IRC Standards:The standard IRC loads specified in IRC : 6-2000 are grouped under four categories as described below : 1. Indian Roads Congress (IRC) Class A Loading IRC class A type loading consists of a wheel load train comprising a truck with trailers of specified axle spacing and loads. The heavy duty truck with two trailers transmits loads from 8 axles varying from a minimum of 27 kN to a maximum of 114 kN. The Class A loading is a 554 kN train of wheeled vehicles on eight axles. Impact has to be allowed as per the formulae recommended in the IRC: 6-2000. The impact factor is inversely proportional to the length of the span and is different for steel and concrete bridges. This type of loading is recommended for all roads on which permanent bridges and culverts are constructed. 2. Indian Roads Congress (IRC) Class B Loading Class B type of loading is similar to Class A loading except that the axle loads are comparatively of lesser magnitude. The axle loads of Class B are a 332 kN train of wheeled vehicles on eight axles. This type of loading is adopted for temporary structures and timber bridges. Combinations of different types of live loads are recommended for the design of bridges in clause 207.4 of IRC: 6-2000. The IRC Code also provides for the reduction of the longitudinal effects on bridges accommodating more than two traffic lanes due to the low probability of all lanes not subjected to the characteristic loads simultaneously. The reduction in longitudinal effect recommended is 10 percent for three lanes and 20 percent for four lanes or more. However, it should be ensured that the reduced longitudinal effects are not less severe than the longitudinal effect resulting from simultaneous load on two adjacent lanes. 3. Indian Roads Congress (IRC) Class 70 R Loading IRC 70 R loading consists of the following three types of vehicles : (a) Tracked vehicle of total load 700 kN with two tracks each weighing 350 kN. (b) Wheeled vehicle comprising 4 wheels, each with a load of 100 kN totaling 400 kN (c) Wheeled vehicle with a train of vehicles on seven axles with a total load of 1000 kN. The tracked vehicle is somewhat similar to that of Class AA, except that the contact length of the track is 4.87 m, the nose to tail length of the vehicle is 7.92 m and the specified minimum spacing between successive vehicles is 30 m. The wheeled vehicle is 15.22 m long and has seven axles with the loads totaling to 1000 kN. The bogie axle type loading with 4 wheels totaling 400 kN is also specified. The 700 kN tracked vehicle is common to both the classes, the only difference being the loaded length which is slightly more for the Class 70 R. The second category is the wheeled type comprising 1000 kN train of vehicles on seven axles for the Class 70 R and a 400 kN bogie axle type vehicle for the Class AA. The Class A loading is a 554 kN train of wheeled vehicles on eight axles. Impact is to be allowed for all the loadings as per the specified formulae which is !fferent for steel and concrete bridges. The various categories of loads are to be separately considered and the worst effect has 10 be considered in design. Only one lane of Class 70 R or Class AA load is considered whereas both the lanes are assumed to be occupied by Class A loading if that gives the worst effect 4. Indian Roads Congress (IRC) Class AA Loading Two different types of vehicles are specified under this category grouped as tracked and wheeled vehicles. The IRC Class AA tracked vehicle (simulating an army tank) of 700 kN and a wheeled vehicle (heavy duty army truck) of 400 kN. All the bridges located on National Highways and State Highways have to be designed for this heavy loading. These loadings are also adopted for bridges located within certain specified municipal localities and along specified highways. Alternatively, another type of loading designated as Class 70 R is specified instead of Class AA loading. 2.3 CLEARANCES To avoid any possibility of traffic striking arty structural part clearance diagrams are specified. The horizontal clearance should be the clear width and the vertical clearance the clear height, available for the passage of vehicular traffic as shown in the clearance diagram in Fig. 2.1. For a bridge constructed on a horizontal curve with superelevated road surface, the horizontal clearance should be increased on the side of the inner kerb by an amount equal to 5 m multiplied by the superelevation. The minimum vertical clearance should be measured from the superelevated level of the roadway.2.4 WIDTH OF CARRIAGEWAY Width of carriageway required will depend on the intensity and volume of traffic anticipated to use the bridge. The width of carriageway is expressed in terms of traffic lanes each lane meaning the width required to accommodate one train of Class A vehicles. Except