Journal of Wind Engineering and Industrial Aerodynamics 48 (1993) 317-328
Elsevier
317
The aerodynamic advantages of a double-effect
large span suspension bridge under wind loading
C. B o r r i a, M. M a j o w i e c k i b a n d P. Spinelli a
aDepartment of Civil Engineering, University of Florence, Via S. Marta 3, Florence, Italy
bInstitute of Construction Technology, University of Bologna, Viale Risorgimento 1,
Bologna, Italy
Summary
In the paper, some recent advances in the design of very large span suspension bridges are
reviewed and a solution based on a design of S. Musmeci is finally investigated. This
solution, based on a double effect cable system, shows many advantages, underlined here,
mainly in providing stiffness and, possibly, damping "reserve", that can face effectively
many design uncertainties.
1. I n t r o d u c t i o n
In t h e design of l a r g e s u s p e n s i o n bridges t h e r e is t o d a y a c l e a r d i c h o t o m y in
design choices b e t w e e n a e r o d y n a m i c a l l y t r a n s p a r e n t d e c k i n g on the one h a n d
a n d v e r y rigid d e c k s t r u c t u r e s p r o v i d i n g a h i g h d e g r e e of r e s i s t a n c e to wind
a c t i o n on t h e other. T h e s e s o l u t i o n s h a v e b e e n d i c t a t e d by the n e e d to p r o v i d e
d e c k i n g w i t h a h i g h d e g r e e of t o r s i o n a l r i g i d i t y a n d at t h e s a m e t i m e m i n i m i s e
the effect of drag, a c r u c i a l f a c t o r on l a r g e bridges.
T h e c o m p l e t e c o n t r a s t b e t w e e n t h e s e t w o design a p p r o a c h e s w a s c l e a r l y
e v i d e n t at the I S L A B 92 S y m p o s i u m on t h e A e r o d y n a m i c s of L a r g e Bridges
( C o p e n h a g e n 1992) [1], widely c o n s i d e r e d to reflect t h e s t a t e of the a r t a n d
c u r r e n t t e n d e n c i e s in l a r g e bridge a e r o d y n a m i c s , and confirmed at t h e r e c e n t
IASS c o n g r e s s (Toronto, J u l y 1992) [2]; t h e differences c a n c l e a r l y be seen in
the c o n t r a s t i n g design c o n c e p t s of two i m p r e s s i v e l a r g e s p a n bridges c u r r e n t l y
under construction:
(i) the StSre B a e l t s u s p e n s i o n bridge in D e n m a r k w i t h a 1624 m c e n t r a l s p a n a n d
highly efficient a e r o d y n a m i c decking, a n d (ii) the A k a s h i K a i k y o s u s p e n s i o n
bridge in J a p a n w i t h a 1990 m c e n t r a l s p a n and a v e r y rigid deck f r a m e w o r k .
Correspondence to: C. Borri, Department of Civil Engineering, University of Florence, Via
S. Marta 3, Florence, Italy.
0167-6105/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
318
C. Borri et al./Double-effect large span suspension bridge under wind loading
°,
~ / a ' -
T
Messina
Akashi Kaikyo
i .
L
Great Belt
Humber
_ ~'-~,,--~
~
Verrazzano Narrow
Fig. 1. Evolution of large span bridges.
We appear therefore to have arrived at a true parting of the ways as regards
design criteria (Fig. 1). On the one hand there is a tendency to reduce the
pressures acting on a structure and on the other an attempt to increase
structural resistance.
It seems reasonable to ask therefore: can we continue to use the classical
suspension bridge design with twin load-bearing cables and vertical hangers
for very large spans without introducing structural innovations? N.J. Gimsing
[3] has shown, in a series of interesting proposals, how considerable modifications to the classical vertical layout of cables and stays enables control of
static and dynamic behaviour over spans far exceeding those currently possible (up to 5 kilometers using today's steels and theoretically up to 20 kilometers using carbon-fibre reinforced material). An equally stimulating contribution in this debate has been made by T.Y. Lin and P. Chow [4] in a proposal
for bridging the Straits of Gibraltar.
