Arches work basically as a structure under compressive stress. The shape is chosen in order to minimise bending moments under permanent loads. The resultant force of the normal stresses at each cross-section, must remain within the central core of the cross-section in order to avoid tensile stresses in the arch. Arches are ideal structures to build in materials which are strong in compression but weak in tension, e.
The ideal "inverted arch" in its simplest form is a cable. Cables are adopted as principal structural elements in suspension bridges where the main cable supports permanent and imposed loads on the deck Figure 6 e.
Design and Construction of Modern Steel Railway Bridges - John F. Unsworth - Google книги
Good support conditions are required to resist the anchorage forces of the cable. In the last few years, a simpler form of cable bridges has been used - the cable stayed bridge. Cable stayed bridges Figure 6 d have been used for a range of spans, generally between m and m, where the suspension bridge is not an economical solution. The range of spans for cable stayed bridges is quite different from the usual range of spans for suspension bridges - from m to m.
Cable stayed bridges may be used with a deck made in concrete or in steel. Generally, cable stayed bridges are designed with very slender decks which are "continuously" supported by the stays which are made of a number of strands of high strength steel. Slab cross-sections are only adopted for small spans, generally below 25m, or where multiple girders are used for the longitudinal structural system, at spacings of 3 - 4,5m. Beam-slab cross-sections Figure 1 are generally adopted for medium spans below 80m where only two longitudinal girders are provided. Box girders are used in prestressed concrete or in steel or composite bridges.
During the industrial revolution of 19th century steel products became more competitive and structural steel began to be adopted for bridge construction. From then on, large truss bridges and suspension bridges where developed. Unfortunately this development was accompanied by several accidents, e. The former was rebuilt with spans of m; the Quebec bridge was only rebuilt in Truss girders or arches built by truss systems have been widely adopted.
An example of an arch-truss bridge designed by G Eiffel the designer of the famous Paris tower is presented in Figure 7. This bridge, built in in Oporto over the Douro River, Portugal, has a central span of m. It is interesting to note that one of the commonest types of modern steel bridge - the box girder bridge was first introduced in bridge engineering in by Stephenson with the "Britannia Bridge" a cast iron m span box girder bridge , yet was only fully developed after the Second World War.
The knowledge of aeronautical engineering of thin-walled structures was used. Between and several accidents occurred to box girder bridges, e. As a result a large research effort was made over the last two decades to investigate the basic structural element of these bridges - the stiffened plate. The behaviour of stiffened plates is now sufficiently known for safe large box girder bridges to be designed in steel. Special consideration during erection and execution phases is given to all aspects of structural stability. Plate girder bridges with only two girders, even for very wide decks Figure 8 , are very often preferred for the sake of simplicity .
However, in bridge construction, a classical solution consists in adopting several I beams hot rolled sections for small spans - up to 25m with 3,0 to 4,5m spacing. Diaphragms may be provided between the beams transverse beams to contribute to transverse load distribution and also to lateral bracing. The top flanges of the beams have continuous lateral support against buckling provided by the deck.
There are two basic solutions for the deck  - a reinforced concrete or partially prestressed concrete slab and an orthotropic steel plate Figure 9. In the former the slab may act independently of the girders a very uneconomic solution for medium and large spans or it may work together with the girders composite bridge deck. The composite action requires the shear flow between the slab and the girders to be taken by shear connectors. Concrete decks are usually more economic than orthotropic steel plates. The latter are only adopted when deck weight is an important component of loading, i.
The orthotropic plate deck, acting as the top flange of the main girders, gives a very efficient section in bending. The deck is basically a steel plate overlain with a wearing surface which may be concrete or mastic asphalt. The steel plate is longitudinally stiffened by ribs which may be of open or closed section. Transversally, the ribs are connected through the transverse beams Figure 9 yielding a complex grillage system where the main girders, the steel plate, the ribs and the floor beams act together.
