In this article we will discuss about:- 1. Introduction to Bridges 2. Types of Steel Bridges 3. Truss Components 4. Economic Span 5. Loads.
Introduction to Bridges:
Bridges are structures meant to support rail road traffic, highway traffic or pedestrian loads across openings or crossings or another set or rail or highway traffic or across any natural or artificial obstacles. Based on the type of traffic for which they are provided, bridges may be classified into- (i) Highway bridges (ii) Railway bridges (iii) Foot bridges for pedestrian traffic. We also at times come across combined Highway and Railway bridges.
Bridges may be made of timber, masonry, reinforced concrete, prestressed concrete and steel. Timber bridges are generally provided for small spans and sometimes as a temporary bridge. For permanent bridges or small spans not exceeding 12 m, masonry bridges may be provided. For greater spans, the dead load of masonry becomes large and hence masonry bridges work out to be uneconomical.
Reinforced concrete bridges are found to be economical for spans exceeding 12 m. Prestressed concrete bridges have been constructed for spans up to 60 m. Arched concrete bridges have been built for still greater spans. Since steel possesses a high working stress compared to other materials, steel bridges work out to be economical for large spans.
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Steel bridges are very common for small as well as long spans in railways. Fabricated components of a steel bridge can be easily transported to the site and assembled, thus considerably reducing the construction time.
A bridge forms mainly the super structure spanning the required length and it comprises of the floor system, the trusses or girders system, support arrangement and lateral bracing system.
The floor system provides a satisfactory surface to afford easy movement of traffic over it. The floor system transmits its weight and loads due to vehicular traffic to the supporting trusses or girders. The trusses and girders in turn transmit all loads received by them to the abutments or supporting piers.
Trusses and girders are provided with end shoe device to safely transmit the reactions to the supporting abutments. Such an arrangement also makes provision for slight longitudinal movements due to temperature changes.
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A lateral bracing system is provided to the bridge, which not only provides adequate stiffness but also minimizes vibrations. Such bracing system also resists lateral forces transmitted by wind action on the structure as well as the moving vehicles.
Steel bridges may be of the following types:
Rolled steel beam bridges – for spans up to 10 m
Plate girder bridges – for spans from 10 m to 40 m
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Trussed bridges – for spans greater than 40 m
Bridges may be classified into Deck Types Bridge and through type bridges, according to the manner of transference of live load to the bridge. In the case of Deck type truss bridges, the floor of the bridge is supported at the top chord joints of the truss. In a Deck type plate girder bridge, the floor is supported on the top flange. In through type truss bridges, the floor is supported at the lower chord joints of the truss and the top chord is provided with lateral bracing.
In a through type plate girder bridge, the floor is supported at the level of the lower flange and the top flanges are braced laterally. Sometimes the floor is supported on the bottom chord or near the bottom chord and the top chords are not braced. Such bridges are called half through or semi-through bridges.
Types of Steel Bridges:
A brief description of some types of steel bridges is given below:
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(i) Beam and Slab Bridge:
These are convenient where the span of the beam exceeds 5 in. For small spans I-section beams may be used. For spans more than 8 m, built-up I-sections or plate girders are used. By providing a combination of main plate girders and cross beams, the bridges can be made for spans up to 20 m.
For very large spans deck and through plate girder bridges may be used. Generally railway deck plate girder bridges are designed to carry one track. Two single-track bridges are made side by side resting on piers and abutments forming a double track bridge. In situations when the clearance below the structure is small it is necessary to provide a through girder bridge.
(ii) Box-Girder Bridges:
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These bridges are found convenient for spans up to 50 m. The box girder consists of steel plates fabricated to box shape and strengthened by angles and channels.
(iii) Trussed Bridges or Open Web Girder Bridges:
These are the most commonly used bridges and are found satisfactory for spans 10 m to as large as 300 m. Bridges of spans 50 m to 60 m are most common. Cross beams are connected to trusses either at the level of the top chord or at the level of the bottom chord. Accordingly the bridges are deck bridges or through bridges.
