CHAPTER 1 INTRODUCTION 1. 1 Introduction A bridge consists of super structure of steel or reinforced concrete member that is supported on one or more points by cables extending from one or more tower is known as cable stayed bridge. The cable-stayed bridge is one of the most modern bridges. It consists of a continuous strong beam (girder) with one or more pillars or towers (pylons) in the middle Cables stretch diagonally between these pylons and the beam, these cables forms intermediate supports for deck and the cables are anchored in the tower rather than at the end.
Most of the cable stayed bridges have been build across the navigable rivers where dimensions of bridge are decided by the navigation requirements. The cable stayed bridge is ideal for spanning the natural barriers of wide rivers, deep valley and for the vehicular and pedestrian bridge crossing the wide highways because there are no pier that will form obstructions. 1. 2 Basic concept The basic concept of cable stayed bridges is to provide intermediate support using inclined cables.
The pre-tension force in cable is design such that the bending moment or deflection at that point is as per design requirements. Closely spaced stay cables reduces the required depth and bending stiffness of girder. This leads to simple cross section and superior dynamic behavior. The multi-cable-stayed system allows main span up to about 200m for concrete and up to 1000m for steel with considerable saving on steel over suspension bridges (Berg, 2003). 01 Figure 1. 1: Force in cable and pylon.
Courtesy: www. intel. com/… /bridge/cablestayed The tower is responsible for absorbing and dealing with compression forces Tension occurs along the cable lines, this works because a moving load is not applied evenly across the bridge, and as it moves one set or the other of the diagonals will find itself in tension (Figure 1. 1). This system is advantageous because it uses single support, A Well-balanced Cables can be fabricated separately and Horizontal loads are contained within the structure.
It is ideal for use when the river banks are fragile for example if the banks are alluvial mud. The cables disperse a load across more area easily. It has Greater inherent rigidity of the triangulated cable-stayed bridges. 1. 3 Structural Advantage of Cable-Stayed Bridge 1) Horizontal compressive forces due the component of cable force are taken by the girder and no massive anchorage is required therefore substructure is economical. 02 2) The orthotropic deck can easily take the amount of axial force developed due to cable with almost no material. ) Excellent aerodynamic stability, by the increase of damping capacity of the system due to large number of stay cables with variable lengths and different natural frequencies. 4) Cable-stayed bridges have a low center of gravity which makes them strong against earthquakes. 5) Ease of replacing the stay cables in case of deterioration, without having to interrupt the traffic on the structure. If any one cable is removed, the distribution of forces in the structure is hardly changed under reduced live load. 1. Comparison with Suspension Bridge A multiple-tower cable-stayed bridge may appear similar to a suspension bridge, but in fact is very different in principle and in the method of construction. In the suspension bridge, a large cable is made up by “spinning” small diameter wires between two towers, and at each end to anchorages into the ground or to a massive structure. These cables form the primary load-bearing structure for the bridge deck. Before the deck is installed, the cables are under tension from only their own weight.
Smaller cables or rods are then suspended from the main cable, and used to support the load of the bridge deck, which is lifted in sections and attached to the suspender cables. As this is done the tension in the cables increases, as it does with the live load of vehicles or persons crossing the bridge. The tension on the cables must be transferred to the earth by the anchorages, which are sometimes difficult to construct due to poor soil conditions. In the cable-stayed bridge, the towers form the primary load-bearing structure.
