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It is therefore essential that the girder of the deck has a sufficient torsional stiffness to transmit any twisting moment from a load with an eccentric resultant, e.
To achieve the required torsional stiffness, the girder will have to be of the box type. The deck girder can simply consist of two I-shaped plate girders directly under the cable planes. And also to give the girder a favourably streamlined shape. An inclined plane, because of being no obstacle for the passing traffic, needs a minimum on pylon height. The most related design items, considering an arrangement of stay-cables, are in the field of: Alternatives on arrangements of stay- cables.
The fan system, also called the radial system, leads to the most efficient structural system. It results in relatively small normal forces in the deck and the longitudinal bending of the pylon remains moderate.
Consequence of cable arrangement on deck normal force. Considering the deck normal force, as shown in figure The construction of the pylon must be finished before starting the construction of the deck. An indication of consequences for design using a kind of cable arrangement is summarised in table 1. Consequences parameters for the main alternative cable arrangements. Because of the positive influences, the semi-harp typology is most commonly used. A typical phenomenon for the harp configuration is the existence of large bending moments in the pylon, which explains the minus sign given in table 1.
Only the tensile force of the longest cable is in fully axial equilibrium. For all other cables, equilibrium os achieved by the combination of axial forces and to a large extend bending moments, see fig. Structural behaviour of a cable stayed bridge with a harp configuration. A practical solution solving the disadvantage on large bending moments is the use of vertical external supports along the side span at the cable — deck connection.
Example of additional support at the side span region. The most relevant aspect in case of an asymmetric cable configuration is the missing of self-weight of the side span needed for the horizontal equilibrium at the top of the pylon.
As a consequence, the backing stay element is heavy loaded which is the reason using a large number of backing stay cables. Normally the most optimal angle of the backing stay cable is 45o.
For the asymmetric bridge sometimes a smaller angle is used which means a reduction of the vertical abutment reaction force. A Dutch example of an asymmetric cable stayed bridge is shown in fig. Asymmetric cable stayed bridge. This system is called self-anchored. This system is called earth-anchored or bi-stayed.
Because of the Dutch soil conditions, mostly the self-anchored system is used. Using a bi-stayed concept results into: The increase of torsional frequency is explained by fig.
For a parallel system a load is carried by one plane of cable only. For the inclined system, both backing stay cables are activated. Therefore, the horizontal displacement of the top of the pylon is for the inclined system much lower than for the parallel system. Influence of cable plane geometry on deck stiffness behaviour.
In cable-stayed bridges, special connections are required to allow the correct transmission of the cable forces to the girder and the pylon. Some examples of the connection cable — deck. Examples of the connection cable — pylon. Examples of fixed connection cable — pylon. An example of a steel-concrete solution is given in fig. The cable material is similar to that used for normal prestressing work and either comprises multi-strand cable made up of cold drawn wires or alternatively as single strand cable mono-strand cable consisting of parallel wires.
Diameters in the range mm are typical. Galvanising each wire can provide protection against corrosion, but a more thorough practice has been to cover the cable in steel or plastic ducting and subsequently inject cement grout after positioning in place. This latter operation is carried out after all dead loads have been applied to avoid too much cracking of the mortar. The cable is normally connected to the pylon with pin-type joints. The cable ends for the pin-type connection have either swaged or filled sockets.
Swaging consists of squeezing a socket onto the wire in a hydraulic press and is generally used with strands having a diameter in the range mm. Filled sockets are more suited to the larger diameter parallel wire type cable with the socket containing the whole bundle of wires. Several alternative types are manufactured differing slightly in the form of dead ending of each wire and the type of filling material. In the simplest form the wires are led through a plate at the base of the socket and finished with a button head or sockets and wedge.
The inside of the socket, conical in shape, is subsequently filled with an alloy of zinc, copper, aluminum or lead, or sometimes with a cold casting compound such as epoxy resin. Thus when the cable is subject to a tension load, wedging action develops, thereby increasing the grip on the wires.
The deck-tocable connection is usually of the 'free' type to accommodate adjustment. A flared arrangement is required for multi-strand cable, while only a single socket is usually needed for mono-strand cable. Initial tensioning of the cable to remove slack is generally carried out with a hydraulic jack similar to that used in prestressed concrete.
The socket is therefore often manufactured with an internal thread for the jack connection and external thread and nut to take up the extension and other adjustments. For the cable erection, the majority of cable-stayed bridges are nowadays designed with monostrand cable, either of the parallel wire or locked coil wire type.