The trusses with parallel chords can be modified to make curved chord trusses. If trusses whose depths vary throughout the length from both ends the forces in the chord members are more or less equalized. Web members of curved chord trusses are likely to be subjected to lesser forces than in the case of parallel chord trusses.
The angle between inclined and vertical members may be 45° to 60°. In order to reduce the lengths of the loaded chords (bottom chords of through trusses and top chords of deck trusses) it is convenient to make subdivided loaded chords.
Truss Components of a Bridge:
The various components of a truss bridge are the following:
1. Chord Members:
These are top and bottom members which act like the flanges of a beam. They resist compressive and tensile forces. The chord members are parallel in a truss of uniform depth. Their profile may however range from uniform depth to variable depth as for example in a bowstring truss. Variable depth profile offers economy.
2. Web Members:
These consist of vertical and diagonal members. In parallel chord trusses, the diagonals offer the required shear resistance. Verticals also carry shear besides providing additional panel points for introduction of loads. Verticals subjected to compression are called posts and those subjected to tension are called hangers.
3. Counters or Counter Bracers:
Counters or counter bracers are a pair of intersecting diagonals in a panel where a single diagonal would be subjected to stress reversal. These are provided in lattice trusses, sway frames and portals.
4. End Posts:
These are compression members provided at supports of single span trusses.
5. The Deck:
This is the structural unit which provides the direct support for vehicular loads.
6. Floor Beams:
These are beams set normal to the direction of traffic. These beams transmit the deck loads to the trusses.
7. Lateral Bracing:
These are members connecting the top chords of two trusses and bottom chords of two trusses. The bracing system forms trusses in the plane of the top chord and in the plane of the bottom chord. These provide stability and offer lateral resistance to wind action.
8. Long Span Bridges:
In the case of a long span bridge truss the members of the truss are likely to be subjected to large forces. In such cases, cantilever bridges, continuous bridges, suspension bridges and arched bridges are found suitable. A cantilever bridge consists of two cantilever trusses supporting between their ends a central simple span truss.
Continuous trusses have more than two supports and are statically indeterminate. In an arch carrying a loading, besides vertical reactions these will also be horizontal thrusts at the supports, which reduce the bending moments. Arches may be three hinged, two hinged or fixed arches.
Economic Span of a Bridge:
The span of a bridge may be so determined that the total cost of the bridge is a minimum. The span to satisfy this condition is called the economic span. The total cost of the bridge consists of the cost of the substructure and that of the superstructure. Very often it is seen that the cost of the substructure forms nearly 50 per cent of the total cost of the bridge.
The cost of pier will not change appreciably for small change in span. Even the cost of the floor-way is not affected much for small variation in span. But it is seen that the cost of the trusses and bracings is directly proportional to the span of the bridge.
But lCt = cost of the trusses and bracings corresponding to one span
Hence, the cost of the whole bridge is a minimum when the cost of one pier and the cost of trusses and bracings corresponding to one span are equal.
Loads on Bridges:
The various loads, forces and stresses to be considered for the design of bridges are the following:
(i) Dead Load:
Dead load is the weight of the floor slab, track stringers, ballast, guard rails, bracing system, rails sleepers etc.
The dead load of the various components may be taken at the following values:
For a single track,
Weight of rails, guide rails and fastening – 3000 N/m
Weight of concrete – 25000 N/m3
Weight of ballast – 1000 N/m3
Wooden tier – 8000 N/m3
The dead load of a bridge depends on various factors like depth of girder or truss, span, number of panels, width of bridge etc.
The dead load of trusses may be estimated by the following methods:
(a) Hudson Formula:
Weight per metre of trusses and bracings = 0.785 A Newton/metre.