A cantilever approach is often used for support of the bridge deck near the towers, but areas further from them are supported by cables running directly to the towers. This has the disadvantage, compared to the suspension bridge that the cables pull to the sides as opposed to directly up, requiring the bridge deck to be stronger to resist the resulting horizontal compression loads; but has the advantage of not requiring firm anchorages to resist a horizontal pull of the cables, as in the suspension bridge. All static horizontal 03 orces are balanced so that the supporting tower does not tend to tilt or slide, needing only to resist such forces from the live loads. Key advantages of the cable-stayed bridge compared to suspension bridge are as follows: 1) Much greater stiffness than the suspension bridge, for half span loaded the maximum deflection is 1/4. 6 times of suspension bridge. (Podolny, 1976) 2) Can be constructed by cantilevering out from the tower – the cables act both as temporary and permanent supports to the bridge deck 3) For a symmetrical bridge (i. . spans on either side of the tower are the same), the horizontal forces balance and large ground anchorages are not required 4) A further advantage of the cable-stayed bridge is that any number of towers may be used. This bridge form can be as easily built with a single tower, as with a pair of towers. However, a suspension bridge is usually built only with a pair of towers. 5) The cable stayed bridge needs almost half cable steel as that required for suspension bridges (troitsky, 1988). 04 CHAPTER 2 CLASSIFICATION OF CABLE STAYED BRIDGE
The number of cable stayed bridges has been designed and build throughout the world for different requirements with different girder, tower and cable arrangement. There are no distinct classifications for cable-stayed bridges. However, they can distinguish by 1) 2) 3) 4) plane of cable longitudinal arrangement of the cable tower and, girder 2. 1 Depending On Plane of Cable 2. 1. 1 Single plane system In this system plane of cable lies at the centre of a road divides the road and through the median strip it is anchored below the roadway. (Figure 2. -a) The cables are supported on single tower or pylon at pier support. This system is not only Economical but aesthetically pleasing. A possible disadvantage is that the large concentrated force in cable requires larger connection and larger girder to support cable force. Also to resist the torsion developed due to asymmetrical traffic or wind the greater stiffness of deck is required hence box girder is used. 2. 1. 2 Double Plane Systems In the double plane system, two principal cable systems are used. One is two vertical planes system (Figure 2. -b) and other is oblique or inclined plane system (Figure 2. 1-c). Using the double plane cable system, the anchorages may be located either on the outside of the deck structure or within the limits of the deck roadway. With the cable arrangements outside the deck, an advantage is gained, because no portion of the deck roadway is required for the connection fittings. A disadvantage is the fact that additional 05 reinforcement is required to transmit the eccentric cable loadings of shear and moment into the main girders of the structure.
Figure 2. 1: plane of cable (troitsky, 1988). (a) Single plane system (b) two plane vertical system (c) two plane inclined system 06 The two vertical planes system is aesthetically preferred over the two inclined planes system. In the two inclined plane system the cables run from the edges of the bridge deck to a point above the centerline of the bridge on an A-shaped pylon. 2. 1. 3Three Plane System In three plane system the three vertical planes of cable are provided, one in median strip and other two are at exterior edges.
This system can be used in urban areas, where it may necessary to introduce mass transit center lane or special bus lane or 3 or 4 vehicular lanes in each direction. 2. 2 Depending On Longitudinal Cable Arrangement The cable arrangement in longitudinal direction depends on proportion of clear spans tower height, design and aesthetic requirements. There are four basic cable configurations generally used. These basic systems are as follows, 2. 2. 1 Radiating System The radiating system or a converging system is an arrangement where in all the cables intersect or meet at a common point at the top of the tower (Figure 2. -a). The angle of all cables with respect to the horizontal is maximum which is the optimum position to support gravity load with minimum axial force, therefore amount of steel required is less, but cable supports can become congested at the tower and the load is concentrated at the top of tower produces large shear and moment for entire height of tower, thus increasing its cost also there is a difficulties in anchoring the cables to the tower or a saddle. 2. 2. 2 Harp System In the harp or parallel system the cables are connected to the tower at different heights and placed parallel to each other (Figure 2. -b). The cable connection is distributed throughout the height of tower, results in efficient tower design. Harp system is more attractive as it is aesthetically more pleasant. The amount of steel required for a harp system configuration of the cables is slightly higher than for radial system arrangement. 07 Figure 2. 2: longitudinal cable arrangement (troitsky, 1988). (a) Radiating System, (b) Harp System, (c) Fan System, (d) Star System. 2. 2. 3 Fan System The fan type is a combination of the radiating and harp types (Figure 2. 2-c).