A complete stay is manufactured in its polyethylene tubing and delivered to site on reels. The simplest erecting procedure is to unreel the cable along the deck and hoist or lift it up to the top of the tower. Unfortunately the natural sag tends to be quite large and therefore considerable take-up has to be provided in the tensioning jack. A more satisfactory procedure is to install a guide rope and pull the cable up with a hauling rope.
Intermediate supports to reduce sag are provided by intermittently spaced sliding hangers. Tensioning is initially carried out at the deck connection end to take up the stack, final tensioning to remove bending moment in the deck and transfer dead load into the cable being supplied after all work on the newly erected section is complete i.
Erection of the Erasmus Bridge, Rotterdam. The pylon may be fabricated from steel plate, or precast concrete elements or occasionally in situ concrete. The various configurations shown in fig.
In bridges with a central cable plane, the pylon can be designed as a free standing column or as a lambda-shaped frame.
Various configurations of pylon. Some examples of pylon configuration. H-frame The cross section of the pylon generally forms a rectangular box with a single cell. Due to dominating compression it is necessary to stiffen the side plates primarily with stiffeners, or to create a larger number of cells within.
Steel pylon cross section. This because of the periodic inspection needed on the cable anchorage at the top of the pylon. An example of a cross section of a pylon is shown in fig.
Cross section of the pylon of the Prins Claus bridge, Utrecht. For a bridge with a single span, two alternatives on layout of the bridge can be used, see fig. The first is an asymmetric bridge with one pylon only.
For the second alternative two pylons are used. As a rule, using two pylons is most cost effective. When one pylon is used, for the same span length, approx. Some reasons for that are: During the construction of the pylon, many times temporary equipment is needed supporting the pylon. Temporary support during the construction of the pylon, Eiland bridge, Kampen. This means an increase of deck width which largely affect the building costs.
The first example a given in fig. The second example b shows a rigid connection between the foundation and the pylon. Examples of a single tower. To avoid the large foundation needed in case of a A-frame, see fig. This type of structure is mostly used when a large distance exist between the deck level and the top of the foundation.
Example of a diamond pylon configuration. For a cable stayed bridge without a backing stay, the bending moments in the pylon constructed as a single structural element will be very large.
Some typical pylon configurations used frequently when a backing stay is missing are shown in fig. Shape of a pylon in case of missing a backing stay.
Combination of esthetics and structural requirements when a backing stay is left. A complete other type of cable stayed bridge is shown in fig. Some main advantageous using such a system are: Both have a large influence on the aerodynamic behaviour of the bridge reduction on normal force in the deck reduction on pylon height and total cable length.
Example of spatial pylon configuration. For timber bridges a distance between 10 — 15can be used. When considering the optimization on cable weight only, it is found that: It is necessary that under all possible loading conditions the anchoring cable is in tension.
Neglecting the bending stiffness of the main deck girder, the following relation can be found, see fig. Relation between span length and anchor cable tension. As shown in figure 40, the side-span la will always be less than half the main span length lm. These examples show that the type of variable loading strongly influences the main geometry of the bridge.
The lines given in fig. Limitation on span length: This because of the following criteria: Especially the geometry of the cross section is an important parameter for the flutter phenomena. This is illustrated by fig. Shape factors for analysing sensitivity to flutter. The main criteria affecting the maximum span of a cable-stayed bridge are cost, stability, strength and construction feasibility. However, for the last 10 years, finalised projects showed e. As an indication, the cable cost premium for self-weight is approx.
Considering the capital cost divided by the roadway deck area, the bridge deck and towers will not contribute to much unit cost increase with span because their costs increase is almost direct proportion to span. Only the cable unit cost increase linearly with span because the length of cable necessary to support an average deck unit increases in length.
The unit costs P. The cost variations due to factors as type of superstructure, complexity and foundations conditions are much larger than unit cost variations due to span length.
Stability criteria Tower buckling In general, tower buckling along the bridge is inhibited by the cable arrangement and therefore, transverse buckling is occurs first. When using splayed cables connected at the outer edge of the superstructure, some transverse restraint to the tower is guaranteed. By using splayed cables, like the Stonecutters Bridge, the transverse tower buckling load is approx. Deck buckling Based on a parameter study of the composite cable stayed Stonecutters bridge it is found that elastic buckling is not a criterion which governs the span of composite cable stayed bridges and closely spaced piers in the side-span are not necessary to inhibit such buckling.