on minor village roads, all bridges must provide for at least two-lane width. The minimum width of carriageway is 4.25 m for a one-lane bridge and 7.5 m for a two-lane bridge. For every additional lane, a minimum of 3.5 m must be allowed. Bridges allowing traffic on both directions must have carriage ways of two or four lanes or multiples of two lanes. Three-lane bridges should not be constructed, as these will be conducive to the occurrence of accidents. In the case of a wide bridge, it is desirable to provide a central verge of et least 1.2 in width in order to separate the two opposing lines of traffic; in such a case, the individual carriageway on either side of the verge should provide for a minimum of two lanes of traffic. If the bridge is to carry a tramway or railway in addition, the width of the bridge should be increased suitably. From consideration of safety and effective utilisation of carriageway, it is desirable to provide footpath of at least 1.5 m width on either side of the carriageway for all bridges. In urban areas, it may be necessary also to provide for separate cycle tracks besides the carriageway. 2.5 VARIOUS TYPES OF LOADING FOR ROAD BRIDGES The loads and forces to be considered in designing road bridges are described below: 1. WIND LOAD Bridge structures are designed for the following lateral wind forces. These forces should 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 should be assumed as a horizontal force of the intensity specified below and acting on an area calculated as follows: (i) For a Deck Structure. The area of the structure as seen in elevation including the floor system and railings. (ii) For a Through or Half Through Structure. The area of the elevation of the windward specified in (a) above plus half the area of de vat ion above the deck level of all other trusses or girders. The pressure given in Table 1 should be doubled for bridges situated in areas such as the Kathiawar-peninsula and Orissa Coasts. The lateral wind force against any exposed moving load should be considered as acting at 1.5 m above the roadway and should be assumed to have the following values: Highway bridges ordinary 300 kg per linear metre. Highway bridges carrying tramway 450 kg per linear metre. The bridges should not be considered to be carrying any live load when the wind velocity at deck level exceeds 130 km per hour. The total assumed wind force should not be less than 450 kg per linear metre in the plane of the loaded chord and 225 kg per linear meter in the plane of unloaded chord on through or half-through truss, latticed or other similar spans and not less than 450 kg per linear metre on deck spans. F = Horizontal velocity of wind in kilometres per hour at height H. A wind pressure of 240 kg per square metre of the unloaded structure should be used if it produces greater stresses than those produced by the combined wind forces as stated above. 2. LATERAL LOADS Forces all Railings and Parapets. The railings and parapets should be designed to resist a lateral horizontal force and vertical force each of 150 kg/m applied simultaneously at the top of the railing or parapet. These forces need not be considered in the design of the main structural members if footpaths are not provided. In case where footpaths are provided, the effect of those forces should be considered in the design of structural system supporting the railing and the footpath up to the face of the footpath Kerb only.Forces on Kerbs. Kerbs should be designed for lateral loading of 750 kg per metre run of the Kerb applied horizontally at the top of the kerb. This load need not be taken for the design of supporting structure. 3. LIVE LOAD Indian Roads Congress has evolved the suitable loading standards for bridges commensurate with the traffic needs of the highway system. The I.R.C. bridge loadings were originally of two typesone known as I.R.C. standard loading and the other as L.R.C. heavy loading both consisting of a uniformly distributed load and a knife-edge load. Later on in 1943 the present 1.R.C. class AA, class A and class B loading were introduced and all of them are still in force. I.R.C. Class AA Loading, The I.R.C. class AA loading corresponds to the class 70 loading and is based on the original classification methods of the Defence Authorities. This loading is to be adopted for design of bridges within certain municipal limits, in certairn existing or contemplated industrial area, in other specified areas and along National Highways and State Highways. Two types of vehicles are specified : (i) Tracked Vehicle. (ii) Wheeled Vehicle. The choice is made, depending upon the anticipated types of vehicles to travel on the bridge Bridges designed for Class AA loading should be checked for Class A loading also, as unde certain conditions heavier stress