The fan arrangement represents a compromise between the extremes of the harp and radiating system and is useful when it becomes difficult to accommodate all the cables at the top of the tower. 2. 2. 4 Star System In the star arrangement, the cables intersect the pylon at different heights and then converge on each side of the tower to intersect the roadway structure at a common point (Figure 2. 2-d). However it contradicts the principle that the points of attachment of the cables should be distributed as much as possible along the main girder. 2. Depending On Type of Tower Towers of cable stayed bridge can have a wide variety of shapes and forms. The pylons are of many shapes and varieties to accommodate different cable arrangements, bridge site conditions, design requirements, aesthetics and economics. 08 The tower (or pylon) of cable stayed bridge may be a single cantilever (Figure 2. 3-a) for single plane cable arrangement or two cantilever tower for double plane cable arrangements. Portal frame towers, ‘A’ frame towers, diamond and modified diamond towers have also been used. Figure 2. : Types of towers (or pylons) (a) Single tower; (b) Double vertical shafts, H; (c) Double cranked shafts; (d) Inclined shafts, A; (e) Modified inclined shafts, diamond; (f) inverted Y. 2. 3. 1 Single shaft tower: The simplest tower form is a single shaft, usually vertical. Sometimes, the single span tower may be inclined longitudinally (Figure 2. 3-a). Stay cables can be arranged in a single plane to align with the tower or be splayed outward to connect with longitudinal edge beams. This form is usually employed for bridges with two-way traffic, to avoid splitting a one way traffic flow. . 3. 2 Double vertical shaft tower: Two vertical shafts straddling the roadway with or without cross struts above the roadway form a simple tower and are used with two planes 09 of cables (Figure 2. 3-b). The stay cables would incline inward to connect to the girder, introducing a tension component across the support system. 2. 3. 3 Two vertical shaft cranked tower: The two shafts of cable-stayed bridges can be cranked inward to keep the plane of cable vertical to avoid tension in the deck. This shaft is connected with beam forms double cranked shaft system (Figure 2. -c). At the point of connection of beam to shaft and at cranks the heavy concentration of stress occurs. 2. 3. 4 Two vertical shaft inclined tower: The two shafts of cable-stayed bridges can be inclined inward to bring the shafts tops together to form an A-frame or inverted Y frame (Figure 2. 3-d&f). The two planes of stay cables are inclined outward, producing a more desirable compression component across the deck support system. For a very long span requiring tall towers, the A-frame can be extended with a single vertical shaft downward (Figure 2. 3-e). 2. Depending On Type of Girder Three basic types of main girders or truss are presently being used for cable stayed bridges: 2. 4. 1 Steel girder Steel girders may be ‘I’ girder or box girder. ‘I’ girder forms a built-up section using number of cover plates to provide required moment of inertia Box girder: This provides the advantage of simplicity of fabrication in comparison with plate girder. A standard section with only the plate thickness varying can be produced in series, which significantly reduces the fabrication cost. Box girder may be rectangular or trapezoidal in the form i. e. he web plate vertical or inclined. The trapezoidal section is often used in order to keep bottom flange area to desired size, whilst the support to the deck plate from the web is provided at an optimum position. Trusses: Trusses may be used instead of girders for aerodynamic reasons. Also in case of combined Railroad Bridge when double deck structures are used. 2. 4. 2. Reinforced or prestressed concrete girders 010 Reinforced or prestressed concrete girders are economical, posses a high stiffness, relatively small deflection and their damping effect is such that there are relatively small vibrations. 11 CHAPTER 3 COMPONENTS OF CABLE STAYED BRIDGE 3. 1 Cable The basic component of all modern cable stayed bridge is steel wire, which is considerably stronger than ordinary steel wire. In most of the case the steel wire is of cylindrical shape with a diameter between 37mm. It contain high carbon of steel than that of structural steel. The strength of high carbon content cable is 5 times more than that of mild steel and 2times more then high strength structural steel. However this increased carbon content causes reduction in ductility.
The elongation at breaking point is 1/5 of that found in structural steel (Gimsing, 1983). The cable used in cable stayed bridge may be composed of helically wound strand, parallel wire strand and locked coil wire ropes. In helically wound strands the wires are wound helically around a central wire in one or more layer (Figure 3. 1). In parallel wire stand all the wires are laid parallel. The locked coil wire ropes have a central portion composed of a number of round wires which is surrounded by several layers of wedge or keystone shaped wires. 012 Figure 3. : Cable of helically wound strand Courtesy: Gimsing, (1983) 3. 1. 1 Modulus of elasticity of cable The modulus of elasticity ‘E’, of the rope is low for low load and increases as the load is increased in to normal working range. Creep may occur for sustained load. 3 2 The modulus of elasticity ranges from 16. 9 ? 10 N / mm for (12. 7mm-65. 1mm) diameter 3 2 Strand and 16. 2 ? 10 N / mm for (66. 66) and larger nominal diameter strand (Troitsky, 1988). Equivalent modulus of elasticity of cable: The axial stiffness of the free hanging cable not only depends on area and modulus of elasticity but also depends on the sag f.
The cable under an axial load under goes an elastic stretch, ? e = ? / Ee . . . . . . . Equation 3. 1 The equivalent modulus of elasticity of cable is defined as Ei =Axial stress / total strain Total strain is due to stress and due to sag. 013 Ei = ? ? f + ? e = E f Ee E f + Ee . . . . . . Equation 3. 2 Ei = Where, Ef EE . 1 + [(? L ) /(12? 3 )] 2 . . . . . . Equation 3. 3 = modulus of elasticity of cable having sag. Ee = modulus of elasticity of straight cable. ? L = specific weight of the cable. = horizontal length of the cable. = tensile stress in the cable. ?
The allowable working load for steel-wire ropes shall be taken as 42% of their calculated breaking load. The effective safety factor against fracture is 2. 4 and for yielding is 1. 5 (Troitsky, 1988). 3. 1. 2 Optimum Inclination of Cable The height of tower greatly affects the stiffness of bridge system. As the angle inclination of cable increases with stiffening girder, the stresses in the cables decrease, but the height of tower increases. Due to this length of cable increases, causing reduction in axial stiffness which leads to greater axial deformation, also with increase in length of cable amount of metal increases.
