Bridges must be designed to carry the specified dead loads, live loads and impact, as well as centrifugal, wind, other lateral loads, loads from continuous welded rail, longitudinal loads and earthquake loads. The forces and stresses from each of these specified loads should be a separate part of the design calculations. Also, because rail cars have changed in size and weight over the years and frequently are run in unit consists, the designer should be alert to live loadings that may be more severe than those used in some specifications (Art. 11.35.2).
Dead loads should be calculated based on the weight of the materials actually specified for the structure. The dead load for rail and fastenings may be assumed as 200 lb per ft of track.
Unit weights of other materials may be taken as follows:
Note that walkway construction may add significantly to the dead load. Also, when a long body rail casting, such as expansion joints, are specified for a bridge, the castings should be supported only on one span of the stringers.
Railroad bridges have been designed for many years using specified Cooper E Loadings. See Fig. 11.16a for the wheel arrangement and the trailing load for the Cooper E80 loading, which includes 80 kip axle loads on the drivers. This configuration can be moved in either direction across a span to determine the maximum moments and shears. With the continuing increase in car axle loads, AREMA has also adopted the Alternate Live Load on four axles shown in Fig. 11.16b. It recommends that bridge design be based on the E80 or the Alternate Loading, whichever produces the greater stresses in the member. A table of live load moments, shears, and reactions for both the E80 and the Alternate Loading may be found in the Appendix of Chapter 15 of the AREMA Manual. The table values are presented in terms of wheel loads (one-half of an axle load).
Some owners may elect to use loadings other than E80 in some cases. Such loadings may be directly proportioned from the E80 loading according to the axle load on the drivers.
For example, an owner specifying a new through truss or girder span may specify an E95 loading for the floor system and hangers, and an E80 loading for the rest of the structure.
It is considered good practice to keep the bridge design loading well above the economical loading capacity of rolling stock and track structure.
The path of the load from the wheels through the rail and into the tie, is either directly to the supporting beams, or through a ballast bed to a deck and thence into the supporting beams. Direct fixation of the rails to supporting members is not considered here.
Figure 11.17a provides a sectional view of an open-deck through-girder span. This type of construction should provide a clear space between ties of no more than 6 in. The guard timber shown at the end of the tie has the function of keeping the ties uniformly spaced and preventing tie skewing. Tie skewing must be prevented because it closes the gage between the rails. Hook bolts or tie anchor assemblies, not shown in the sketch, are used to fasten the tie to the support beam. The guard timbers are fastened to the ties with 5â„8-in-diameter washerhead drive spikes, through bolts, or lag bolts.
Figure 11.17b provides a sectional view of a ballast-deck through-girder span. Many such spans are designed with closely spaced floorbeams, thus eliminating the stringers.
Load on Multi-Track Structures
To account for the effect of multiple tracks on a structure, the proportion of full live load on the tracks should be taken as follows:
Two tracks Full live load.
Three tracks Full live load on two tracks, one-half live load on third track.
Four tracks Full live load on two tracks, one-half live load on one track, one-quarter live load on remaining track.
The tracks selected for these loads should be such that they produce the maximum live load stress in the member under consideration. For bridges carrying more than four tracks, the track loadings should be specified by the owners engineer.
Impact loads, I, are expressed as a percentage of the specified axle load and should be applied downward or upward at the top of the rail. For open-deck bridge construction, the percentages are obtained from the applicable equations given below. For ballast-deck bridges designed according to specifications, use 90% of the impact load given for open deck bridges.
For rolling equipment without hammer blow (diesel or electric locomotives, tenders, rolling stock):
In the above equations, RE = 10% (RE represents the rocking effect, acting as a couple with a downward force on one rail and an upward force on the other rail, thus increasing or decreasing the specified load); for stringers, transverse floor beams without stringers, longitudinal girders and trusses, L = length, ft, center to center of supports; for floor beams, floor beam hangers, subdiagonals of trusses, transverse girders, supports for longitudinal and transverse girders, and viaduct columns, L = length, ft, of the longer supported stringer, longitudinal beam, girder, or truss.
