Cable stay bridge design

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Cable stayed bridges D. J. Farquhar Mott Macdonald Following a brief history of cable stayed bridges this chapter describes the various materials and forms of construction that have been adopted for the major structural components of these bridges, focussing in turn on the cable system, the pylon and the deck. By the use of examples the most appropriate use of these materials and component forms is discussed. A step-by-step approach is given for the preliminary design of the cable stayed bridge from outline proportions of the structure to the static and dynamic analysis including requirements for erection calculations and wind loading on stays. The dynamic behaviour for the cable stayed bridge includes the phenomenon of stay oscillation, which is reviewed in detail including discussion of the various types of dynamic cable response together with the available preventative measures. Introduction The use of inclined stays as a tension support to a bridge deck was a well-known concept in the nineteenth century and there are many examples, particularly using the inclined stay as added stiffness to the primary draped cables of the suspension bridge. Unfortunately, at this time, the concept was not well understood. As it was not possible to tension the stays they would become slack under various load conditions. The structures often had inadequate resistance to wind-induced oscillations. There were several notable collapses of such bridges, for example the bridge over the Tweed River at Dryburgh (Drewry, 1832), built in 1817, collapsed in 1818 during a gale only six months after construction was completed. As a result the use of the stay concept was abandoned in England. Nevertheless, these ideas were adapted and improved by the American bridge engineer Roebling who used cable stays in conjunction with the draped suspension cable for the design of his bridges. The best known of Roebling’s bridges is the Brooklyn Bridge, completed in 1883. The modern concept of the cable-stayed bridge was first proposed in postwar Germany, in the early 1950s, for the reconstruction of a number of bridges over the River Rhine. These bridges proved more economic, for moderate spans, than either the suspension or arch bridge forms. It proved very difficult and expensive in the prevailing soil conditions of an alluvial floodplain to provide the gravity anchorages required for the cables of suspension bridges. Similarly for the arch structure, whether designed with the arch thrust carried at foundation level or carried as a tied arch, substantial foundations were required to carry these large heavy spans. By comparison the cable-stayed alternatives had light decks and the tensile cable forces were part of a closed force system which balanced these forces with the compression within the deck and pylon. Thus expensive external gravity anchorages were not required. The construction of the modern multi-stay cable-stayed bridge can be seen as an extension, for larger spans, of the prestressed concrete, balanced cantilever form of construction. The tension cables in the cable-stayed bridge are located outside the deck section, and the girder is no longer required to be of variable depth. However, the principle of the balanced cantilever modular erection sequence, where each deck unit is a constant length and erected with the supporting stays in each erection cycle, is retained. The first modern cable-stayed bridge was the Stroms- mund Bridge (Wenk, 1954) in Sweden constructed by the firm Demag, with the assistance of the German engineer Dischinger, in 1955. At the same time Leonhardt designed the Theodor Heuss Bridge (Beyer and Tussing, 1955) across the Rhine at Dusseldorf but this bridge, also known as the North Bridge, was not constructed until 1958. The first modern cable-stayed bridge constructed in the United Kingdom was the George Street Bridge over the Usk River (Brown, 1966) at Newport, South Wales which was constructed in 1964. These structures were designed with twin vertical stay planes. The first structure with twin inclined planes connected from the edge of the deck to an A-frame pylon was the Severins Bridge (Fischer, 1960) crossing the River Rhine at Cologne, Germany. This bridge was also the first bridge designed as an asymmetrical two-span structure. The economic advantages described above are valid to this day and have established the cable-stayed bridge in its unique position as the preferred bridge concept for major crossings within a wide range of spans. The long- est-span cable-stayed bridge so far completed is the Tatara Bridge in Japan with a main span of 890 m. At the time of writing (2008) several other bridges are planned, or are in construction, with main spans in excess of 1000 m, notably the Sutong Bridge (1088 m) and the Stonecutters Bridge (1018 m), which are both in China. ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers www.icemanuals.com 357 ice | manuals doi: 10.1680/mobe.34525.0357 CONTENTS Introduction 357 Stay cable arrangement 358 Stay oscillations 364 Pylons 367 Deck 372 Preliminary design 376 References 380 Further reading 381 More free ebooks : http://fast-file.blogspot.com Stay cable arrangement Two basic arrangements have been developed for the layout of the stay cables: 1 the fan stay system (including the modified fan stay system) 2 the harp stay system. These alternative stay cable arrangements are illustrated in Figure 1. Fan cable system The fan system was adopted for several of the early designs of the modern cable-stay bridge, including the Stromsmund Bridge (Wenk, 1954). The method of supporting the stays on top of the pylon was taken from suspension bridge tech- nology where the cable is laid within a pylon top deviator saddle. The floor of the saddle is machined to a radius so that each cable stay anchored in the main span can pass over the pylon and be anchored directly within the back or anchor span. This arrangement is structurally efficient with all the stays located at their maximum eccentricity from the deck and a minimum moment is applied to the pylon. The fan arrangement initially proved suitable for the moderate spans of the early