2. The evolution o f design aspects o f long span suspension bridges
The two large suspension bridges mentioned earlier and currently under
construction, both share the same main structural system, i.e. a classical
suspension bridge design with decking on vertically parallel planes suspended
on vertical hangers of variable length from two load-bearing cables. Given the
well-known problems of aerodynamic stability in this type of bridge, recent
C. Borri et al./Double-effect large span suspension bridge under wind loading
319
theoretical and experimental research has been directed mainly towards the
definition of aerodynamically efficient decking.
After the historic failure of the Tacoma Narrows bridge in 1940, caused by
aerodynamic instability, most research analyses up until the 1960's concentrated on deck design.
An initial tendency was to provide suspension bridges with a high degree of
torsional rigidity (see for example the heavy, stiff deck structures of the
Verrazzano Narrows, Tago and Firth of Forth Road bridges). Rigid decking
provides satisfactory aerodynamic resistance and stability but increases
decking weight, construction costs, wind drag and lateral deflection (up to
14 meters on the Akashi Kaikyo [5]). Not to be forgotten are the maintenance
and inspection problems of this type of construction.
The end of the 1960's saw the introduction of a second approach to the
problem: the basic strategy employed was to reduce the effects of wind action
by concentrating exclusively on the aerodynamics of deck profile. Because of
their shape and behaviour under wind action, decks designed according to
such criteria are defined as streamlined or aerodynamically transparent.
Streamlined decks usually have a single- or multi-box girder construction with
single or multiple cells and with an orthotropic decking plate to support and
transmit loads. This type of construction reduces wind action, especially drag
(either pseudo-static or turbulent), and significantly contributes to overall
torsional rigidity.
The single box girder solution does not, however, provide sufficient reliability on very large spans. A comparative study of some streamlined decks during
preliminary design work for the Akashi Kaikyo bridge showed that the maximum span for a single box girder deck is 1700 meters. For this reason the
height of the deck section, on two recent bridges the StSre Baelt (1624 m) and
the Humber (1100 m), has been increased in order to provide the torsional
rigidity needed to counteract aeroelastic instability.
Another question currently debated is about the deck type that should be
used for spans of over 2000 m. An initial reply has been given by the Japanese
designers of the Akashi Kaikyo bridge who ensure aerodynamic stability by
means of rigid deck framework despite the high price to be paid in terms of drag
resistance and turbulence (buffeting and vortex shedding).
At 1624 meters the StSre Baelt bridge was the longest of its type until the
arrival of the Akashi Kaikyo at 1990 meters. The adoption of a rigid deck on
the Akashi Kaikyo at the same time as this marked "jump" in scale from 1624
to 1990 m represents a historical departure in the development of suspension
bridge design and raises a considerable number of questions for future applications. Even greater "jumps" in length are foreseen for the future: 3300 meters
for the Straits of Messina; 5000 meters for a multi-span bridge over the Straits
of Gibraltar.
The solution put forward by the designers of the Messina bridge [6] involves
the use of a ventilated deck, i.e. a deck of three box sections separated by grill
sections which permit the vertical passage of air (see Fig. 2). This drastically
320
C. Borri et al./Double-effect large span suspension bridge under wind loading
Cmd.ABRI AN SIDE
SICILY SlOE
960 e~ - ~ -
('.-.":~:"
O
I --EL" "~6 M . . . . . . . . .
•
3300 M
II10 I~
I
....................
.~t
",:.~.,.,~¢.~,JU,,7~4~I. "~-- . . . . . .
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L . . . . . . . . . . . . . .
SEA |OTTOH AT - 150 ~
~
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~
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'" '!
.,~.-;,.:~.,:.~::.~:-.~.=: ~ ...,:..'~....