may be obtained under class A loading. I.R.C. Class A Loading. The class A loading was proposed by I.R.C. with the object of covering the worst combination of axle loads and axle spacings likely to arise from the various types / vehicles that are normally expected to use the road. This load train is reported to have beer arrived at aft ac an exhaustive analysis of all lorries made in all the countries of the world. The load train is composed of a driving vehicle and two trailers of specified axle spicing and loads. This loading is to be normally adopted on all roads on which permanent bridges and culvert are constructed. I.R. C. Class B loading. The I.R.C. Class B loading is similar to class A train of vehicles wilt reduced axle loads and type contact dimensions. This loading is to be normally adopted temporary structures and for bridges in specified areas. Structures with timber spans are regarded as temporary structures. Apart from these, the I.R.C. has also given a load classification of I.R.C. Standard Specification east and Code of Practice for Road Bridge Section II (I.R.C. 6-1966) conforming to the revised system of load classification by the Defence Authorities which gives loadings varying from class 3 to 7: I The new class 7,9 R loading given in this chart is nothing hut a revision of the class 70 loading: the original classification (in other words-the class AA loading) incorporating certain changesNotes : The nose to tail spacing between two successive vehicles should not be less than 90 m. z. For multilane bridges and culverts, one train of class AA tracked or wheeled vehicles whichever creates severer conditions should be considered for every two traffic lane widths. No "Other live load should be considered on any part of the said 2-lane width carriageway of the bridge when the above mentioned train of Tracked Vehicle crossing bridge. The maximum loads for the wheeled vehicle should be 20 tonnes for a single axle or 40 tonnes for a bogie of two axles spaced not more than 1.2 m centres.4. DEAD LOAD The dead load is the weight of the structure and the weight of the portion of the superstructure which is supported wholly or in part by the structure. The dead load initially assumed should be checked after the design is completed and the design should be revised if the actual calculated dead load exceeds the assumed dead load by more than 2.5%. The dead load of the structure depends upon the following factors: (1) Live load. (2) Type of design. (3) Working stresses employed. (4) Length of span. (5) Character of the details. On the basis of the above factors the approximate weight of the structure is roughly estimated by means of the following empirical formulae : Empirical Formulae/or R.C.C. Bridges (A) T-Beam Bridges. The formula is applicable only for 6-15 m span T -beam bridges: W= 415 +80L Here, W = Total weight in kg/m2 L = Clear span in metres. (B) Spandrel Filled R. C. C. Arches. The average dead load in kg/m of road surface is given by the following formulae: (i) Formula for rise-span ratio, 1: 4 ; W= 198.5 L (ii) Formula for rise-span ratio, 1: 5 ; W = 166 L (iii) Formula for rise-span ratio, 1 : 6 ; W= 144 L Here, L = Span in metres W=Average dead load in kg/m. Empirical Formula for Steel Bridges (a) Plate Girder Bridges: (i) Kempe's formula: Here, P = Weight in kg of small plate girder. W = Total load supported in kg. L = Span in metres. d = Total depth of girder in cm. (ii) Wisconsin Highway Commission Formula. For through plate girders of steel, the weight it kg per metre run of span from 10.5 to 24.0 m is given by (i) W = 446.4 + 15.8 L (for 5.4 m wide roadway) (ii) W= 476 + 19.5 L (for 6 m wide roadway) (iii) Boston Bridge Work Standard Formulae. The weight of plate girder bridges in kg/m2 is given by (i) For Deck Girders with side Walks: W = 122 + 3.64 L (ii) For through Girders with Side Walks : W= 16.1 + 2.86L (iii) For Through Girders without Side Walks : W = 14.6 + 3.78L Here, L = Span in metres. (b) Truss Bridges (i) America Bridge Company Formula W = 275 + 171L (For 6.2 m wide roadway) This formula is applicable for low truss spans of 10 m to 30 m without stringers. Here, W = Weight in kg per metre run. (ii) Wisconsin Commission Formula W= 119 + 19.5L This formula is applicable for load truss spans of 10 metres to 25 metres. (iii) Illinois Commission Formula This formula is applicable for steel high truss spans of 30 metres to 50 metres. 