The Journey Of Cable Bridges
Prof. Prem Krishna
Based on the growth in analytics,
computing, material strength and quality, construction technology, facilities for experimental work, small spans made
from non-metallic natural materials have given way to the magnificent and imposing bridges
of great aesthetic appeal
One very great contribution to the development of Civil and Structural engineering generally has come from the exponential growth of electronics in the last 100 years, leading to computing capabilities, which are hard to believe, besides instrumentation for experimentation on both models as well as prototypes of structures, automation and robotics. Another big factor is the continuing improvement in materials of construction. Bridge development has been a beneficiary likewise. Above all however, the story of bridge engineering, with cables or otherwise, is an epitaph to the great qualities of human endeavour and ingenuity.
This paper is an effort to give the reader a commentary of some of the above developments with time, and, look at the prospects for cable bridges, in the Indian as well as the global context. The text brings out reviews of ‘Design related to analytical approaches’, ‘Aerodynamics a crucial issue’, ‘Developments in Materials and Technology’, with the example of Akashi Kaikyo bridge, the most outstanding of the day.
Tension structures are essentially utilised in longer span applications, often in span ranges where other systems would not compete easily. This can be explained by the fact that a cable element is inherently efficient in as far as material usage is concerned. Figure 7 gives a straightforward explanation. Not only is the cable cross-section uniformly stressed, the variation of this stress along the cable length is small. Thus, the entire material can be stressed almost to capacity. Thus, the efficiency of a cable and use of high tensile strength steel (steels with strengths of 1,800 N/mm2 are now available), results in smaller dead weights – a major load in the design for longer span structures. It may be pertinent to mention here that in a culvert, live/dead load stresses may be of the order of 4 to 6, whereas, in a suspension bridge cable of long span, this value may be 1/10 to 1/15.
During the years (1850s onwards) that the first cable bridges were designed and built, both the tools for computing as well as the analytical methods were greatly limiting. The designs were thus more intuitive than based on any kind of complex analysis. However, the Niagara Falls suspension bridge (1855) and the Brooklyn Bridge (1883) by J.A. Roebling, would indicate the understanding of the designer about the inherent flexibility and the possibilities of aerodynamic vulnerability of a suspended system. In hindsight one could say that the bridges, more so the Niagara falls than the Brooklyn, went overboard in providing stiffness in the girders, while additionally using cable stays. With only the linear Elastic Theory by Rankine being available those days, the design and construction of these bridges must be considered as an act of courage. During the period beginning 1880, the ‘Deflection’ theory was developed with the efforts of Levy and Melan. The use of this theory afforded much relief in the bending moments in the girder, and, allowed the use of shallower girders. However, as an intuitive measure to ensure adequate stiffness there existed minimum threshold limits on width and depth. Better understanding of the suspension bridge system and developments in analytical methods, enabled bolder designswith greater slenderness. The Tacoma Narrows suspension bridge completed in 1940 had plate girders 1/350 of span (compared with 1/40 of Brooklyn Bridge), and, a width of 1/72 of span (which was almost two/thirds of the value for the Golden Gate bridge, which tended to undergo large aerodynamic oscillations, and, had to be strengthened). The design was very much a result of the benefits of using the Deflection theory. The open deck of the Tacoma narrows bridge was thus left with a limited torsional stiffness, and one that attracted large wind forces through the plate girders. While it was still adequate to cater to the effects of vertical loading, the design had not catered to the effects of wind oscillations, and, resulted in the most dramatic failures in bridging history, within 4 months of its completion, due to wind flutter, see figure 8. This sent the bridge engineers scurrying to their desks to understand more fully the intricacies of bridge aerodynamics. Following extensive research on the subject the confidence of bridge engineering community for building long span bridges was restored by the 1950s. It was nevertheless fully realised that wind induced dynamic effects were to remain a prime consideration in the design of cable bridges. The next section of the paper presents this aspect in some detail.
Aerodynamics - A Crucial Issue
Both static and dynamic effects of wind are important for cable bridges. There are several cases of small cable bridges having suffered damage or failure due to wind. The most catastrophic being the failure of the Tacoma Narrows Bridge already mentioned. The Forth road suspension bridge suffered high amplitude oscillations of its towers while still under construction. It is noteworthy that besides the geometry and mass characteristics of a bridge, the site peculiarities can often manifest themselves into a dramatic influence on the aerodynamic effect on such bridges (Fig. 9).
The static response of the bridge can be best seen in terms of the force coefficients CD, CL and CM, representing drag, lift and pitching moment respectively, which are dependent upon the shape of the deck as well as the angle of incidence of wind (measured in the vertical plane). The dynamic behaviour of the bridge under the action of wind loads is dependent upon the flow; particularly in terms of the turbulence characteristics, and the structural as well as aerodynamic characteristics - the mass, stiffness, frequency, geometrical shape and damping. These characteristics are often related to the bridge form and span, the various forms of aerodynamic response can be described as - buffeting, vortex induced oscillations, and, self-excited oscillations such as in vertical bending, torsional bending, galloping in towers, or, flutter. There is a close link between bridge aerodynamics and the Cable Bridge form. It is best, therefore, to proceed by studying the problem in terms of the three major components in a cable bridge superstructure - the deck, towers and cables.