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(RAIL)
(SERVICE)
(ROAD)
(ROAD)
2~000
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24000
I
375~,
I
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:
L 8250~
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52000 ~
6450
I.
I
61150
k~
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3oooo
c..~
oooo
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4000
Fig. 2. Design of the Messina Bridge [6].
reduces the quasi-static coefficients of a e r o d y n a m i c r e s i s t a n c e to lifting and
t o r q u e (moment).
I n n o v a t i o n s in overall s t r u c t u r a l design can also be found in the large scale
plans of the feasibility studies for bridging the Straits of G i b r a l t a r (Fig. 3) [4].
In this case a t t e n t i o n is no longer exclusively c o n c e n t r a t e d on the aerod y n a m i c p e r f o r m a n c e of the deck but r a t h e r is m a i n l y directed towards the use
of purely s t r u c t u r a l methods for i n c r e a s i n g the r e s i s t a n c e of a classic suspension bridge design so as to enable the large i n c r e a s e in scale involved in this
project.
The discussion above will have made it clear t h a t bridge designers are faced
with two choices: a rigid deck or an a e r o d y n a m i c a l l y t r a n s p a r e n t deck. Rigid
decks can provide the a e r o d y n a m i c c h a r a c t e r i s t i c s needed to e n s u r e efficiency
and stability but entail increases in weight and t h e r e f o r e increases in the costs
C. Borri et al./Double-effect large span suspension bridge under wind loading
.
5km
i
i
-,.~,
I_ 1kin
A
321
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3krn
1kin
J
A'
Fig. 3. Design of the Gibraltar bridge [4].
of structural works. Transparent decks reduce transverse pressures but are
limited to use on spans of less than 1700 meters (as shown by Japanese studies)
in those cases where considerable increases in length are not matched by
corresponding increases in width.
The lack of a synthetic solution combining these two design approaches is
due mainly to the uncertainties in physical system modelling and more especially in the modelling of actions. Physical modelling does not yet make it
possible to evaluate the sensitivity and degree of reliability of the overall
design process especially in the analysis of large bridges where wind action is
undoubtedly a dominant factor.
Uncertainties arise from our incomplete knowledge of the stochastic properties of actions, the modelling and behaviour of materials, mathematic modelling and the modelling of structural properties such as mass, damping and
rigidity. All these uncertainties mean that the whole design and construction
322
C. Borri et al./Double-effect large span suspension bridge under wind loading
process must be subject to general reliability testing [7]. In a study of the
Humber bridge [8], the uncertainties of the mathematical aeroelastic model
were checked on the basis of structural parameter and aerodynamic uncertainties. For bridges of a similar type this study provides general indications
concerning analytical model uncertainties through the use of critical flutter
speed definitions.
An interesting debate during the ISALB 92 symposium gave the impression
that from an engineering point of view the overall design process and structural system testing is reliable only on simple, classical suspension bridges of
spans up to 2000 meters. In order to remove some of these uncertainties, special
wind tunnels have been constructed which are wide enough to take 1:100
aeroelastic bridge models complete with access viaducts. The wind tunnel for
the Japanese project, for example, has a test width of 43 meters. This was the
only way of decreasing the degree of u n c e r t a i n t y when studying structural
characteristics and wind-structure interaction (frequency, damping and inertial scaling) and the only way of faithfully modelling towers, decks and cable
systems.
Another method for solving the problem is to deal with the " a c t i o n " side of
the equation. That is, by designing a deck section that is aerodynamically
t r a n s p ar en t or ventilated and which, as a consequence, drastically reduces the
"actions" operating on the structure. To be applicable, however, this method
presupposes th at the methods for extrapolating from models to the finished
project are reliable, i.e. that the uncertainties have been estimated on the basis
of comparisons with existing constructions. In the case of large bridges,
however, such a comparison is not practicable and extrapolation is not immediately possible. It should also be said t hat theoretical numeric methods for
extrapolating from models to reality are also affected by numerous uncertainties which cannot be ignored.
