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Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016
Editors J.F. Silva Gomes and S.A. Meguid
Publ. INEGI/FEUP (2016)
-1443-
PAPER REF: 6405
SEISMIC BEHAVIOR OF A DUAL-DECK CABLE-STAYED BRIDGE
WITH INVERTED-Y TOWERS
Pedro Almeida1, Rui Carneiro Barros
2(*)
1PhD student of PRODEC at FEUP, Dept of Civil Engineering, Structural Division, Porto, Portugal 2Habilitation - PhD - MSc - Civil Engineer, Prof at Dept Civil Engng, Structural Division, FEUP, Porto, Portugal (*)Email: [email protected]
ABSTRACT
The Third Tagus Crossing (TTT) proposed to cross the Tagus River between Lisbon and the
southern side, is a cable-stayed bridge with double composite steel/concrete deck. If final
decision is taken towards the design contest and bridge construction, this bridge will have the
longest cable-stayed crossing for simultaneous road and high-speed railway use in Europe.
The dual deck supported by two Warren type trusses, consists of two platforms: at the top, for
the road traffic circulation, with six lanes; the other lower platform, for high-speed railway
traffic with four lanes. In this work are detailed results of the seismic analysis for two possible
typologies of the bridge towers, for this third crossing of the Tagus River. The main objective
is to analyse the dynamic behaviour under seismic actions varying the tower typology
comparing the response in terms of moments and displacements between the H-shaped
(inverted Y shape with cross-bracings) and inverted Y (classic single Y shape). Without the
immediate objective of analysing in detail the deck elements, use is made of an equivalent
beam with the properties of the proposed deck cross section. The equivalent beam is the same
for the analysis of two types of towers, so the main difference in this study is in the shape of
towers.
Keywords: Cable-stayed bridge, seismic analysis, towers typologies.
INTRODUCTION
The tower is the defining element that expresses the visual form of any cable-stayed bridge
giving opportunity to give a different style to the bridge. The primary function of the tower is
of a structural nature, whose main function is to transmit the forces resulting from the
anchoring of tie rods to the foundations, leading compression efforts and minimizing load
eccentricities.
The towers can in general have a variety of shapes, and through the construction process may
be adjusted to facilitate anchoring of tie rods with different configurations. The tower’s
shapes depend, in addition to the structural requirements of the site conditions of implantation
of the bridge, also on: aesthetic requirements, economic, geological, topographical and
constructive constraints (Farquhar 2008, Podolny and Scalzi 1986).
The principal structural factor for the tower shape selection is on the kind and form of
anchoring the tie-rods to the deck. As secondary factor, according to Podolny and Scalzi
(1986), should also be taken in consideration the various methods and building techniques,
which can help the designer and the bridge owner to develop the best tower project for the
proposed bridge crossing.
Symposium_24: Structural Dynamics and Control Systems
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CASE STUDY
The longitudinal configuration of the Third Tagus Crossing (TTT), is a classic case of large
cable-stayed bridge (Figure 1), which is similar to other two existing bridges already built in
China: Tianxingzhou bridge and Tongling bridge.
The longitudinal configuration of the cable-stayed TTT structure, is a bridge with two towers,
one central span and two side spans. The bridge has a total length of 7200 m including the
access viaducts, in a straight development, with the brim of the deck set to 52.30 m above the
water level. The cable-stayed part consists of three spans: a main span of 540 m and two side
openings offsets (side-spans) with 300 m each. These side spans have two middle pillars
dividing the span into two sections of 210 m + 90 m (Fig. 1). Structurally these two
intermediate supports prevent the vertical displacement of the deck, and the retention tie-rods
limit the longitudinal displacement at the top of the towers; additionally the tie-rods also
decrease the deformability of the central span when actuated by overhead service loads
(Manterola 2006). The ratio between the length of the main span and the length L of the
cable-stayed zone (main span plus compensation spans) is 0.56L, which corresponds to a
solution above the classic values between 0.40L and 0.50L. The side suspension of the deck is
in multiple cables in two planes, with 68 pairs of tie rods distributed over two towers, in semi-
harp configuration.
Fig. 1 - Longitudinal configuration TTT (dimensions in m)
The two towers have a height of 190.00 m, 137.70 m above the deck brim, and the
relationship between the height of the towers and the length of the main span lies within the
optimum relationship according to various authors (Farquhar 2008, Leonhardt 1986,
Leonhardt 1987). The main frame is comprised of a mixed steel/concrete composite deck,
suspended in the longitudinal plane. The cross section is formed by Warren type trusses; the
structural main beams are the main part of the deck support and are connected by upper and
lower crossbeams. The two platforms, top and bottom, are in reinforced concrete; in the lower
deck there are four longitudinal beams, one below each rail track. Figure 2 shows the
geometry of the towers, the cross-sectional geometry type and the properties of the equivalent
beam used for this study, as considered earlier by Almeida and Barros (2015).