5. LONGITUDINAL FORCES in all road bridges, provision should be made for longitudinal forces arising from any one or more of the following causes: (1) Tractive effort caused through acceleration of the driving wheels. (2) Braking effect resulting from the application of the brakes to braked wheels. Braking effect is invariably greater than tractive effort. (3) Frictional resistance offered to the movement of free bearings due to change of temperature or any other cause. The braking effect on a simply supported span or a continuous unit of spans or on any other type of bridge unit should be assumed to have the following value: (i) In the case of a single lane or a two lane bridge: Twenty per cent of the first train load plus ten per cent of the load of the succeeding trains or part thereof, the train loads in one lane only being considered for the purposes of this sub-clause. Where the entire first train is not on the full span, the braking force should be taken as equal to twenty per cent of the loads actually on the span. (ii) In the case of bridges having more than two lanes: As in (i) above for first two lanes plus five per cent of the loads on the loads in excess of two. Note. The loads in this clause should not be increased on account of impact. The force due to braking effect should be assumed to act along a line parallel to the, roadway and 1,20 metre above it: while transferring the force to the bearing, the change in the vertical reaction at the bearings should be taken into account. The longitudinal force at any free bearing should be limited to the sum of dead and live load reactions at the bearing multiplied by the appropriate co-efficient of friction. The co-efficient of friction at the . bearing should be assumed to have the following values: For roller bearing 0.03 For sliding bearings of hard copper alloy 0.15 For sliding bearings of steel on cast iron or steel on steel 0.25 For sliding bearings of steel en ferro asbestos 0.20 For other types ........ To be decided by engineer in-charge. The longitudinal force at the fixed bearing should 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 barking effect on the wheels as mentioned above. The effect of braking force on bridge structures with out bearings such as arches, rigid frames, etc. should be calculated in accordance with approved methods of analysis of indeterminate structure. The effect of the longitudinal forces and ,dl other horizontal forces should be calculated up to a level where the resultant passive earth resistance of the soil below the deepest scour level (lower level in case of a bridge having pucca floor) balances these forces. 6. FORCES DUE TO EARTHQUAKE For the purpose of determining seismic forces, the country is divided into five zones (IS : 1893) cm. Both horizontal and vertical seismic forces have to be taken into account for design of bridge structures. The horizontal seismic force to be resisted is computed from Equation 4.1. Fh=Wm.h where Fh= horizontal seismic force to be resisted; Wm= weight of mass under consideration ignoring reduction due to buoyancy h= .1.0; 0= basic horizontal seismic coefficient, taken as 0.08, 0.05, 0.04, 0.02 and 0.01 for zones V. IV, III, II and I, respectively.l = a coefficient depending on the importance of the structure, taken as 1.5 for major bridges of over 300 m linear waterway, and as 1.0 for other bridges. = a coefficient depending upon the soil foundation system, the value varying from 1.0 to 1.5 as given in the code. The vertical seismic force to be resisted (Fv) is estimated from Equation 4.2 Fv = Wm.vwhere v= 0.5h The bridge as a whole and every part of it should be designed and constructed to resist the stresses produced by seismic effects. For horizontal acceleration, the stresses should be calculated as the effect of force applied horizontally at the centre of mass of the elements of the bridges into which it is conveniently divided for the purpose of design. The forces can come from any horizontal direction. Seismic forces need not be considered for bridges in zones I to III and for bridges of spans less than 15 m. 7. CENTRIFUGAL FORCE Where a road bridge is situated on a curve, all portions of the structure effected by centrifugal action of moving vehicles are designed to carry safely the stress induced by this action in addition to all other stresses to which they may be subjected to. This centrifugal force should be determined from the following formula:C=WV2/127R Here, C = Centrifugal force in tonnes acting normally to traffic (i) at the point or action of the wheel loads (ii) uniformly distributed over every metre 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 and (ii) in tonnes per liner metre in case of uniformly distributed live load. V = The design speed of the vehicle using the bridge in km. p.h. R = The radius of curvature in metres. The centrifugal force should be considered to act at a height 1.2 m above the level of the carriageway. This force is not increased for impact effect. 8. ERECTION FORCES The forces which may act temporarily during erection should be considered. It is permissible to allow for stresses during erection different from those which the member will be subjected to during actual working. 