Aerodynamic stability criteria This criteria is most critical and the most governing form of aerodynamic instability is torsional divergence, where the torsional amplitude of oscillation in the wind stream increases rapidly in amplitude with small increase in wind speed at the critical wind velocity Vcrit.
The critical velocity is a function of the lowest torsional frequency of the bridge deck fT and the overal bridge width b. This figure can be ued to derive approx. Torsional natural frequency versus span. For large span, such as Stonecutters Bridge at m, it is necessary to split carriageways with an air gap between.
This air gap effectively increases dimension b and also improves the characteristic aerodynamic stability of the section, see fig. Typical cross section to avoid aerodynamic instability. Strength criteria Strength of cable stays For a given stay spacing, the cable strength demand is the mainspan is a function of the bridge width, not span. Even for a composite concept, the cable stays are within currently available sizes.
Lateral bending and axial load in the main girder Lateral bending caused by static wind loading becomes a critical load case and increases in proportion to the span to a power greater than 2, due to the additional drag from cables.
This because, the critical location bending moment in the girder at the tower is the same as for the maximum axial load. For the composite deck, long term distribution of axial load due to creep must be considered in reviewing the worst effect in both concrete and steel components. As is the case for aerodynamic stability, a structural system with divided carriageways has advantages in lateral bending, provided the full effective girder width is achieved by transverse framing.
Construction criteria The characteristic aerodynamic behaviour and stability of a cable-stayed bridge during construction is quite different from that of the complete bridge. If the bridge is constructed by the balanced cantilever method, as is common, the pylon base becomes subject to very large buffeting forces originating from responses, at a time when the tower is lacking the buckling restraint it receives form the cables in the completed bridge.
There are two possible modifying factors which van reduce the impact of the construction loading. The first is the statistics of occurrence of extreme winds, which permit a much lower design windspeeds for the period during construction. The second is the use of temporary TMD tuned mass damper , to reduce the dynamic component of wind buffeting response during construction. Consequences of stiffness properties on member forces.
Therefore, as a start of the design, the horizontal displacement of the pylon top can be analysed according to: Example on pylon top support condition. The translated stiffness located at the top of the pylon, because of permanent tensile forces in the anchor cable, is equal to: Relation between support stiffness and buckling length.
The n-value is analyzed according to: In general, the n-value information about the consequences of geometrical non-linearity is an indication of properly chosen dimensions. The following guidance can be used: The most common form is the box section, which offers good torsional restraint.
Plate girders are sometimes used with a double plane system of hangers, where erection procedures require assembly in small light elements. Trusses are also an option, but the high fabrication cost, expensive maintenance to counteract corrosion and poor aerodynamic characteristics now render this method relatively uneconomic in case of one layer highway bridge.
While in early cable-stayed bridges the deck and towers were of steel, today towers are normally of concrete. The decks of highway bridges up to meters span and of railway bridges up to meters span can also advantageously be built in concrete. Span length increase of cable-stayed bridges in the last fifty years. Currently a steel deck is chosen where lightweight is important due to poor soil conditions, where an unusually long span is required or because of the erection method.
Steel box sections are ideally suited to modern fabrication methods. In particular automatic numerically controlled cutting, drilling, milling and welding machines are a positive encouragement towards manufacturing as much of the deck as possible under workshop conditions and bringing finished units to the site.
Furthermore, recent advances in welding technology such as submerged arc, C02, etc. The time required to erect and weld deck units into place depends upon the amount, type of weld, plate thickness, etc.
While moments are mainly taken by the steel structure, the reinforced concrete slab largely absorbs normal forces. In order to reduce the influence of shrinkage and creep, slabs can be prefabricated. Competitive designs 26 Cablestayed bridges with concrete decks are especially suitable for railway bridges. Due to their large self-weight, dynamic and fatigue considerations are less important than for bridges with steel decks. Some examples of composite bridge decks of cable-stayed bridges.
Influence of supports and expansion joints The design of a deck a much related to the position of expansion joints and support conditions. Three examples of support and expansion joint conditions. For system A, the so-called bi-concept is used with expansion joints at the pylon position. For this situation, the deck is loaded by a tensile normal force. The end support should resist a large horizontal component.