A first series of uncertainties concerns the significance of the wind tunnel
testing of models. According to Scanlan [9]: " ... the Reynolds number of the
test will typically be two to three orders of magnitude low ... The usual
argument that the effects of the Reynolds number are negligible for structural
elements with sharp edges remains to be fully substantiated . . . "
Scanlan himself draws attention to some of the limits of his theory of
aeroelastic instability: " ... in the discussion reported above it is supposed that
flutter and buffeting forces can be separated and do not i n t e r a c t . . . Since
the physical phenomena of flow over bluff bodies and its interaction with
them are intrinsically nonlinear effects, this analytical separation, made for
engineering analysis, is convenient but does not allow, in principle, certain
complexities of the flow-structure i n t e r a c t i o n . . . ".
Here it should also be emphasised that, even though model analyses and
t r e a tmen t might be exact, numeric extrapolation using algorithms to simulate
wind storms over time can itself lead to further uncertainties.
Firstly, a simulation must comprise at least 20 or 30 case histories of suitable
duration (10 20 min) if it is to be statistically significant.
C. Borri et al./Double-effect large span suspension bridge under wind loading
323
Secondly, all the algorithms used to generate histories in time do not take
into account the quadrature components of the cross spectrum. This means
that the phases cannot be simulated correctly. The same applies to the lee
eddies caused by the shape of the object hit by wind currents or by the presence
of transversal elements and roughnesses. The same is also true in case of cross
winds causing eddies running the entire length of a bridge which can trigger
oscillations. These phenomena cannot be correctly simulated given the current
stage of development of generation methods.
The considerations raised in the discussion above make it reasonable to ask
the question: can we continue to propose the classical layout of a simple
suspension bridge for large spans without introducing some structural innovations? In other words, can we hope to dominate all the problems which might
arise through the zealous application of analyses to what is, in effect, an "old"
layout without at the same time implementing on overall synthesis of
! |5e
Fig. 4. [10].
324
C. Borri et al./Double-effect large span suspension bridge under wind loading
structural concepts? Working along these lines, Lin and Chow [4], suggest
increasing the deflection/span ratio from 1/10 to 1/5 so as to reduce the stresses
on the load-bearing cables. According to these authors, the increase in cost due
to the higher towers required in their hypothesis would be offset by the
reduction in cable diameter.
N.J. Gimsing [3] has shown, in a series of interesting proposals, how considerable modifications to the classical vertical arrangement of cables and
stays enables control of static and dynamic behaviour over spans far exceeding
those currently possible. K. Ostenfeld and A. Larsen [10] (see Fig. 4) have
Fig. 5.
2000
3300
Fig. 6.
C. Borri et al./Double-effect large span suspension bridge under wind loading
325
proposed the introduction of a system of horizontal wires in order to control
and limit lateral movement of the deck.
We are firmly convinced that theoretical and experimental analyses,
the production, construction and maintenance of free spans greater than
2000 meters must all be based on clear design concepts which remove,
or at least substantially reduce, the uncertainties indicated by many leading
authorities on the subject.
3. S o m e r e m a r k s a b o u t a p r o p o s e d d o u b l e e f f e c t t e n s i l e s t r u c t u r e
The aim of this paper is, therefore, to study the behaviour of a double-effect
suspension bridge under the effect of wind action. To do this we will use
a model inspired by S. Musmeci's design for the Straits of Messina bridge and
we will be studying the reductions in aeroelastic instability provided by this
model.
The model is based on four guidelines:
(i) Reduction of bridge weight by means of a streamlined deck with high
flutter stability.
(ii) Considerable increase in torsional rigidity (even though the deck is not
torsionally rigid) by means of the double-effect produced by pull (or stabilising)
cables with counteropposing curvature.
(iii) Increase in drag resistance through the adoption of multiple decks and
the effect of second-order rigidity produced by a spatial system of load-bearing
and pull cables.
(iv) Increase in resistance to lift forces due to the double-effect in (iii).