In the other hand if the angle of inclination is small, unnecessary large axial force will be developed in the girder and also the vertical component of cable force will be less which is undesired. The optimum angle of inclination with girder is 45 o and it may very in the reasonable limit of 25 ? 65o (Troitsky, 1988). 3. 2 Main Girder The stiffening girder with its integrated bridge deck is a structural element subjected to major part of external load being applied to a cable stayed bridge. The stiffening girder 014 re designed to resist bending, torsion and compression due to gravity load, wind load and the axial force component induced by cable. Due to the support of cable system bending moment reduces significantly in the deck and it also assist the cable system by transmitting the horizontal component of cable force. 3. 2. 1Concrete Girder Reinforced or prestressed concrete deck system posses a high degree of rigidity, a relatively small deflection and their damping effect is such that there are relatively small vibrations.
Generally this system consists of a stiffening girder separated in to two cantilevers which are connected by a middle single-span girder. This system is very convenient for a free cantilevering construction. Multi-span structure could be very economical; usually these spans are equal, so the dead load is compensated. The main advantages are (Troitsky, 1988) 1) The horizontal component of inclined cable forces causes compression combined with bending, which is very favorable as it is in opposite nature of gravity load. 2) The depth of the main girder is very shallow, like that of tied arch bridge with suspended deck. ) The amount of steel used for cable is comparatively less. An optimum solution can be achieved by correct choice of height of tower. 4) The erection of cables, as well as of reinforced concrete deck, is comparatively easy. Besides that, construction with free cantilevering system is very suitable. Due to small amount of steel and ease of erection, this system can be highly recommended with regard to cost. 5) The deflection is small, and therefore this system is applicable for railroad bridges. 015 3. 2. 2 Prestressing effect on girder: The inclined cables connected between tower and girder produces the compression in the deck.
This compression can effectively utilize to reduce the banding tension produced at the bottom of girder. This compression can be utilized as prestress force in reinforced concrete deck. 3. 2. 2. 1 Basic Theory of Prestressing: A prestress force is applied to a concrete member and this induces an axial compression that counteracts all or part of the tensile stresses set up in the member by applied loading. In the field of bridge engineering, the introduction of prestressed concrete has aided the construction of long-span concrete bridges.
These often comprise precast units, lifted into position and then tensioned against the units already in place, the process being continued until the span is complete . The prime function of prestressing is to ensure that only limited tensile stresses occur in the concrete under all conditions within the working range of loads The compression induced in the girder act as the prestressing force, thus giving the following advantages (Chompreda, 2007): 1) The moment resistance capacity is increased as the full section is effective in resisting bending. ) 3) 4) The shear resistance of the section is greatly improved because of compression. Self-weight of the girder is less because the smaller section is required. The axial force from prestressing reduces the principal tensile stress and helps close the cracks; thus, increase shear resistance. 5) Un-cracked section is more durable. 3. 2. 2. 2. Loss of prestressing force: The effective force in the cable can be determined after deducting the following losses in the cable force. 1.
Loss due to elastic shortening of the concrete: After the cable force is transferred to the girder, girder shortens hence the cable, this leads to reduction in the effective prestressing force. 016 2. Loss due to shrinkage of concrete: The shrinkage of concrete depends on the amount of water used in the preparation of concrete. For ordinary concrete the average shrinkage strain can be taken as 0. 0003. (Lin T. Y, 1976) The shrinkage of concrete causes shortening of concrete and hence of cable, this results in loss of prestressing force. . Loss due to creep of concrete: The creep is time and stress dependent phenomena. Amount of creep is often 1 or 2 times the elastic shortening, hence it is very important to consider in design. 4. Loss due to creep of steel: The amount of creep varies with type of steel and level and duration of stress. The loss of prestress due to creep of steel is generally overcome by over-tensioning. 5. Loss due to anchorage slip: When jack is released and the prestress is transferred to anchorage, the anchorage fixtures are subjected to stress at his transfer will lead to deform, thus allowing tendon to slacken slightly. Friction wedges employed to hold the wires will slip a little distance before the wires can be firmly gripped. This slip depends on the type of wedge and stress in the wire. This slip will produce loss in strain of wire hence the prestressing force. 3. 2. 3 Analysis Basis A cable-stayed bridge consists of three principal components, namely girders, towers and inclined cable stays. The girder is supported elastically at points along its length by inclined cable stays (Figure 3. ) so that the girder can span a much longer distance without intermediate piers. The dead load and traffic load on the girders are transmitted to the towers by inclined cables. High tension forces exist in cable-stays which induce high compression forces in towers and part of girders. The assembly of girder supported on number of cables makes structure highly statically indeterminate and the nonlinearity involve in the problem makes it more complicated to analyze, this demands high computational efforts. 017 Figure 3. 2: Forces in the girder Courtesy: www. elsevier. com/locate/compstruct 018
The non linearity in the problem is because of beam column effect cable sag effect due to its self weight, large deflections due to change in geometry and nonlinear material behavior if stress exceeds elastic limits. Cable sag effect. – The inclined cable stay of cable-stayed bridges is generally quite long and it is well known that a cable supported at its end and under the action of dead load and axial tensile force will sag into a catenary shape. The axial stiffness of a cable will change with changing sag. When a straight cable element for a whole inclined cable stay is used in the analysis, the sag effect must be taken into account.