cable-stay designs, with a small number of stay cables or bundled cables supporting the deck. There were, however, obvious difficulties, with the corrosion protection of cables at the pylon head, their sus- ceptibility to fretting fatigue arising from bending and hori- zontal shear stresses within the cable bundle and with the replacement of any individual stay in the event of damage. In addition, when this arrangement was adopted for larger spans the size of the limited number of cables increased, eventually becoming uneconomically large and difficult to accommodate within the fan configuration. The anchorages were also heavy and more co mplicated and the dec k n e eded to be further strengthened at the termination point. Therefore when a greater number of stays were required the modified fan layout was introduced whereby the stays are individually anchored near the top of the pylon. This is now the more commonly adopted system. In order to give sufficient room for anchoring, the cable anchor points are spaced vertically at 1.5–2.5 m. Providing the anchor zone is maintained close to the pylon top there is little loss of structural efficiency as the behaviour of the cable system will be dominated by the outermost cable which is still attached to the top of the pylon and anchored at the supported end of the back span. The advantages of this arrangement are as follows. n The large number of stays distribute the forces with greater uniformity through the deck section, providing a continuous elastic support. Hence the deck section can be both lighter and simpler in its construction. n As each stay supports a discrete deck module, each module can be erected by the progressive cantilever method without resort to any additional temporary supports. Thus increased speed and efficiency of the deck erection is possible. n The concentrated forces at each anchor point are much reduced. n With the modified fan layout it is also possible to completely encapsulate each stay, thus giving a double protective system throughout its length and, should damage occur, replacement of the stay can be undertaken as a routine maintenance task. n The large number of stays of varying length and natural frequency increases the potential damping of the structure. Freyssinet International has recently reintroduced the concept of a deviator saddle at pylons in conjunction with a modified strand system, for use in smaller-span cable- stayed bridges and extradosed bridges. The modified strand, known as Cohestrand 1 , is protected by a poly- ethylene sheath but is filled internally with polymer resin instead of petroleum wax. The resin compound is hydro- phobic, resistant to water vapour and oxygen and is capable of transferring both compression and shear forces from the polyethylene sheath to the steel wires of the strand. The strand can thus be continuous through the deviator saddle without the need to remove the polyethylene sheath. This enables more slender pylons to be constructed without having to provide a cross-over stay arrangement. The disadvantages of earlier saddle designs have been addressed in that the corrosion protection of each strand is continuous through the saddle, individual strands are not in contact and thus not subject to fretting corrosion and the system is replaceable strand by strand. The deviator saddle is made of a bundle of tubes placed within a larger steel saddle tube. All voids between the tube bundles are filled with a high-strength fibre concrete in the factory. If (a) (b) (c) Figure 1 Alternative stay cable arrangements: (a) fan stay system: (b) modified fan stay system; and (c) harp stay system 358 www.icemanuals.com ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com necessary, the external surface of the polyethylene sheath can be locally treated, at the saddle location, to ensure that the friction coefficient between the saddle and the strand is greater than 0.5. The arrangement of the strands and saddle is illustrated in Figure 2. This arrangement of multi-tube saddle and Cohestrand 1 has been incorporated in a number of bridges worldwide: in Malaysia, Vietnam, Korea, Lithuania and the Sudan. A typical design is that of the Sungai Muar Bridge, a 132 m main span cable-stayed bridge in Malaysia. Harp cable system With the harp system the individual stays are anchored at equal spacing over the height of the pylon and are placed parallel to each other. This arrangement provides a visual emphasis of the flow of forces from the back span to the main span and, in examples that are well proportioned, is aesthetically pleasing. However, the arrangement is not as structurally efficient as the fan layout and relies on the bending stiffness of the pylon and/or deck for equilibrium under non-symmetrical live loading. When loading one end only of the stay system the load may be divided into symmetrical and antisymmetrical components of loading. The symmetrical loading will be resisted by the triangle of forces formed by the stays, pylon and deck but the anti- symmetrical loading can only be resisted by bending of the deck, the pylon or a combination of both depending on their relative stiffness. This disadvantage can be over- come by anchoring the back stay cable at approach pier locations so that any unbalanced load is resisted by the pier. An elegant example of this arrangement is the Knie Bridge over the River Rhine at Dusseldorf with its single pylon and 320 m main span. Multiple span bridges The main concern with multiple-span cable-stayed bridges is the lack of longitudinal restraint to the top of the inner pylons, which cannot be directly anchored to an approach pier. Without providing additional longitudinal restraint a multiple-span structure would be subject to large deforma- tions under the action of live load. Increasing the stiffness of either the pylons or the deck can provide this additional restraint. However, increasing the deck stiffness will be accompanied by an unacceptable increase in the dead load and thus, the more practical approach is to stiffen the pylon. A typical example of the stiffened pylon is the A-frame braced pylon shown in Figure 3(a). However, such an arrangement requires a substantial increase in the pylon materials