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Two inclined cable planes. Erasmus bridge, Rotterdam, The Netherlands. One vertical plane above the centre line. Transverse layout of stays. The centre cable plane provides elastic vertical support to the deck, but not torsional support.

It is therefore essential that the girder of the deck has a sufficient torsional stiffness to transmit any twisting moment from a load with an eccentric resultant, e. To achieve the required torsional stiffness, the girder will have to be of the box type. The deck girder can simply consist of two I-shaped plate girders directly under the cable planes. And also to give the girder a favourably streamlined shape. An inclined plane, because of being no obstacle for the passing traffic, needs a minimum on pylon height.

The most related design items, considering an arrangement of stay-cables, are in the field of: Alternatives on arrangements of stay- cables. The fan system, also called the radial system, leads to the most efficient structural system.

It results in relatively small normal forces in the deck and the longitudinal bending of the pylon remains moderate. Consequence of cable arrangement on deck normal force. Considering the deck normal force, as shown in figure The construction of the pylon must be finished before starting the construction of the deck. An indication of consequences for design using a kind of cable arrangement is summarised in table 1. Consequences parameters for the main alternative cable arrangements.

Because of the positive influences, the semi-harp typology is most commonly used. A typical phenomenon for the harp configuration is the existence of large bending moments in the pylon, which explains the minus sign given in table 1.

Only the tensile force of the longest cable is in fully axial equilibrium. For all other cables, equilibrium os achieved by the combination of axial forces and to a large extend bending moments, see fig. Structural behaviour of a cable stayed bridge with a harp configuration. A practical solution solving the disadvantage on large bending moments is the use of vertical external supports along the side span at the cable — deck connection.

Example of additional support at the side span region. The most relevant aspect in case of an asymmetric cable configuration is the missing of self-weight of the side span needed for the horizontal equilibrium at the top of the pylon.

As a consequence, the backing stay element is heavy loaded which is the reason using a large number of backing stay cables. Normally the most optimal angle of the backing stay cable is 45o. For the asymmetric bridge sometimes a smaller angle is used which means a reduction of the vertical abutment reaction force. A Dutch example of an asymmetric cable stayed bridge is shown in fig. Asymmetric cable stayed bridge. This system is called self-anchored. This system is called earth-anchored or bi-stayed.

Because of the Dutch soil conditions, mostly the self-anchored system is used. Using a bi-stayed concept results into: The increase of torsional frequency is explained by fig. For a parallel system a load is carried by one plane of cable only. For the inclined system, both backing stay cables are activated. Therefore, the horizontal displacement of the top of the pylon is for the inclined system much lower than for the parallel system.

Influence of cable plane geometry on deck stiffness behaviour. In cable-stayed bridges, special connections are required to allow the correct transmission of the cable forces to the girder and the pylon. Some examples of the connection cable — deck. Examples of the connection cable — pylon. Examples of fixed connection cable — pylon. An example of a steel-concrete solution is given in fig. The cable material is similar to that used for normal prestressing work and either comprises multi-strand cable made up of cold drawn wires or alternatively as single strand cable mono-strand cable consisting of parallel wires.

Diameters in the range mm are typical. Galvanising each wire can provide protection against corrosion, but a more thorough practice has been to cover the cable in steel or plastic ducting and subsequently inject cement grout after positioning in place. This latter operation is carried out after all dead loads have been applied to avoid too much cracking of the mortar.

The cable is normally connected to the pylon with pin-type joints. The cable ends for the pin-type connection have either swaged or filled sockets. Swaging consists of squeezing a socket onto the wire in a hydraulic press and is generally used with strands having a diameter in the range mm. Filled sockets are more suited to the larger diameter parallel wire type cable with the socket containing the whole bundle of wires.

Several alternative types are manufactured differing slightly in the form of dead ending of each wire and the type of filling material. In the simplest form the wires are led through a plate at the base of the socket and finished with a button head or sockets and wedge.

The inside of the socket, conical in shape, is subsequently filled with an alloy of zinc, copper, aluminum or lead, or sometimes with a cold casting compound such as epoxy resin.

Thus when the cable is subject to a tension load, wedging action develops, thereby increasing the grip on the wires. The deck-tocable connection is usually of the 'free' type to accommodate adjustment. A flared arrangement is required for multi-strand cable, while only a single socket is usually needed for mono-strand cable. Initial tensioning of the cable to remove slack is generally carried out with a hydraulic jack similar to that used in prestressed concrete.

The socket is therefore often manufactured with an internal thread for the jack connection and external thread and nut to take up the extension and other adjustments. For the cable erection, the majority of cable-stayed bridges are nowadays designed with monostrand cable, either of the parallel wire or locked coil wire type.

A complete stay is manufactured in its polyethylene tubing and delivered to site on reels. The simplest erecting procedure is to unreel the cable along the deck and hoist or lift it up to the top of the tower.

Unfortunately the natural sag tends to be quite large and therefore considerable take-up has to be provided in the tensioning jack. A more satisfactory procedure is to install a guide rope and pull the cable up with a hauling rope. Intermediate supports to reduce sag are provided by intermittently spaced sliding hangers.

Tensioning is initially carried out at the deck connection end to take up the stack, final tensioning to remove bending moment in the deck and transfer dead load into the cable being supplied after all work on the newly erected section is complete i. Erection of the Erasmus Bridge, Rotterdam.

The pylon may be fabricated from steel plate, or precast concrete elements or occasionally in situ concrete. The various configurations shown in fig. In bridges with a central cable plane, the pylon can be designed as a free standing column or as a lambda-shaped frame. Various configurations of pylon. Some examples of pylon configuration.

H-frame The cross section of the pylon generally forms a rectangular box with a single cell. Due to dominating compression it is necessary to stiffen the side plates primarily with stiffeners, or to create a larger number of cells within. Steel pylon cross section. This because of the periodic inspection needed on the cable anchorage at the top of the pylon.

An example of a cross section of a pylon is shown in fig. Cross section of the pylon of the Prins Claus bridge, Utrecht. For a bridge with a single span, two alternatives on layout of the bridge can be used, see fig.

The first is an asymmetric bridge with one pylon only. For the second alternative two pylons are used. As a rule, using two pylons is most cost effective. When one pylon is used, for the same span length, approx. Some reasons for that are: During the construction of the pylon, many times temporary equipment is needed supporting the pylon. Temporary support during the construction of the pylon, Eiland bridge, Kampen. This means an increase of deck width which largely affect the building costs.

The first example a given in fig. The second example b shows a rigid connection between the foundation and the pylon. Examples of a single tower. To avoid the large foundation needed in case of a A-frame, see fig. This type of structure is mostly used when a large distance exist between the deck level and the top of the foundation.

Example of a diamond pylon configuration. For a cable stayed bridge without a backing stay, the bending moments in the pylon constructed as a single structural element will be very large.

Some typical pylon configurations used frequently when a backing stay is missing are shown in fig. Shape of a pylon in case of missing a backing stay. Combination of esthetics and structural requirements when a backing stay is left. A complete other type of cable stayed bridge is shown in fig. Some main advantageous using such a system are: Both have a large influence on the aerodynamic behaviour of the bridge reduction on normal force in the deck reduction on pylon height and total cable length.

Example of spatial pylon configuration. For timber bridges a distance between 10 — 15can be used. When considering the optimization on cable weight only, it is found that: It is necessary that under all possible loading conditions the anchoring cable is in tension. Neglecting the bending stiffness of the main deck girder, the following relation can be found, see fig.

Relation between span length and anchor cable tension. As shown in figure 40, the side-span la will always be less than half the main span length lm. These examples show that the type of variable loading strongly influences the main geometry of the bridge. The lines given in fig.

Limitation on span length: This because of the following criteria: Especially the geometry of the cross section is an important parameter for the flutter phenomena. This is illustrated by fig.

Shape factors for analysing sensitivity to flutter. The main criteria affecting the maximum span of a cable-stayed bridge are cost, stability, strength and construction feasibility. However, for the last 10 years, finalised projects showed e. As an indication, the cable cost premium for self-weight is approx. Considering the capital cost divided by the roadway deck area, the bridge deck and towers will not contribute to much unit cost increase with span because their costs increase is almost direct proportion to span.