On the consideration of the sag nonlinearity in the inclined cable stays, it is convenient to use an equivalent straight cable element with an equivalent modulus of elasticity which can well describe the catenary action of the cable (Weon, 2006). Beam-column effect. – Since a high pretension force exists in inclined cables, the tower and part of the girder are subjected to a large compression action; this means that the beam-column effect has to be taken into consideration for girders and towers of the cablestayed bridge.
In a beam-column, lateral deflection and axial force are interrelated such that its bending stiffness is dependent on the element axial forces, and the presence of bending moments will affect the axial stiffness. The element bending stiffness decreases for a compression axial force and increases for a tension force. The beam-column effect can be evaluated by using the stability functions. Geometric nonlinearity-For longer span deflection becomes significant and hence the geometric nonlinearity has to be considered.
For analysis of span over 600 meters, large deformations should be taken into consideration (Wang and Fu, 2002). 3. 2. 4 Design Basis Moment of resistance-The moment of resistance of the girder can be determined by using the basics of pre-stress concrete beam theory. The gravity load produces tensile stress at bottom at mid span and at top near cable support. The compressive force from the cable causes reduction in the tensile stress of concrete therefore the moment of resistance is increased. 019 Figure 3. 3: 3D view of ‘T’ beam type girder
For single plane of cable system the deck and girder can be constructed as ‘single-T’ beam and for two plane system it can be constructed as ‘Double T’ beam (Figure 3. 3). And Moment of resistance of the Tee beam can determine as per IS 456-2000, by taking effective flange width of compression side as: beff = l0 + bw ? l0 ? ? ? +4 ? b? . . . . . . Equation 3. 4 Shear resistance: The shear resistance of prestressed concrete members at the ultimate limit state is dependent on whether or not the section in the region of greatest shear force has cracked.
The mode of failure is different for the two cases. If the section is un-cracked in flexure, then failure in shear is initiated by cracks which form in the webs of I or T sections once the principal tensile strength has been exceeded. If the section is cracked, then failure is initiated by cracks on the tension face of the member extending into the compression zone, in a similar manner to the shear mode for reinforced concrete members. The permissible shear stress for the member under compression (un-cracked) can be increased by multiplying the permissible shear stress by factor 20 ? = 1+ 5P , but not exceeding 1. 5 . Ag f ck . . . . . Equation 3. 5 P = axial compressive force in N, Ag = Gross area of the concrete section id mm2, f ck =characteristic compressive strength of concrete. 3. 3 Tower The tower may be foxed or pinned at base. With fixed base the large bending moment may be induced at base, while pinned base does not. Fixed base may be more practical to erect and may be less costly than inserting a heavy pinned bearing, which requires tower to be externally supported until the cables are connected. 3. 3. 1 Design Considerations
Imagination combined with engineering economics can produce many variations of tower designs, each type satisfying particular design conditions and requirements better than other conventional types (Troitsky, 1988). In selecting a specific type of tower, the designer must consider several factors. For example, when a large clearance is required below the superstructure, the A-frame has a decided disadvantage a large pier width is required to accommodate the legs of the frame. In some cases a modified A-frame with a short cross top member may be the best solution considering all the factors involved.
The towers are normally constructed of cellular sections and are fabricated of structural steel or reinforced steel. The towers have to carry heavy loads, usually several thousands of tons. Therefore, box sections with large kern width are best to provide safety against buckling with minimum amount of material. Box sections can be kept slender without unnecessary wasting of the material. Towers may be built of metal or of reinforced concrete or prestressed concrete. The advantage of metal towers lies in their faster fabrication and erection.