and a much larger foundation. An alterna- tive to increasing the bending stiffness of the pylon is the introduction of an auxiliary cable system to provide the additional stiffness and stability. Two cable systems are illustrated. The first system, in Figure 3(b), connects the tops of the pylons and thus directly transfers any out-of- balance forces to the anchor stays in the end spans. The second system, in Figure 3(c), connects the top of the inter- nal pylons to the adjacent pylon at deck level so that any out-of-balance forces are resisted by the stiffness of the pylon below deck level. An example of this latter arrange- ment can be seen with the design of the Ting Kau Bridge, Hong Kong, which is a four-span cable-stayed bridge. The disadvantage of such an auxiliary cable system is that the individual cables are very long and the large sag will be visually dominant when compared with the adjacent stay cable plane. Special measures are necessary to limit the propagation of wind-induced oscillations in these very long stays (see the section on Stay oscillations). Number of cable planes The cable layout may be arranged as either a single-plane system or as a twin-plane system. Outer steel tubes Aluminium tubes Ultra-high performance fibre concrete Temporary support bracket α Figure 2 Deviator saddle for Cohestrand 1 (courtesy of Freyssinet International) (a) (b) (c) Figure 3 Multiple span bridges: (a) A-frame braced pylon; (b) additional cable system where tops of pylons are connected; and (c) additional cable system where tops of internal pylons are connected to adjacent pylon at deck level ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers www.icemanuals.com 359 Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com The twin-plane system may either be formed as two vertical planes connected from the edge of the deck to two pylon legs located outside the bridge cross-section or as twin inclined planes connected from the edge of the deck to either an A- frame or inverted Y-frame pylon. The A-frame pylon was first adopted for the Severins Bridge (Fischer, 1960). The ver- tical twin-plane system, with its tensioned stay geometry, pro- vides considerable rigidity between the deck and pylon when compared with the free-hanging cables of the suspension bridge. Inclined stays further increase the stiffness and stability of the structure, with the stays and deck forming a transverse frame. Inclined stays are of particular benefit when adopted for longer spans as they improve the torsion response of the structure to both eccentric live load and aero- dynamic effects. When comparing the alternative stay sys- tems, when supporting a deck with low torsional stiffness, the inclined stay system connected to an A-shaped pylon will have approximately half the rotation under eccentric loading when compared with the vertical twin-plane system. The inclined stay system is also aerodynamically superior, reducing the magnitude of vortex shedding oscilla- tions and increasing the critical wind speed of the structure. However, the geometry of the inclined stay planes must be carefully checked in relation to the traffic envelope and the clearances required may result in an increase in the overall width of the deck. The single-plane system creates a classic structural form avoiding the visual interference often associated with twin-cable planes. However, the single plane is not able to resist torsion loading from eccentric live loading and there- fore this configuration requires the deck to be in the form of a strong torsion box. A deck section of this form is likely to have excess resistance to the longitudinal bending of the deck, particularly when a multi-stay arrangement is used. The single pylon has to be located within the central median of the carriageway and as such an additional width of deck is required to provide for the necessary clearances to traffic. Two outstanding examples of cable-stayed bridges with a single-stay plane are the Rama IX Bridge (Gregory and Free- man, 1987) (see Figure 4) and the Sunshine Skyway Bridge (Figure 5). The Rama IX Bridge crosses the Chao Phraya River, Bangkok with a 450 m main span and has an orthotro- pic steel box deck section which is 4 m deep. The deck section carries three lanes of traffic in each direction and is 33 m wide. The Sunshine Skyway Bridge crosses Tampa Bay, Florida with a 366 m main span and a 4.27 m deep trapezoidal concrete box deck section. The deck section carries two lanes of traffic in each direction and is 29 m wide. It is possible to combine the use of twin- and single-plane arrangements in the single structure as incorporated into the Rama VIII Bridge, Bangkok, completed in 2002 (Figure 6). This bridge has a single inverted Y-pylon with twin inclined stay planes supporting a main span of 300 m, whereas the back span has a single stay plane anchored directly to a piled abutment. Stay design Many factors must be considered in the design of the stay system including the characteristic breaking strength and the effective stay modulus. The proportion of the breaking strength that can be realised depends on the relaxation of the stay under permanent loads. The irreversible strain arising from relaxation increases rapidly when the perma- nent load in the stay exceeds 50% of the breaking load. The Post-Tensioning Institute (PTI) Recommendations (2001) limit, for normal load combinations, the maximum load in the stay to 45% of the stay breaking load and to 50% for exceptional load combinations. The French Inter- ministerial Commission on Prestressing Recommendations for Cable Stays (2002) limit the maximum load in the stay, at the serviceability limit state, to 50% of the stay breaking load and, at the ultimate limit state, to 70% of the stay breaking load. This slightly higher loading is Figure 4 Rama IX Bridge, Bangkok Figure 5 Sunshine Skyway Bridge, Florida, USA (courtesy Parsons Brinckerhoff ) 360 www.icemanuals.com ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com permitted providing detailing recommendations to limit bending effects due to eccentricity at the anchorages and cable stay vibration are incorporated into the design. The permissible load in the stay may also be limited by