9. FORCES DUE TO WATER CURRENTS Any part of a bridge which may be submerged in running water should be designed to sustain safely the horizontal pressure due to the force of the current. In case of piers parallel to the direction of water current, the intensity of pressure should be calculated from the following formula: P = 52KV2 Here, P = Intensity of pressure in kg/m2 due to the water current, K = A constant having the following values for different shapes of the piers. V = The velocity of the current in metres/see. 10. SECONDARY STRESSES In steel structures, secondary stresses are caused due to eccentricity of connections, floor beam loads applied at intermediate points in a panel, cross girders being connected away from panel points, lateral wind loads on the end posts of through girders, and movement of supports. Secondary stresses are brought into play in reinforced concrete structures due either to the movement of supports or to the deformations in the geometrical shape of the structure or its member, resulting from causes such as rigidity of end connection or loads applied at intermediate points of trusses or restrictive shrinkage of concrete floor beams. For reinforced concrete members, the shrinkage coefficient for design purposes may be taken as 0.0002. All bridges should be designed and constructed in such a manner that the secondary stresses are reduced to a minimum and these stresses should be allowed for in the design. 11. ERECTION STRESSES The stresses that are likely to be induced in members during erection should be considered in design. It is possible that the erection stresses may by different from those which the member will be subjected to in actual service. 12. TEMPERATURE EFFECTS Daily and seasonal variations in temperature occur causing material to shorten with a fall in temperature and lengthen with a rise in temperature. These variations have two components: a uniform change over the entire bridge deck and a temperature gradient caused by the difference in temperatures at the top and the bottom of the deck. Suitable provisions should be made for stresses or movements resulting from variations in temperature. The probable rise and fall in temperature shall be determined from meteorological records for the locality in which the bridge is located. In case of massive concrete members the time lag between air temperature and the interior temperature should be considered. The coefficient of expansion per degree centigrade shall be taken as 11.7 x 10-6 for steel and reinforced concrete structures and as 10.8 x 10-6 for plain concrete structures. 13. DEFORMATION STRESSES Deformation stresses are considered for steel bridges only. A deformation stress is defined as the bending stress in any member of an open-web girder caused by the vertical deflection of the girder combined with the rigidity of the joints. No other stresses are included in this definition. The design, manufacture and erection of steel bridges should be so arranged as to keep the deformation stresses to a minimum. If detailed computations are not made to provide otherwise, the deformation stresses should be assumed to be not less than 16 per cent of the dead and live load stresses. 2.6 INDIAN RAILWAY BRIDGE LOADING STANDARDS Railway bridge loadings should conform to the specifications of the Indian Railway Standards (IRS) prescribed by the Ministry of Railways, Government of India. The various loads to be used are specified in the IRS Bridge rules. Specific recommendations are available for the design of steel. R.C.C, P.S.C. masonry and plain concrete arch bridges in the relevant bridge codes. The railway tracks are classified according to the importance of traffic as main and branch lines. The three types of gauges used in the Indian Railways are : (i) Broad gauge (BG): 1676 mm (5'-6") (ii) Metre gauge (MG): 1000 mm (3-3.375) (iii) Narrow gauge (NG): 762 mm (2'-6") At present, the Indian Railway have adopted the unigauge policy with the broad gauge as the standard gauge throughout the country. Consequently many important old lines are being converted into broad gauge.The various loads and forces to be considered in the design of the bridge are: i) dead and live loads ii) Dynamic effects iii) Centrifugal force due to curvature of track iv) Temperature and frictional effects v) Racking force vi) Wind and earthquake forces. 