Summary

From since 2006 we have enterprises an intensive studies of about an innovative solution for a design of a very long suspension bridge. The proposal consist in a suspended bridge that connects the 15Km of the Gibraltar Straits with a “ultra-long” central span of 10Km, based on a new type of suspended structure combined with the use of CFRP technologies.

The aim of this paper is to present the latest result of this research that has brought in this last years, to the complete computer analysis of the entire structure and confirm the structural scheme that we have thought in origin.


1.Introduction

For more than twenty years, the governments of Spain and Morocco have been studying different solutions for crossing the Gibraltar Strait, that divide the African and the European continents.

Here we present a structural scheme that represents a new type of bridge system that was thinking at first as a proposal for the Gibraltar Strait crossing with a central free span of 10Km but can be used even for smallest spans. Our solution, that held his basis on the researches of Le Ricolais and Sergio Musmeci, is an one sheet hyperboloid-like three-dimensional tensile structure: that means a 3D net with the ropes interlaced to each other to form a wicker basket containing inside a series of sub-bridges that brought the deck of the bridge.


2.The design project proposal

In 1991 professors T.Y.Lin and Chow, theoretically demonstrated the feasibility of the plan, even if only at the preliminary stage, proposing a solution consisting in a suspended bridge with two central 5000mt long spans and two 2500mt long lateral ones, in order to cover the 15Km jump of the Strait. 

Lin and Chow proposed a bridge with three towers with the foundations of the central tower resting at a approximately 400mt under the sea level.

In spite of the great effort needing to cover the distance between the two continental borders, all projects that have been presented until now, do not show a real new system for suspension: we have always seen solutions that integrate, in a hybrid so-called system, the cable stayed with the suspended bridge.

We want instead to propose a new innovative static system: a tension-structural system that not only allows to stabilize the bridge against the wind effects but that also does not need the central tower (that would involve complex foundations designs resting on not safe soil layers) and cover the straits with a single span of 10Km.

This structural scheme represents a new type of structural bridge system that can be used even for smaller spans, but at least more than 4-5Km.



2.1The bridge design idea

In 1965, for the Messina Strait crossing, architect Sergio Musmeci already proposed a “double effect” tensioning system, which for the first time in the design of infrastructures of such importance took into consideration the aero-elastics phenomena.

Musmeci’s plan, that won an international competition, consisted in a suspended bridge with, among other important innovations, an inferior stabilizing rope system that, with his intrinsic torsional damping, was contrasting the action of flutter and increases therefore the critical design speed wind.


Also Christian Menn, in collaboration with Prof. David Billington, proposed a solution for a 5Km suspended bridge with the introduction of two lateral stabilized system ropes. Even in the ‘800 there were some studies about stabilizing bridge systems.

Not in the last, even Le Ricolais has studied a bridge concept based on hyperboloid 3d surfaces and in particular this studied confirm to me the necessity to developed this type of solution.

Developing the concepts proposed by Le Ricolais and Musmeci, my solution for the Gibraltar Strait is a three-dimensional tensile structure with a hyperboloid shape: this consists of a 3D net with the ropes interlaced to each other to form a wicker basket containing inside the deck of the bridge. The employment of the hyperboloid for the bridge makes part of my research in the tension structures during the years 1991-92. In this period I have thought an application of the hypar shape in a early tulle model.




Il modello in tulle

 

2.2Description of the bridge structure

The model that I propose is based on this guidelines:

Considerable increase in torsional and lift rigidity by means of the double-effect produced by the 3D cable net in hyperboloid configuration with anti-clastic opposite curvature. Reduction of bridge weight by use of CFRP cables in combination with a streamlined deck (like the Musmeci scheme for Messina) that allow to reduce the dead load of the bridge.

The principal net rope, beginning from two towers at the extremities of the bridge 1900mt high above the sea level, has been designed with carbon fibre (CFRP) cables of approximately 1.2mt diameter and is developed around an elliptic sections that gradually reduces towards the midspan of the bridge.