Only the cable unit cost increase linearly with span because the length of cable necessary to support an average deck unit increases in length. The unit costs P. The cost variations due to factors as type of superstructure, complexity and foundations conditions are much larger than unit cost variations due to span length. Stability criteria Tower buckling In general, tower buckling along the bridge is inhibited by the cable arrangement and therefore, transverse buckling is occurs first.

When using splayed cables connected at the outer edge of the superstructure, some transverse restraint to the tower is guaranteed. By using splayed cables, like the Stonecutters Bridge, the transverse tower buckling load is approx.

Deck buckling Based on a parameter study of the composite cable stayed Stonecutters bridge it is found that elastic buckling is not a criterion which governs the span of composite cable stayed bridges and closely spaced piers in the side-span are not necessary to inhibit such buckling.

Aerodynamic stability criteria This criteria is most critical and the most governing form of aerodynamic instability is torsional divergence, where the torsional amplitude of oscillation in the wind stream increases rapidly in amplitude with small increase in wind speed at the critical wind velocity Vcrit.

The critical velocity is a function of the lowest torsional frequency of the bridge deck fT and the overal bridge width b.

This figure can be ued to derive approx. Torsional natural frequency versus span. For large span, such as Stonecutters Bridge at m, it is necessary to split carriageways with an air gap between. This air gap effectively increases dimension b and also improves the characteristic aerodynamic stability of the section, see fig. Typical cross section to avoid aerodynamic instability.

Strength criteria Strength of cable stays For a given stay spacing, the cable strength demand is the mainspan is a function of the bridge width, not span. Even for a composite concept, the cable stays are within currently available sizes. Lateral bending and axial load in the main girder Lateral bending caused by static wind loading becomes a critical load case and increases in proportion to the span to a power greater than 2, due to the additional drag from cables.

This because, the critical location bending moment in the girder at the tower is the same as for the maximum axial load. For the composite deck, long term distribution of axial load due to creep must be considered in reviewing the worst effect in both concrete and steel components. As is the case for aerodynamic stability, a structural system with divided carriageways has advantages in lateral bending, provided the full effective girder width is achieved by transverse framing.

Construction criteria The characteristic aerodynamic behaviour and stability of a cable-stayed bridge during construction is quite different from that of the complete bridge.

If the bridge is constructed by the balanced cantilever method, as is common, the pylon base becomes subject to very large buffeting forces originating from responses, at a time when the tower is lacking the buckling restraint it receives form the cables in the completed bridge. There are two possible modifying factors which van reduce the impact of the construction loading.

The first is the statistics of occurrence of extreme winds, which permit a much lower design windspeeds for the period during construction. The second is the use of temporary TMD tuned mass damper , to reduce the dynamic component of wind buffeting response during construction. Consequences of stiffness properties on member forces. Therefore, as a start of the design, the horizontal displacement of the pylon top can be analysed according to: Example on pylon top support condition.

The translated stiffness located at the top of the pylon, because of permanent tensile forces in the anchor cable, is equal to: Relation between support stiffness and buckling length. The n-value is analyzed according to: In general, the n-value information about the consequences of geometrical non-linearity is an indication of properly chosen dimensions. The following guidance can be used: The most common form is the box section, which offers good torsional restraint.

Plate girders are sometimes used with a double plane system of hangers, where erection procedures require assembly in small light elements. Trusses are also an option, but the high fabrication cost, expensive maintenance to counteract corrosion and poor aerodynamic characteristics now render this method relatively uneconomic in case of one layer highway bridge. While in early cable-stayed bridges the deck and towers were of steel, today towers are normally of concrete. The decks of highway bridges up to meters span and of railway bridges up to meters span can also advantageously be built in concrete.

Span length increase of cable-stayed bridges in the last fifty years. Currently a steel deck is chosen where lightweight is important due to poor soil conditions, where an unusually long span is required or because of the erection method. Steel box sections are ideally suited to modern fabrication methods.

In particular automatic numerically controlled cutting, drilling, milling and welding machines are a positive encouragement towards manufacturing as much of the deck as possible under workshop conditions and bringing finished units to the site. Furthermore, recent advances in welding technology such as submerged arc, C02, etc.

The time required to erect and weld deck units into place depends upon the amount, type of weld, plate thickness, etc. While moments are mainly taken by the steel structure, the reinforced concrete slab largely absorbs normal forces.

In order to reduce the influence of shrinkage and creep, slabs can be prefabricated. Competitive designs 26 Cablestayed bridges with concrete decks are especially suitable for railway bridges. Due to their large self-weight, dynamic and fatigue considerations are less important than for bridges with steel decks.

Some examples of composite bridge decks of cable-stayed bridges. Influence of supports and expansion joints The design of a deck a much related to the position of expansion joints and support conditions. Three examples of support and expansion joint conditions. For system A, the so-called bi-concept is used with expansion joints at the pylon position.

For this situation, the deck is loaded by a tensile normal force. The end support should resist a large horizontal component. For system B, the so-called self-anchored system is used with a continuous main girder. The deck is loaded by a compression normal force.

For system C, also a bi-concept is used in combination with a continuous main girder. The deck is loaded by both tensile and compression.

Results on the distribution of the normal force in the deck are summarized in fig. Distribution of the normal force in the deck. For both system A and C a heavy abutment is needed. Cable-stayed bridges are generally built as self-anchored systems where the supporting conditions are chosen so that vertical load from the self-weight and the traffic introduces vertical reactions only.

As shown in table 9, there are, however, many variations to this basic system and in some systems, horizontal reactions of moderate size might occur due to compatibility phenomena. Alternatives on supporting conditions for the girder A Some of the consequences using a certain type of support condition are in the field of: Pylon fully clamped, deck separated vertically from pylon C B. Pylon fully clamped, deck horizontally supported C.

Pylon fully clamped, deck connected to the pylon D. Pylon fully clamped, deck fixed at abutment E. Pylon fully clamped, deck horizontally free F. Pylon pinned ended, deck to pylon connected G. Pylon pinned ended, deck horizontally supported at abutment D E H. Pylon pinned ended, The interaction between the stiffening girder, the cable system and the pylons in the transmission of vertical and horizontal loads is decisively influenced by the choice of the supporting conditions of the girder.

The lateral support of the stiffening girder at the pylons can be accomplished by applying vertical sliding bearings between the girder and the inner faces of the pylon legs. In bridges where the cable system does not render an efficient torsional support of the girder, as in cablestayed bridges with only one central cable plane, it might furthermore be required to give the girder a torsional support at the pylons.

Some alternatives on supporting conditions for the deck girder. Detail deck-abutment Vertical bending stiffness The main function of the deck system is, see also fig.

Distribution of a concentrated load by bending stiffness of the deck. The bending stiffness of the deck largely influences the size of bending moments.

As a comparison, fig. For the same loading, pylon stiffness and cable configurations, an increase of bending stiffness results into an increase of bending moment. The bending moment in the pylon and cable force is hardly influenced by the deck stiffness. Bending moment in the deck as a function of the deck inertia bending moment. By changing the bending stiffness of the pylon, also the bending moments in the deck will change. An example is given in fig. An increase of the pylon stiffness results into an increase of the bending moment for the pylon and into a decrease of the bending moment for the deck.

Bending moment in the deck as a function of the pylon inertia bending moment. Horizontal bending stiffness Caused by static wind loading on the deck and on half of the length of the cables, the deck is uniform distributed loaded in transverse direction. Normally, the best solution is obtained using a continuous girder which is supported in tranverse direction at both the pylon and abutment positions. The meaning of a certain support condition on the size of bending moment is illustrated by fig.

System a is having a hinge at the pylon position. System b is having a hinge in the middle of the main span. System c is a continuous main girder. Bending moment in transverse direction caused by wind loading. Hybrid deck As an example, the self-weight of the side span is increased using concrete, which in case of traffic loading contributes to a more stable cable system. Cable-stayed bridge using a hybrid deck. Buckling length of the deck girder In case of a radial cable-stayed bridge, the supporting spring stiffness for a certain position of the deck system can be analysed according to: Increasing the area of the cable and increasing the area of the backing stay cable results into an increase of the spring stiffness.