3.2 VARIOUS TYPES OF R.C.C. BRIDGES Reinforced concrete bridges may be of following types as described below : (1) Dack Slab Bridge A deck slab bridge as shown in Figs. 3.1(a) and (b) or solid slab bridge is the simplest type of construction, used mostly for culverts or small bridges with a span not exceeding 8 m. Though the thickness of deck slab is considerable, its construction is much simpler and the cost of form work is also minimum. Wearing coat Deck Slab or" (a) Deck slab bridge Foot path Wearing coat 4/11WAl21.11.11,Kor Abutment Slab Beam (b) T-beam bridge Fig. 3.1. (2) T-beam Bridge As shown in Fig. 3.1(b), T-beam bridge is another type of a simple R.C. bridge used for spans between 10 to 20 metres. The number of longitudinal girders depends upon the road width. The slab is generally built monolithic with girders so that T-beam effect is achieved. (3) Hollow Girder Bridges Reinforced concrete hollow girder bridges are economical in the span range of 25 to 30 m. The closed box shape provides torsional rigidity, and the depth can be varied conveniently along the length as in continuous deck or in balanced cantilever layout. The cross-section can consist of a single cell or can be multi-cellular. The extra torsional stiffness of the section makes this form particularly suitable for grade separations, where the alignment is normally curved in plan. The cells can be rectangular or trapezoidal, the latter being used increasingly in prestressed concrete elevated highway structures. Reinforced concrete hollow girder bridges are currently not favoured. A typical cross-section of a reinforced concrete hollow girder superstructure suitable for two-lane traffic on a National Highway for a simply supported clear span of 30 m is shown in Fig. 3.2. The components of the girder are: (i) the cantilever portion including the kerb; (ii) the top slab carrying the roadway; (iii) the webs, in this case two exterior webs and one central web; and (iv) diaphragms, typically two end diaphragms and three intermediate diaphragms. The design of the simply supported hollow girder can be performed on similar lines as for a T-beam superstructure with a few modifications. The tensile bars are mainly spread over a larger 3.2 VARIOUS TYPES OF R.C.C. BRIDGES Reinforced concrete bridges may be of following types as described below : (1) Dack Slab Bridge A deck slab bridge as shown in Figs. 3.1(a) and (b) or solid slab bridge is the simplest type of construction, used mostly for culverts or small bridges with a span not exceeding 8 m. Though the thickness of deck slab is considerable, its construction is much simpler and the cost of form work is also minimum.(2) T-beam Bridge As shown in Fig. 3.1(b), T-beam bridge is another type of a simple R.C. bridge used for spans between 10 to 20 metres. The number of longitudinal girders depends upon the road width. The slab is generally built monolithic with girders so that T-beam effect is achieved. (3) Hollow Girder Bridges Reinforced concrete hollow girder bridges are economical in the span range of 25 to 30 m. The closed box shape provides torsional rigidity, and the depth can be varied conveniently along the length as in continuous deck or in balanced cantilever layout. The cross-section can consist of a single cell or can be multi-cellular. The extra torsional stiffness of the section makes this form particularly suitable for grade separations, where the alignment is normally curved in plan. The cells can be rectangular or trapezoidal, the latter being used increasingly in prestressed concrete elevated highway structures. Reinforced concrete hollow girder bridges are currently not favoured. A typical cross-section of a reinforced concrete hollow girder superstructure suitable for two-lane traffic on a National Highway for a simply supported clear span of 30 m is shown in Fig. 3.2. The components of the girder are: (i) the cantilever portion including the kerb; (ii) the top slab carrying the roadway; (iii) the webs, in this case two exterior webs and one central web; and (iv) diaphragms, typically two end diaphragms and three intermediate diaphragms. The design of the simply supported hollow girder can be performed on similar lines as for a T-beam superstructure with a few modifications. The tensile bars are mainly spread over a larger area in the soffit slab. A few of the rods can be accommodated in the webs as shown in Fig. 3.2. If curtailment of bars is desired, the curtailed portion may be provided with nominal (smaller diameter) bars. In situations of higher labour costs and relatively lower material costs as in developed countries, it may even be desirable to extend the bars straight avoiding addition of different sized bars for part length. The webs are designed to carry the shear. The main bars in higher rows provided in the webs may be cranked as per bar curtailment from bending moment consideration and anchored at the top. Vertical stirrups are provided to cater to the requirements of shear. Usually two-legged stirrups of 12 mm of 16 mm diameter are adopted with variable spacing. Rectangular openings are provided in the diaphragms to enable removal of formwork from inside the cells after casting. Detailing of reinforcement should