Top flanges of box girders, e. The biggest disadvantage of orthotropic steel plate decks is their initial cost and the maintenance required when compared to a simple concrete slab. However, for box girders the maintenance cost may be lower than for an open orthotropic deck. Plate girder bridges can provide a very competitive solution for short and medium span bridges. They are almost always designed to act compositely with the concrete slab. The plate girders are fabricated with two flanges welded to a thin web which usually has transverse stiffening and may have longitudinal stiffening.
Three types fo bridge cross-section may be used. For shorter spans, up to 60m, multiple girders at spacings of 3 to 4,5 m enable a simple reinforced concrete slab to be used, as shown in Figure 13 a. For medium spans 50 to m it is usually more economic to use only two plate girders, Figure 13 b. A prestressed concrete slab, usually of varying depth, may be used that sits directly on the two girders.
Alternatively cross girders may be adopted with twin longitudinal girders that support the slabs at 3 to 4,5 m centres. For short spans a low slenderness is feasible with a web that is unstiffened except at cross bearing positions and supports. For medium spans the web will usually need to be of intermediate slenderness and require vertical transverse stiffening. For larger spans the web is likely to require both transverse and longitudinal stiffening, as shown in Figure 13 b. The distance between transverse stiffeners is of the order of magnitude of the depth of the girder. The Thebes bridge, constructed in , consists of five pin-connected through truss spans, of which two spans are ft fixed double anchor spans anchoring four The Quebec Bridge, an example of economical long-span steel cantilevered truss construction for railroad loads, was completed in after two construction failures Figures 1.
Baker may not have known of the work of engineers C. Shaler Smith or C. Schneider who had already constructed cantilever railway bridges in the United States. In , the suspended span truss fell while being hoisted into place. It was quickly rebuilt and the Quebec Bridge was opened to railway traffic in Figure 1. Another major cantilever-type bridge was not to be constructed until after It remains the longest span cantilever bridge in the world.
Continuous spans were often used for long-span steel railway bridge construction in Europe but seldom in North America due to the practice of avoiding statically indeterminate railway bridge structures. The first long-span continuous steel truss railway bridge was built by the Canadian Pacific Railway over the St. Lawrence River at Montreal in Figure 1.
The Viaur Viaduct, built in , was the first major steel railway bridge in France. Carleton University Civil Engineering Exhibits. Following the collapse a design was submitted by H. Vautelet, but the redesign of the bridge was carried out by G. Duggan under the review of C. Schneider, R. Modjeski, and C. Nickel steel was also used extensively by J.
Waddell for long-span railway bridge designs. Talbot conducted tests of nickel steel connections for the Quebec Bridge reconstruction. Many engineers believe that the design was inappropriate for railroad loading. Chesterfield, Library and Archives Canada. Lawrence River at Quebec City, Canada. Many iron and steel railway bridges were replaced in the first decades of the twentieth century due to the development of substantially more powerful and heavier locomotives.
Lawrence Bridge built in at Montreal, Canada. It was built to carry four heavily loaded railroad tracks of the New England Connecting Railroad and Pennsylvania Railroad when it was completed in Figure 1. It is the largest arch bridge in the world and was erected without the use of falsework. It was also the first major bridge to use high carbon steel members in its construction. This bridge remains the largest continuous span bridge in the world.
Railroads were the catalyst for material and construction technology innovation in the latter half of the nineteenth century as the transition from wood and masonry to iron and steel bridges occurred in conjunction with construction methods that minimized interference with rail and other traffic. Library of Congress from Detroit Publishing Co.
- Stanford Libraries?
- Account Options.
- In a New Land: A Comparative View of Immigration.
- The Design of Modern Steel Bridges | Wiley Online Books;
- Bridges by Structure?
Navier on the subject of the theory of elasticity laid the foundation for the rational analysis of structures. France led the world in the development of elasticity theory and mechanics of materials in the eighteenth century and produced well-educated engineers, many of whom became leaders in American railway bridge engineering practice. Engesser, a German railway bridge engineer, further developed compression member stability analysis for general use by engineers.