For system B, the so-called self-anchored system is used with a continuous main girder. The deck is loaded by a compression normal force. For system C, also a bi-concept is used in combination with a continuous main girder. The deck is loaded by both tensile and compression.
Results on the distribution of the normal force in the deck are summarized in fig. Distribution of the normal force in the deck. For both system A and C a heavy abutment is needed. Cable-stayed bridges are generally built as self-anchored systems where the supporting conditions are chosen so that vertical load from the self-weight and the traffic introduces vertical reactions only.
As shown in table 9, there are, however, many variations to this basic system and in some systems, horizontal reactions of moderate size might occur due to compatibility phenomena. Alternatives on supporting conditions for the girder A Some of the consequences using a certain type of support condition are in the field of: Pylon fully clamped, deck separated vertically from pylon C B.
Pylon fully clamped, deck horizontally supported C. Pylon fully clamped, deck connected to the pylon D. Pylon fully clamped, deck fixed at abutment E. Pylon fully clamped, deck horizontally free F. Pylon pinned ended, deck to pylon connected G. Pylon pinned ended, deck horizontally supported at abutment D E H. Pylon pinned ended, The interaction between the stiffening girder, the cable system and the pylons in the transmission of vertical and horizontal loads is decisively influenced by the choice of the supporting conditions of the girder.
The lateral support of the stiffening girder at the pylons can be accomplished by applying vertical sliding bearings between the girder and the inner faces of the pylon legs. In bridges where the cable system does not render an efficient torsional support of the girder, as in cablestayed bridges with only one central cable plane, it might furthermore be required to give the girder a torsional support at the pylons.
Some alternatives on supporting conditions for the deck girder. Detail deck-abutment Vertical bending stiffness The main function of the deck system is, see also fig. Distribution of a concentrated load by bending stiffness of the deck. The bending stiffness of the deck largely influences the size of bending moments. As a comparison, fig. For the same loading, pylon stiffness and cable configurations, an increase of bending stiffness results into an increase of bending moment.
The bending moment in the pylon and cable force is hardly influenced by the deck stiffness. Bending moment in the deck as a function of the deck inertia bending moment. By changing the bending stiffness of the pylon, also the bending moments in the deck will change. An example is given in fig. An increase of the pylon stiffness results into an increase of the bending moment for the pylon and into a decrease of the bending moment for the deck. Bending moment in the deck as a function of the pylon inertia bending moment.
Horizontal bending stiffness Caused by static wind loading on the deck and on half of the length of the cables, the deck is uniform distributed loaded in transverse direction. Normally, the best solution is obtained using a continuous girder which is supported in tranverse direction at both the pylon and abutment positions. The meaning of a certain support condition on the size of bending moment is illustrated by fig.
System a is having a hinge at the pylon position. System b is having a hinge in the middle of the main span. System c is a continuous main girder. Bending moment in transverse direction caused by wind loading. Hybrid deck As an example, the self-weight of the side span is increased using concrete, which in case of traffic loading contributes to a more stable cable system.
Cable-stayed bridge using a hybrid deck. Buckling length of the deck girder In case of a radial cable-stayed bridge, the supporting spring stiffness for a certain position of the deck system can be analysed according to: Increasing the area of the cable and increasing the area of the backing stay cable results into an increase of the spring stiffness.
The cable force is analyzed by assuming the load and half of the length of the adjacent deck structure. Caused by the horizontal component, the normal force in the deck increases into the direction of the pylon stepwise. Development of the normal force in the deck caused by self-weight.
The normal force in the pylon is equal to the summation of the vertical component of all cable forces supporting the deck plus the vertical component of the cable force of the anchor cable.
For analyzing the vertical spring value, neglecting the axial displacement of the anchor cable and pylon, the following equations can be used. The member properties of the main girder area and inertia bending moment should be analyzed taken into account the theory on effective width. Schematization of the bridge deck by continuous girder supported by spring elements.
When the girder as shown in fig. The results on bending moment and vertical displacement show clearly the existence of a situation far from optimal. An optimization is achieved by prestressing the cables, each on their own level. The level of prestressing should be based on the intended situation like zero vertical displacement caused by self-weight of the bridge, which automatically means a nearly optimal line on bending moment as illustrated in fig.
The size of cable prestressing can be solved analytically using the theory of Troitsky. This theory will be explained considering the cable stayed bridge shown in fig. Optimal bending moments and displacement caused by self weight for the main girder of the deck achieved by prestressing of the cables Mr is defined as the maximum value for bending moment in the deck at position r.
