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
328 6 Examples for typical cable-stayed bridges
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.
3296.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge
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
330 6 Examples for typical cable-stayed bridges
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
3316.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge
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
332 6 Examples for typical cable-stayed bridges
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
3336.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge
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
334 6 Examples for typical cable-stayed bridges
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
3356.1 Cable-stayed concrete bridges with precast beams – Pasco-Kennewick Bridge
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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