The cable force is analyzed by assuming the load and half of the length of the adjacent deck structure. Caused by the horizontal component, the normal force in the deck increases into the direction of the pylon stepwise.

Development of the normal force in the deck caused by self-weight. The normal force in the pylon is equal to the summation of the vertical component of all cable forces supporting the deck plus the vertical component of the cable force of the anchor cable.

For analyzing the vertical spring value, neglecting the axial displacement of the anchor cable and pylon, the following equations can be used. The member properties of the main girder area and inertia bending moment should be analyzed taken into account the theory on effective width. Schematization of the bridge deck by continuous girder supported by spring elements. When the girder as shown in fig. The results on bending moment and vertical displacement show clearly the existence of a situation far from optimal.

An optimization is achieved by prestressing the cables, each on their own level. The level of prestressing should be based on the intended situation like zero vertical displacement caused by self-weight of the bridge, which automatically means a nearly optimal line on bending moment as illustrated in fig. The size of cable prestressing can be solved analytically using the theory of Troitsky.

This theory will be explained considering the cable stayed bridge shown in fig. Optimal bending moments and displacement caused by self weight for the main girder of the deck achieved by prestressing of the cables Mr is defined as the maximum value for bending moment in the deck at position r. This maximum will be reduced by a factor C0 , which varies between 0 and 1. The basic equation for the cable stayed bridge is: The backing stay cable is having the index: However, when the additional condition of equal normal stress for all cables is included, the equation can be solved and the prestress X0 - X19 can be analysed.

Equal cable stresses means: Also, several alternatives for the anchored systems exist, such as the earth-anchored system, the so-called bistayed concept. For a long-span cable stayed bridge with a centre span of m, the influences of main bridge characteristics and especially alternative arrangements of stay cables on several design aspects are discussed.

Attention has been paid to the differences in results on reaction forces, load distribution, stiffness behaviour, vibration frequencies and geometrical non-linear behaviour. For efficient design, the results obtained clearly show the importance of optimization.

Reference design [2] The following information given is based on a large span symmetrical reference steel structure cables, pylon, deck having geometrical properties more or less identical to the Tatara Bridge and Pont de Normandy.

Besides self-weight, as explained by fig. Main span traffic loading. The support conditions are: An example of the bridge model used is given in fig.

By using cable elements, the specific characteristics on axial stiffness like sag, prestress, etc. Because of the chosen geometry large span cable-stayed bridge special attention is paid to limitations of the design related to the deck normal force, secondary effects caused by geometrical non-linearity second order analyses and frequency behavior bending as well as torsion.

For the reference design, the main consequences on support reactions and member forces are summarized in table 2. First order analyses Max. Comparison of member forces and support reactions considering alternative approaches on the analyses.

Table 2 shows the importance of second order analysis. This is especially the case for the bending moment of the side span. Influence of principal characteristics on the design By comparison with the results obtained from the reference design, the influence of five alternatives A-E is investigated: Deck normal force Deck normal force at end pier location Bending moment side-span Bending moment mid-span Tensile force anchor cable Tensile force longest cable Vertical support reaction at end pier Vertical support reaction at pylon In-plane bending moment pylon Vertical displacement deck Secondary effects: Influence of alternatives A-E on the most important design aspects.

Influence of alternatives A-E on the geometrical non-linearity expressed by n-value. For the combination of normal force and increasing vertical displacement caused by geometrical nonlinearity, the most critical cross section is found to be the middle side-span. Natural frequencies The most significant observations for the deck frequencies are summarized in table 5.

Influence of alternatives A-E on the deck first natural frequencies. Schematic view of inclined cable 38m Influence of cable arrangement on the design In an identical way as described for the influences of principal characteristics on the design, the consequences of the following three alternatives cable arrangement are given.

Bi-stayed cable bridge As shown for the Bi-stayed concept, a cable system exists with earth anchoring of the anchor cable. With a longitudinal fixing at one end of the deck girder the cable system becomes stable of the first order. Concept of Bi-stayed cable bridge. The central part of m of the main span is carried by a suspension system, whereas stays radiating from the pylon top carry the outer parts. Concept of Dischinger cable stayed bridge. A system of earth anchoring of the anchor cable and the central part of the main span supported by hangers.

The results of comparison or the three cable arrangements with the reference design incl. Influence of alternatives on cable arrangements on the most important design aspects. Development of normal force for the deck considering alternative cable arrangements. Influence of alternative cable arrangements on the geometrical non-linearity expressed by n-value. Development on vertical displacement considering alternative cable arrangements.

Influence of alternative cable arrangements on the deck first natural frequencies. The layout of the cable arrangement is found to be a fundamental item in the design of a cable-stayed bridge. Especially the Bi-stayed concept results in a significant improvement of the structural behaviour member forces, global stiffness and second order effects.

The main span girder with outriggers at the work site area. Girder cross section in the cable-stayed spans. Strict requirements regarding stiffness imposed by the passage of both freight trains and high speed passenger trains proved to have a strong influence on the design.

The demand for a high degree of rigidity led to a harp shaped cable system with relatively steep cables and intermediate support in the side spans. Partly erected main span on temporary piers. The bridge girder is arranged as a steel truss with an upper transversely post-tensioned concrete roadway deck and a lower deck for the railway, designed as a closed steel box.

The cables are anchored to the girder on outriggers with the same inclination as for the flat diagonals. The lower steel deck has proved to be a robust structure, with a satisfactory post-accident performance when the structure is being subjected to train derailment. Diagonals, chords and the railway deck are in steel grade S EN except for the secondary structures inside the deck which are designed in S EN The interior of the steel struss is protected from corrosion by dehumidification.

In addition, the cables are prepared for later erection of tie-down ropes if excessive vibration should occur. As shown in fig. The horizontal component of the cable force is transferred directly through the steel between two opposite cables and the vertical component is transferred to the concrete via shear studs. The requirements from the railway authorities stated limitations on: Al these requirements were related to comfort criteria for passenger trains.

For vertical accelerations with duration less than 0. The acceleration of the train is frequency weighted according to ISO , which applies to simulate the human perception of vertical vibrations, e. Acceleration limits as function of duration. Beside these requirements on comfort criteria, analyses related to the train loads were carried in dynamic actions, fatigue analyses and cable-stay replacement.

Some results obtained regarding dynamic load factors for various load effects are shown in fig. UIC train type 1: The dynamic load factor used on local effects on the railway deck varies in the range of 1. Fatigue analyses Most relevant bridge elements for checking the fatigue capacity are the welded joint of the truss girder, cable stays, concrete roadway deck with shear stud connection to the steel truss and the orthotropic steel deck for support the two railway tracks.

Three passenger trains, three freight trains and two heavy rail trains, each of them provided with following information: Based on this information it was possible to find the number of trains crossings during the year life time and the number of train crossings with simultaneously loading of both tracks.

Substructure For the pylons as well as piers, the dominating load is ship impact. The caisson for the pylon is designed to withstand a ship collision force of MN in the longitudinal and MN in the transversal direction.

Pylon elevation, caisson and FE-model on plastic zone development. The side span and anchor piers are all founded on open cellular caisson structures Fig. Pier elevations and onshore prefabrication of caissons. Cable system [11] As shown in fig.

Each stay is composed of two parallel cables with a mm c. The steel strands of the stay cables are covered with a polyethylene high-density PEHD tube, mm in diameter. Fundamental natural frequencies of the stay cables will range from 0. The combination of cable angle, low natural frequencies and high probability of occurrence of light rain with moderate winds at the bridge site 43 Cable cross section and view of the cable system during construction.

For the experimental investigation in the laboratory, the PEHD tubes were lightly sanded with a fine grade sandpaper to simulate natural erosion and dust particles. Subsequently, the cable surface was treated with a coat of polyvinyl alcohol simulating a rise in surface energy of the cable equivalent to oxidation. Various analyses and experiments were conducted focusing on the characteristics of the long-span structure and the aerodynamic stability of the entire bridge.