However, for large cable-stayed bridges, the can be built more economically with concrete than steel. 021 The Height of the Tower The height of the tower is determined from several considerations, such as the relation of tower height to span length, the type of cable arrangement, and the general aesthetic proportions of all the towers visualized as an entity To find the optimum height of tower the expression given by (troitsky, 1988) may be used: The height of tower as the function of the panel length (n a) is expressed as H= n a * tan250 = 0. 465na. . . . . . . Equation 3. 6
Where, ‘n’ is the number of panels on one side of the pylon and ‘a’ is the panel length i. e. the spacing of cable along the deck. For example: with 4 cables on each sides of cable, H=0. 465X4a=1. 86a . . . . . . . Equation 3. 7 The middle panel is usually longer than the remaining panels. The optimum size of the middle part is determined under the assumption of full use of the material of the girder. Generally it is 20-30% larger than other panels. It may be taken as 1. 3 times of other panels In this case the ratio of the tower height to the length of the mid span, for six panels, h 1. 4a l = ? l (6 + 1. )a 5. 2 . . . . . . . Equation 3. 8 The number and length of the panels are basically determined by the bridge system and its structural characteristics. 3. 4 Cable Anchorage 3. 4. 1 Cable Anchorage at Deck The cable anchorages at the deck are often consisting of transverse inclined beam which span between internal web plates. The ends of the cables which are suitably socketed are attached to these beams. The concentrated cable forces requires substantial strengthening 022 of the deck, web and bottom plates to ensure the very large forces are distributed over the full width and depth of the stiffening girder.
Figure 3. 4: Details of cable anchorage The cable normally passes between the two webs of the girder and are anchored by their cable sockets to a cast steel anchor body. The anchor body is so arranged that hydraulic jacks can be positioned to control the cable tension so as to adjust for the creep of the cable, the error in the cable length, variation of the elastic modulus and to modify the stress distribution due to dead load. When the cables is anchored in to the transverse bracket, connected to one web of the main girder in longitudinally inclined plane, Cantilever moments acting transversely are induced i. . the transverse compressive force must be carried by the orthotropic plate of the bridge deck, while transverse tensile force has to be resisted by strong ties between the flanges of the main cantilever. 3. 4. 2cable Support on the Tower Cable supports on the tower may be either fixed or movable or a combination of both. Fixed support may be in the form of cable socket provided with eyes attached to the ribs of the tower-head bearing by pins or by direct bearing (Figure 3. 5). They cannot slide but 023 are free to pivot in a vertical plane.
With concrete towers, the anchoring of strand is done in a manner similar to that in prestressed concrete. Alternatively the cables are continuous over the tower; they may be situated on top of saddle where sometimes an upper clamp is provided. With fixed connection, all the cable forces are transmitted to the tower. With movable supports the appropriate rocker or roller bearings are provided which provides horizontal and rotational movement. The rocker bearing can provide a large amount of rotational movement while a small amount of horizontal movement of cable is allowed.
With a roller bearing, a large amount of horizontal movement is permitted while rotational movement is somewhat restricted. Figure 3. 5: Cable anchorage at the tower 024 CHAPTER 4 AERODYNAMIC STABILITY The modern long-span cable-stayed bridges are more flexible and slender, and thus are more susceptible to the disturbances of the dynamic excitations due to wind loads. The principle aero-dynamic stability problems of cable stayed bridges are vortex shedding, buffeting and flutter. Figure 4. 1: Aerodynamic response with wind speed Courtesy: Bergman (2007) 4. 1 Vortex Shedding
Vortex shedding is the instance where alternative low pressure zones are generated on the downwind side of the structure. These alternating low pressure zones cause the structure 025 to move towards the low pressure zone, causing movement perpendicular to the direction of the wind. The periodic shedding of vortices alternatively from the upper and lower surfaces of the bridge deck (Figure 4. 1) causes periodic fluctuation of the aerodynamic forces on the structure. The periodicity is directly proportional to the wind speed. . At critical wind speed the frequency of dynamic load (i. e. ortices) coincides with the natural frequency and resonance occurs which produces large deformations in the structure. The magnitude of the amplitude is depends on the unsteady air-load, response characteristic of the structure and mode of vibration (Nunen, 1981) Figure 4. 2: Vortex shedding behind a circular cylinder. Courtesy: www. elsevier. com/locate/jweia 4. 2 Flutter Aerodynamic instabilities involving rotation are called ‘flutter’ Flutter is a self starting and potentially destructive vibration where aerodynamic forces on an object couple with a structures natural mode of vibration to produce rapid periodic motion. t is a phenomenon of aerodynamic instability can seriously affect safe working of bridge and may cause a destructive failure of bridges. It must thus be avoided for any real bridges (Cheng, 2003). 026 During flutter, the bridge deck will oscillate in both modes vertical and torsional. Flutter can occur in any object within a strong fluid flow, under the conditions that a positive feedback between the structures natural vibration and the aerodynamic forces. That is, that the vibrational movement of the object increases an aerodynamic loads which in turn drives the object to move further.