This maximum will be reduced by a factor C0 , which varies between 0 and 1. The basic equation for the cable stayed bridge is: The backing stay cable is having the index: However, when the additional condition of equal normal stress for all cables is included, the equation can be solved and the prestress X0 - X19 can be analysed.
Equal cable stresses means: Also, several alternatives for the anchored systems exist, such as the earth-anchored system, the so-called bistayed concept. For a long-span cable stayed bridge with a centre span of m, the influences of main bridge characteristics and especially alternative arrangements of stay cables on several design aspects are discussed.
Attention has been paid to the differences in results on reaction forces, load distribution, stiffness behaviour, vibration frequencies and geometrical non-linear behaviour. For efficient design, the results obtained clearly show the importance of optimization. Reference design  The following information given is based on a large span symmetrical reference steel structure cables, pylon, deck having geometrical properties more or less identical to the Tatara Bridge and Pont de Normandy.
Besides self-weight, as explained by fig. Main span traffic loading. The support conditions are: An example of the bridge model used is given in fig.
By using cable elements, the specific characteristics on axial stiffness like sag, prestress, etc. Because of the chosen geometry large span cable-stayed bridge special attention is paid to limitations of the design related to the deck normal force, secondary effects caused by geometrical non-linearity second order analyses and frequency behavior bending as well as torsion.
For the reference design, the main consequences on support reactions and member forces are summarized in table 2.
First order analyses Max. Comparison of member forces and support reactions considering alternative approaches on the analyses. Table 2 shows the importance of second order analysis. This is especially the case for the bending moment of the side span. Influence of principal characteristics on the design By comparison with the results obtained from the reference design, the influence of five alternatives A-E is investigated: Deck normal force Deck normal force at end pier location Bending moment side-span Bending moment mid-span Tensile force anchor cable Tensile force longest cable Vertical support reaction at end pier Vertical support reaction at pylon In-plane bending moment pylon Vertical displacement deck Secondary effects: Influence of alternatives A-E on the most important design aspects.
Influence of alternatives A-E on the geometrical non-linearity expressed by n-value. For the combination of normal force and increasing vertical displacement caused by geometrical nonlinearity, the most critical cross section is found to be the middle side-span. Natural frequencies The most significant observations for the deck frequencies are summarized in table 5.
Influence of alternatives A-E on the deck first natural frequencies. Schematic view of inclined cable 38m Influence of cable arrangement on the design In an identical way as described for the influences of principal characteristics on the design, the consequences of the following three alternatives cable arrangement are given.
Bi-stayed cable bridge As shown for the Bi-stayed concept, a cable system exists with earth anchoring of the anchor cable. With a longitudinal fixing at one end of the deck girder the cable system becomes stable of the first order. Concept of Bi-stayed cable bridge. The central part of m of the main span is carried by a suspension system, whereas stays radiating from the pylon top carry the outer parts.
Concept of Dischinger cable stayed bridge. A system of earth anchoring of the anchor cable and the central part of the main span supported by hangers. The results of comparison or the three cable arrangements with the reference design incl.
Influence of alternatives on cable arrangements on the most important design aspects. Development of normal force for the deck considering alternative cable arrangements. Influence of alternative cable arrangements on the geometrical non-linearity expressed by n-value. Development on vertical displacement considering alternative cable arrangements. Influence of alternative cable arrangements on the deck first natural frequencies.
The layout of the cable arrangement is found to be a fundamental item in the design of a cable-stayed bridge. Especially the Bi-stayed concept results in a significant improvement of the structural behaviour member forces, global stiffness and second order effects. The main span girder with outriggers at the work site area. Girder cross section in the cable-stayed spans. Strict requirements regarding stiffness imposed by the passage of both freight trains and high speed passenger trains proved to have a strong influence on the design.
The demand for a high degree of rigidity led to a harp shaped cable system with relatively steep cables and intermediate support in the side spans. Partly erected main span on temporary piers. The bridge girder is arranged as a steel truss with an upper transversely post-tensioned concrete roadway deck and a lower deck for the railway, designed as a closed steel box.
The cables are anchored to the girder on outriggers with the same inclination as for the flat diagonals. The lower steel deck has proved to be a robust structure, with a satisfactory post-accident performance when the structure is being subjected to train derailment.
Diagonals, chords and the railway deck are in steel grade S EN except for the secondary structures inside the deck which are designed in S EN The interior of the steel struss is protected from corrosion by dehumidification.