ensure that the edges are duly strengthened. It is desirable to provide one access opening of 750 mm diameter in the soffit slab for each cell near one of the abutments. This opening will enable maintenance personnel to inspect the inside of the cells if necessary. Additional reinforcement of 2-14 at top and bottom on all four sides totaling to 16 bars about 1400 mm long each should be provided to locally strengthen the soffit slab at the opening. (4) Balanced Cantilever Bridge A balanced cantilever bridge consists of spans simply supported. It can be used for spans varying from 35 to 60 metres. In yielding river beds, where foundations are expensive and small spans are uneconomical, it can be used with advantage. They are also provided over deep gorges to be crossed by a single span where the use of centering is not possible. The connection between the suspended span and the edge of the cantilever is known as articulation. The bearings at articulations should be alternatively of fixed and expansion types. The cantilever span is usually 20 to 25% of the supported span. The suspended span is designed as a simply supported span with supports at the articulations. In order to design the supported or main span the maximum negative moment at the supports is determined when the cantilever and suspended spans are subjected to full live load with no live load on the supported span. The maximum positive moment at the mid-span would occur with full live load on the main span and no live load on the cantilever and suspended span. The cross-section of a balanced cantilever bridge can be of T -beam or Hollow Girder type. The depth at supports is kept greater than at mid-span because the negative moments are usually large in magnitude than the positive moments at mid-span. The soffit can be arranged as two inclined lines with a central horizontal line a parabolic profile. When compared to simply supported bridges, it requires more elaborate detailing of reinforcements. The balanced cantilever bridges have the following advantages over simply supported girder bridges: (z) This requires lesser quantities of materials, i.e., There is saving in material cost e.g., concrete and steel cost and form-work cost. (it) This requires slender piers because reaction at every pier is vertical and central. (iii) Only one bearing is required at every pier, whereas in case of simply supported bridges two bearings are required. Hence, the width of the pier can be smaller. (iv) This requires lower initial and maintenance cost because of fewer expansions bearings. (5) Rigid Frame Bridges Rigid frame bridges are structures consisting of a number of parallel girders (or slab instead of girders) which are rigidly connected to the supporting columns or piers Usually the decking and substructure are cast monolithically.The arrangement of Type (a) [Fig. 3.4(a)] is suitable for single span openings as in the case of bridges over railway tracks. Type (b) [Fig. 3.4(b)] shows a two-span bridge with the base of the column fixed. If the base is hinged, which is a more common condition, the column is tapered downward. This type can also be used for bridges with greater number of spans by adding the required number of intermediate columns. Type (c) [Fig. 3.4(c)] offers an aesthetically pleasing structure over restricted access highways and has been used extensively over expressways in USA and Germany. Rigid frames possess the advantages listed for continuous bridges and have the following additional advantages: (z) No bearings are needed at the supports. (ii) The rigid connections result in more stable supports, than possible with independent piers of comparable dimensions. (iiz) In view of the slender dimensions, the supporting piers or columns cause the least obstruction to view for the traffic below the bridge. (6) Arch Bridges Arch bridges are very commonly used from times immemorial. They are more graceful, pleasing in appearance and suited for deep gorges within rocky sides. These bridges can be economically used up to spans of about 200 m. The arches may be of barrel type or rib type. (1) Barrel Type or Filled Spandrel Arches: Barrel type arches resemble a curved slab. Their deck ;s generally supported on earth, filling placed on the arch slab and retained by spandrel walls. That is why it is also known as filled spandrel arch. (ii) Rib Type or Open Spandrel Ribbed Arches: A typical opens spandrel ribbed arch is shown in Fig. 3.6. They are similar to curved beams spaced suitably along the width of the bridge. In this case, the deck is supported on the columns which are in turn supported on arch ribs.The type of arches used are : (i) Three Hinged Arch : This consists of a hinge at each springing and a hinge at the crown. Three hinged arch is best suited for yielding foundation as small movement