Towers The steel towers are m high and shaped like an inverted Y after examining the wind resistance, the structural efficiency and aesthetics. A full aero-elastic model of an inverted Y-type tower was tested in the wind tunnel to optimize the shape of the column and its rectangular section with notched corners to reduce vortex shedding. Cables The stay-cables have two-plane multi-fan shape. A total of cables were made of semi-parallel wire strands consisting of a galvanized wires 7 mm in diameter, covered with polyethylene tube in shops.

The ends of the strands are fixed by sockets that are resistant enough to fatigue due to bending vibration as well as that of axial force. Girders The steel girders have the cross-section of a streamlined box with two fairings in both ends.

They are elastically supported on elastomer bearings at the towers for vertical movement and fixed bearings for restraining lateral movement.

Since the side spans are short in proportion to the center span, PC girders at 45 Innovative technical features 1 Buckling tests for the girders with large compressions The analysis shows that the ultimate loading capacity of longspan cable-stayed bridges is determined by buckling of girders, since the extremely large compressions are applied to towers and girders.

The test result shows that the maximum gust response displacement at mid-span was within design tolerance. This provides sufficient dumping instead of the ties between cables. A typhoon came along while the center span was at its furthest extension with the installation of the remaining final segment. After the bridge had been structurally completed, the vertical and horizontal vibrations were measured by means of heavy-duty exciters, so as to confirm the accuracy of the vibration characteristics applied in the design.

At m in length, the bridge is one of the longest cable-stayed structures in the world and is one of only a few multi-span cable-stayed bridges in existence. Ting Kau cable-stayed bridge completed and general arrangement. Considering a multi-span cable-stayed bridge, the system on equilibrium, structural behaviour, is very different compared to a classical three-span cable-stayed bridge. The adjacent pylons deflect towards the loaded span and the adjacent spans move upwards without any other restrains than their own rigidity.

A series of more or less acceptable solutions for multiple cable-stayed spans is shown in fig.

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Caravane hobby kmfe 6 Places -. The cost of the Kronprinzenbridge Berlin is very high because of prestigious influences. Please stay us informed like. Exploring in Yahoo I ultimately stumbled upon this site. By changing the bending stiffness of the pylon, also the bending moments in the deck will change. video porno tube escort meaux Oferta de empréstimo entre particular -. As is the case for aerodynamic stability, a structural system with divided carriageways has advantages in lateral bending, provided the full effective girder width is achieved by transverse framing. The ends of the strands are fixed by sockets that are resistant enough to fatigue due to bending vibration as well as that of axial force. Services ménagers - Services -. Sweat Yves Saint Laurent Homme pas cher frmagasin.

Beside these requirements on comfort criteria, analyses related to the train loads were carried in dynamic actions, fatigue analyses and cable-stay replacement. Some results obtained regarding dynamic load factors for various load effects are shown in fig. UIC train type 1: The dynamic load factor used on local effects on the railway deck varies in the range of 1.

Fatigue analyses Most relevant bridge elements for checking the fatigue capacity are the welded joint of the truss girder, cable stays, concrete roadway deck with shear stud connection to the steel truss and the orthotropic steel deck for support the two railway tracks. Three passenger trains, three freight trains and two heavy rail trains, each of them provided with following information: Based on this information it was possible to find the number of trains crossings during the year life time and the number of train crossings with simultaneously loading of both tracks.

Substructure For the pylons as well as piers, the dominating load is ship impact. The caisson for the pylon is designed to withstand a ship collision force of MN in the longitudinal and MN in the transversal direction.

Pylon elevation, caisson and FE-model on plastic zone development. The side span and anchor piers are all founded on open cellular caisson structures Fig. Pier elevations and onshore prefabrication of caissons.

Cable system [11] As shown in fig. Each stay is composed of two parallel cables with a mm c. The steel strands of the stay cables are covered with a polyethylene high-density PEHD tube, mm in diameter.

Fundamental natural frequencies of the stay cables will range from 0. The combination of cable angle, low natural frequencies and high probability of occurrence of light rain with moderate winds at the bridge site 43 Cable cross section and view of the cable system during construction.

For the experimental investigation in the laboratory, the PEHD tubes were lightly sanded with a fine grade sandpaper to simulate natural erosion and dust particles. Subsequently, the cable surface was treated with a coat of polyvinyl alcohol simulating a rise in surface energy of the cable equivalent to oxidation. Various analyses and experiments were conducted focusing on the characteristics of the long-span structure and the aerodynamic stability of the entire bridge. Towers The steel towers are m high and shaped like an inverted Y after examining the wind resistance, the structural efficiency and aesthetics.

A full aero-elastic model of an inverted Y-type tower was tested in the wind tunnel to optimize the shape of the column and its rectangular section with notched corners to reduce vortex shedding. Cables The stay-cables have two-plane multi-fan shape. A total of cables were made of semi-parallel wire strands consisting of a galvanized wires 7 mm in diameter, covered with polyethylene tube in shops.

The ends of the strands are fixed by sockets that are resistant enough to fatigue due to bending vibration as well as that of axial force. Girders The steel girders have the cross-section of a streamlined box with two fairings in both ends. They are elastically supported on elastomer bearings at the towers for vertical movement and fixed bearings for restraining lateral movement.

Since the side spans are short in proportion to the center span, PC girders at 45 Innovative technical features 1 Buckling tests for the girders with large compressions The analysis shows that the ultimate loading capacity of longspan cable-stayed bridges is determined by buckling of girders, since the extremely large compressions are applied to towers and girders.

The test result shows that the maximum gust response displacement at mid-span was within design tolerance. This provides sufficient dumping instead of the ties between cables. A typhoon came along while the center span was at its furthest extension with the installation of the remaining final segment.

After the bridge had been structurally completed, the vertical and horizontal vibrations were measured by means of heavy-duty exciters, so as to confirm the accuracy of the vibration characteristics applied in the design.

At m in length, the bridge is one of the longest cable-stayed structures in the world and is one of only a few multi-span cable-stayed bridges in existence. Ting Kau cable-stayed bridge completed and general arrangement. Considering a multi-span cable-stayed bridge, the system on equilibrium, structural behaviour, is very different compared to a classical three-span cable-stayed bridge.

The adjacent pylons deflect towards the loaded span and the adjacent spans move upwards without any other restrains than their own rigidity. A series of more or less acceptable solutions for multiple cable-stayed spans is shown in fig. A series of solutions for multiple cable-stayed spans. Influence of cable arrangement on the design of a cable-stayed bridge, W.

Challenges in the Construction Process. Box girder bridge Until the structural possibilities for box girders were limited; structures had to be assembled from rolled sections, plates and riveted connections. Box girder bridge with composite concrete deck: Notwithstanding these limitations, the first steel box girder, the Conway bridge with a single span of The Conway bridge tubular bridge.

The basic concept of using hollow sections was only occasionally repeated with riveted construction. A box girder is more material consuming than a truss girder, and material was much more expensive than labor in those days. Here a corrosion problem arose. Riveted boxes are not completely watertight.

Humid airs sucked in, condensed and water collected at the bottom. With the development of electric welding and precision flame cutting, the structural possibilities increased enormously. It is now possible to design large welded units in a more economical way, e. A box girder consists of: The great torsion rigidity makes a box girder a particularly appropriate solution where the bridge is curved in the horizontal plane, fig.

Many bridges over European highways may serve as examples. Launching as an erection method is then still possible as long as the curvature is constant. Section of a steel box girder bridge. In wide cross-sections the box is sometimes subdivided into cells, figure 5.

Nowadays, composite steel-concrete box girder bridges are commonly used in curved bridges. They generally consist of one or more U-girders attached to a concrete deck through shear connectors. Diaphragms connect individual steel U-girders periodically along the length to ensure that the bridge system behaves as a unit. The cross section of a steel box is flexible i. Web and bottom plates stiffeners are required to improve stability of the relatively thin steel plates that make up the steel box.

During construction, overall use of top bracing members enhances stability and torsional rigidity of the girder. These bracing members become unimportant once the concrete deck hardens, but is left in place anyway.

Example composite steel-concrete bridge using diaphragms connecting individual steel U-girders. Transportation of box section with stiffened flange. Welded connection on site. Because of the limited space caused by the present railway lines, single columns could be used only, see fig. Reasons like minimization of train traffic delay and minimization of scaffolding, results into the application a composite cross section. Because of the available area, the use of cranes was also not an option.