Where, A = Maximum net area of the tension chord
(b) Fuller’s Formula:
Weight per metre of truss bridges = (150 L + 5500) Newton/metre
(spans 30 m to 90 m)
Weight per metre of plate girders = (200 L + 1000) Newton/metre
(spans 10 m to 30 m)
where L = span of the bridge in metres
(c) For a Single Track Railway:
Weight of both the girders including bracings system, per metre = (52 to 53) L √w N/w
where, L = span in metres,
w = Heaviest axle load of the engine in kN
(ii) Live Load:
Live Load on Highway Bridges:
Live Loud on Footways (Foot Bridges):
The live load on foot bridges shall be taken as follows:
For all parts of bridge floors accessible to pedestrians and animals and for all foot ways, the loading shall be 4000 N/m1. Where crowd loads are likely to occur, such as a foot bridge located near towns which are either centres of pilgrimage or where congregational fairs are held seasonally, the intensity of the footway loading shall be increased from 4000 N/m2 to 5000 N/m2.
Kerbs 0.6 m or more in width shall be designed for the above loads. If the kerb width is less than 0.6 m no live load shall be considered.
The main girder, trusses, arches or other members supporting the footways shall be designed for the following live loads per square metre of the footway area, the loaded length of the footway taken in each case being such as to produce the worst effects on the member under consideration.
(a) For effective spans of 7.5 m or less – 4000 N/m2, but for crowded locations – 5000 N/m”
(b) For effective spans of over 7.5 m but not exceeding 30 m – The intensity of the load be determined according to the equation.
(c) For effective spans of over 30 m, the intensity of the load shall be determined according to the equation-
Each part of the footway shall be capable of carrying a wheel load of 40 kN which shall be deemed to include impact, distributed over a contact area 300 mm in diameter. The working stresses shall be increased by 25 per cent to meet this provision. This provision need not be made where vehicles cannot mount the footway as in the case of a footway separated from the roadway by means of an insurmountable obstacle, such as truss on a main girder.
Railings, Parapets or Guide Posts:
(1) High Level Bridges:
(a) Substantial railings or parapets along each side of the bridge shall be provided for the protection of traffic. Consideration shall be given to the architectural features of the railing or parapet to obtain proper proportioning of its various members and its harmony with the structure as a whole. Consideration shall be given also to avoiding, as far as is consistent with safety and appearance, obstruction of the view from passing motor cars.
(b) Railings or parapets shall have a minimum height above the adjacent roadway or footway surface, of one metre less one-half the horizontal width of top rail or top of the parapet. They shall be designed to resist a lateral horizontal force and a vertical force each of 1500 N per metre run applied simultaneously at the top of the railing or parapet.
These forces shall also be considered in the design of the main structural members if the bridge is provided with footpaths. Where, however, footpath are not provided, these forces need not be considered in the design of main structural members.
(c) The clear distance from the lower rail to the top of the kerb shall not exceed 150 mm unless that space is filled by vertical or inclined members, the clear distance between which is not more than 150 mm. The strength of the lower rail shall be at least as great as that of the top rail.
The space between the lower rail and the top rail shall be filled by means of vertical, horizontal or inclined members, the clear distance between, which shall be fixed, with due regard to the safety of persons and animals using the structure.
(2) Submersible Bridges:
Railing shall be either collapsible or removable:
(a) Collapsible railings shall be used where it is necessary to put up the railings immediately the bridge is open to traffic after a submerging flood. Care shall be taken in the structural design of these railings to ensure that they sit well in their grooves and are not liable to be dislodged by floods.
(b) Removable railings may be adopted when there is no danger to the traffic using the bridges for short periods without railing. Care shall be taken in the structural design of these railings to ensure that the various members are interchangeable and can be easily removed and refitted.
(c) Collapsible or removable railings shall be designed to resist as far as possible the same forces as specified in (1) b for railings or parapet on high level bridges.
All structures shall be designed for the following lateral wind forces. These forces shall be considered to act horizontally and in such a direction that the resultant stresses in the member under consideration are the maximum.