the fatigue performance of the stay under repeated live load cycles. However, this will depend on the magnitude of the live load cycles as a proportion of the permanent loads. Thus it is only the most heavily loaded stays of a highway structure that are possibly limited by fatigue whereas the stays for a railway structure where the live load has greater dominance will be much more fatigue sensitive. Fatigue endurance of a component is usually given in a plot of the stress range (Á) against the number of load cycles (N) known as the Wo ¨ hler curve. When the Wo ¨ hler curve is represented on a log–log scale the plot is represented by a series of straight lines. The PTI Recommendations relate the design limit to the test acceptance criteria of each type of stay material, such as strand, bar or wire, and the test cri- teria of the assembled stay. The recommendations for par- allel wire strand (PWS) and parallel strand are given in Figure 7. The fatigue endurance of the assembled stay will not only result from variations in the applied axial tension but also be influenced by any secondary bending in the stay, arising from either wind- or structure-induced vibrations at the anchorage or bending of the stay in a saddle. The response to these factors is extremely important though complex and varies according to the manufacturing characteristics of the stay and its anchor. Because of this the PTI Recommendations propose that at least three represen- tative samples of the stay assembly to be used in a project be fatigue tested. Testing is usually undertaken over two million cycles. The stress range depends on the generic type of stay being tested but the upper limit of the stress range is always taken as 45% of the breaking load. Acceptance criteria for the test are based upon a limit to the number of individual wires in the stay that may break and that a tensile test, undertaken after the fatigue test, achieves at least 95% of the guaranteed breaking load of the stay. The French CIP Recommendations for Cable Stays (2002) include the effect of coincident bending through a modified fatigue test whereby the cable specimen is made to deviate sinusoidally from the anchorage centreline at the same frequency as it is being subject to an axial stress variation. Stay types Problems arose with the stays of early cable stay bridges as a result of deficiencies with the anchorage design, steel material problems and inadequate corrosion resistance. The development of modern stay systems has largely overcome these problems providing designs that minimise bending of the stay at the anchorage face and incorporate a double corrosion protection system throughout. Avail- able stay systems include: n locked coil (prefabricated) n helical or spiral strand (prefabricated) n bar bundles n parallel wire strand (PWS) n new PWS (prefabricated) n parallel strand n advanced composites. Locked coil stays Locked coil stays have been incorporated into many of the earliest cable-stay bridges. The stays are factory produced on planetary stranding machines, each layer being applied in a single pass through the machine and contra-laid between each layer. The core of the stay is composed of conventional round steel wires while the final layers Figure 6 Rama VIII Bridge, Bangkok (courtesy A. Yee) 400 300 200 100 0 Life: number of cycles 10 5 10 6 10 7 145 110 Allowable d e s ig n fa t igue stress rang e : M P a Parallel strand Parallel wire 345 310 Figure 7 Wo¨ hler enduran ce curves for parallel wire and parallel strand stays ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers www.icemanuals.com 361 Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com comprise Z-shaped steel wires which lock together creating an extremely compact stay cross-section. A typical example of a locked coil stay is illustrated in Figure 8. Modern locked coil stays provide all the wires in a finally galvanised condition and will achieve a tensile strength of up to 1770 N/mm 2 . The stays are commonly anchored by zinc- filled sockets although sometimes stays that are sheathed with a polyethylene protection have their sockets filled with epoxy resin. The largest locked coil stays manufac- tured to date are the 167 mm diameter stays supplied for the Rama IX Bridge over the Chao Phraya River, Bangkok. Helical or spiral strand stays Helical or spiral strand stays, which are illustrated in Figure 9, are also factory fabricated on a planetary stranding machine similar to the locked coil stay but are entirely manufactured from finally galvanised round steel wires. The wires are usually of 5 mm diameter with a tensile strength of either 1570 N/mm 2 or 1770 N/mm 2 . The largest spiral strand stays manufactured to date are 164 mm diameter, as supplied for the Queen Elizabeth II Bridge over the River Thames at Dartford. Bar bundles Bar bundles contain up to ten threaded steel bars with a tensile strength of 1230 N/mm 2 coupled together in 12 m lengths. The bars have been conventionally placed within a steel tube and protected with a cement grout. The use of couplers connecting the bars will give a much reduced fatigue resistance when compared with the equivalent wire or strand systems. Coupled bar systems are thus rarely used where significant variations in the stay load are likely to occur. Tests have also been undertaken to assess the effective- ness of cement grout as a protective medium. These tests concluded that transverse and longitudinal cracking of the grout rapidly develops due to temperature effects, live load strains and wind vibration. It may be assumed that the cement grout provides little protection against corrosion. Parallel wire strand stays Parallel wire strand (PWS) most commonly comprises 7 mm diameter finally galvanised round steel wires with a tensile strength of 1570 N/mm 2 . PWS stays may either be prefabricated or assembled on site, the wires being installed without a lay or helix within a polythene tube and injected with cement grout or wax. When manufactured without a lay the prefabricated stays are difficult to handle and coil on to the reel and the system also suffers from the doubts associated with grouted stays. New parallel wire strand stays The new PWS system, as illustrated in Figure 