Svensson: Cable-Stayed Bridges (Sample Chapter)

Holger Svensson

CABLE-STAYED

BRIDGES 40 Years of Experience Worldwide

326

6 Examples for typical cable-stayed bridges

6 Examples for typical cable-stayed bridges

Cable-Stayed Bridges. 40 Years of Experience Worldwide. First Edition. Holger Svensson. Š 2012 Ernst & Sohn GmbH & Co. KG. Published 2012 by Ernst & Sohn GmbH & Co. KG.

6.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge

6.1 Cable-stayed concrete bridges with precast beams 6.1.1 General Cable-stayed concrete bridges with beams from precast elements have not been built very often. The first major examples are the Pasco-Kennewick Bridge and the East Huntington Bridge, both in the USA, which were completed in 1978 and 1985.

6.1.2 Pasco-Kennewick Bridge 6.1.2.1 General layout The Pasco-Kennewick Bridge was the first cable-stayed bridge which the author had to design on his own during the years 1973 to 1978, see appendix. What he learned from this work he published in [1.15], which forms the basis for the following description.

The roadway bridge across the Columbia River between the cities of Pasco and Kennewick, WA, Fig. 6.1, 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.

Figure 6.1 Location of bridge

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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, a clear flowing outline over the complete bridge length and slender towers and piers.

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, see Fig. 6.4. The large number of thin white cables has the tendency to blur against the sky and creates the impression of a veil, Fig. 6.2.

Overall system The bridge comprises two approaches and the inner three-span symmetrical cable-stayed bridge with a beam supported by 144 cables in two planes, Fig. 6.3. 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.

Cross-sections The beam cross-section comprises two outer triangular boxes and the inner roadway slab supported by cross girders, Fig. 6.4. The shape of the boxes was confirmed in the wind tun-nel tests outlined in [6.1]. A longitudinal section through the cross girders and roadway slab is shown in Fig. 6.5.

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.

Precast elements 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

6 Examples for typical cable-stayed bridges

elements were match-cast against one another. The bulkheads of the precast elements were not provided with a profile for shear interlock, because the shear forces remained always below 5 % of the overall compression forces.

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, Fig. 6.6. The upper roadway reinforcement was welded for sustainability. This was costly and has not been repeated. Some additional post-tensioning is more economic.

In order to reduce the local wheel load moments in the roadway slab, the joints were placed at the quarter point between cross girders.

Post-tensioning The spans of the approach bridges were post-tensioned with 24 continuous 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 overlapping 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 from where they are distributed in strut action to the tendon anchorages of the adjacent cross girders, Fig. 6.7.

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 St 1450/1650 (fy/GUTS) in accordance with ASTM A 421. 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, Fig. 6.8. 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, Fig. 6.9. 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.

6.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge

Figure 6.2 Completed bridge

Figure 6.3 General layout

Figure 6.6 Steel dowels with sleeves in precast joints Figure 6.4 Cross-sections

Figure 6.5 Longitudinal section along bridge center

Figure 6.7 Transverse post-tensioning of main bridge

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The transition between the inner HiAm casting and the cement grout of the free cable length is filled with epoxy resin plus zinc dust. A detailed description of this HiAm anchorage is provided in Section 3.4.

The short steel pipe at the tip of the anchor head serves for the airtight, tension and com-pression resistant anchorage of the PE pipe to the anchor head.

Stay cable anchorages At the superstructure the stay cables are anchored into the outer edge beams, Fig. 6.10. 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, Fig. 6.7. 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. A hole in the lower steel plate serves as drainage in case the upper seal does not work or condensation water appears.

At the tower head the stay cables are individually anchored in the steel tower heads, Fig. 6.11. The large cable forces required thick steel plates, each steel tower head weighing 63 t.

In order to approach the ideal fan arrangement of the cables with a common point of intersection, the stay cables are anchored in three parallel vertical planes.

6 Examples for typical cable-stayed bridges

Bearings 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 [6.3]. For this purpose the longitudinal bearing at the abutment and the transverse bearings at the towers were provided with the desired failure joints, Fig. 6.13, which fail when earthquake forces occur which are larger than those assumed for service conditions. The relative movements between beam and piers are limited to 25 cm in all directions.

Between the beam and the abutments a movement of 25 cm is only possible in the longitudinal direction. This limitation is necessary to prevent the shearing-off of the pendulums and to protect the roadway joints as far as possible.

Cable tests 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 [6.2]. The results of the fatigue tests and the tensile tests as well as the slip at room temperature and at 80 °C were satisfactory and in accordance with former tests outlined in [3.19 – 3.21].

Tension pendulums At the hold-down piers uplift forces occur, together with longitudinal movements of the superstructure, for which tension pendulums, Fig. 6.14, from parallel wire cables with 157 wires each are arranged.

They stress the beam down in such a way that even under increased service loads no uplift from the bearings takes place.

In order to prevent a kink in the wires at the entrance into the anchor heads, these anchor heads can freely rotate on spherical bearings, Fig. 6.15. 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 – see Fig. 4.26 – a strong steel pipe with a longitudinal hinge at its center ensures the rotation of the anchor heads, Fig. 6.14.

In order to avoid the strong increase of compression forces in the bearings, which would be created by the elongation of the steel pipe for beam movements of ± 21 cm at pier 5 under service loads (during earthquake ± 25 cm), 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, Fig. 6.15.

