svensson: cable-stayed bridges (sample chapter)

40 Years of ExperienceWorldwide

Holger Svensson

CABLE-STAYED

BRIDGES

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.

© 2012 Ernst & Sohn GmbH & Co. KG. Published 2012 by Ernst & Sohn GmbH & Co. KG.

3276.1 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 favor-

able 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 perma-

nent loads, simplifies the construction and improves the aerodynam-

ic 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 driv-

ing 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. Con-

sequently, 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


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 per-

mits good quality control and rapid erection. The high compression

at the cable anchorages acts on completely cured concrete from ma-

ture 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 pur-

pose, 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 in-

creased 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 sym-

metrical 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 road-

way 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, under-

neath which the bearings are located in order to reduce the trans-

verse 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 an-

chorage 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. 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 join-

ing of the precast elements and the temporary shear during erection,

Fig. 6.6. The upper roadway reinforcement was welded for sustain-

ability. 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 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-ten-

sioning 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 bend-

ing 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 transverse-

ly with a 2.25 MN tendon. The stiff triangular edge boxes distribute

the cable forces in the longitudinal direction so that at the cable an-

chorages 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 mini-

mum distance to the surrounding PE pipe, Fig. 6.8. The black

PE pipes are wrapped with white UV-resistant PVF tapes for color-

ing.

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

bet ween the wires and the inner cone. The steel balls are secured in

place by epoxy resin filled with zinc dust.


Figure 6.2 Completed bridge

Figure 6.3 General layout

Figure 6.5 Longitudinal section along bridge center

Figure 6.4 Cross-sections

Figure 6.7 Transverse post-tensioning of main bridge

Figure 6.6 Steel dowels with sleeves in precast joints


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 be-

tween 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.

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 exe-

cuted [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].

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 add-

ition, 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 trans-

verse inclination as the corresponding cable plane.

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 neces-

sary to prevent the shearing-off of the pendulums and to protect the

roadway joints as far as possible.

Tension pendulums

At the hold-down piers uplift forces occur, together with longitudi-

nal 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 an-

chor heads, these anchor heads can freely rotate on spherical bear-

ings, Fig. 6.15. Since even the moment from the friction in the spher-

ical 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 superstruc-

ture requires the cable anchor heads to be anchored with support

nuts, Fig. 6.15.

Design calculations

The design calculations followed the principles outlined in Chapter 4.

For the various static and dynamic calculations a modified STRUDL-

program was used. The action forces for the final stage were deter-

mined 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


Figure 6.8 Stay cable cross-section with 283 wires

Figure 6.9 Longitudinal section of anchor head

Figure 6.10 Cable anchorage at beam

Figure 6.11 Steel tower head

Figure 6.12 Tower layout

Figure 6.13 Longitudinal bearings at the abutment and transverse bearings

at the towers with the desired failure joints


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 intro-

duced 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 signifi-

cantly 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 out-

side the assumed wind spectrum as shown in Fig. 6.18.

When comparing the test results with flutter calculations in ac-

cordance 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 simi-

lar cross-sections.

6.1.2.2 Construction engineering

General

The construction engineering was performed backwards by dismant-

ling 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 short-

enings 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 loca-

tion 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 ambi-

ent temperature during casting because the steel forms expand simi-

larly 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 direc-

tion 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 calcu-

lated 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


Figure 6.14 Pendulum layout Figure 6.15 Rotating pendulum anchorage at top and bottom

Figure 6.16 Aerodynamic shape factors Figure 6.17 Correlation between wind speed and angle

of attack

Figure 6.18 Results of the dynamic wind tunnel tests Figure 6.19 Change of fixed points during construction

1 Spherical bearing

2 Longitudinal joint in point

of counter flecture

3 Additional bearing during

construction

4 Pendulum

5 Axis of end cross girder

Section A–A

Wind angle of attack α in °

Win

d s

pe

ed

v in

km

/h

Win

d s

pe

ed

v in

km

/h

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

Movements in

final stage

System


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

super imposed 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 dis-

mantled, taking into account shrinkage and creep and the construc-

tion 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 cy-

cles 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 elem-

ents required special measures. These tensile stresses were caused by

the moment from the eccentric action of the horizontal support re-

action 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 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 be-

came 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 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, 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 ap-

proaches 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 elem-

ent. 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 for-

ward 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

Figure 6.20 Initial overlength of stay cables at installation


Figure 6.21 Casting of tower legs

Figure 6.24 Starter piece

Figure 6.25 Steel form

Figure 6.26 Match-casting

Figure 6.27 Portal crane

Figure 6.22 Tower heads before installation

Figure 6.23 Tower head

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