The aim of returning to the Musmeci project was to prove that it is possible
to construct a large span suspension bridge through the introduction of certain
structural innovations and rather than by simply attempting to reduce the
effects of actions to a minimum. Using the Musmeci structural layout means,
in effect, giving a bridge design "structural reserves" in the form of pull cable
rigidity, a rigidity which can be regulated. Structural reserves can also be
provided in this layout by means of mechanical (but not aerodynamic) damping
whereby the anchor points of the pull cables are fitted with viscous or hysteretic dampers. Put in other terms, the structure in this case is no longer
unprotected against external actions and we are no longer obliged to predict
actions precisely (something which is in any case not possible). Rather, the
structure is equipped with a rigidity and resistance which constitute the
structural reserves needed to cope with the large increases in scale involved in
this type of construction.
Therefore, following the main advantages can be summarised as follows.
Increase of torsional a n d lateral stiffness
The increment of torsional stiffness leads, for bridges of about 3000 m span,
to a reduction of the rotation at the mid span to 80% of that computed for
a classical suspension system (see Tables 1, 2).
326
C. Borri et al./Double-effect large span suspension bridge under w i n d loading
Table 1
Input data of the example
Central span of the bridge
Main cable's sag
Stabilizing cable's sag
Initial slope of the lower cable
Vertical rigidity
Lateral flexural rigidity
Torsional rigidity
IeMl~=o
3300 m
300 m
80 m
30°
1.40 m 4
276.1 m 4
2.80 m 4
0.007
dCM/d~[~ =o
O.irad + I tad
M e a n wind velocity at the deck of the bridge
Af(main)
Af (stabilizing)
5.6 m 2
0.8 m 2
60 m/s
Table 2
Results
dCM/d~[~=o
A~a} (%)
Ad b~ (%)
0.1
0.5
1
20.36
25.28
36.21
27.37
a~Aa=(Re-Rd)/Rc × 100, in which Rc is the quasi static rotation at mid span (classical layout), and
Rd is the quasi static rotation at mid span (double effect layout).
b)Ad = (Dr - Dd)/D¢ × 100, in which D¢ is the quasi static displacement at mid span (classical layout),
and Rd is the quasi static displacement at mid span (double effect layout).
This amount becomes significantly higher if one considers the variation of
CM ( a e r o d y n a m i c m o m e n t coefficient). T a b l e 2 s h o w s t h e p e r c e n t i l e d i f f e r e n c e
f o r s o m e v a l u e s o f t h e i n i t i a l CM d e r i v a t i v e .
The stiffness increase has also an advantageous influence on the dynamic
behaviour. In fact, the higher eigenfrequency interacts with lower spectral
intensity of the wind turbulence. This will lead to a reduced dynamic response.
N u m e r i c a l t e s t s o n a 3D m o d e l a r e o n g o i n g , w h o s e r e s u l t s c o n f i r m s u b s t a n t i a l l y t h i s effect.
Improvement
of structural
resources
The double effect suspension system allows to attribute an additional design
p a r a m e t e r f o r c o n t r o l l i n g t h e s t r u c t u r a l b e h a v i o u r . T h i s is g i v e n b y t h e c o n t r o l
o n e c a n a c t i v a t e o n t h e p r e t e n s i o n o f t h e l o w e r c a b l e s . T h i s f o r c e is, p r i m a r i l y ,
an independent parameter, which can be easily changed. On the contrary in
t h e c l a s s i c a l s u s p e n s i o n l a y o u t t h e f o r c e i n t h e c a b l e s is g i v e n b y t h e e q u i l i b r i u m c o n d i t i o n for g i v e n g e o m e t r y a n d l o a d s .
C. Borri et al./Double-effect large span suspension bridge under wind loading
327
One should also stress the f u r t h e r a d v a n t a g e given by dampers, which can
be easily installed at the e x t r e m i t i e s of the lower stabilizing cables, giving
t h e r e f o r e a decisive c o n t r i b u t i o n to the s t r u c t u r a l a n d a e r o d y n a m i c damping.