The wind force on a structure shall be assumed as a horizontal force of the intensity specified below and acting on an area calculated as follows:
(a) For Deck Structures:
The area of the structure as seen in elevation including the floor system and railing, less area of perforations in the hand railing or parapet wall (while calculating the wind pressure on live load, or clear distance between the trailers of a train of vehicles shall not be omitted).
(b) For a through or Half through Structure:
The area of the elevation of the windward truss as specified in- (a) above, plus half the area of the elevation above the deck level of all other trusses or girders.
The following table gives the wind pressure intensities corresponding to various velocities of wind. The pressure given in this table shall however be doubled for bridges situated in the areas such as the Kathiawar Peninsula, and the Bengal and Orissa coasts.
In the above table-
H = The average height in metres of the exposed surface above the mean retarding surface (ground or bed level or water level).
V = Horizontal velocity of wind in Kilometres per hour at height H.
P = Horizontal wind pressure in N/metre2 at height H.
The lateral wind force against any exposed moving live load shall be considered as acting at 1.5 metre above the roadway and shall be assumed to have the following values:
(a) Highway bridges, ordinary = 3000 N/m run
(b) Highway bridges, carrying tramway = 4500 N/m run
while calculating the wind pressure of live load, the clear distance between the trailers of a train of vehicles shall not be omitted.
The bridges shall not be considered to be carrying any live load when the wind velocity at deck level exceeds 130 kilometres per hour.
The total assumed wind force as calculated according to the above paragraphs shall however not be less than 4500 N per metre run in the plane of the loaded chord and 2250 N per metre run in the plane of the unloaded chord on through or semi-through truss, latticed or similar span and not less than 4500 N per metre run on deck spans.
A wind pressure of 2400 N per metre2 on the unloaded structure applied as specified in the above paragraphs shall be used if it produces greater stresses than those produced by the combined wind forces mentioned above.
(iv) Longitudinal Forces:
In all road bridges, provision shall be made for longitudinal forces arising from any one or more of the following causes:
(a) Tractive efforts caused through acceleration of the driving wheels
(b) Braking effect resulting from the application of brakes to braked wheels, and
(c) Frictional resistance offered to the movement or free bearings due to change of temperature or any other cause.
Note:
Braking effect is invariably greater than the tractive effort.
The braking effect on a simply supported span of a continuous unit of spans or any other type of bridge unit shall be assumed to have the following value:
(a) In the case of a single lane or a two lane bridge. 20 percent of the first train load plus 10 percent of loads of the succeeding trains or part thereof, the train loads in one lane only being considered for the purposes of this clause. Where the entire first train is not on the full span, the braking force shall be taken as equal to 20 percent of the loads actually on the span.
(b) In the case of bridges having more than two lanes. As in (a) above for the first two lanes plus 5 percent of the loads on the lanes in excess of two.
Note:
The loads in this clause shall not be increased on account of impact.
The force due to braking effect shall be assumed to act along a line parallel to the roadway and 1.2 metres above it. While transferring the force to the bearings, the change in the vertical reaction at the bearings should be taken into account.
The longitudinal force at any free bearing shall be limited to the sum of dead and live load reactions at the bearing multiplied by the appropriate coefficient of friction.
The coefficient of friction at the bearing shall be assumed to have the following values:
For simply supported reinforced concrete and prestressed concrete superstructure, the span upto which plate bearing can be used shall be limited to 15 metres.
The longitudinal force at the fixed bearings shall be taken as the algebraic sum of the longitudinal forces at the free bearings in the bridge unit under consideration and the force due to the braking effect on the wheels, mentioned in (a) and (b) above.
The effect of braking force on bridge structures without bearings such as arches, rigid frames etc., shall be calculated in accordance with approved methods of analysis of indeterminate structures.
The effects of braking force on bridge structures without bearings such as arches, rigid frames etc., where the resultant passive earth resistance of the soil below the deepest scour level (floor level in case of a bridge having pucca floor) balances these forces.