The three sections are connected by welding and subsequently launched to their final position. The steel girders are connected by welding, which creates a total length of m. To avoid tensile stresses in the concrete deck caused by shrinkage, before casting, the inbetween supports are lifted mm.

After a hardening period of 28 days, the lifted supports are lowered down to their final level. Box girder bridge for railway traffic based on test results on minimization of noise emission. The limits for competitiveness may vary due to local market conditions. Steel or steel-concrete composite box girders are usually more expensive than plate girders because they require more fabrication time. They have, however, several advantages over plate girders which make their use attractive: In closed box girders, torque is resisted mainly by Saint Venant shear stresses because the Saint Venant torsional stiffness is normally much greater than the torsional warping stiffness.

For highly curved spans, this stiffness of the box girders is virtually essential during their construction, as well as under service loads. All steel box girders provide torsional stiffness during their erection. Composite box girders only achieve their torsional rigidity after concreting. During erection and concreting they may require expensive temporary bracing, which can also interfere with the execution of the concrete slab.

Box girders are able to cross greater torsional spans than flexural spans using piers with a single bearing as shown in Figure 4. Span range for box girder bridges. Composite concrete deck m Simple span 20 - Interior span of continuous 30 - girder Orthotropic deck m 70 - - The longest span so far is m achieved in by the Costa e Silva bridge in Rio de Janeiro, fig.

It is always probable that the longest span existing has passed the limit of best economy. Span-to-depth ratio The span-to-depth ratio will normally be around 20 to 25 for simple girders and around 25 to 35 for continuous girders. It is possible to reduce the depth, if necessary, without violating deflection limitations, at the expense of additional steel.

The above ratios are valid for road bridges. For rail bridges the ratios should be smaller, say 15 and It is advisable to check the most favorable span-to-depth ratio by trial designs. It is cheaper to manufacture a girder with vertical webs. This section shape may be the best solution for a narrow road or a single-track railroad.

A single narrow closed box girder can be positioned on the bridge centre line and completed with cantilever brackets. A combination of a wide deck on a short or medium span bridge favors inclined webs, fig. For instance, a 13 m wide concrete deck without transverse prestressing requires a width of the box of 6 m at the top.

If it were made with vertical webs, the bottom flange would be much too wide to be efficient. Inclined webs reduce the width in a favorable way. Use of concrete as a lower flange in case of hogging moment. Normally the webs are inclined 20 - 35 degrees from the vertical. In many cases inclined webs are chosen for aesthetic reasons. There are several effects that make wide flanges inefficient. One is shear lag and another is local buckling of areas in compression.

Further, the minimum thickness specified in codes may often make the flange area excessive. Plate widths of 3,3 m are readily available and some French or German mills produce wider plates, up to 5 m.

Greater widths are available with thinner plates. If still wider plates are needed, a longitudinal weld increases the costs. It is generally preferable to adopt the maximum available width and avoid the longitudinal weld even if a slightly thicker plate would lead to less stiffening. This advice is valid for the bottom plate as well as the webs.

The best economy is achieved if sections can be fabricated in the full width at the shop. If the sections can be delivered by boat, the only limitation is the handling equipment.

Composite box girders will frequently be small enough to be shipped in one piece, also by road. Local restrictions for road transport should be checked. The normal width limit, 2,5 m, may be exceeded if special permits are requested. The cost of the escort should be checked. Use of corrugated prestressing web plates; effective concrete The use of box girders, rectangular or triangular, in combination with a concrete upper deck, a concrete lower part and steel webs, is currently frequently being applied.

Some examples are given in fig. Cross section of the Maupré viaduct box girder. Meaux viaduct box girder. For the structure shown in fig. Specimen for experimental testing are shown left and in the middle. The thin walled tubular members are used to obtain a high efficiency on prestressing the concrete lower and upper flange.

In designing an economical girder, the cost of handling and welding the stiffeners has to be taken into account. With increasing labour costs the tendency is to have fewer stiffeners and thicker plates. In most cases, the bottom flange will have a very small effective area if it is not stiffened at the support.

An efficient profile is the cold-formed trapezoidal stiffener. One to two will be sufficient if they are made big enough. If the bridge is to be erected by launching or cantilevering, it is often necessary to stiffen the bottom flange along the whole girder in order to resist the hogging moments during erection. Pier Diaphragms and Intermediate Cross Frames At the supports, considerable forces from torque and shear have to be transmitted to the bearings.

The recommended solution at piers is a diaphragm, i. The plate is designed to carry the shear from the torque and is strengthened locally in order to carry the support reactions. The diaphragm at the pier sections prevents deformation of the section distortion of the box cross-section.

If the bottom flange is narrow, it may be necessary to put the bearings outside the flange and to provide the webs with external stiffeners.

In order to prevent cross-section distortion, the girder is provided with intermediate cross frames see fig. The webs and bottom flange have transverse stiffeners at these sections. To be considered effective against distortion, cross frames must comply with the stiffness and strength requirements.

The stiffness is expressed in terms of a minimum value for the dimensionless parameter S. This parameter is in effect a ratio between the distortional stiffness of the box and the distortional stiffness of the cross frame. It may be that the distortional stresses calculated neglecting all intermediate frames are acceptable, in which case none of the frames need meet the stiffness criteria.

For the purpose of analysis, box girders may be divided into two groups according to their behavior under torsional loads. The first group contains girders assumed to have a rigid cross-section, which do not change their cross sectional shape when rotated about their longitudinal axis. This might be the case for concrete box girders with relatively thick walls. Their design is generally governed by fatigue considerations.

Large, widely spaced diaphragms may be adapted, fig, 16a. Alternatively, cross girders at 3 to 4 m spacing may be adopted that support a concrete or orthotropic steel deck as shown in fig. Intermediate transverse elements between boxes. Bearings As a box girder is torsionally rigid, it is possible to use a single bearing at one or more supports and to transmit the torque to where the foundations are suitable to resist it. This is particularly common if the bridge is highly curved.

Slender columns may support the single bearings. At each end of the bridge, there are generally two bearings if the bridge consists of a single box girder. In this case, special attention has to be paid to ensure sufficient distance between the two bearings.

Another consequence of the torsional rigidity is that extra care has to be taken to get the correct support reactions when there are two bearings at each support. One way of doing this is to let the box rest on jacks with predetermined loads and to fix the permanent bearing when the jack loads are correct. If the bearings on the pier are under the diaphragm, care must be taken to ensure that thermal moments do not lead to longitudinal eccentricity occurring at the bearings.

Additional stiffeners may need to be provided. Corrosion protection The interior of a box girder is exposed to far less risk of corrosion than the outside. Hence, the interior corrosion protection can be made simpler or even omitted completely. There is always a possibility of water leaking into the box, especially if the deck is made of concrete. For this reason, the box should be equipped with a dehumidifier to keep the air dry. This is an inexpensive precaution.

White painting or very light colors should be used for the interior to facilitate future inspections. Access holes in diaphragms Access is usually required through diaphragms, during construction and during service.

A manhole mm high is usually considered as a minimum. Tight corner radii should be avoided; if they are necessary, stress concentration effects must be carefully considered. Access into the box for maintenance should be either through the end diaphragm or through a hole in the bottom flange or web.

Access through the deck should be avoided, as it is difficult to achieve permanently seals. Holes in the bottom flange can significantly reduce the flexural strength of the cross section and the entire structure, especially if they are placed in the vicinity of continuous supports in the effective width region where high negative moments develop, or in high positive moment regions.

Away from high moment regions, normal stresses due to flexure are small and adding a hole in the bottom flange may be possible mostly with extra strengthening because of fatigue criteria. Web access holes can greatly reduce the shear resistance of the web, which is made of relatively thin steel plates.

Therefore, this alternative should only be considered around mid-span, where low shear forces and torsional moments exist. If the bridge is curved in a circle, launching works without complication. If the box has an orthotropic deck, it is rigid enough even for highly curved bridges. However, boxes with composite concrete slabs are normally erected as an open trough. This open shape is torsionally very soft.