of one foundation relative to other does not cause enomous stress. The disadvantage of this type is that the thickness at the quarter point being more than that at springing, masking is required for aesthetic purposes as shown in Fig. 3.7. (ii) Two Hinged Arch : This consists of hinges placed at the abutments. In this case, only reactions are transmitted to the supports, there being no bending moment in the arch at springings as shown in Fig. 3.8. (iii) Fixed Arch : This form is most commonly employed for good unyielding foundations. In this case the construction is much similar than the three or two hinged type arch as shown in Fig. 3.9. Broadly there are two types of hinges provided in archespermanent one in the hinged arches and temporary ones in the fixed arches. The temporary hinges are built as an expedient to reduce moment caused by shrinkage, plastic flow, elastic strain due to trust, and the settlement of the abutment due to the push of the arch. (iv) Bow String Girder Bridge : Bow string arches are economical when sufficient headroom is required under a bridge. In this type horizontal thrust is resisted by horizontal ties and vertical reaction by supports. The floor beams are suspended from the arches by means of vertical suspenders. The main supporting system is known as bow-string girder, because of the resemblance of the arch ring with a bow and the tie beam with a string. Slight vertical or angular displacement of the abutments do not matter in the case of either two hinged arch or the bow string girder. A bow string girder is unaffected even by small horizontal displacements of the abutments. The details of bow-stung girder bridge are sketched in Fig. 3.10. They are commonly adopted for arch bridges having spans of 30 to 45 metres. (7) Continuos Bridges: They are used for large spans and where unyielding foundations are available, as high stresses are introduced even if slight settlements of piers or abutments occur. Usually, end spans are made about 16 to 20% smaller than the intermediate spans. The deck can be in the form of slab, T-beam or box-section. Generally, the bending moment at support is of larger magnitude than that at mid span and is negative in nature. Therefore, at supports the thickness of slab is generally 1.3 to 1.8 times the minimum thickness at mid-span and the length of launched portion will be about 20 to 25% of the span. 3.3 COURBON'S METHOD Courbon's theory or distribution of live load on longitudinal beams is applicable when the following, conditions are satisfied : (i) The span-width ratio is greater than 2 and less than 4. (i) There are atleast five symmetrical cross-girders or diaphragms connecting the longitudinal girders. (iii) The depth of the cross-girders or diaphragms is atleast 3/4th of the depth of longitudinal girders. (a) For Bending Moment When the live loads are eccentrically placed with respect to the axis of the bridge (or C.G. of girder system), then reaction factor Rx for any given girder distant x from the bridge axis can be represented by the linear law. Rx=c+d.x ...(3.1) where c and d are constants. The above law is justified if the cross beams are so rigid that the deflections vary linearly in the transverse direction, so that the load supported by each beams is proportional to its deflection. (c + d.x) =P ...(3.2) and (c + d .x)x = P.e ...(3.3) where e is the eccentricity of load P with respect to the axis of the bridge. Measuring x to be positive towards the load P and ve in the other direction, we have x = 0 Also, c=n.c where n is the number of longitudinal girders. P Hence, from (3.1), c+ dx=P or nc+ 0 = P or c=P/n(3.4) Also, from (3.3), cx+ dx2 =P.e or 0 +dx2=P.e d=P.e/x2or Substituting the values of c and d in

If there are several point-loads

where e is the eccentricity of C.C. of loads. Knowing Rx,the B.M. in the longitudinal girder can be computed. (b) For S.E : Two cases for S.F. may arise. Case 1: This case arises when the load is placed beyond the diaphragm (or cross beam) closest to the support. The reaction factors are found as for B.M. Case 2 : This case arises when the load is placed between the support and the first intermediate diaphragm. Figure 3.12 shows this case with four longitudinal girders, A, B, C and D, with the load P placed between beams A and B. The load P is distributed to A and B, as PA and PB by considering the slab to be simply supported. The loads PA and PB are distributed to the support AB and diaphragm A'B', considering the beam as simply supported. The portion of the load. going to the support is the direct S.F. in the beam, while that going to the diaphragm is redistributed among all the beams by normal Courbon's method. Hence, S.F. QA due to PA is given by

where 1= span of the bridge, q = distance between support first intermediate diaphragm.