During that period, due to continually increasing locomotive loads, it was not uncommon for railway bridges to be replaced at year intervals. The associated demand for stronger and longer steel bridges, coupled with failures that were occurring, compelled engineers in the middle of the nineteenth century to engage in the development of a scientific approach to the design of iron and steel railway bridges.
American railway bridge engineering practice was primarily experiential and based on the use of proven truss forms with improved tensile member materials. Many early Town, Long, Howe, and Pratt railway trusses were constructed without the benefit of a thorough and rational understanding of forces in the members. The many failures of railway bridge trusses between and attest to this. This empirical practice had served the burgeoning railroad industry until heavier loads and longer span bridges, in conjunction with an increased focus on public safety, made a rational and scientific approach to the design of railway bridges necessary.
In particular, American engineers developed a great interest in truss analysis because of the extensive use of iron trusses on U. In response, Squire Whipple published the first rational treatment of statically determinate truss analysis the method of joints in At this juncture, European engineers were also interested in the problems of truss analysis and elastic stability. Clapyron developed the three-moment equation in and used it in an postanalysis of the Britannia Bridge. Following Whipple, two European railway bridge engineers, D. Karl Culmann, an engineer of the Royal Bavarian Railway, was a strong and early proponent of the mathematical analysis of trusses.
Investigations, conducted primarily in England in the s, into the effects of moving loads and speed were beginning. Fairbairn considered the effects of moving loads on determinate trusses as early as Schwedler, a German engineer, presented the fundamental theory of bending moments and shear forces in beams and girders in Earlier he had made a substantial contribution to truss analysis by introducing the method of sections.
Also in , A. The spans were erected simply supported, and then sequentially jacked up at the appropriate piers and connected with riveted plates to attain continuous spans. Culmann also developed an analysis for the continuous beams and girders that were often used in the s by railroads. Later, in , he published a general description of the cantilever bridge design method. Bridge engineers were also given the powerful tool of influence lines for moving load analysis, which was developed by E. Winkler in Heavier and more frequent railway loadings were also creating an awareness of, and initiating research into, fatigue notably by A.
Wohler for the German railways. North American engineers recognized the need for rational and scientific bridge design, and J. Waddell published comprehensive books on steel railway bridge design in and Furthermore, Waddell and others promoted independent bridge design in lieu of the usual proprietary bridge design and procurement practice of the American railroad companies. The Erie Railroad was the first to establish this practice and only purchased fabricated bridges from their own scientific designs, which soon became the usual practice of all American railroads.
- The Homeowners Energy Handbook: Your Guide to Getting Off the Grid.
- The Cayman Islands Alive! 2nd Edition (Hunter Travel Guides);
- The cannabinoids: chemical, pharmacologic, and therapeutic aspects.
- Navigation menu!
- Topics in Algebraic and Topological K-Theory!
- Skin Cancer after Organ Transplantation?
In particular, between and almost bridges collapsed in the United States. As could be expected, some bridge companies had good specifications for design and construction but others did not. Maxwell and O. Mohr between and Maxwell and W. The first specification for iron railway bridges was made by the Clarke, Reeves and Company later the Phoenix Bridge Co. This was followed in by G. Bouscaren of the Cincinnati Southern Railroad published the first specifications with concentrated wheel loads in By the practice of bridge design by consulting engineers working on behalf of the railroads became more prevalent in conjunction with the expanding railroad business.
By Cooper provided his first specification for steel railway bridges. This latter specification has been continuously updated and is the current recommended practice on which most North American railroad company design requirements are based. Louis Bridge Co. Paul Railway Co. I This was not a general specification but was the first use of specification documents in the design and construction of railway bridges in the United States. The specification also included the first requirements for the inspection of material.
This can be a critical consideration as most railway bridge construction projects are privately funded by railroad companies. Steel arch, girder, and truss forms remain commonplace. These material enhancements, combined with a greater understanding of hydraulics, geotechnical, and construction engineering, have enabled the design of economical, reliable, and safe modern railway bridges.