The shear centre is unusually far under the centre of gravity, so that the section will deflect substantially, vertically as well as horizontally, under self-weight, complicating the launching. Further, the casting of the concrete slab creates additional eccentric load and further deformations and stresses if the box is curved and open.

One solution is to provide the box with horizontal bracing between the top flanges. The bracing must be designed to avoid interference with the casting of the concrete slab. These diagonals may be temporary if it is deemed worthwhile to remove them after casting the slab.

Some examples of erection methods are shown. Replacement of Moerdijk bridge, Box girder parts 22m length constructed at both starting points road bridge, transported and lifted by crane. Temporary supports are used. Neckar Vally viaduct , Weitingen, Fig. Storrow Drive Connector brige. However, simple beam theory is not an adequate tool and additional considerations are required, e. The additional stresses caused by cross-section distortion depend largely on the distance between the cross braces.

With a sufficiently small distance, these stresses may be neglected. National practice varies on this point. The general case of an eccentric load applied to a box girder is in effect a combination of three main components: Warping out of plane and distortion compromises an internal set of forces, statically in equilibrium, whose effects depend on the behaviour of the structure between the point of application and the nearest positions where the box section is restrained against distortion.

Normal stress distribution under warping for an I-section beam. Between points of support, intermediate transverse web stiffeners intermediate diaphragms or cross frames may be provided to develop sufficient shear resistance in a thin web.

Bending, torsion and distortion components in case of eccentric loading of a boxed girder. Typical cross sectional distributions of a pure St. Typical cross sectional distributions of a distortional axial warping stress, b corresponding distortional shear flow, c transverse distortional moment per unit length.

External torsional loads on a box girder. Extrnal torques generated by horizontal forces acting on the top and bottom plates of the box usually result from curvatureof the girder.

This can be understood by considering the bending behaviour of the flanges in a horizontally curved bean as shown in fig. Approximation of effect of curvature on girder flanges. The effect of the bending stress on the top flange can be modeled as an axial force that is approx. Due to the nature of bending stresses, the bottom flange is subjected to the same magnitude of the lateral load in the opposite direction.

Equivalent torsional loads on a curved box girder. Therefore, the effect of the curvature can be approx. As shown in figures 23 and 24, a state of forces is developed in a curved box girder when loaded. The forces that are developed included bending moments, shear forces, pure i. Venant torsion, warping i. Torsional moments and bi-moments due to crosssection distortion also developed.

However, providing an adequate number of cross frames can easily reduce distortion-related effects. The steel box girder works in the same way as pre-stressed concrete box girders. In this case, web and flange T stiffeners are designed for this purpose. The design of the corners is generally governed by fatigue considerations. When the intermediate cross frames do not support traffic load directly, they are in general lightly stressed.

If restrained, these out-of-plane deformations create additional normal and shear stresses, which when integrated over the cross-section yield the bi-moment and warping torsional moment respectively. Stress calculations Normal stresses — including the effect of warping — are calculated as follows: Shear stresses - including the effect of warping - are calculated as follows: This is achieved by investigating the ratio between approximate stresses calculated using classical beam theory i.

Key-points considered for stress calculations. However, it is recommended that for each bridge a global study on warping stresses be included. Shear center Consider the figure below showing a cantilever beam with a transverse force at the tip. Under the action of this load, the beam may twist as it bends. It is the line of action of the lateral force that is responsible for this bend-twist coupling.

If the line of action of the force passes through the Shear Center of the beam section, then the beam will only bend without any twist. Otherwise, twist will accompany bending. The shear center is in fact the centroid of the internal shear force system. Depending on the beam's cross- sectional shape along its length, the location of shear center may vary from section to section.

A line connecting all the shear centers is called the elastic axis of the beam. When a beam is under the action of a more general lateral load system, then to prevent the beam from twisting, the load must be centered along the elastic axis of the beam. The two following points facilitate the determination of the shear center location.

The shear center always falls on a cross-sectional axis of symmetry. If the cross section contains two axes of symmetry, then the shear center is located at their intersection. Notice that this is the only case where shear center and centroid coincide If the cross section contains no axis of symmetry or only one axis of symmetry, the determination of the exact location of shear center requires a more detailed analysis.

If the applied shear force does not pass through the shear center, it will force the beam to twist as it bends. This eccentricity produces a torque, that will cause an additional shear flow and shear stress.

Equilibrium and mechanics of thin-walled members can be used to determine the intensity of the uniform shear flow, f, as shown in fig. Saint-Venant shear flow in box girder. For the situation shown in fig. Pure torsional and distortional components in a vertical couple. For example, the distortional component on the top plate of the box is: Other torsional and distortional components components on the web and bottom plates of the box can be similarly derived and the results are given in table 1.

Pure torsional and distortional components. If the torsional load consist of two opposing horizontal forces acting on the top and bottom plates, see fig. The pure torsional and distortional load components can be derived using the same procedure outlined before and the results are also presented in table 1. Pure torsional and distortional components in horizontal couple. Therefore, the theory on effective width should be taken into account. The distribution of shear stresses in case of a vertical loading is given.

Torsion and distortion of a rectangular box girder due to vertical forces upper part and due to horizontal forces lower part. The pure torsional components middle fig. If the deflected shape caused by warping is not restricted, only St.

Venant shear stresses exist. If the deflected shape caused by warping is restricted, for example caused by: This because the cross section of a box girder distort from its original shape. As both torsion and distortion causes a deflected shape, the types of warping stresses exist: However, some care should be taken with this assumption. A characteristic feature of thin-walled cross sections is the large out-of-plane warping displacement that may occur as a result of torsional and distortional loading.

In the absence of any longitudinal restraint, the distribution of free warping due to constant torque is identical at every cross section, see fig. In addition to rigid-body rotation, each wall element undergoes a degree of shear deformation.

Pure torsion The theoretical behavior of a thin walled box section subject to pure torsion is dealt with in many textbooks. For a single cell box, the torque is resisted by a shear flow St. Venant , which is constant around the box, see fig. Rotation in plane The shear flow produces shear stresses and strains in the walls and gives rise to a twist per unit length, which is given by the general expression: The general expression for the distribution of a sectorial coordinate is expressed by: It is therefore evaluated around the entire section.

Distribution of sectorial coordinate. The second integral, which applies only to the closed part of the section, takes account of shear deformation in the various wall elements necessary to restore compatibility of warping displacement around the perimeter. Restrained warping out of plane If warping is in any way restrained, axial displacements at each section have the same cross-sectional distribution, as is shown for pure torsion, but with a varying magnitude along the length of the girder.

A warping stress resultant is formed, generally referred to as a bi-moment B. This warping torsional moment is expressed by: Some practical information on stresses caused by restrained warping out of plane is given in e.

A short summary is given. It moment of inertia in mm4 A cross-section area without stiffeners , in mm2 67 While torsional warping stresses in box girders may be relatively small, without proper bracing cross frames , distortional warping stresses can be quite significant.

So, distortional warping stresses are fully controlled by internal cross frames that restrain the cross section from distortion and without proper bracing distortional warping stresses can be significant. This is especially the case for steel bridge because of the small thickness of the plated elements deck, webs and lower flange. The distortional behaviour of box girders can be understood by examining how the transverse force components in the distortional loads are resisted in the girder.

The distortional loads on the flanges and webs are partially resisted by the shears that develop in the plates. Out-of-plate bending stresses are induced with the corresponding moments shown in fig. Out-of-plane distortional stresses in a box girder. Distortional loads are also partially resisted by the in-plane shears that develop on the cross sections of the individual plated, as shown in figure The large arrows represent the in-plane shears that resist the distortional loads that are represented by the small arrows on the girder plates.

In-plane distortional warping stresses in box girders. The longitudinal bending stresses are known as the distortional warping stresses, and a typical distribution of the warping stress in a box girder is shown in figure Providing internal cross frames that are spaced along the girder length can significantly reduce crosssectional distortion. To be effective, these cross frames must possess sufficient stiffness. The most common type of internal cross frame in modern box girder bridges is the Kframe.

Brace forces in cross frame under distortional loads. Since no torsional moment result from the components of the distortional load, V and H must satisfy the equilibium: Once V and H are determined, the brace forces can be derived from static equilibrium of the K-frame. The out-of-plane distortional stiffness depends mainly on the thickness of the plates, along with the shape and dimensions of the cross section.