Removing of the hangers at the extremities of the mid span
As confirmed by the p r e l i m i n a r y design of G i b r a l t a r S t r a i t Bridge by Lin and
Chow, Musmeci's proposal allows to i n c r e a s e the rigidity of the v e r t i c a l
h a n g e r s n e a r the tower, w h i c h would become e x t r e m e l y low in the classical
solution.
The factors listed above a p p e a r t h e r e f o r e to provide the hoped for synthesis
of the two a p p r o a c h e s in suspension bridge c o n s t r u c t i o n . The solution proposed seems to satisfy all the p r i m a r y r e q u i r e m e n t s of large suspension bridges
t h u s r e c o n c i l i n g the two, p r e v i o u s l y opposing, design approaches.
4. Concluding r e m a r k s
R e p r o p o s i n g the c o n c e p t s of the design of S. Musmeci, the a u t h o r s tried to
show an a l t e r n a t i v e way to face the design problems of long span suspension
bridges, t h r o u g h the i n t r o d u c t i o n of a p p r o p r i a t e i m p r o v e m e n t s in the struct u r a l layout. This c o n c e p t is i n n o v a t i v e with respect to the " c l a s s i c a l " s t r a t e g y
of o n l y r e d u c i n g the loads due to the wind.
Double effect suspension bridges can provide some additional s t r u c t u r a l
r e s o u r c e s to the designer consisting in the c o n t r o l of the stabilizing cable's
rigidity as well as in the i n c r e a s e d s t r u c t u r a l damping.
C o m p a r a t i v e a n a l y s e s into a e r o e l a s t i c b e h a v i o u r are still in progress, via
n u m e r i c a l simulations on a 3D model. However, any w o r s e n i n g of the characteristics studied can be ruled out given t h a t the proposal made does not
influence deck a e r o d y n a m i c s .
References
[1] Prec. Int. Symp. on Aerodynamics of large bridges, Copenhagen, Denmark, 19-21
February 1992, A. Larsen (Ed.) (Balkema, Rotterdam, 1992).
[2] IASS-CSCE International Congress, Innovative large span structures: concept, design,
construction, Toronto, Canada, 1992.
[3] N.J. Gimsing, Large bridges of the future, Prec. Int. Symp. on Aerodynamics of Large
Bridges, Copenhagen, Denmark, 19 21 February 1992.
[4] T.Y. Lin and P. Chow, Gibraltar Strait crossing - a challenge to bridge and structural
engineers, Structural Engineering International, Vol. 2 (1991).
[5] T. Miyata et al., Aerodynamics of wind effects on the Akashi Kaikyo bridge, Atti del
Convegno ANIV [N VENTO'92, Capri, Italy.
[6] L. Finzi and A. Castellani, Innovative structural systems for a 2 miles span suspension
bridge, IASS-CSCE Int. Congr., Innovative large span structures: concept, design,
construction, Toronto, Canada, 1992.
[7] H.O. Madsen and P. Ostenfeld-Rosenthal, Wind criteria for long span bridges, Prec. Int.
Symp. on Aerodynamics of Large Bridges, Copenhagen, Denmark, 19-21 February 1992.
328
C. Borri et al./Double-effect large span suspension bridge under wind loading
[8] G. Diana, Falco Indagine analitico sperimentale su un ponte sospeso di grande luce
soggetto all'azione del vento, Atti del Convegno ANIV IN VENTO'90.
[9] R.H. Scanlan, Wind dynamics of long-span bridges, Proc. Int. Symp. on Aerodynamics of
Large Bridges, Copenhagen, Denmark, 19-21 February 1992.
[10] K. Ostenfeld and A. Larsen, Bridge engineering and aerodynamics, Proc. Int. Symp. on
Aerodynamics of Large Bridges, Copenhagen, Denmark, 19-21 February 1992.