Modern structural analysis has also enabled considerable progress regarding the safety and economics of modern railway superstructures. Vast advancements in the theory of elasticity and structural mechanics were made in the nineteenth century as a result of railroad expansion. Furthermore, modem methods of structural design that facilitate the efficient and safe design of modem stmctures have followed from research.
Advances in manufacturing and fabrication technologies have permitted plates, sections, and members of large and complex dimensions to be fabricated and erected using superior fastening techniques such as welding and high-strength bolting. Modern fabrication with computer-controlled machines has produced economical, expedient, and reliable steel railway superstructures. Baker, B. Bennett, R. Billington, D. Chatterjee, S. Cooper, T. Gasparini, D. Ghosh, U. Griggs, F. Johnson, A. Kuzmanovic, B. Marianos, W. Morison and the development of bridge engineering. Middleton, W. Petroski, H.
New York. Plowden, D. Ryall, M. Timoshenko, S. Troitsky, M. Tyrrell, H. Tyrell, Chicago, IL. Unsworth, J. Waddell, J. Whipple, S. Carbon is the principal element controlling the mechanical properties of steel. The strength of steel may be increased by increasing the carbon content, but at the expense of ductility and weldability.
Steel also contains deleterious elements, such as sulfur and phosphorous, that are present in the iron ore. Steel material development in the latter part of the twentieth century has been remarkable. Mild carbon and high-strength low-alloy HSLA steels have been used for many years in railway bridge design and fabrication. Recent research and development related to high-performance steel HPS metallurgy has provided modern structural steels with even further enhancements to physical properties.
An increase in strength is associated with plastic behavior due to strain hardening until the ultimate tensile stress is attained Figure 2. Yield stress in tension can be measured by simple tensile tests ASTM, Yield stress in compression is generally assumed to be equal to that in tension. Two theories, the Tresca and von Mises yield criteria, meet the necessary requirement of being pressure independent. The von Mises criterion is most suitable for ductile materials with similar compression and tensile strength, and also accounts for the influence of intermediate principal stress Chen and Han, ; Chatterjee, It has also been shown by experiment that the von Mises criterion best represents the yield behavior of most metals Chakrabarty, Substitution of these values into Equation 2.
Therefore, a theoretical relationship is established between yield stress in shear and tension. Example 2. AREMA recommends the allowable shear stress for structural steel to be 0. Ductility is necessary in railway bridges and many civil engineering structures to provide advance warning of overstress conditions and potential failure. Adequate ductility also assists in the prevention of lamellar tearing in thick elements. Only ductile steels are used in modern railway bridge fabrication. In steel railway bridges, this fracture can be initiated below the yield stress.
Welding can also create hardened heat-affected zones HAZ , hydrogen-induced embrittlement, and high residual tensile stresses near welds. All of these may be of concern with respect to brittle fracture. Other factors that affect brittle fracture resistance are galvanizing hot-dip , poor heat treatments, and the presence of nonmetallic alloy elements. Normal railway bridge strain rate application is relatively slow in comparison to, e. Brittle fracture can, however, be caused by high strain rates associated with large impact forces from live loads.
Thick elements are often more susceptible to brittle fracture due to the triaxial stress state.
Normalizing, a supplemental heat treatment, can be beneficial in improving material toughness through grain size reduction in thick elements Brockenbrough, Adequate material toughness for the coldest service temperature likely to be experienced by the bridge generally a few degrees cooler than the coldest ambient temperature is critically important. Temperature changes the ductile to brittle behavior of steel. CVN testing is done at a rapid load rate, so adjustments are made to the specified test temperature to account for the greater ductility associated with the slower strain rate application of railway traffic.
Tables 2. Higher-strength steels, where increased strength is attained through increased carbon and manganese content, will become hard and difficult to weld. The addition of other alloy elements to increase strength Cr, Mo, and V and weathering resistance Ni and Cu will also reduce the weldability of steel. Carbon equivalence CE of about 0. Weld cracking generally results from resistance to weld shrinkage upon cooling.
