hardening of the epoxy under favorable conditions.
Lifting traveler: From early on it was planned to use some slab lifting equipment from building construction readily available in the USA to lift the element from the pontoon. The hydraulic jacks with the pull rods rested longitudinally movable on the two traveler main girders which were tied back by two erection cables to the tower strut. The weight of the precast elements was transmitted in tension via the erection cables to the tower heads and in compression via the traveler main girders and shear corbels into the beam. The horizontal component of the erection cables was carried back to the approach beam, and the compression in the beam was carried via the temporary corbels at the towers into the foundation. These temporary corbels were active until the side span joint was closed.
Joint closure: The free-cantilevering took place from the towers out- wards to both sides until the side span joint was closed by cast-in-place concrete. The closure joints to the side spans and at the bridge center were closed with cast-in-place concrete.
Cable installation: The completely shop-fabricated parallel wire cables in their PE pipes were pulled up with a pull rope, supported by movable hangers from a highline as erection cable. Since PE pipes become brittle at low temperatures, the reels were placed in cubicles on the pontoons in which the air was heated during delivery to site. Then the PE pipes were pulled up via so-called ‘bananas’ to ensure a minimum bending radius. The lower anchor heads are supported by corbels underneath the beam. They are guided to their anchorages through cast-in steel pipes. The lower anchor heads were led to the upper end of the cast-in steel pipe by adjusting the sag of the highline into such a position that the tension rod of a 10 MN center hole jack could be threaded- in. In order to create compression in the second joint back, most cables had to be installed longer than required in the final stage. Only after two further beam elements were installed were the cables stressed to their final lengths. After installation, the PE pipes were grouted for corrosion protection. The required grout pressure at the top was ensured by stand pipes, through which the grout was wasted. The grout had a water/cement ratio of 0.38 and contained 1% by weight of expanding agent. For coloring, the black PE pipes were wrapped with self-adhesive off-white tape.
Construction by geometry
A large bridge from precast elements and shop-fabricated cables with well-known predetermined lengths is advantageously constructed by. The measurements of forces and deformations during construction serve only as controls. If the weights and the lengths of all individual members and the assumptions for shrinkage and creep are correct, then the bridge with its desired shape and internal forces must result, independently of the selected construction method and intermediate construction steps. On the other hand, deviations from the theoretical geometry of the individual members result in a final bridge stage in which the desired geometry and action forces cannot be reached together. Therefore, the individual members have to be fabricated as accurately as possible. During each erection stage the results of several control measurements were compared with the theoretical values:
Force measurements: The weight of each of the precast elements was measured by the precisely calibrated draft of the transport barges. On average, the elements were 3% heavier than assumed. The differences between the actual and theoretical values were within the measurement tolerances. Therefore, no re-stressing of stay cables was required at the end of construction.
Geometry controls: The thickness of the joints was measured by the distance between two bolts cast into the precast elements. It was determined that their distance immediately after concreting and at the end of construction increased on average by only 0.6 mm. During construction the theoretical and actual beam levels tallied well initially. Only towards the end did the beam become higher than assumed – at the center joint about 17 cm. This geometry deviation could be reconciled with the following deviations against the theo-retical assumptions.
- The modulus of elasticity of the beam concrete was not 35000 MN/m2 as given by AASHTO, but for the average 28-day cylinder compression strength of 51.3 MN/m2 it came to about 39000 MN/m2 due to the use of high-quality crushed granite aggregate.
- The shortenings due to shrinkage and creep were smaller than assumed, equal to code assumptions for a humidity of 90%.
- The towers shortened by only 2⁄3of the assumed values due to the higher concrete strength and lower foundation settlement.
The resulting changes in gradient in the bridge center were: Higher concrete modulus of elasticity 1.4 cm; Smaller shrinkage 5.9 cm; Smaller creep 8.1 cm; Smaller tower shortening and pier settlement 2.0 cm; Total 17.4 cm.
These geometry deviations were taken into account by the installation of the final cables only in so far that the angular deviations between the two beam tips before joint closure were taken out; otherwise the beam was left slightly too high. The horizontal deviations of the beam axis remained within the small range of + 2 cm and – 0.4 cm.
Excerpt from: Svensson, Holger; Cable-Stayed Bridges, Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH, Berlin (Germany), ISBN 343302992X; pp. 327-345. References to figures and literature were omitted.
Relevant Web Sites
- Spanning Washington, Washington State University Press, Pullman (USA); pp. 109-111
- Great American Bridges and Dams, John Wiley & Sons, New York (USA), ISBN 0471143855, 1984; pp. 314
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