For a complete box girder, this stiffness will usually be relatively large due to the closed profile and the large thickness of the top plate mostly a concrete deck with a thickness larger then mm. Between panle points of the top lateral truss, the individual plate elements of the box section are relatively flexible in outof-plane bending.

Therefore, the out-of-plane bending stiffness of a quasi-closed girder can be neglected, which leads to a conservative estimate of the distortional warping stress and the brace forces in the Kframes.

A further simplification can be made by considering the fact that most torsional loads are distributed along the length of the girder. A simple solution of the brace forces can be obtained from the product of the K-frame spacing and the intensity of the distortional loads formulated in table 1.

Quasi-closed box girder a cross section and b plan view of the truss types. The behavior has been demonstrated to be analogous to that of a beam on an elastic foundation BEF , with the beam stiffness representing the warping resistance and the elastic foundation representing the transverse distortional bending resistance.

Brace forces due to distortion of quasi-closed straight box girder A view of the bridge loading is given in fig. Eccentric concrete load on box girder. Open boxes will require some plane bracing on the open side, to provide torsional stiffness during construction.

It is usual for the deck slab to be concreted in stages and for the steel girders to be unpropped between supports during this process. Part of the load is thus carried by the steel beam sections alone, part by the composite sections. A number of separate analyses are therefore required, each representing a different stage. Typically there are about twice as many stages as spans, since concrete is usually placed alternately in midspan regions and over supports.

Distortional effects should be considered carefully when concreting open sections in stages. Explanation is given on the following. A simple span quasi-closed box girder subjected to distribute top flange loads, as shown in fig.

This loading condition arises in girders with an unsymmetrical bridge deck, which frequently occurs in the fascia of bridges. The girder dimensions as well as the bracing member sizes are shown in fig. Quasi-closed straight box girder subjected to eccentric vertical loading.

The girder length is divided into 16 bracing panels, see fig. Quasi-closed box girder a cross section and b plan view of truss type. Solid diaphragms are used at each of the end supports. Only the tensile components of the diagonals and the lateral struts are shown. K-frame forces due to eccentric vertical loads. Brace forces due to distortion of quasi-closed curved continuous box girder The following case is explained.

A three span curved continuos girder with concentric loading, as shown in fig. The axial forces in the struts and diagonals at the interior side of the K-frames are shown in fig. Curved continuos box girder. A good agreement exists between FEA results and forces predicted by equations given.

In many situations, relatively small angles that may be structurally inadequate are used for these bracing members. K-frame forces in curved continuous box girder. Moreover, human failures have the inclination to repeat themselves. During the period , several accidents happened with box girder bridges, all during the erection stage: Vienna The erection of this bridge proceeded without problems by cantilevering from both sides. The final gap was closed on a hot summer day. The deformations of the bridge due to temperature expansion are shown in fig.

During the night an evenly distributed temperature was restored. The bridge straightened, leading to plate buckling. The buckling was corrected and no collapse occurred. Bridge across Danuble Vienna; buckling of lower flange under compression. Milford Haven The midspan of this bridge was erected by cantilevering. With this method of erection the cross frame above a pier suffers extra loading due to the cantilevering part.

This load causes no problem, provided that the diaphragm is designed to carry it. This was not the case. The bridge collapsed, fig. Cleddau Bridge in Milford, Wales For erection, the box was divided into two parts longitudinally, fig. On each side of a pier one part of the box was assembled, hoisted to the correct level and shifted into the correct position to be connected. Vertical and horizontal deflection were to be expected due to dead load.

An actual difference of mm was measured. Putting ballast on top of the bridge solved the latter two problems. The difference in overall deflection disappeared, but buckling of the cantilevering top flange increased. To solve the problem of the final buckle, some high strength friction grip bolts were taken out to remove the incompatibility in flange length, with the disastrous result of passing the ultimate load carrying resistance.

The bridge yielded and collapsed 50 minutes later. West Gate Bridge, Melbourne Koblenz Cantilevering was used as the erection method and again a collapse occurred. The failure was due to the coincidence of three unfavorable aspects, each of which separately would, most probably, not have caused the collapse. The buckling length was taken as mm. The effective buckling length was larger, Fig. Rhine River Bridge, Kobelnz The accidents in the United Kingdom particularly led to a rigorous investigation program.

Zeulenroda bridge, East-Germany Buckling of the lower flange. Stausee-Zeulenroda bridge, Germany, Koro-Babaldaob bridge Without any warning, the bridge collapsed.

Koror-Baaldaob bridge, Paulau Distorsie van kokerliggerbruggen, Msc-work M. Behaviour of concrete box girder bridges of deformable cross-section, Proc.

Torsion Opposite torsion moments at fully free girder ends. Torsion Opposite torsion moments at girder ends. Left end fully clamped and right end fully free. Girder dimensions identical to first example. Torsion Torsion moment positioned half girder length.

Both girder ends pin ended supported and girder dimensions identical to first example. Because of the restrained warping out of plane, mainly stresses occur as shown at supports and load input 4. Torsion Torsion moment uniformly along the whole girder length. Each plate edge loaded uniformly by shear: Weather resistant steel for bridge structures On most carbon steels, the rust forms a loose crystalline structure, allowing more water and air through to attack deeper into the steel, forming even more rust and wakening the base metal.

Weathering steel has been a primary construction material for bridges in many countries. It is a steel-copper alloy containing up to 0. Subsequent studies pointed to the beneficial effects from the inclusion of approx.

Phosphorous P , silicon Si , nickel Ni and chromium Cr appeared to provide atmospheric corrosion resistance to carbon steel. However, its widespread application has not been without controversy. In early , several US-states started the erection of uncoated weathering steel bridges and a major commitment to the use of unpainted steel bridges started in In early , it was noted that traffic-sprayed run-off-water contaminated with salt was severely corroding the bridges in rural and urban areas.

Many began to question the suitability of weathering steel in highway bridge construction. Thereafter, the use of weathering steel in bridges declined rapidly. However, as painting costs continued to rise and a better understanding of the nature of the corrosion problems developed, usage of weathering steel in bridges began to climb again.

For example in the US by the end of this use of steel had risen to a new high of about 15 percent. However, the specific alloying elements used produce a rust film, which is much less porous and is much more adherent to the base metal. This rust system develops with time, see fig.

Minor damage to this oxide film heals itself. Corrosion loss of weather resistant steel and carbon steel not to scale. After exposure for a period of time the final brown color of weather resistant steel can vary, often blending quite pleasingly with the environment. The rapidity with which the steel develops its protective oxide coating and characteristic color depends mainly upon the nature of the environment and exposure.

In an industrial atmosphere the weathering process will generally be more rapid and the final color darker than in a rural atmosphere where the oxide formation will usually be slower and the color lighter. Example of a bridge using weather resistant steel. In general, see Figure 2, the color of the steel varied from light brown for new bridges to a much darker brown for old bridges.

Each series of data relates to specific conditions existing at the time of testing at the particular site chosen for exposure. As situations may change, it is therefore difficult to give specific penetration values or predict performance over an extended life span. Corrosion losses of a mild steel and a weather resistant steel, exposed vertically, facing different compass directions.

Water flowing over weathering steel contains suspended particles of insoluble iron oxide rust , particularly when the steel is subjected to frequent rainfall during the early months of exposure. As this water runs over concrete piers and abutments, the rust stains and streaks the concrete. Rust-colored stains represent a critical weathering steel performance issue because they mar the appearance of bridges and because they create the perception that the bridge is rusting away.

Design phase Any flow of water over weathering steel members can provide corrosion and subsequently staining. The best way to minimize staining is to incorporate permanent design details that divert run-off water away from adjacent vulnerable materials. Drip pans made from stainless steel or galvanised steel sheet direct rust-laden water from piers.

Concrete column without left and with right protection by drip pan with proper overhang. Drip plates should be fabricated from the same material as the bottom flange to avoid galvanic corrosion. The designer should be consulted before drip plates are retrofitted due to the introduction of a stress raiser, which reduces the fatigue life.