Centrifugal Forces:
In case a road bridge is situated on a curve, all portions of the structure affected by the centrifugal action of moving vehicles are to be proportioned to carry safely the stress induced by this action in addition to all other stresses to which they may be subjected.
The centrifugal forces shall be determined from the following equations:
C= Centrifugal forces acting normally to the traffic (1) at the point of action of the wheel loads or (2) uniformly distributed over every metre length on which a uniformly distributed load acts.
W = Live load (1) in TV in case of wheel loads, each wheel load being considered as acting over the respective ground contact length and (2) in N/m per metre in case of a uniformly distributed live load.
V = The design speed of vehicles using the bridge in kilometres per hour and
R = The radius of curvature in metres
The centrifugal force shall be considered to act at a height of 1.2 m above the level of the carriageway.
No increase for impact effect shall be made on the stresses due to centrifugal action.
The overturning effect of the centrifugal force on the structure as a whole shall also be duly considered.
Temperature Effect:
Provision shall be made for stresses and moments from variations in temperature.
The rise and fall in temperature shall be fixed for the locality in which the structure is to be constructed and shall be figured from an assumed temperature at the time of erection.
Due consideration shall be given to the lag between air temperature and the interior temperature of massive concrete members or structures.
Except where stated otherwise, the following range of temperature shall generally be assumed in the design:
Moderate climate: from – 18°C to + 50°C
Extreme climate: from – 35°C to + 50°C
But, in both cases (a) and (b) above, intermediate values can be allowed at the discretion of the Engineer responsible for the design.
The coefficient of expansion per degree centigrade shall be taken as 0.0000117 for steel and reinforced concrete structures and 0.0000108 for plain concrete structures.
Secondary Stresses:
These are the additional stresses brought into play due either to the movement of supports or to the deformations in the geometrical shape of the structure or its members resulting from causes such as rigidity of end connection or loads applied at intermediate points of trusses or restrictive shrinkage of concrete floor beams.
All bridges shall be designed and constructed in a manner such that the secondary stresses are reduced to a minimum; and they shall be allowed for in the design.
For reinforced concrete members the shrinkage coefficient for purposes of design may be taken as 2 × 10-4.
Erection Stress:
Allowance shall be made in the design for stresses set up in any member during erection; such stresses may be different from those which the member will be subjected to during actual working.
Seismic Force:
If a bridge is situated in a region subject to earthquake, allowance shall be made in the design for the seismic force and earthquake-resistance features shall be embodied in the structural details of the design.
The seismic force shall be taken as a horizontal force equal to the approximate fraction (specified below) of the weight of dead and live leads acting above the section under consideration (parts of the structure embedded in soil shall not be considered to produce any horizontal force).
Regions liable to minor damage: 1/20 of Gravity
Regions liable to severe damage: 1/10 of Gravity
For bridges situated in epicentral tracts where large devastations have occurred in the past due to earthquakes, the percentages shall be fixed by the engineer responsible for the design, with due regard to the local conditions regarding the intensity of earthquakes generally experienced in these regions.
The horizontal forces due to seismic force shall be taken to act through the centre of gravity of all the loads under consideration. The direction of this force should be such that the resultant stresses in the member under consideration are maximum.
Seismic and wind forces shall not be considered to act simulaneously. The magnitude of the seismic force shall not be reduced on account of reduction in weight due to buoyancy obtained in a submerged mass.
Loading on Footways:
For foot bridges meant for pedestrians and animals the loading shall be 490 kg/metre2. In the case of a footpath on a road-rail bridge, the live load including impact may be taken as 415 kg/metre1, (but where crowd loading is likely this may be increased to 490 kg/metre2).
Kerbs 0.6 m or more in width, shall be designed for the above loads. If the Kerb width is less than 0.6 m no live load shall be applied.
For purposes of design of main girders the live loads on the footpaths shall be taken as follows:
In the case of footpaths provided as a combined road-rail bridge the loading on the footpaths for purposes of designing the main girders shall be taken as 195 kg/metre2.