In addition, the cables are prepared for later erection of tie-down ropes if excessive vibration should occur. As shown in fig. The horizontal component of the cable force is transferred directly through the steel between two opposite cables and the vertical component is transferred to the concrete via shear studs.
The requirements from the railway authorities stated limitations on: Al these requirements were related to comfort criteria for passenger trains.
For vertical accelerations with duration less than 0. The acceleration of the train is frequency weighted according to ISO , which applies to simulate the human perception of vertical vibrations, e. Acceleration limits as function of duration. Beside these requirements on comfort criteria, analyses related to the train loads were carried in dynamic actions, fatigue analyses and cable-stay replacement. Some results obtained regarding dynamic load factors for various load effects are shown in fig.
UIC train type 1: The dynamic load factor used on local effects on the railway deck varies in the range of 1. Fatigue analyses Most relevant bridge elements for checking the fatigue capacity are the welded joint of the truss girder, cable stays, concrete roadway deck with shear stud connection to the steel truss and the orthotropic steel deck for support the two railway tracks.
Three passenger trains, three freight trains and two heavy rail trains, each of them provided with following information: Based on this information it was possible to find the number of trains crossings during the year life time and the number of train crossings with simultaneously loading of both tracks.
Substructure For the pylons as well as piers, the dominating load is ship impact. The caisson for the pylon is designed to withstand a ship collision force of MN in the longitudinal and MN in the transversal direction. Pylon elevation, caisson and FE-model on plastic zone development. The side span and anchor piers are all founded on open cellular caisson structures Fig.
Pier elevations and onshore prefabrication of caissons. Cable system  As shown in fig. Each stay is composed of two parallel cables with a mm c. The steel strands of the stay cables are covered with a polyethylene high-density PEHD tube, mm in diameter. Fundamental natural frequencies of the stay cables will range from 0. The combination of cable angle, low natural frequencies and high probability of occurrence of light rain with moderate winds at the bridge site 43 Cable cross section and view of the cable system during construction.
For the experimental investigation in the laboratory, the PEHD tubes were lightly sanded with a fine grade sandpaper to simulate natural erosion and dust particles. Subsequently, the cable surface was treated with a coat of polyvinyl alcohol simulating a rise in surface energy of the cable equivalent to oxidation. Various analyses and experiments were conducted focusing on the characteristics of the long-span structure and the aerodynamic stability of the entire bridge.
Towers The steel towers are m high and shaped like an inverted Y after examining the wind resistance, the structural efficiency and aesthetics. A full aero-elastic model of an inverted Y-type tower was tested in the wind tunnel to optimize the shape of the column and its rectangular section with notched corners to reduce vortex shedding.
Cables The stay-cables have two-plane multi-fan shape. A total of cables were made of semi-parallel wire strands consisting of a galvanized wires 7 mm in diameter, covered with polyethylene tube in shops.
The ends of the strands are fixed by sockets that are resistant enough to fatigue due to bending vibration as well as that of axial force. Girders The steel girders have the cross-section of a streamlined box with two fairings in both ends. They are elastically supported on elastomer bearings at the towers for vertical movement and fixed bearings for restraining lateral movement. Since the side spans are short in proportion to the center span, PC girders at 45 Innovative technical features 1 Buckling tests for the girders with large compressions The analysis shows that the ultimate loading capacity of longspan cable-stayed bridges is determined by buckling of girders, since the extremely large compressions are applied to towers and girders.
The test result shows that the maximum gust response displacement at mid-span was within design tolerance. This provides sufficient dumping instead of the ties between cables. A typhoon came along while the center span was at its furthest extension with the installation of the remaining final segment.
After the bridge had been structurally completed, the vertical and horizontal vibrations were measured by means of heavy-duty exciters, so as to confirm the accuracy of the vibration characteristics applied in the design. At m in length, the bridge is one of the longest cable-stayed structures in the world and is one of only a few multi-span cable-stayed bridges in existence.
Ting Kau cable-stayed bridge completed and general arrangement. Considering a multi-span cable-stayed bridge, the system on equilibrium, structural behaviour, is very different compared to a classical three-span cable-stayed bridge. The adjacent pylons deflect towards the loaded span and the adjacent spans move upwards without any other restrains than their own rigidity.
A series of more or less acceptable solutions for multiple cable-stayed spans is shown in fig.