SEISMIC ACTION
The study of the bridge seismic response was done by nonlinear analysis of the time-histories
imposed by earthquakes, assuming a non-linear behavior. The seismic action was modeled by
acceleration series, of accelerograms compatible with the regulatory response spectrum of the
seismic action. In the simulations, a set of 8 artificially generated accelerograms
(SeismoArtif. 2015) were used to enable a nonlinear dynamic time-domain analysis (Time
History), where the accelerograms were set individually in both horizontal directions. The
Proceedings of the 5th International Conference on Integrity-Reliability-Failure
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integration time, of the selected accelerograms with duration of 20 seconds, was divided into
2000 analysis time-steps each with 0.01 seconds, as considered earlier by Almeida and Barros
(2015).
Seismic action in the longitudinal direction
The bending stress in the base portion of the towers (zones T1 and T3) with the simulated
seismic action in the longitudinal direction of bridge development, has a similar value for the
two shapes of the towers (MYY moments, Figure 3).
Greatness Properties
Area (m2) 3.89
Shear area AY (m2) 3.89
Shear area AZ (m2) 2.38
IY (m4) 83.43
IZ (m4) 313.94
Constant torsion (m4) 131.00
Fig. 2 - Geometry of the towers on the left; Geometry simplified cross-section type, right up and properties of
the equivalent beam right below
Fig. 3 - Tower bending moments MYY and tower longitudinal displacements,
for earthquakes in the longitudinal direction
0
20
40
60
80
100
120
140
160
180
200
-600 -400 -200 0 200 400 600
[m]
[MN.m]
Torre Y Inv. Torre H
T3
T2T4
T1
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
[S]
Displacments, X m
-300
-150
0
150
300
450
[S]
T2MN.m
-450
-300
-150
0
150
300
450
600
[S]
T1MN.m
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
[S]
Displacments, X m
-500
-350
-200
-50
100
250
400
[S]
T4MN.m
-450
-300
-150
0
150
300
450
600
[S]
T3MN.m
Symposium_24: Structural Dynamics and Control Systems
-1446-
In the risers anchoring zone (above the deck tower zones T2 and T4), the bending stress are
higher for the tower of inverted Y shape. It should be noted that for the tower H-shaped the tie
rods are distributed by two shafts, while for the tower inverted Y the tie rods are anchored in a
single shaft. The displacements at the top of the towers, along the longitudinal direction of
bridge development, have a similar value of about 0.12 m (Fig. 3).
With the seismic action in the longitudinal direction, the bending stress resultants (moments)
in the transverse direction of the towers (MXX moments, Figure 4) are of the same magnitude
or higher than at the base of the tower for the H-shaped (T1).
The displacements at the top of the towers have significant differences: for the tower in H-
shape reach values of 0.13 m, well above those that occur for the tower in inverted Y (0.03
m). In Figure 4 it can be seen the development over time of both the displacements and the
bending stresses.
By analysis of graphs (side graphics, Figure 4) during the time-history analysis of the towers,
associated with the seismic action in the longitudinal direction, it is possible to verify that the
maximum moments Mxx and displacements in transverse direction occur within the first 10
seconds and are more significant for the tower H-shaped.
Fig. 4 - Tower bending moments MXX and tower transverse displacements,
for earthquakes in the longitudinal direction
0
20
40
60
80
100
120
140
160
180
200
-300 -200 -100 0 100 200 300
[m]
[MN.m]
Torre Y Inv. Torre H
T3
T2T4
T1
-0,05
-0,025
0
0,025
0,05
[S]
Displacments, Y m
-300
-200
-100
0
100
200
300
[S]
T4MN.m
-250
-150
-50
50
150
250
[S]
T3MN.m
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
[S]
Displacments, Y m
-100
-50
0
50
100
[S]
T2MN.m
-300
-200
-100
0
100
200
300
[S]
T1 MN.m
Proceedings of the 5th International Conference on Integrity-Reliability-Failure
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Tower Y Inv. node
50 Tower Y Inv. node
30 Tower H node 50 Tower H node 30
Fig. 5 - Displacements of the deck, for longitudinal earthquakes
Figure 5 and Figure 6 represent the displacement and moments of the deck, for base
earthquake in the longitudinal direction. The node 50 is at the center of the bridge, the node
30 is the node in the center of the side span, A2 is the frame in the middle of the bridge, A25
is the frame in the mid of the side span.