If the energy during the period of aerodynamic excitation is larger than the natural damping of the system, the level of vibration will increase. Because of this, structures exposed to aerodynamic forces are designed carefully within known parameters to avoid flutter. Several analytical theories indicate that the magnitudes of the torsional and bending frequencies should be different from each other in order to avoid flutter. The wind speed which causes flutter depends on the mass and the ratio of the torsional and vertical bending natural frequencies. 4. 3 Buffeting
Buffeting is a forced vibration caused by the turbulence existing inherently in natural wind in conjunction with the ‘‘structural-induced signature turbulence’’ (Wang 2007). Turbulence or gusts of natural wind produces a narrow oscillation called buffeting. In this case the bridge structure will respond randomly in one or more of its natural modes. In long span bridge decks the buffeting is caused by those components of turbulence which have frequencies high enough to produce a dynamic response are of low intensity and therefore exert very small dynamic loads.
Only the structures with light damping are the dynamic response to the buffeting likely to be high. 027 CHAPTER 5 METHODS OF ERECTION Commonly used methods for the erection of bridges: 1) 2) In-situ – assembly of bridge components on temporary false-work. Lifting: e. g. beams and trusses placing of individual beams or a complete deck by crane suspension bridges lifting of pre-fabricated deck modules which are then hung from the deck hangers connected to the previously installed main cables, slung between the main towers and anchorages. 3) Launching: sequential construction (on rollers or tracks) of a continuous deck at one end of the bridge.
As each new section is added the whole deck is pushed or pulled out (usually over multiple spans). 4) Sliding or rolling: construction of a complete new bridge (usually alongside a busy existing bridge) which is then jacked into place over a few hours or days, to replace the existing structure. 5) Cantilevering: for arches successive construction from the two springing points which is temporarily tied back until the two halves can be joined at mid-span for cable-stayed bridges successive cantilevering out from the pylons of deck units suspended from the stay cables. . 1 Cantilever Method In this method the symmetrical construction is started from the tower, the girders are lift by the derrick cranes and supported by the stay cables. Cantilever method does not require temporary support (Gimsing, 1983). The erection by the cantilever method involves following steps (Figure 5. 1): 1) 2) The central tower is erected fixed to the pier. A work station is constructed on the central tower to place derrick crane over the tower to lift the deck. 028 Figure 5. 1: Cantilever method of erection Courtesy- www. encyclopedia/.. britannica 3) Deck units are lifted and the stay cables are installed and stressed initially to take the load. Temporary supporting cables may be provided to support tower for eccentric load. 4) The bridge is closed at the centre span and additional load from wearing coat, railing e. t. c. is applied 5. 2 Large Block Method The large block erection method is one of the simplest methods. In these method large sections of the bridge or in some cases the entire bridge is put in place at one time. 029 The advantages of this method are: 1) It reduces the amount of work that must be done at the site.
Since the bridge or block can be assembled before shipping, it can be done in a safer and more controlled environment. If this work is done at the production workshop, this can reduce costs, as there is no need to mobilize large amounts of people and equipment. 2) There is less risk involved. Since the bridge is assembled on the ground workers are not placed at risk in high or dangerous places. There is also less risk of the bridge collapsing midway through the erection process or of damage to the individual parts during shipping or erection. ) One other advantage is that large block erection can significantly shorten the length of time required for a project. The amount of time spent erecting temporary supports or scaffolding can be cut to almost zero. On the other hand, large block erection can only be performed in certain special cases. The location must be one that will allow the entire bridge or large block to be transported from the fabricator to the job site. This method also requires the use of a crane or cranes large enough to lift the entire bridge or block. Sufficient heavy equipment and a route of travel for it must be available 5. Cable and Tower Method In many cases the conditions under the bridge are not suitable for the use of temporary supports. This can happen when the valley is too deep, the flow of a river is too rapid, or environmental reasons prevent the use of temporary supports under the bridge. If conditions on both sides of the bridge are suitable to erecting towers and placing cable anchorages (just like a suspension bridge,) the cable erection method can be used. There are two basic types of the cable erection method the diagonal cable method (much like a cable stayed bridge) and the vertical cable method (much like a suspension bridge. In both methods, cables stretched between the two towers suspend a crane that carries the parts to their location for placement and attachment. 030 In the diagonal method, cables extended directly from the tower tops to the girder support the semi-complete bridge, the tension in each individual cable must be carefully monitored and adjusted to maintain balance and keep the structure in its proper position. In the vertical method, a structure much like a suspension bridge is created to support the bridge during erection Support girders are hung from each hanger rope and serve as temporary supports.