The particular interlaced cables conformation formed a “closed system“ extremely stable with respect to the horizontal, vertical and torsional effects of the wind loads. As a consequence of the material and shape designed for, all the ropes that build the bridge structural system have an extremely light weight and, thanks to their form, contribute together to the resistance and stability of the construction.

The use of CFRP materials is ideal for such type of structure, thanks to their high tensile strength (generally in excess of 2000Mpa), small relaxation (typically below 3% of service applied load) and excellent corrosion resistance. In addition to such great properties, the reduced weight of CFRP tendons represents an additional benefit, especially when installed over such long spans.
For the construction of the bridge, it is estimated that about 1.000.000 t of carbon fiber are needed!

The two A-shaped towers are 1900mt high and in top of each of them there are wind turbine generators that make the bridge “energy self-sufficient”.

In a first scheme (2006), inside the hyperboloid shape rope net, hanging from a second order of cables with an approximate diameter of 0.20mt, are carried the three decks that are suspended from the bridge structure.

The decks run inside the cable net and are composed by two 30mt width steel box girders with an orthotropic deck: each deck contains five motorway lines and is conformed like a “thin airfoil” section, in order to oppose minimal resistance to wind blows and is connected to the other decks by cross-sectional box girders set every 50mt in correspondence of the hanging ropes. 

Such connecting structures allow maintenance staff to move from each motorway’s deck and the railway one below, and in addition will carry an inward damping system like those installed on the top of many skyscrapers, with the scope of reducing horizontal movements. 

But this solution involved only some of the external net ropes that were therefore more stressed than the others. And so I have thought of a new scheme based on the frames necessary for the bridge construction.

The new development of the bridge design (2009) consist in a series of internal cable stayed bridge (called sub-bridges), independent one to each other, hanging on the same frames that allow to build the cable nets. 

In fact, the construction of the three-dimensional net is possible by assembling great temporary steel frames that allow “to guide” the ropes that have already been assembled “in situ” with the technique of “areal spinning” to constitute the hyperboloid shape. 

These frames should be at first assembled near the towers and then turned in position (from the two parts symmetrically) with the help of two temporary main ropes; at the same time the frames should be stabilized by two lower ropes.

So, the structural philosophy is: the means of the internal bridges (Fig.8) are made in a traditional and consolidated solution with a relative small span. The innovation is in the external structural net-system that carried the complex.

2.3The use of cfrp cables

As we had already said, the reduced weight of CFRP tendons of about 1.5g/cm3 represents an additional benefit, especially when installed over such long spans that allow benefitting of their excellent performances with a small portion of their strength invested in carrying self weight of the complex cable’s net involved in this particular type of structure. One of the main challenges induced by this design will be in developing appropriate deviators in order to reduce stress concentrations where the cables cross.


One of the main drawbacks of using CFRP cables is indeed in the extra care that must be taken with respect to friction and changes from a perfectly aligned geometry that may induce extra stresses in the cables. Recent research studies on this kind of issues have shown that CFRP cables may be well protected by using a grid of Ultra-High molecular weight (UHMW) piping so the individual tendons could move through this connection, the radius of which would need to be about 1 meter at each point as recent studies on similar technological issues have shown.

 

2.4The computer analysis

In this last year we have started a series of study on simplify FEM computer models to control the distribution of the forces in the net.

The first structural scheme that I analyzed focused on the version of the single 6Km free span bridge that I proposed for the Messina Strait in a site crossing more near to the Messina city. The vertical loads and the horizontal wind actions were applied to the intermediate elliptical beam elements (that support the inner sub-bridges) supposed with adequate stiffness to transmit the action on each rope of the network.

The final computer model consist in tension-only elements for the ropes and in beam elements for towers and frames elements.

A non-linear static analysis was performed at first to determinate the deformation of the bridge under permanent and live loads, under the pretension loads and the moving loads.

The results showing a 11mt vertical deformation  under overall live and permanent loads and a 12m horizontal deformation under the static wind actions.

The tensions in the cables of about 80000tons.

It was also performed an eigenvalue dynamic analysis to assess the modes of vibration of the structure. The first horizontal flessional mode is of about 13sec and the torsional one of about 4.70sec.