Tower Y Inv. A2 Tower Y Inv. A25 Tower H A2 Tower H A25
Fig. 6 - Bending moments of the deck, for longitudinal earthquakes
Seismic action in the transverse direction
For the considered seismic actions (8 artificially generated accelerograms using SeismoArtif.;
2015) acting in the transverse direction of the bridge, both tower bending moments Myy and
tower longitudinal displacements (Figure 7) are lower than the one´s obtained during the
excitation by the same as longitudinal earthquakes. The bending stress resultants (moments)
at the base of the towers (zones T1 and T3) for simulated seismic action in the transverse
direction, perpendicular to the direction of bridge development, is greater for the tower H-
shaped (MYY, Figure 7) in the anchoring zone of the risers, than the corresponding moments
for the tower inverted Y (zones T2 and T4). The longitudinal displacements at the top of the
towers, for transverse earthquakes, have similar values for both solutions (H shaped and
inverted Y shaped), but are much smaller than when the towers were excited by longitudinal
earthquakes.
-0,1
-0,05
0
0,05
0,1
[S]
Displacements X m
-0,1
-0,05
0
0,05
0,1
[S]
Displacements X m
-0,1
-0,05
0
0,05
0,1
[S]
Displacements X m
-0,1
-0,05
0
0,05
0,1
[S]
Displacements X m
-0,05
-0,025
0
0,025
0,05
[S]
Displacements Y m
-0,05
-0,025
0
0,025
0,05
[S]
Displacements Y m
-0,05
-0,025
0
0,025
0,05
[S]
Displacements Y m
-0,05
-0,025
0
0,025
0,05
[S]
Displacements Y m
-150
-100
-50
0
50
100
150
[S]
MYYMN.m
-300
-200
-100
0
100
200
300
[S]
MYYMN.m
-250
-150
-50
50
150
250
[S]
MYYMN.m
-350
-200
-50
100
250
[S]
MYYMN.m
-300
-200
-100
0
100
200
300
[S]
MXXMN.m
-250
-150
-50
50
150
250
[S]
MXXMN.m
-150
-100
-50
0
50
100
150
[S]
MXXMN.m
-150
-100
-50
0
50
100
150
[S]
MXXMN.m
Symposium_24: Structural Dynamics and Control Systems
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Fig. 7 - Tower bending moments MYY and tower longitudinal displacements,
for transversal earthquakes
The maximum moments (and corresponding bending stresses) occur for this case of
transverse seismic action across the bridge longitudinal direction (Figure 8). The bending
stress resultants (moments) at the tower base for the H-shaped tower (zone T1, Fig. 8) are
higher than those obtained for the tower inverted Y shaped (zone T3, Fig. 8); about 36%
increase in moments MXX. With the earthquake acting in the transverse direction, the
displacements at the top of the inverted Y tower show significantly lower values (0.11 m)
than those of the tower H-shaped (0.41 m).
Fig. 8 - Tower bending moments MXX and tower transversal displacements,
for transversal earthquakes
0
20
40
60
80
100
120
140
160
180
200
-1000-750 -500 -250 0 250 500 750
[m]
[MN.m]
Torre Y Inv. Torre H
T3
T2T4
T1
-650
-400
-150
100
350
600
[S]
T3MN.m
-800
-500
-200
100
400
700
[S]
T4MN.m
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
[S]
Displacments, Y m
-1000
-700
-400
-100
200
500
800
[S]
T1MN.m
-0,45
-0,3
-0,15
0
0,15
0,3
0,45
[S]
Displacments, Y m
-400
-200
0
200
400
[S]
T2MN.m
0
20
40
60
80
100
120
140
160
180
200
-200 -100 0 100 200
[m]
[MN.m]
Torre Y Inv. Torre H
T1
T3
T2T4
T1
-100
-50
0
50
100
[S]
T4MN.m
-100
-50
0
50
100
[S]
T3MN.m
-75
-50
-25
0
25
50
75
[S]
T2MN.m
-100
-50
0
50
100
[S]
T1MN.m
-0,05
-0,025
0
0,025
0,05
[S]
Displacments, X m
-0,05
-0,025
0
0,025
0,05
[S]
Displacments, X m
Proceedings of the 5th International Conference on Integrity-Reliability-Failure
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The reason for the more favorable tower performance for the inverted Y shaped, in relation to
the tower in H-shape, is justified by the inverted Y tower having a greater inertia in the
locking area of the ties; still the materialization of the connection of the tie rods to their shafts,
in last third of the inverted Y tower, somehow contributes to a better solidarization which
makes it less vulnerable when seismically excited in this direction.