On multi-track bridges, the impact should be applied as follows:
When load is received from two tracks:
The longitudinal loads from trains on bridges are generally attributed to tractive or braking effort. With the current use of high adhesion locomotives and the development of better braking systems, bridges may be subject to greater longitudinal loads than in the recent past.
The current AREMA recommendation is to assume the longitudinal load as 15% of the specified live load without impact for braking and 25% for traction.
Field measurements are being made on selected bridges to determine longitudinal loads associated with high adhesion locomotives. Until additional information is available for noncontinuous rail across bridges, such as on structures with lift joints or expansion joints, the designer can consider locomotives as developing a draw bar effort of 0.90 x 0.37 x weight of the locomotive axles. Bridges in pull-back, push-in areas and on grades requiring heavy tractive effort, may experience greater than normal longitudinal loads.
The longitudinal load should be applied to one track only and should be distributed to the various components of the supporting structure, taking relative stiffnesses into account where appropriate, as well as the type of bridge bearings. The braking effort is assumed to act at 8 ft above the top of the rail, and tractive effort at 3 ft above the top of the rail.
On curves, a centrifugal force corresponding to each axle should be applied horizontally through a point 6 ft above the top of the rail. This distance should be measured in a vertical plane along a line that is perpendicular to and at the midpoint of a radial line joining the tops of the rails. This force should be taken as a percentage C of the specified axle load without impact. Any eccentricity of the centerline of track on the support system requires the live load to be appropriately distributed to all components.
C = 0.00117S^2D
where S train speed, mph
D degree of curve 5729.65/R
R radius of curve, ft
When the superelevation is 3 in less than that at which the resultant flange pressure between
wheel and rail is zero,
On curves, each axle load on each track should be applied vertically through the point defined above, 6 ft above top of rail. Impact should be computed and applied as indicated previously.
Preferably, the section of the stringer, girder, or truss on the high side of the superelevated track should be used also for the member on the low side, if the required section of the lowside member is smaller than that of the high-side member.
If the member on the low side is computed for the live load acting through the point of application defined above, impact forces need not be increased. Impact forces may, however, be applied at a value consistent with the selected speed, in which case the relief from centrifugal force acting at this speed should also be taken into account.
Lateral Loads From Equipment
In the design of bracing systems, the lateral force to provide the effect of the nosing of equipment, such as locomotives (in addition to the other lateral forces specified), should be a single moving force equal to 25% of the heaviest axle load (E80 configuration). It should be applied at the base of the rail. This force may act in either lateral direction at any point of the span.
On spans supporting multiple tracks, the lateral force from only one track should be used.
Resulting vertical forces should be disregarded.
The resulting stresses to be considered are axial stresses in the members bracing the flanges of stringers, beams and girders, axial stresses in the chords of trusses and in members of cross frames of these spans, and the stresses from lateral bending of flanges of longitudinal flexural members, which have no bracing system.
The effects of the lateral load should be disregarded in considering lateral bending between brace points of flanges, axial forces in flanges, and the vertical forces transmitted to the bearings.
Stability of spans and towers should be calculated using a live load, without impact, of 1200 lb per ft. On multitrack bridges, this live load should be positioned on the most leeward side.
The lateral bracing of the compression chord of trusses, flanges of deck girders, and between the posts of viaduct towers, should be proportioned for a transverse shear force in any panel of 2.5% of the total axial force in both members in that panel, plus the shear force from the specified lateral loads.
AREMA recommended practices consider wind to be a moving load acting in any horizontal direction. On unloaded bridges, the specified load is 50 psf acting on the following surfaces:
Girder spans: 11â„2 times vertical projection Truss spans: vertical projection of span plus any portion of leeward truss not shielded by the floor system Viaduct towers and bents: vertical protection of all columns and tower bracing On loaded bridges, a wind load of 30 psf acting as described above, should be applied with a wind load of 0.30 kip per ft acting on the live load of one track at a distance of 8 ft above the top of the rail. On girder and truss spans, the wind force should be at least 0.20 kip per ft for the loaded chord or flange and 0.15 kip per ft for the unloaded chord or flange.
The above specified loads were generally based on traditional rail cars with a vertical exposure of approximately 10 ft. Today, equipment such as double stack containers may have a vertical exposure of 20 ft and move in long blocks of cars. The designer should consider locations where high wind velocity and vehicle exposure may justify using greater loadings.