10, was devel- oped with a tensile strength up to 1770 N/mm 2 . The stay is prefabricated and with a long lay helix to improve coiling on to the reel. The largest stays can contain up to 400 wires and a coating of high-density polyethylene (HDPE) is applied in the factory using the continuous extrusion process. The stays can be socketed using a patented Figure 8 Locked coil cable (courtesy Bridon International Ltd) Figure 9 Spiral strand cable (courtesy Bridon International Ltd) Polyethylene coating Filament tape 7 mm dia. galvanised wire Figure 10 New parallel wire strand (PWS) system 362 www.icemanuals.com ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com system such as BBR’s DINA or HiAm anchorages. The individual wires within these anchorages incorporate button heads transferring the full load to the anchor. The socket is then filled with a proprietary epoxy compound that is claimed to enhance the fatigue resistance of the stay. Other manufacturers provide these stays with con- ventional socketed anchorages filled with zinc or epoxy resin. Parallel strand stays Parallel strand stays are usually manufactured from 15.7 mm (or 15.2 mm) diameter seven-wire strands, which are usually galvanised and have a tensile strength of 1770 N/mm 2 , to give a characteristic breaking load per strand of 265 kN. Some manufacturers also supply strand with a tensile strength of 1860 N/mm 2 . The strand bundle can typically comprise up to 110 strands and anchoring is by means of a pre-stressing anchor head with individual strands gripped by wedges. In order to provide adequate fatigue resistance it is essential that rotation of the strands at the face of the wedge grips, due to changes in stay load or wind oscillation, is minimised. Guides or dampers located some distance in front of the anchor face provide the necessary restraint (see the section on Stay flexure at the anchorage ). An outer polyethylene tube covers the strand bundle, providing protection against impact damage and prevents dynamic oscillation or rattling of the individual strands. Early designs filled the tube with cement grout or wax as corrosion protection but in later designs each strand is manufactured with a continuously extruded HDPE coating over a corrosion-inhibiting petroleum wax. With this level of protection further cement or wax injection is unnecessary. European and Japanese practice has been to use galvanised strands but some American bridges have been constructed using epoxy-coated strand. The risk with epoxy-coated strand is that small pinholes or minor damage can propagate corrosion, forming a notch in the strand, which will create a local stress concen- tration. The use of Galfan, a licensed zinc and aluminium mixture, gives two to three times the protection for the equivalent weight of zinc coating, but the fatigue properties of the strand are reduced. The outer covering to the stay has conventionally been manufactured from steel or polyethylene pipe. Where polyethylene pipe is used, UV resistance was achieved by the use of carbon black pigment in the material. The design temperature differential between the stays and the deck or pylon can vary considerably. The PTI Recom- mendations (2001) note that values of 98C and 228C have been used for white painted or taped stays and black stays respectively. The use of black stays is not preferred, particularly in tropical zones where there is a high solar gain. Early attempts to wrap the stays, as in the case of the Pasco-Kennewick Bridge over the Columbia River USA, where a white plastic wrapping was used, were unsuccessful as the coating deteriorated within a few years. Later coverings using Tedlar, as in the case of the Second Severn Bridge (Mizon et al., 1997), have been more successful. Subsequently a range of light-coloured polyethylene pipe has been developed with a high UV resis- tance. The pipe is manufactured in a bi-extrusion process where a thin coating of light-coloured polyethylene is extruded over a black pipe core. Advanced composite stays Advanced composite stays are manufactured from aromatic polymide fibres, abbreviated to arimid, developed by Dupont in the 1970s under the trade name Kevlar. Kevlar is manufactured in three grades and has an exceptionally good strength-to-weight ratio. The structural grade ‘Kevlar 49’ has a tensile strength in the range 3600– 4100 N/mm 2 and a density of 14.4 kN/m 3 . Due to its good resistance to corrosion the material has found favour in the manufacture of rope for use in a marine/offshore environment. An experimental cable-stayed footbridge has also been constructed in Aberfeldy, Scotland. The structure, which has a main span of 63 m, utilises Kevlar aramid stays, protected with a low-density polyethylene coating. For further information on the use of non-metallic stay systems reference should be made to the chapter titled Advanced fibre polymer composite structural systems used in bridge engineering. Stay behaviour The behaviour of the stay under load must be represented in the analysis of the structure. The modulus of the stay under load is a characteristic of the stay manufacture and a non- linear variation with respect to both stay length and axial tension. When comparing the modulus of various types of stay that are manufactured, parallel wire strand (PWS) achieves the highest modulus at 205 kN/mm 2 . This is close to the modulus of the steel wire itself. Seven-wire strand achieves a modulus of some 195 kN/mm 2 while locked coil will be approximately 155 kN/mm 2 . The modulus of helical strands will be within the range 155– 175 kN/mm 2 . The modulus of both locked coil and helical strands is variable depending on the lay angle, the galvanis- ing and the stay diameter. Factory-produced locked coil and helical strand cable, which are pre-stressed as part of the manufacturing process, will give the stays a predictable elongation in service. Pre-stressing, where the cable is supported in a bed and preloaded, is the method used to remove the non-elastic stretch, resulting from the initial compaction of the strand. Pre-stressing is not required for PWS or parallel strand stays. The non-linear behaviour of the stay may be represented by an equivalent modulus taking into account