Towers The towers are designed as frames with vertical legs and struts, fixed to the foundations, Fig. 6.12. 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. In order to avoid deviating forces from the stay cables, each tower head axis has the same transverse inclination as the corresponding cable plane.

Design calculations The design calculations followed the principles outlined in Chapter 4.

For the various static and dynamic calculations a modified STRUDLprogram 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 which was kept constant because the change of sag for live loads was negligible.

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

6.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge

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Figure 6.8 Stay cable cross-section with 283 wires

Figure 6.9 Longitudinal section of anchor head

Figure 6.12 Tower layout

Figure 6.10 Cable anchorage at beam

Figure 6.11 Steel tower head

Figure 6.13 Longitudinal bearings at the abutment and transverse bearings at the towers with the desired failure joints

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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.

Some of the difficulties due to the limited computer capacity in 1976 are mentioned in the Appendix, and the action forces of the overall system are given in Fig. 4.10.

Earthquake 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, Fig. 6.13, 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 [6.1]. Five different edge configu-rations were investigated but they did not give significantly different results. The aerodynamic shape factors are shown in Fig. 6.16.

Fig. 6.17 gives the relation between wind speed and wind angle of attack as measured for the Severn Bridge [6.4], and confirmed on other occasions. This results in the design wind speed with angles of attack up to ± 2 °. The corresponding drag factor in accordance with Fig. 6.16 comes to 1.17, referred to the beam depth. 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, see Figs 3.90 and 3.91, and that for the bluff tower legs with 2.0, see Fig. 4.81.

Aerodynamic stability Since the bridge is located in the vicinity of the infamous Tacoma Narrows Bridge, Fig. 6.1, 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 [6.5]. It was found that wind oscillations of any kind only occur outside the assumed wind spectrum as shown in Fig. 6.18.

When comparing the test results with flutter calculations in accordance with Klöppel/Thiele [4.17], the shape reduction factor against an air foil comes to about 0.6 for a wind angle of attack of about 4 °, see Fig. 4.237. This tallies with earlier test results for similar cross-sections.

6 Examples for typical cable-stayed bridges

6.1.2.2 Construction engineering General The construction engineering was performed backwards by dismantling the final bridge as outlined in Section 5.2.

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 elas-ticity, shrinkage and creep determined the location of four characteristic points, Fig. 6.19 – 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. The temperature during closure of the side span and main span joints was taken into account by moving the cable suspended beam with jacks at the towers into that position which corresponds with the position in the final stage. In this way the joint closure temperature did not enter into the final geometry.

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), Fig. 6.10

6.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge

Section A–A

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1 Spherical bearing 2 Longitudinal joint in point of counter flecture 3 Additional bearing during construction 4 Pendulum 5 Axis of end cross girder

Figure 6.15 Rotating pendulum anchorage at top and bottom

Wind speed v in km/h

Figure 6.14 Pendulum layout

Wind angle of attack α in °

Figure 6.16 Aerodynamic shape factors

Figure 6.17 Correlation between wind speed and angle of attack

Wind speed v in km/h

System

Wind angle of attack α in ° Region of resonant vibrations Flutter vibrations for rising wind speeds Flutter vibrations for decreaseing wind speeds Statistical wind limitations Design wind speed max v = 160 km/h Figure 6.18 Results of the dynamic wind tunnel tests

Movements in final stage Figure 6.19 Change of fixed points during construction

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6 Examples for typical cable-stayed bridges

Figure 6.20 Initial overlength of stay cables at installation

– – – – –

elastic elongations sag 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, Fig. 6.9 – additional length for button heading the wires, 12.5 mm each – additional 10 mm to avoid too short cables (the cable fabricator guaranteed the cable lengths to ±10 mm).

Geometry and action forces during construction: As mentioned earlier, the construction engineering was done backwards by dismantling the system, see Section 5.2.2.1. 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 ‘center 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, see Fig. 5.85.

Both side span joints were opened similarly to the center joint. At the end of the construction engineering the straight towers with their original heights remained. 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. These tensile stresses were caused by the moment from the eccentric action of the horizontal support reaction on the beam during lifting of a precast element, see Fig. 6.35.

In order to introduce additional compression into the critical joint during construction most stay cables were initially installed too long, Fig. 6.20, 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 loadbearing 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, Fig. 6.21.

The steel tower heads were fabricated in Japan. The up to 21 mm filled welds of the corbels for the cable anchorages were stressedrelieved. 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, Fig. 6.22.

Figure 6.23 shows an installed tower head with all cables after concreting the external concrete ‘ears’.

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, Fig. 6.24. 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, Fig. 6.25. 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.

Fig. 6.26 shows the match-casting arrangement: after curing, each element was moved forward to serve as bulkhead for the next element. 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.

After steam curing and breaking the bond between concrete and the steel forms with com-pressed air, the precast elements were lifted out of the forms by a portal crane, Fig. 6.27, moved one length forward for the next casting operation, and finally transported to the storage area where they were kept wet for another two weeks. 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

6.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge

Figure 6.24 Starter piece

Figure 6.21 Casting of tower legs

Figure 6.25 Steel form

Figure 6.22 Tower heads before installation

Figure 6.26 Match-casting

Figure 6.23 Tower head

Figure 6.27 Portal crane

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Date of information: June 2012 homepage_sample_chapter