Railway bridges are designed for the following standard loadings.
Loading for Broad gauge 1676 mm
Fig. 13.24 shows the standard loading for main line.
The following table shows the equivalent uniformly distributed load on one track for computing the maximum bending moments and shear forces.
For metre gauge 1000 mm.
Fig. 13.24 shows the loadings for standard main line, standard branch line and standard C.
The equivalent uniformly distributed loads for each track for purpose of determining bending moments and shear forces are given in Table 13.4.
For narrow gauge 762 mm
The following three loading used:
(i) H class loading (Heavy class loading)
(ii) A class loading
(iii) B class loading.
Equivalent uniformly distributed load in tonnes on each track and impact factors for the 762 mm. gauge are shown in the following table:
Impact Foot Bridges:
No impact allowance need be made for foot bridges. Road bridges. Provision for impact or dynamic action shall be made by an increment of the live load by an impact allowance expressed as a fraction or a percentage of the applied live load. The impact fraction shall be determined from the following equations which are applicable for spans between 3 metres and 45 metres.
For Class AA Loading:
The impact percentage shall be taken as follows:
(a) For spans less than 9 metres
(i) For tracked vehicles – 25 percent for spans upto 5 metres, linearly reducing to 10 percent for spans of 9 metres.
(ii) For wheeled vehicles – 25 percent.
(b) For spans of 9 metres or more
For steel bridges-
(i) Tracked vehicle: 10 percent for all spans.
(ii) Wheeled vehicles: 25 percent for spans up to 23 metres and in accordance with the curve indicated in Fig. 13.28 for spans in excess of 23 metres.
Class A or class B loading:
In the members of any bridge designed either for class A or class B loading the impact percentage shall be determined from the following equation which is applicable for spans between 3 metres and 45 metres.
Where. L is the span is metres. For spans 3 metres and less the impact factor will be 0.545 or 54.5 percent.
In any bridge structure where there is filling of not less than 0.6 metre including the road crust the impact percentage to be allowed in the design shall be assumed to be one-half of what is stipulated above.
For calculating the pressure on bearings and on the top surface of the bed blocks, full value of the appropriate impact percentage shall be allowed, but, for the design of piers, abutments and structures, generally below the top of the bed block, the appropriate impact percentage shall be multiplied by the factor given below:
(a) For calculating the pressure at the bottom surface of the bed block ……………………………………. 0.5
(b) For calculating the pressure on the top 3 metres of the structure below the bed block decreasing uniformly to zero. … 0.5
(c) For calculating the pressure on the portion of the structure more than 3 metres below the bed block ….. Zero
For Broad and Metre Gauge Railway, the impact effect shall be taken as equal to the live load giving the maximum stress in the member under consideration multiplied by an impact factor i obtained as follows:
(v) Centrifugal Force:
Road bridges:
Where a road bridge is situated on a curve, all portions of the structure affected by the centrifugal action of moving vehicles are to be proportioned to carry safely the stress induced by this action in addition to all other stresses to which they may be subjected.
The centrifugal force shall be determined from the following equation:
where, C = Centrifugal force in tonnes acting normally to the traffic (1) at the point of action of the wheel loads or (2) uniformly distributed over every metre length on which a uniformly distributed load acts.
W = Live load (1) in tonnes in case of wheel loads, each wheel load being considered as acting over the ground contact length and (2) in tonnes per linear metre in case of a uniformly distributed live load.
V = The design speed of the vehicles using the bridges in km per hour, and
R = The radius of curvature in metres.
The centrifugal force shall be considered to act at a height of 1.2 metres above the level of the carriageway.
No increase for impact effect shall be made on the stresses due to centrifugal action.
The overturning effect of the centrifugal force on the structure as a whole shall also be duly considered.
Railway Bridges:
For Railway bridges the horizontal load and load due to centrifugal force which may be assumed to act at a height of 1830 mm above the rail level, is-