the sag or catenary effect in the loaded stay. The variation in the equivalent modulus of elasticity of the stay (E eq ) is given in Figure 11 and may ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers www.icemanuals.com 363 Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com be expressed as: E eq ¼ E 1 þð 2 Â L 2 Â E=12 Â 3 Þ ð1Þ where E is the guaranteed modulus of the straight stay, L is the horizontal length of the stay,  is the specific weight of the stay and  is the tensile stress in the stay. Allowance must be made during the erection of the deck for the dead load extension of the stay. In the case of a prefabricated stay this is achieved in manufacture, by reducing the stay length to compensate for this extension. In the case of the stay fabricated on site, using a strand system, the calculated extension of the stay is taken up within the anchorage. The length of the stays will also vary with changes in temperature and it is therefore necessary to measure the temperature of the stay and deck at the time of stay installation and calibrate the stay load accordingly. Stay flexure at the anchorage Some stay systems are designed with rotational adjustment, through a pin and clevis arrangement, which assists with the proper alignment of the stay during its erection. However, when the cable is subject to small angular deviations in ser- vice the inertia of the anchorage components will inhibit the cable end from rotating and thus the anchorage connection, whatever arrangement is adopted, should be considered fixed ended. Angular deviations at the anchorage may arise through a number of cumulative effects as follows: n installation error when the anchorage is built into the structure n vibration of the cable stay due to wind and other effects causing an oscillating rotation at the anchorage n structural displacements causing a varying rotation of the anchorage with respect to the stay cable n varying load in the stay cable due to the effect of imposed loading on the structure causing varying rotation of the stay cable at the anchorage due to the catenary effect. When no guide is installed to limit the rotation of the stay the maximum bending is at the face of the anchorage and decreases exponentially over a characteristic length, which depends upon the bending stiffness of the cable. The bending stresses at the face of the anchorage are high, are located where they are most damaging, and are typically of the same order as those for live loading. However, they are identical whether the stay is monolithic, such as with a spiral or locked coil strand, or is composed of separate tensile components that can slide over each other, such as parallel strand or parallel wire stays. Monolithic stays vary from separate tensile components in that the charac- teristic length is much longer and this has to be considered when designing any guide system. To limit these harmful bending effects a guide system should be provided at a distance from the anchor face. The guide, acting as a simple support, is usually located at the end of the anchor pipe that is an integral part of the bridge pylon or girder, so that the stay is subject to continuous bend- ing over the guide. When adopting a rigid guide, subject to it being located a sufficient distance from the face of the anchor, the moment will be reduced by half the original moment at the face of the anchor. However, by manufacturing the guide from an elastic material, typically poly-butadiene, with an optimum spring stiffness designed for each individual cable arrangement, the bending stress in the cable can be further reduced to a third of the original moment. This effect is illustrated in Figure 12 . Stay oscillations A phenomenon peculiar to cable-stay bridge construction is the effect of stay oscillation. During cantilever erection a slender deck may be particularly prone to wind-induced movement. This can in turn excite the stays, producing violent oscillations which, in some projects, have had to 0.2 0.4 0.6 0.8 1.0 E eq /E 100 200 300 400 500 Stay length L: m 700 MPa 500 MPa 300 MPa 200 MPa L: m Figure 11 Equivalent modulus of elasticity of stay cable (based on E ¼ 205 000 N/mm 2 ) Sprin g constant of g uide Stress in stay Moment at anchor Moment at guide Optimum spring stiffness Figure 12 Effect of guides on stay anchor bending 364 www.icemanuals.com ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com be restrained with temporary straps. In service the wind- induced vibration of stay cables has also occurred on a range of cable-stayed bridges under a variety of wind and traffic conditions. Both standing waves and travelling waves have been observed and these oscillations can reach amplitudes of more than a metre. This behaviour was reported to have occurred with the Helgeland Bridge (Svensson and Jordet, 1996). A cable’s natural frequency for the fundamental mode may be calculated from the following: N ¼ 1 2L ffiffiffiffi T m r ð2Þ where L is the chord length of the cable (see note below), T is the cable tension and m is the cable mass per unit length. (Note: It is normal to provide an anchor guide system which gives an apparent fixity to the cable. In this case the chord length of the cable may be assumed to be the length between guides at the top and bottom of the cable.) Cable vibrations can occur as a result of a number of effects which can be categorised under the following headings: n vortex shedding n wake-induced vibrations n rain–wind instability n cable galloping n parametric instability n rattling appropriate measures need to be planned to suppress cable vibration due to these phenomena. Vortex shedding This effect is due to the alternate shedding of vortices from opposite sides of the strand, inducing a periodic load in the cable. As steady wind is required for this effect to occur, the most damaging vibrations generally occur at low wind velocities. They can be mitigated by reducing or eliminating the underlying excitation along the lengths of the stay cables that drives stay oscillation by introducing projec- tions, or texturing, of the stay pipe. This roughens the surface of the cable and presents an irregular surface to the wind flow. Vortex shedding is expected to occur