Single panel simple span bridges designed in accordance with generally accepted practices for anchor bolts, bridge seat widths, edge distance on masonry plates, continuous rail, etc.
may not require analysis for earthquake loads. In other cases, earthquake loads may be very important. The designer must take into account the owners requirements and should refer to AREMA Chapter 9, Seismic Design for Railway Structures, for specific requirements.
Load From Continuous Welded Rail
Evaluation of the loads to be taken in the bridge components from continuous welded rail is very subjective. The sources of internal stress in the rail are generally temperature, braking, tractive effort of locomotives, rail creep, load from track curvature, and gravity in long track grades. The loads generated by these conditions depend upon the type of fastenings used.
Thus, the bridge designer must be familiar with the fastening systems for rail and ties on open deck and ballast deck bridges. The rail must be adequately constrained against vertical and lateral movement as well as longitudinal movement, unless provision is made for expansion and contraction of the rail at one or more points on the bridge. Railroad bridge owners may have their own specifications for fastening rail on bridges that the designer must follow. Also, refer to AREMA Chapter 15, Part 8, for recommended practices.
Combination Loads Or Wind Load Only
Every component of substructure and superstructure should be proportioned to resist all combinations of forces applicable to the type of bridge and its site. Members subjected to stresses from dead, live, impact, and centrifugal loads should be designed for the smaller of the basic allowable unit stress or the allowable fatigue stress.
With the exception of floorbeam hangers, members subjected to stresses from other lateral or longitudinal forces, as well as to dead, live, impact, and centrifugal loads, may be proportioned for 125% of the basic allowable unit stresses, without regard for fatigue. But the section should not be smaller than that required with basic unit stresses or allowable fatigue stresses, when those lateral or longitudinal forces are not present. Note that there are two loading cases for wind: 50 psf on the unloaded bridge, or 0.30 kip per ft on the train on one track and 30 psf on the bridge.
Components subject to stresses from wind loads only should be designed for the basic allowable stresses. Also, no increase in the basic allowable stresses in high strength bolts should be taken for connections of members covered in this article.
Distribution of Loads Through Decks
The AREMA Manual contains recommended practices for distribution of the live loads described in Art. 11.35.2 to the ties in open deck construction and to the deck materials in ballast deck bridges. Attention is called to the provision that, in the design of beams and girders, the live load must be considered as a series of concentrated loads.
On open-deck bridges, ties within a length of 4 ft, but not more than three ties, may be assumed to support a wheel load. For ballasted-deck structures, live-load distribution is based on the assumption of standard crossties at least 8 ft long, about 8 in wide, and spaced not more than 2 ft on centers, with at least 6 in of ballast under the ties. For deck design, each axle load should be uniformly distributed over a length of 3 ft plus the minimum distance from bottom of tie to top of beams or girders, but not more than 5 ft or the minimum axle spacing of the loading. In the lateral direction, the axle load should be uniformly distributed over a length equal to the length of tie plus the minimum distance from the bottom of tie to top of beams or girders. Deck thickness should be at least 1â„2 in for steel plate, 3 in for timber, and 6 in for reinforced concrete.
For ballasted concrete decks supported by transverse steel beams without stringers, the portion of the maximum axle load to be carried by each beam is given by
For end shear, D = d. At each rail, a concentrated load of P/2 should be assumed acting on each beam.
D should be taken equal to d for bridges without a concrete deck or where the concrete slab extends over less than the center 75% of the floorbeam.
If d > S, P should be tile maximum reaction of the axle loads with the deck between beams acting as a simple span.
For ballasted decks supported on longitudinal girders, axle loads should be distributed equally to all girders whose centroids lie within a lateral width equal to length of tie plus twice the minimum distance from bottom of tie to top of girders.
Design requirements for use of timber and concrete for bridge decks is included in Chapters 7 and 8 of the AREMA Manual.
The designer should be aware of any pertinent requirements of the bridge owner for such items as concrete slab overhang, derailment conditions, composite action, waterproofing and drainage.
IF the design axle load is at 22.5t , what is the AREMA recommendation for the track design load if the annual tonnage is about 11million tonnes