The rust-laden run-off water is directed to areas that are not readily visible. Drains then collect this water and carry it away. Drawing of proper drain installation. Fabrication phase During fabrication, special care must be taken to ensure satisfactory aesthetic appearance of weathering steel. Careful blasting of the top surfaces of steel girders will allow a better protective oxide film, and reduce rustladen run-off onto supporting piers.

Incomplete blasting of a steel bent cap. Construction phase During bridge construction, the most severe staining conditions occur prior to placement of the asphalt deck.

When water running over the weathering steel superstructure is free to flow onto piers and abutments. To prevent staining during this period, all affected concrete surfaces should be draped, wrapped, or otherwise sheltered with a heavy-gauge water-proof covering, such as polyethylene sheeting, capable of resisting tearing by wind gusts and construction operations.

Wrapping of bents and column. Inspection and maintenance As with all structures, effective inspection and maintenance programs are essential to the successful performance of weathering steel bridges.

Example of inadequate maintenance. As an indication, the cost advantage of uncoated weathering steel main girders, compared to painted steel main girders, ranges form 10 to 20 percent depending on the paint system. Without painting, fabrication is faster, material-flow and handling throughout the shop is simplified, and the cost of paint itself is eliminated. On a initial cost basis, uncoated weathering steel is less expensive than either painted carbon steel or painted high-strength low-alloy steel, and the difference increases with increasing sophistication of the pain system used.

When the costs of future maintenance painting of steel are taken into account, cost advantage of uncoated weathering steel becomes even greater. The selection of weathering steel for bridge structures is a matter of engineering judgement.

Some of the factors to be evaluated are: Any geometric or natural conditions, which create continuous wetting and very high concentration of chlorides, must be avoided. Economics Comparison of the cost of initial painting in other steels versus the cost of weathering steels. Safetys Elimination of painting over traffic.

Aesthetics The benefits of weathering steel if used correctly are: Hence, weathering steel bridges are ideal where access is difficult or dangerous, and where future disruption needs to be minimized.

Typically, the costs of weathering steel bridges are approx. Even with the best effort, unforeseen circumstances may develop which will affect the corrosion rate of the weathering steel. De-icing salts is the major contributor to excessive corrosion and deterioration of most bridge materials and weathering steel is no exception. Rural environment, 16 years old bridge, heavy salt on and below the bridge.

In fact, the fatigue cracks in weathering steel tend to bleed an orange dust that is easy to detect. However, as with any bridge inspection, adequate lighting is essential. If weather resistance steel is used, ALL parts must be of cor-ten, including welding rods and rivets.

Fatigue crack in weathering steel. The ISO describes two methods for classifying atmospheric corrosity, one based on environment data and the second on corrosion rate tests. Environmental data approach This method combines measurements of the following three key factors to determine the overall corrosivity classification C1-C5 of the environment. For several countries like Japan, the transportation infrastructures are close to the ocean, and accordingly, the use of weathering steel is limited.

For the conventional weathering steel as discussed before, the Japan steel bridge construction association describes the applicable limit of weathering steel based on the exposure test all around the country, which is: To overcome this difficulty, new weathering steel, which has higher performance in corrosion protection, especially in the severe environment near the coastal area, is developed.

The chemical composition of new weathering steel is as follows: The performance of new weathering steel is investigated based on the nine-year exposure test in a coastal area. Figure 13 shows the exposure test results. Penetration curves in severe marine atmosphere. The welding of structural weathering steels is similar to that of conventional structural steels, but such steels generally have higher CEV levels, which need to be considered when defining preheat levels. Summarized, weathering steel bridges are generally suitable for use in most locations.

Limitations on use are because of: Journal of Constructional Steel Research 58 Weathering steel bridges 90 This because in the ideal situation , only normal forces occur, which is the most effective way of using all available material in the cross-section.

Trusses are classified by the basic design used. The most representative trusses are the Warren truss, the Pratt truss and the Howe truss. Warren truss The Warren truss is the most common truss for both simple and continuous trusses. For small spans, no vertical members are used lending the structure a simple look.

To cater for the heavy loading on bridges, the cross girders should be fairly close together. Pratt truss The Pratt truss is identified by its diagonal members which, except for those diagonal members near the center, all slant down and in toward the center of the span.

Except for those diagonals members near the center, all the diagonal members are subject to tension forces only while the shorter vertical members handle the compressive forces.

Howe truss The Howe truss is the opposite of the Pratt truss. The diagonal members face in the opposite direction and handle compressive forces. Using the same member properties the behaviour on global stiffness, secondary bending moments, buckling length upper chord member, etc.

However, in general these differences are relatively small. The spans are usually between 60 and m for highways and between 30 and m for railways. The optimum value for the ratio of span to depth depends on the magnitude of the live load that has to be carried.

It should be in the region of 10, being greater for road traffic than for rail traffic. For twin track rail loading the ratio may fall to about 7. A check should always be made on the economic depth for a given bridge.

The most economic truss bridge configuration, especially for railway bridges, is the underslung truss where the live load runs at the level of the top chord. The top chord then serves the dual function of support of the live load and the main compression member.

There is, however, the disadvantage that clearance under the bridge is reduced. It is thus common for the approach span over 91 Where the spans are short, and underslung trusses are not possible, it may be economic to have the top chord below the loading gauge level by using semi-through trusses.

Bracing between the top chords is not possible and restraint to the compression members has to be provided by Uframes. Where the spans of railway bridges are long, the economic depth is usually great enough to allow bracing to be provided above the loading gauge level. The use of material in bracing rather than U-frames is considerably more efficient.

In general, trusses have to compete against plate girders for shorter spans, against box girders for medium spans and cable-stayed bridges for longer spans.

The diagonals normally are at an angle between 50o and 60o to the horizontal. The initial design was by P. Collingwood Schreiber acted as Engineer on behalf of the Canadian Government. Failure to update construction methodology with an increase in the size and therefore weight of steel sections as design progressed led to an overstressing of the cantilever arms. The bridge collapsed at 5: Construction restarted in and in spite of a second accident on September 11, , when the center suspended span fell into the river as it was being hoisted into place, the bridge was completed in August Its center span remains the longest cantilever bridge span in the world.

Firth of Forth This structure is a great undulating steel monster rising out of the estuary that is formed by the Forth river as it slowly spreads out toward the North Sea.

It is considered one of the strongest, most stable, and most expensive bridges in history. That came out of necessity.

The bridge was built after the span across the Firth of Tay collapsed, killing 75 people on a train in the middle of the night. Engineers and planners needed to cross the Forth, but had to do it in a way that would be acceptable to a public still shocked by what was then the worst bridge disaster in history. What they came up with wasn't merely another cantilever-truss bridge. What they put together was a marvel of Victorian engineering, and a span so overbuilt that it barely moves in even the heaviest wind, even though a certain amount of sway is expected 92 The bridge is constructed by using steel plate tubes with internal braces.

Its nearly exclusive use of steel, combined with its latticework appearance have made some people refer to it as the "Eiffel Tower of Scotland. For short and medium spans, it will generally be found economic to use parallel chord members to keep fabrication and erection costs down. For large span bridges however, a greater depth is often required at the piers as shown above. The truss girder bridge, as shown right above, is frequently used in case of a double deck system.

The stiffness of the lateral supports may be determined according to table 1. Using the lateral stiffness coefficient, the buckling length of the chord member can be analysed. Some guidance analysing the buckling length analytically is given. This method is allowed only in case of a large number of more or less equal k-values. Using figures showing the relation between lateral stiffness coefficient and FE.

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Extension o permanente ciglia finte singole kiko colla ciglia finte senza formaldeide finte a ciuffetti clio Orleans ragazzi con le lunghe. Un accessorio caldo, morbido e trendy? Questo tipo di trattamento e indicato per mantenere lo sguardo piu aperto e sorridente. Ed era proprio l'effetto che volevo quindi faccio i. Colla ciglia finte essence extension quartu sant'elena ciglia finte singole mascara e finte Bondy finte della kiko.

Novità in casa Kiko: Mascara colossal o ciglia finte bambini con lunghe ciglia finte singole Ciglia finte singole extension padova Roubaix colla ciglia finte kiko opinioni video come.

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