when its frequency becomes approximately the same as the natural frequency of a stay, that is to say, a wind velocity approaching the reso- nance-inducing velocity. In order to avoid this phenomenon the French CIP Recommendations for Cable Stays (2002) require that the natural frequency of stays should not be the same as the vortex-shedding frequency described below: N ¼ US t D ð3Þ where U is the wind velocity, D is the outer diameter of the stay and S t is the Strouhal number 0.20 for a circular cable. Wake-induced vibrations Wake-induced vibrations occur when the leeward stay lies in the wake of a windward obstacle, such as another stay. This effect has most often occurred in moderate winds, which are not turbulent, and the effect is sometimes related to rain or ice accretion. The effect can be mitigated by improving the cable system stiffness through tying the cables together using cross-cables. These couple the modes of the different stays and thus stiffen the combined cable system so that any excitation causes less oscillation and self-excited modes are avoided. This method of mitigat- ing cable oscillation was employed on both the Normandy and Helgeland Bridges. Rain–wind instability Rain–wind instability results from perturbing the smooth surface of a stay and has occurred when water rivulets form on the top and bottom of a stay, with wind in the direction of the span, and for stays that slope downwards in the direction of the wind, as illustrated in Figure 13. The French CIP Recommendations for Cable Stays (2002) note the results of research which show there is a possibility of rain–wind excitation if the steady wind velocity is in the range 8–15 m/s. The wind must be from an oblique direc- tion, between 308 and 808 from the perpendicular to the cable, so that the wind will tend to lift the cable. The frequency of the cable oscillation is typically 1–3 Hz. Below the stated wind speed range, the top rivulet does not form because the wind is insufficient to prevent it from running down the side of the stay. Above the range, the wind forces tend to blow the rivulets off the stay. Wind turbulence also prevents the rivulets from forming. In order to avoid the onset of rain–wind oscillation it has been suggested that the Scruton number (S c ) for the stay should be at least 10 according to the following formula Stay Bottom rivulet Top rivulet Wind Figure 13 Wind–rain oscillation of stays ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers www.icemanuals.com 365 Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com specified in the PTI Guide Specifications (2001): m D 2 5 10 ð4Þ where m is the mass per unit length of the stay,  is the damping ratio (typically in the range 0.5–1%),  is the density of air and D is the outer diameter of the stay. Rain–wind excitation is therefore unlikely to occur if the damping ratio satisfies the above formula. Where stay cable pipes have effective surface texturing it has been suggested that the above requirement may be relaxed such that S c 5 5. However, this conclusion is based on limited testing of regularly spaced stay arrangements and a study by Jones et al. (2003) recommends that a careful case-by-case evaluation of the above limits be undertaken. Cable galloping The possibility of galloping oscillations of either single cables or groups of cables should also be investigated. The PTI Recommendations (2001) propose the following equation to check if cable galloping occurs: U crit ¼ cND ffiffiffiffiffiffiffiffiffi m D 2 s ð5Þ where c ¼ 40 (PTI) and 35 (CIP) for circular cables. The French CIP Recommendations for Cable Stays (2002) raise doubts as to the validity of the above formula; how- ever, no other advice is given. Clearly, as the wind speed increases there could be instances of cable galloping occur- ring, but usually increasing wind speed is accompanied by the wind becoming more turbulent and in this state the likelihood of galloping will be reduced. Parametric excitation Parametric excitation can occur when the frequency of an applied load, derived from either vehicular or wind excita- tion of the girder/pylon, causes small vibrations of the deck or pylon cable anchorages which match a stay frequency or any multiple (harmonic) thereof. Stays with an oscillation amplitude of several metres can occur although these more pronounced effects are usually when the deck is poorly streamlined, such as when twin I girders are adopted. The deck anchorages are usually the main driver for such oscillations but it is possible for an unbraced pylon to vibrate under wind loading. The Øresund Bridge for example, is reported to have experienced stay oscilla- tions due to this phenomenon. The new Stonecutters Bridge in Hong Kong has 300 m high pylons which were originally conceived as tapered tubular steel members above the deck level. However, the transverse frequency of the pylons was found to be close to the cable frequencies and consequently vulnerable to parametric oscillation under longitudinal wind conditions. The pylons were modified to concrete construction, with a composite steel skin, in order to increase the pylon mass and hence their fre- quency. It is therefore possible to set limits on the wind- induced motions and frequencies of the girder and pylon so as to limit or preclude objectionable parametric excita- tion of the stays, by ensuring separation between the deck/pylon frequencies and the stay frequencies. Rattling A stay that is made up of a bundle of sheathed strands experiences aerodynamic interaction whereby the outer strands will move in and out of the bundle and slap against the inner strands, eventually initiating a general motion of the whole cable. The solution is to encase the strand bundle within an HDPE pipe and this forms an integral component within all modern stay cable designs. Methods of damping stay oscillations There are three methods of damping stay oscillations: 1 incorporating internal and external damping mechanisms 2 texturing the external surface of the cable cover 3 installing stabilising cables. Dampers The damping ratio of a cable stay is the sum of its intrinsic damping, which will vary according to the type of stay and the aerodynamic damping which increases with