Thicker elements are more difficult to weld. Preheat and interpass temperature control, in conjunction with the use of low hydrogen electrodes, will prevent welding-induced hardening and cracking. Modern structural steels have been developed with excellent weldability. This type of corrosion protection works well where there are alternate wetting and drying cycles. It may not be appropriate in locations where deicing chemicals and salts are prevalent, in marine environments, or where there is a high level of sulfur content in the atmosphere.
Weldability is slightly compromised because CE is raised through the addition of alloy elements for weathering resistance. As-rolled plates shall be sampled at each end of each plate-as-rolled. Normalized plates shall be sampled at one end of each plate-as-heat treated. Quenched and tempered plates shall be sampled at each end of each plate-as-heat-treated. The bar stock so furnished need not conform to the CVN impact test requirements of this table. A numeral 1, 2, or 3 shall be added to the F marking to indicate the applicable service temperature zone.
A numeral 1, 2, or 3 should be added to the T marking to indicate the applicable service temperature zone. TABLE 2. Nonweathering steels can be protected with paint or sacrificial coatings hot-dip or spray applied zinc or aluminum. Shop applied three-coat paint systems are currently used by many North American railroads.
Two, and even single, coat painting systems are being assessed by the steel coatings industry and bridge owners. An effective modern three-coat paint system consists of a zinc-rich primer, epoxy intermediate coat, and polyurethane top coat. For aesthetic purposes, steel with zinc or aluminum sacrificial coatings can be top coated with epoxy or acrylic paints. Mild carbon steel has a carbon content of 0.
Mild carbon steel is not of high strength but is very weldable and exhibits well-defined upper and lower yield stresses Steel 1 in Figure 2. Therefore, it is not desirable to increase strength by increasing carbon content and manipulation of the steel chemistry needs to be considered. HSLA steels have increased strength attained through the addition of many alloys. Alloy elements can significantly change steel phase transformations and properties Jastrewski, The addition of small amounts of chromium, columbium, copper, manganese, molybdenum, nickel, silicon, phosphorous, vanadium, and zirconium in specified quantities results in improved mechanical properties.
These steels typically have a well-defined yield stress in the ksi range Steel 2 in Figure 2. A Grade 42, 50, and 55 steels are used for bolted or welded construction. Higher-strength A steel Grades 60 and 65 is used for bolted construction only, due to reduced weldability. A, A, and A steels are not material toughness graded at the mills and often require supplemental CVN testing to ensure adequate toughness, particularly for service in cold climates. A and A Grade 50W steels are atmospheric corrosion-resistant weathering steels. Further increases in strength, ductility, toughness, and weathering resistance through steel chemistry alteration have been made in recent years.
HSLA steels with 70 ksi yield stress have been manufactured with niobium, vanadium, nickel, copper, and molybdenum alloy elements. These alloys stabilize either austenite or ferrite so that martensite formation and hardening does not occur, as it would for higher-strength steel attained by heat treatment. A concise description of the effects of various alloy and deleterious elements on steel properties is given in Brockenbrough A disadvantage of higher-strength steels is a decrease in ductility.
Heat treatment restores loss of ductility through quenching and tempering processes.
Tempering improves ductility and toughness through temperature relief of the high internal stresses caused by martensite formation. Even HPS steel with ksi yield stress has been quench and temper heat treated to provide good ductility, weldability, and CVN toughness Chatterjee, In such cases, the yield stress is determined at the 0. Use of these steels may result in considerable weight reductions and precipitate fabrication, shipping, handling, and erection cost savings.
High-strength steel can also allow for design of shallower superstructures. However, none of these steels are typically used in ordinary railway bridges.
National Steel Bridge Alliance
HPS 70W and W steels are produced by a combination of chemistry manipulation and quench and temper operations or, for longer plates, thermo-mechanical controlled processing TMCP. The first HPS steels were produced with a yield stress of 70 ksi. However, HPS with 50 ksi yield stress soon followed due to the weldability, toughness, and atmospheric corrosion resistance property improvements of HPS. HPS plates with ksi yield stress are also available. Weldability is increased by lowering the carbon content e.