A following computer model involved the 10Km version of the bridge, designed for crossing the Gibraltar Strait. The structural pattern is the same as that proposed for the 6Km version but of course it was necessary to increase the diameter of the principal cables to 1.6m.

This model has brought a 46m vertical deformation without pretension and 23m of deformation with 200000KN of cable pretension. The first natural period of vibration is increased to 19sec showing however, also in this case, a very stiffness structure while considering the great span.

During the end of 2010 we have also developed a model of the entire bridge in scale 1:4000 made with epoxy resin and elastic wire.


3.Conclusions

As Joerg Schlaich and Manabu Ito said (in some e-mail that they sent me in answered to my advice requirement): “the idea seems analytically and structurally feasible, but more investigation will be needed for its realization, such as the development of the details of cable-to-cable connection, the method of introducing necessary cable tension during the erection stage and so on”. As Schlaich said: “The concept of a tube with circular or elliptic cross-section is very efficient ... I am sure you are aware that all depends on finding the right way to prestress it, so that under vertical load not only the upper suspension cables work in tensions but also the lower cables in compression, i.e. reduction of tension.”

Manabu Ito also said that “Another problem is the availability of FRP wire material. Of course, it has already applied to small footbridges, but is supply of such large amount of FRP cables possible? Is their durability for more than 100years approved in our structural engineering community?

With the introduction of cfrp cable of course new problems come up: the fabrication (spinning is not possible), the anchorages (how to anchor a bundle of 1.2 m diameter) and the clamping at joints (these cables do not stand large transversal pressure)”.
Following the advice of this two great engineers, I conclude that I hope that this amazing idea (or a similar concept even less longer...) should be now developed in an executive design with the aid of the scientific and technical community and eventually became a reality if there was an occasion with the economic feasibility.


4.References

TADAKI K, “History of the Modern Suspension Bridge – Solving the Dilemma between Economy and Stiffness”, Richard Scott, ASCE PRESS , 2010

BORRI C. et al, “The aerodynamic advantages of a double-effect large span suspension bridge under wind loading”, Space Structures 4, Thomas Telford/U.K, 1998

MAEDA K. et al. “Applicability of CFRP cables to ultra long-span suspension bridges”, Proc. of IABSE Conference in Seoul (2001), IABSE Report, Vol. 84, pp. 224-225.

SCOTT R., “In the wake of Tacoma”, ASCE PRESS, 2001

PETROSKI H. “Design Paradigms: Case History of Error and Judgments in Engineering”, Cambridge University Press, Cambridge, UK, 1994

ITO M. “Wind induced vibration on bridge”, IABSE Report

BRANCALEONI F. et al. “The Messina Strait Bridge – A challenge and a dream”, CRC Press, Taylor & Francis Group, 2010

GIMSING N. “Cable supported bridges”, second edition, Wiley, 1998


I primi schizzi di progetto (1990)



 

Il crollo del Tacoma Narrows Bridge

Questo video è molto istruttivo perchè tratta del crollo del ponte di Tacoma accaduto nel Novembre del 1940 appena qualche mese dopo l’inaugurazione del ponte. Dimostra come la fiducia degli ingegneri nel calcolo e nei mezzi della scienza vada vista sempre in relazione con la forza della natura che talvolta, anzi spesso, può fare brutti scherzi all’ingegno dell’uomo.


Questo crollo esemplare, fortunatamente senza vittime (se non per il povero cagnolino del cineoperatore...) ha posto le basi per i successivi studi sull’aeraodinamica dei ponti sospesi e quindi è servito da scuola e a monito per i tecnici a seguire.



Da vedere assolutamente anche questo video con una interessante intervista a Mario Salvadori che è stato uno dei più brillanti ed influenti strutturisti del secolo scorso, autore di libri stupendi come “Perchè le strutture stanno in piedi”.

http://dailymotion.virgilio.it/video/xaxjh9_the-tacoma-narrows-bridge_tech

THE GIBRALTAR STRAIT CROSSING

A NEW PROPOSAL