increasing wind speed. The intrinsic damping of a cable stay is low with a typical range of 0.1–0.3% (logarithmic decrement of 0.6–1.8%). Wind–rain instability can be avoided if the total stay damping exceeds 0.5% (logarithmic decrement of 3.0%). Various devices are available to supplement the cable damping. External dampers are hydraulic devices which apply a transverse damping force to the stay and are mounted on structures which are fixed to the deck close to the stay anchorages. Internal dampers are ring shaped and placed between the stay and the steel anchorage tube which is built into the structure. Internal dampers use the distorsion of a dissipating material (specially formulated neoprene) or viscous friction or dry friction. The object of a damper is to minimise the amplitude of any cable stay vibration. However, unlike a guide, which would com- pletely inhibit cable displacement, a damper must permit some displacement if it is to effectively dissipate energy. Texture of the stay pipe Applying a texture to the external surface of the stay is also an effective method of preventing wind–rain instability as it helps prevent the rivulets forming long continuous lengths. Initially on Japanese bridges longitudinal fins were adopted but when this type of profile is adopted the drag coefficient increases dramatically to 1.35. Later helical 366 www.icemanuals.com ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers Cable stayed bridges ice | manuals More free ebooks : http://fast-file.blogspot.com [...]... form of any cable- stayed bridge, giving an opportunity to impart a distinctive style to the design The design of the pylon must also adapt to the various stay cable layouts, accommodate the topography and geology of the bridge site and carry the forces economically The primary function of the pylon is to transmit the forces arising from anchoring the stays and these forces will dominate the design of... – Sunshine Skyway Bridge, USA (all dimensions in metres) Crossbeam tendons Stay cable anchorage Precast anchor block Formwork bolts Figure 33 Precast anchorage and edge beam – Helgeland Bridge 374 www.icemanuals.com More free ebooks : http://fast-file.blogspot.com ICE Manual of Bridge Engineering # 2008 Institution of Civil Engineers ice | manuals Cable stayed bridges a number of stays as a beam with... 0.8 is typically adopted; the French CIP Recommendations for Cable Stays suggest a value of 0.7, which allows for some increase in surface roughness of the stay as the stay cover ages The drag factor adopted must also account for any protuberances incorporated on the stay cover as a stabilisation measure against stay oscillations Cable- stayed bridges with streamlined deck shapes will commonly have a drag... Early cable- stay pylon designs were predominantly constructed as steel boxes, and bridges such as the Stromsmund Bridge (Wenk, 1954) took the form of a steel portal frame, which was intended to provide transverse restraint to the stay system However, this restraint is largely unnecessary as sufficient transverse restraint can be provided within the stay system itself When a single mast supports each stay. .. the stays and the effective length of the mast in buckling will be approximately 0.7 times the height Connecting the back stays to an independent gravity anchorage is an equally effective solution Early cable- stay pylon designs, such as for the Stromsmund Bridge (Wenk, 1954), incorporated a pin at the pylon foot so as to ensure that the mast did not have to be designed for large bending moments Later designs... any eccentricity of the stay anchor within the pylon is accurately modelled as part of the analysis of the structure When the inclination of the back stay and main stay cables are identical, with both anchors at the same level, the axes of the stay, and hence the stay forces, will intersect on the pylon centreline However the inclination of the back span stays and main span stays Figure 26 Fabricated... horizontal component of the stay force The economic solution for the suspension bridge is a minimum-weight deck section With the cable- stayed bridge the greater participation of the deck in the overall structural behaviour gives the opportunity to consider alternative deck forms, particularly with concrete being an efficient material when used for compressive members As such, cable- stayed bridge deck forms have... Point Bridge, USA (all dimensions in metres) 9.78 29.05 single central plane of stays The first of such designs was the Brotonne Bridge crossing the River Seine near Rouen, France A similar design, using precast segmental units for the deck, was adopted for the Sunshine Skyway Bridge, USA, as illustrated in Figure 31 In common with a number of major bridge projects in the United States, this design. .. occurred in early designs, with insufficient pre-stress, where they were subject to repeated shock following unloading The trajectory of the stay cables will be modified by the stabilising cables so kinking of the stay cable at the anchorage will occur The setting of the rigid anchor tubes at deck and pylon needs to be corrected so that they follow the modified cable geometry Stabilising cables cannot therefore... platform at the time the cantilever erection within the main span commences Preliminary design The cable- stayed bridge, incorporating multiple stays, is a highly redundant structure where the deck acts as a continuous beam with a number of elastic supports with varying stiffness The deck and pylon of the cable- stayed bridge are both in compression and therefore bending moments in these elements will be . multi -stay cable- stayed bridge can be seen as an extension, for larger spans, of the prestressed concrete, balanced cantilever form of construction. The tension cables in the cable- stayed bridge. layout of the stay cables: 1 the fan stay system (including the modified fan stay system) 2 the harp stay system. These alternative stay cable arrangements are illustrated in Figure 1. Fan cable system The. have established the cable- stayed bridge in its unique position as the preferred bridge concept for major crossings within a wide range of spans. The long- est-span cable- stayed bridge so far completed