Toughness is significantly increased through reductions in sulfur content 0. The fracture toughness of HPS is, therefore, much improved with the ductile to brittle transition occurring at lower temperatures the curve shifts to the left in Figure 2. Higher toughness also translates into greater crack tolerance for fatigue crack detection and repair procedure development. Chromium, copper, nickel, and molybdenum are alloyed for improved weathering resistance.
Improved weathering resistant steels are under development that might provide good service in even moderate chloride environments. Also, because fatigue strength depends on applied stress range and detail see Chapter 5 , there is no increase in fatigue resistance for higher-strength steels. Therefore, the material savings associated with the use of higher-strength steels with greater than 50 ksi yield stress may not be available because deflection and fatigue criteria often govern critical aspects of ordinary steel railway superstructure design.
The steel bridge designer must carefully consider all design limit states strength, serviceability, fatigue, and fracture , fabrication, and material cost aspects when selecting the materials for railway bridge projects. All A, Grade 36 36, 58, min 80, max To 4 incl. All A b 46, 70, min Over incl. All A b 42, 63, min Over incl. All A, Grade 42 42, 60, min To 6 incl. In many applications these steels can be used unpainted. Also, as seen in Table 2. Since A Grades 42 and 50 are recommended for welded and bolted construction, with higher grades used for bolted construction only, the AREMA recommendations for structural steel do not include A grades higher than Grade Barsom, J.
Brockenbrough, R. Brockenbrough and F. Chen, W. Fisher, J. Hill, R.. Jastrewski, Z. Kulak, G. Lwin, M. Railroad and other transportation entity operating practices also need careful deliberation. In , it was estimated that there were about 77, bridges of all materials with a cumulative length of miles on , miles of track.
In the cumulative length of steel bridges was estimated as miles. The weight of typical locomotives currently used on North American railroads approaches Trains with loads causing many cycles of stress ranges that might accumulate significant fatigue damage did not occur until the latter half of the twentieth century when typical train car weights increased from , lb to over , lb on a regular basis. This information is required for the selection of span lengths, types, and materials for preliminary design.
Preliminary design concepts are often the basis of regulatory reviews, permit applications, and budget cost estimates. Detailed design of the bridge for fabrication and construction can proceed following preliminary design. Construction methods that minimize the interference to normal rail, road, and marine traffic enable simple erection and are cost-effective must be carefully considered during the planning process.
These methodologies may add cost to the reconstruction project that are acceptable in lieu of the costs associated with extended interruption to railway or marine traffic. Therefore, site reconnaissance surveying and mapping and route selection are performed on the basis of business, technical, and public considerations. The railroad operating environment presents specific challenges for bridge design, maintenance, rehabilitation, and construction. Existing records and drawings of previous construction are of considerable value during planning of railway bridges being reconstructed on the same, or nearby, alignment.
Regulatory requirements relating to railway bridge location, construction, and environmental mitigation vary by geographic location and jurisdiction. Environmental protection vegetation, fish, and wildlife and cultural considerations are often critical components of the bridge planning phase. Land ownership and use regulations also warrant careful review with respect to potential bridge crossing locations. Railway bridge construction project managers and engineers must be well versed in the jurisdictional permitting requirements for bridge crossings. Regulatory concerns regarding bridge location and construction that may affect bridge form must be communicated to the railway bridge designer during the planning phase.
The basic form of the bridge may depend on whether the flood plain is stable. Stable flood plains may be spanned with shorter spans unless shifting channel locations require the use of longer spans. Hydraulic studies must also consider the potential for scour at substructures. Discharge flows that exceed subcritical at, or even immediately downstream of, the bridge may also be acceptable with adequate scour protection. Published values of C c for various constriction geometries are available in the literature on open channel hydraulics Chow, It determines a base coefficient of discharge, C', for four opening types in terms of the opening ratio, N, and constriction length ratio, Lib.