The Deck: The deck is the most important component of a bridge from the standpoint of the aerodynamic behaviour of a cable bridge, and, is therefore the one most investigated. Initially cable bridges used stiffening girders of trusses along with a concrete or a steel deck. Collapse of the Tacoma Narrows suspension bridge led to the idea of using box girder decks to meet the requirements of adequate flexural as well as torsional stiffness, as well as to minimise wind loading. The shape of the deck cross section can have a profound effect on the wind effects. As seen from Fig. 10, the trusses attract a large drag compared to streamlined boxes.
One of the major design concerns in this respect has been to choose a deck and stiffening system to raise the critical wind speed for the initiation of flutter above the design wind speed, while introducing adequate stiffness. From that point of view, the comparison of the flat plate to a box, a truss, and, a split - box has shown that the critical wind speed for the initiation of flutter for a flat plate is the maximum. The split-box (Fig. 11) is better than a single box, which is better than a truss. It is also possible to use fairings on the edges of the deck along parts of its length, in order to reduce its oscillatory motion. It is being investigated too whether the use of passive controls such as the use of control surfaces or ‘wings’, or, pendulums can be of advantage in suppressing deck oscillations.
Towers: For long bridges, towers may rise to 200 m plus above the foundation level. This is almost as high as the Eiffel tower. These towers therefore have similar problems of dynamic response to wind as tall buildings or other tall structures. The aerodynamic behaviour of these towers is significant for their own safety as also because it influences the behaviour of the bridge as a whole. Even more important is to ensure the aerodynamic stability of bridge towers during the erection stage before the cables are erected. The tower legs experience both along-winds as well as across-wind oscillations for which the design must cater. One such measure, whereby the corners of the tower are modified, and, its advantageous effect on the across-wind tower oscillation is seen in figure 12 (a) and (b).
Developments in Materials and Technology
The various aspects of major concern in this section, which are specifically associated with the construction of cable bridges are, high strength steel cables, availability of testing facilities to prove the design, fabrication of large quantities of steel or placement of large volumes of concrete, lifting and erection of large precast or prefabricated components, strict geometrical control during erection, and, so on.
Strands assembled from thin wires provide for a structural element unique to cable bridges. The wires could be 3 mm or 5 mm diameter ones made from high strength steel several times stronger than structural steel. The various configurations of ropes or strands are shown in Fig. 16. Ropes are made up from strands twisted in the desired configuration. Parallel wire strands, being superior in their mechanical properties, are the most commonly employed. Suspension bridge cables used to be made by ‘spinning’ thin wires, and this consumed much time. Instead, now this can be achieved by assembling strands of small diameters. The big advantage of employing parallel wire strands, or, parallel strands is in making the stays in cable stayed bridges. Not only do these give a value of elastic modulus almost as high as that of the wire, it is possible to vary the overall cross-sectional dimension of the stay as required. Another important development in respect of cables has been in the protection measures for these. Whereas one started with Zinc coatings alone, it is now possible to provide multi-level protection against even the most aggressive environments.
In the author’s opinion, the Akashi Kaikyo suspension bridge in Japan, at present the longest span in the world (may be overtaken some day when the Messina Sraits Bridge, 3,300 m main span gets built) is one of the best examples of how a large project can push the frontiers of a field of engineering (in this case of Civil). It is with the intension of a demonstration that certain features related to this bridge are brought out below:
The bridge was conceived almost 10 years before its opening to the traffic. It has spans of 960 m, 1,991 m, and, 960 m. The towers rise 216.2 m above the deck. The bridge is designed for 6 lanes of traffic. Higher strength steel was developed (1,800 N/mm2) for the cable wires which a diameter of 1,100 mm. 3, 00,000 km length of wire was used in the cables. The accuracy achieved in obtaining the cable profile was 1/20,000 (approximately 10 mm in a 200 m sag). The substructure used 9, 67,000 m3 of concrete, and, the capacity for pouring concrete was 180 m3/hr. The quantity of structural steel used, mostly in the superstructure, was 224,000 tonnes.
The foundation caissons were 80m in diameter. These were fabricated and towed into position by boats, see figure 17. A wind tunnel was specially designed, fabricated, and, instrumented with the most sophisticated equipment, to test a 1/100 scale model of the full bridge. The tunnel was 41.5 m wide, 4 m high, and the largest such tunnel in the world. Figure 18 shows the model being tested.
Each one of the aspects of construction and technology brought out above are setting up new bench marks.
The paper has attempted to trace the path of development of cable bridges from the primitive times. It is seen how, based on the growth in analytics, computing, material strength and quality, construction technology, facilities for experimental work, small spans made from non-metallic natural materials have given way to the magnificent and imposing bridges of great aesthetic appeal. It is also seen that the development of the ‘Deflection’ theory for suspension bridges, so useful in designing the system more economically and to truly bring out its essence, led designers to go one too far in making these bridges slenderer than what nature could tolerate, and, led to the embarrassing Tacoma Narrows disaster. This nevertheless led to the required breakthroughs in bridge aerodynamics, and, perhaps also a fuller utilisation of the cable stayed bridge system, which is much more stable aerodynamically.
India too is adopting the use of cable bridges more frequently, as its engineering prowess grows.
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