Figure 9 and Figure 10 represent the displacements and moments of the deck for the base
earthquake in the transverse direction. Nodes 50 and 30 are respectively at the bridge center
and side span center; the same applies for the sectional frames A2 and A25 of the bridge
spans.
Tower Y Inv. node
50 Tower Y Inv. node
30 Tower H node 50 Tower H node 30
Fig. 9 - Displacements of the deck, for transversal earthquakes
Tower Y Inv. A2 Tower Y Inv. A25 Tower H A2 Tower H A25
Fig. 10 - Bending moments of the deck, for transversal earthquakes
CONCLUSIONS
In this work was comparatively studied the seismic response of two structural solutions of the
proposed Third Tagus Crossing. The two types of towers studied (H-shaped and inverted Y-
shaped), have the same height and the tie rods are anchored in the towers also at the same
height. Both towers are subjected to a set of 8 earthquakes in the longitudinal direction or in
-0,05
-0,025
0
0,025
0,05
[S]
Displacments X m
-0,05
-0,025
0
0,025
0,05
[S]
Displacments X m
-0,05
-0,025
0
0,025
0,05
[S]
Displacements X m
-0,05
-0,025
0
0,025
0,05
[S]
Displacements X m
-0,2-0,15-0,1-0,05
00,050,10,150,2
[S]
Displacements Y m
-0,1
-0,05
0
0,05
0,1
[S]
Displacements Y m
-0,2
-0,1
0
0,1
0,2
[S]
Displacements Y m
-0,1
-0,05
0
0,05
0,1
[S]
Displacements Y m
-50
-25
0
25
50
[S]
MYYMN.m
-100-75-50-250255075100
[S]
MYYMN.m
-50
-25
0
25
50
[S]
MYYMN.m
-100
-50
0
50
100
[S]
MYYMN.m
-800-600-400-200
0200400600800
[S]
MXXMN.m
-750
-500
-250
0
250
500
750
[S]
MXXMN.m
-500
-300
-100
100
300
500
[S]
MXXMN.m
-750
-500
-250
0
250
500
750
[S]
MXXMN.m
Symposium_24: Structural Dynamics and Control Systems
-1450-
the transversal directions. Basically, both tower shape solutions lead to similar values of
moments and displacements, when excited by longitudinal earthquakes. However the seismic
action along the transverse direction is the one that in fact controls the design process and the
potential selection of the tower shape, since for this case occur the major differences in results
obtained for the two shapes studied. In fact when the towers are loaded by transversal
earthquakes, the bridge tower solution in inverted Y is itself more efficient than that for the
tower in H-shape.
REFERENCES
[1]-Almeida, P, Barros, RC. Análise do Comportamento Sísmico de Duas Formas de Torres
para a Ponte Atirantada Proposta para a Terceira Travessia do Tejo. ICEUBI 2015 –
International Conference on Engineering, UBI-Covilhã, 2-4 December 2015.
[2]-Farquhar, D.J. -- Cable stayed bridges, ICE Manual of Bridge Engineering. Editado por
Gerard Parke, and e Nigel Hewson. Second Edition ed. London, UK: Thomas Telford Ltd.,
2008.
[4]-Kawashima, K., Unjoh, S., and Tunomoto, M. – “Estimation of Damping Ratio of Cable
Stayed Bridges for Seismic Design”. Journal of Structural Engineering no. 119 (4): 1015-
1031, 1993.
[5]-Leonhardt, F. -- L'esthétique des Ponts (Puentes: estética y diseño). Presses
Polytechniques Romandes, Lausanne, 1986.
[6]-Leonhardt, F. – “Cable Stayed Bridges with Prestressed Concrete”. PCI Journal no. 32
(5): 52-80, 1987.
[7]-Manterola, J. – Puentes: apuntes para su diseño, cálculo y construcción. Colegio de
Ingenieros de caminos canales y puertos, Madrid, 2006.
[8]-Podolny, W., and Scalzi, J.B. -- Construction and design of cable-stayed bridges. 2nd ed.,
Wiley series of practical construction guides. New York, 1986.
[9]-SeismoArtif – “A computer program for generating artificial earthquake accelerograms,
version 2.1.0”. http://www.seismosoft.com , 2015.