The coefficient of discharge, C , is further modified by adjustment factors based on the opening ratio, Froude number, F, and detail abutment geometry to obtain the discharge coefficient, C. In terms of the USGS method, the coefficient of contraction is ,3 - 71 where C is the USGC discharge coefficient, which depends on N, L, b, F, and other empirical adjustment factors based on skew angle of the crossing, the conveyance, K, details the geometry and flow depth at the constriction; N is the bridge opening ratio and is equal to QJQ , where Q c is the undisturbed flow that can pass the bridge constriction and Q is the flow in the not constricted channel; L is the length of channel at the constricted bridge crossing; K — AT?
In these cases, many piers are required that may create an obstruction to the flow and consideration of the contraction effects due to obstruction is also necessary Equation 3. Hydraulic Research methods are also used. The degree of contraction is usually less for obstructions than constrictions. Published values of C c for various obstruction geometries are available in the literature on open channel hydraulics Yarnell, ; Chow, The flow about an obstruction consisting of bridge piers was extensively investigated Nagler, and Equation 3.
When pier drag forces constitute the predominate friction loss through the contraction, the momentum balance or Yarnell equation methods are applicable. The momentum balance method yields more accurate results when pier drag becomes more significant. The Yarnell equation is based on further experiments summarized by Yarnell, with relatively large piers typical of railway bridge substructures that were performed to develop equations for the afflux for use with Equation 3.
The afflux depends on whether the flow is subcritical or supercritical Hamill, For supercritical flow conditions which will cause downstream hydraulic jump , the analysis is more complex and design charts have been made to assist in establishing the discharge past obstructions Yarnell, Scour can occur when the streambed is composed of cohesive or cohesionless materials.
However, scour generally occurs at a much higher rate for cohesionless materials, which will be the focus of the present discussion. General scour may also occur due to degradation, or adjustment of the river bed elevation, due to overall hydraulic changes not specifically related to the bridge crossing. This component of the general scour may occur with live-bed scour the streambed material upstream of the bridge is moving conditions. Accurate assessment methods for general scour, dg , are available TAC, ; Richardson and Davis, Scour will cease when the rate of sediment deposit equals the rate of loss by contraction scour.
During dear- water conditions sediment is not transported into the contraction scour depth increase creating channel bed depressions or holes. Scour will equilibrate and cease when the velocity reduction caused by the increased area becomes less than that required for contraction scour. Equation 3. In some cases, substructure depth must also be designed anticipating extreme natural scour and channel degradation events. Also, it is often beneficial to consider the use of fewer long piles than a greater number of short piles when the risk of foundation scour is relatively great.
Provision for changes in elevation of the under-crossing i. The minimum railway bridge clearance envelope recommended by AREMA is generally 23 ft from the top of the rail and 9 ft each side of the track center- line. These dimensions must be revised to properly accommodate track curvature. Soil borings should generally be taken at or near each proposed substructure location. For the purposes of railway bridge design, the subsurface investigation should yield a report making specific foundation design recommendations.
Although typically more costly than driven piles, concrete piles may also be installed by boring when required by the site conditions. However, tolerable settlements may depend on longitudinal and lateral track geometry regulations, which are often specified as maximum permissible variations in rail profile and cross level. In some cases it is possible that, due to geotechnical conditions, foundations must be relocated. This will result in significant changes in the proposed bridge arrangement and should be carefully and comparatively cost estimated.
A geotechnical engineer experienced in shallow and deep bridge foundation design and construction should be engaged to manage geotechnical site investigations and provide recommendations for foundation design. Track profile, or vertical alignment, is composed of constant grades connected by parabolic curves. The magnitude of the force depends on the track curvature and live load speed and is applied at the center of gravity of the live load see Chapter 4.
Track alignment and superelevation also affect vertical live load forces including impact in supporting members based on geometrical eccentricity of the live load. The central angle subtended by a ft chord in a simple curve, or the degree of curvature, D, is used to describe the curvature of North American railroad tracks. The track is superelevated to accommodate the centrifugal forces that occur as the train traverses through curved track Figure 3. Transition curves are required between tangent and curved tracks to gradually vary the change in the lateral train direction.