The main cable tension must be adjusted to keep the structure from sagging during erection. Cable erection is a complex and difficult erection method. Steel cables stretch and elongate under heavy loads. As more weight is added to each support cable, it stretches changing the balance. This makes calculations and management of the erection quite difficult. The cable erection method is frequently used for arches. 5. 4 Launching Method The launching method is one of the highly mechanized erection methods used in bridge construction.
The method consists of manufacturing the superstructure of a bridge by sections in a prefabrication area behind one of the abutments . Each new unit is concreted directly against the preceding one and after it has hardened the resultant structure is moved forward by the length of one unit (Figure 5. 2) 031 Figure 5. 2: Launching method of erection of cable stayed bridge Courtesy: www. matsuo-bridge. co. jp/english/bridges/erection/block 032 CHAPTER 6 CONCLUSIONS 1) The cable-stayed bridge is considered as the most suitable one for medium- to longspan bridges with spans ranging from 200 m to about 1000 m. s the system is self supporting. It does not require heavy end anchorage like in suspension bridge. 2) A reinforced or prestressed concrete deck is more suitable for cable stayed bridge as the component of the cable force along the deck can be advantageously utilized as the prestressing force for the deck. This will lead to effective utilization of the material. 3) The analysis of the cable stayed system is more complex as the system of the deck supported by the cable together with forms a highly indeterminate structure. Furthermore the behavior of the cable is nonlinear because of the sag effect of the cable.
This demands high computational effort for analysis. 4) The modern cable stayed bridges are more flexible and slender (light weight. ) and thus they are more susceptible to wind. Hence the wind is one of the major governing factors for the cable stayed bridge. 033 LIST OF REFERANCES 1. Troitsky, M. S. (1988). “Cable-stayed bridge, theory and design” Second Edition, BSP Professional Books. 2. Podolny, W. , and Scalzi, J. B. (1982) “Construction and design of cable-stayed bridges” John Wiley and Sons Ltd. 3. Gimsing, N. J. , (1983) “Cable-stayed bridges: Concept and design” second edition, John Wiley & Sons Ltd. . Weon-keun song, Seung-Eock Kim (2006). “Analysis of overall collapse mechanism of cable-stayed bridges with different cable layouts”. Engineering structures (29), 2133-2142. 5. Wang, P. H. , Tseng, T. C. , and Yang, C. G. (1993). “Initial shape of cable-stayed bridge. ” Computers & Structures, 46(6), 1095-1106. 6. Wang, Chung C. Fu, (2002). “Static and stability analysis of long span cable stayed steel bridges. ” Steel bridges A2C02. 7. Wang P. H. and Yang C. G. (1996). “Parametric studies on cable-stayed bridges. ” Computers & Structures, 60(2), 243-260. 8. Chen, D. W. Au, F. T. K. , Tham, L. G. , and Lee, P. K. K. (2000) “Determination of initial cable forces in prestressed concrete cable-stayed bridges for given design deck profiles using the force equilibrium method” Computers & Structures, 74(1), 1-9. 9. Podolny W (1976) “Construction & Design of Cable-Stayed Bridges” John Wiley & Sons Inc. 10. L. D. Zhu_, M. Wang, D. L. Wang, Z. S. Guo, F. C. Cao (2007) “Flutter and buffeting performances of Third Nanjing Bridge over Yangtze River under yaw wind via aeroelastic model test” Journal of Wind Engineering 1579–1606. 11. S. H. Cheng, D.
T. Lau, M. S. Cheung (2003), Comparision for 3D flutter analysis of cable-stayed bridges. ” Computers and Structures 2811–2822 034 12. 13. Lin T. Y, (1976). “Design of prestress concrete structure” Asia Adam Berg & David Jacobson (2003) “Erection of Cable-Stayed Bridges Having Composite Decks with Precast Concrete Slabs” CEE 949 14. J. W. G. van Nunen and A. J. Persoon, (1981), “Investigation of the vibrational behaviour of a cable-stayed bridge under wind loads. ” CM 1059 15. Indian Standard 456-2000, “Code of practice, Plain and Reinforced Concrete” BIS2000, ICS 91. 100. 0 16. .http://www. vsl. net/Portals/0/vsl_techreports/PT_Incremental_Launching_Method. pdf 17. 18. 19. http://www. fhwa. dot. gov/bridge/pt/pttoc. cfm www. elsevier. com/locate/jweia http://www97. intel. com/en/ThinkingTools/SeeingReason/ProjectExamples/UnitPlan s/BridgeTheGap/Cable-stayed_Bridges6. htm 20. http://www. matsuo-bridge. co. jp/english/bridges/erection/block 21. Chopreda, (2007), “Prestressed concrete design-basic principle” bridge design ECGE 406 22. Don Bergman (2007), “Design of John James Audubon Bridge. ” Bridge engineering-buckland and taylor ltd. 035
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