The cubic parabola is used by many freight railroads as a transition from the tangent track to an offset simple curve. The length of the transition curve is based on the rate of change of superelevation. For example, with a rate of change of superelevation that is equal to 1. Right spans must be laid out on a chord to form the curved track alignment. However, fabrication effort and costs must be carefully considered prior to designing offset floor systems. The superelevated and curved track creates horizontal eccentricities based on the horizontal curve geometry track curvature effect , e c , and vertical superelevation track shift effect , e s.
These eccentricities must be considered when determining the lateral distribution of live load forces including dynamic effects to members stringers, floorbeams, and main girders or trusses. The shift effect eccentricity, e s , is Figure 3. These effects are often negligible for short spans or shallow curvature Waddell, However, if necessary, they can be determined in terms of the main member shear force and bending moment for the tangent track across the span as Figure 3. For the condition of equal shear from Equations 3.
Example 3. The railroad has specified a 5 in. The track tie depth and rail height are taken as 7in. Determine the geometrical effects of the curvature on the design live load shear and bending moment for each girder. The effect of the offset of the live load center of gravity is Equation 3. The outside girder forces will be reduced by, and the inside girder forces increased by, [2 9. The curve mid-ordinate over a 70 ft span Equation 3.
Design for equal shear at the girder ends and use a track offset at the centerline of 7.
The effect of the curvature alignment Equations 3. It should be noted that these shear and bending moment forces do not include the effects of the centrifugal force. Section The bridge deck must be superelevated as indicated in Section 3. The required superelevation is easily accommodated in ballasted deck bridges Figure 3.
Varying the elevation of the deck supporting members may be problematic from a structural behavior, fabrication, and maintenance perspective and, generally, is not recommended. Curved spans must be designed for flexural and torsional effects. Dynamic behavior under moving loads is particularly complex for curved girders as flexural and torsional vibrations may be coupled. These analyses are complex and often carried out with general purpose finite element or grillage computer programs.
A synthesis of the research is available from the FHWA. Nevertheless, curved girders are often effectively utilized for light transit applications. There are many salient design and construction reasons for avoiding skewed bridge construction. Torsional moments and unequal distribution of live load occur with larger skew angles and compromise performance.
Also, skewed spans generally require more material than square spans and include details that increase fabrication cost. Many railroads have specific design requirements regarding skew angle and type of construction for skewed railway bridges. Skew connections and bent plates may be prohibited requiring that the track support at the ends of skewed spans be perpendicular to the track. This can be accommodated many ways depending on bearing and span types.
Figure 3. The length of spans is generally governed by site conditions, such as hydraulic or geotechnical considerations, or transportation corridor clearances railroad, highway, or marine. Width is controlled by the number of tracks and the applicable railway company and regulatory clearances. Bridge aesthetics is of particular importance in urban or accessible natural environments. However, there are some basic tenets of aesthetic bridge design that appear to be generic in nature Leonhardt, ; Billington, ; Taly, ; Bernard-Gely and Calgaro, Harmony is often of primary importance to the public who generally desire bridges to integrate and be compatible with their environment.
The bridge should also be expressive of function' and materials. However, the economical proportioning of bridges does not necessarily produce aesthetic structures and other issues, in addition to harmony and expression of function, also warrant careful deliberation. Proportion and scale are important. The deck plate forms the top flange of the bridge deck. There are different types of bridge deck structure; most of them vary in the form of the longitudinal stiffeners.
These longitudinal stiffeners can be divided into two types: open stiffeners such as flat bars, angles and bulb sections and closed stiffeners with a trapezoidal, V or rounded form. Fatigue is a well known phenomenon related to orthotropic bridge decks and is a worldwide problem. Several bridge cases are known and, despite years of research made in the Netherlands, United Kingdom, Hungary, Japan, Brazil and many other countries, a good solution was, until now, not available for a fast and definite rehabilitation.