DESIGN OF T-BEAM RAIL-OVER BRIDGE SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR BACHELOR OF TECHNOLOGY IN CIVIL ENGINEERING BY VASAV DUBEY (109526) MADHURESH SHRIVASTAV(109833) LOKESH KUMAR (109822) AMAN AGARWAL (109814) SHOBHIT DEORI (109281) KULDEEP MEENA(109821) PRADEEP KUMAR (109695) ANIMESH AGARWAL(109788) MANJEET GOYAT(109597) BATCH OF 2009-2013 UNDER THE GUIDANCE OF DR. H. K. SHARMA NATIONAL INSTITUTE OF TECHNOLOGY KURUKSHETRA MAY 2013
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DESIGN OF T-BEAM RAIL-OVER BRIDGE
SUBMITTED IN PARTIAL FULFILMENT
OF THE REQUIREMENTS FOR
BACHELOR OF TECHNOLOGY
IN
CIVIL ENGINEERING
BY
VASAV DUBEY (109526) MADHURESH SHRIVASTAV(109833)
LOKESH KUMAR (109822) AMAN AGARWAL (109814)
SHOBHIT DEORI (109281) KULDEEP MEENA(109821)
PRADEEP KUMAR (109695) ANIMESH AGARWAL(109788)
MANJEET GOYAT(109597)
BATCH OF 2009-2013
UNDER THE GUIDANCE OF
DR. H. K. SHARMA
NATIONAL INSTITUTE OF TECHNOLOGY
KURUKSHETRA
MAY 2013
Contents
Acknowledgement i
List of Figures ii
1 Introduction 1
1.1 General 1
1.2 Classification of Bridges 1
1.3 T-Beam Bridges 3
1.4 Background 4
1.5 History 5
1.6 Construction Materials and Their Development 6
1.7 Design 7
1.8 Construction Procedure 8
1.9 Problem Statement 10
2 Deck Slab 12
2.1 Structural Details 12
2.2 Effective Span Size of Panel for Bending Moment Calculation 12
2.3 Effective Span Size of Panel for Shear Force Calculation 12
2.4 Moment due to Dead Load 16
2.5 Moment due to Live Load 16
2.6 Design of Inner Panel 45
2.7 Shear Force In Deck Slab 45
3 Cantilever Slab 54
3.1 Moment due to Dead Load 54
3.2 Moment due to Live Load 55
3.3 Design of Cantilever Slab 55
4 Design of Longitudinal Girders 60
4.1 Analysis Longitudinal Girder by Courbon's Method 60
4.2 Shear Force in L-girders 65
4.3 Design Of Section 69
5 Design Of Cross Girders 73
5.1 Analysis of Cross Girder 73
5.2 Design of Section 79
6 Design of Bearings 82
6.1 Design Of Outer Bearings 82
6.2 Design Of Inner Bearings 85
7 Conclusion 90
7.1 Deck Slab 90
7.2 Cantilever Slab 90
7.3 Longitudinal Girders 90
7.4 Cross Girders 91
7.5 Bearings 91
References 93
Appendix-A : IRC Loadings 94
Appendix-B: Impact Factors 98
Appendix-C: K in Effective Width 100
Appendix-D: Pigeaud's Curve 101
i
Acknowledgement
We wish to record our deep sense of gratitude to Dr. H.K. Sharma, Professor,
Department of Civil Engineering, National Institute of Technology, Kurukshetra for
his able guidance and immense help and also the valuable technical discussions
throughout the period which really helped us in completing this project and
enriching our technical knowledge.
We also acknowledge our gratefulness to Dr. D.K. Soni, Head of Department,
Department of Civil Engineering, National Institute of Technology, Kurukshetra for
timely help and untiring encouragement during the preparation of this
dissertation.
ii
List of Figures
Figure 1.1: Cutaway view of a typical concrete beam bridge.
Figure 2.1: Plan of Bridge Deck
Figure 2.2: Section X-X of Bridge Deck Plan
Figure 2.3: Section Y-Y of Bridge Deck Plan
Figure 2.4: Class AA Track located for Maximum Moment on Deck Slab
Figure 2.5: Both Class AA Track located for Maximum Moment on Deck Slab
Figure 2.6: Disposition of Class AA Wheeled Vehicle as Case 1 for Maximum
Moment
Figure 2.7: Disposition of Class AA Wheeled Vehicle as Case 2 for Maximum
Moment
Figure 2.8: Disposition of Class AA Wheeled Vehicle as Case 3 for Maximum
Moment
Figure 2.9: Disposition of Class A Train of Load for Maximum Moment
Figure 2.10: Class AA Tracked loading arrangement for calculation of Shear Force
Figure 2.11: Class AA Wheeled loading arrangement as Case 1 for Shear Force
Figure 2.12: Disposition of Class AA wheeled vehicle as Case 2 for Shear Force
Figure 2.13: Disposition of Class A Train of load for Maximum Shear
Figure 3.1: Cantilever Slab with Class A Wheel
Figure 3.2: Reinforcement Details in Cross Section of Deck Slab
Figure 3.3: Reinforcement Details in Longitudinal Section of Deck Slab
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Figure 4.1: Class AA Tracked loading arrangement for the calculation of reaction
factors for L-girders
Figure 4.2: Influence Line Diagram for Moment at mid span
Figure 4.3: Class AA Wheeled loading arrangement for the calculation of
reaction factors for L-girders
Figure 4.4: Computation of Bending Moment for Class AA wheeled Loading
Figure 4.5: Class A loading arrangement for reaction factors for L-girder
Figure 4.6: Computation of Bending Moment for Class A Loading
Figure 4.7: Class AA tracked loading for calculation of shear force at supports
Figure 4.8: Dead Load on L-girder
Figure 4.9: Reinforcement Details of Outer Longitudinal Girder
Figure 4.10: Reinforcement Details of Inner Longitudinal Girder
Figure 5.1: Triangular load from each side of slab
Figure 5.2: Dead Load reaction on each longitudinal girder
Figure 5.3: Position of class AA tracked loading in longitudinal direction
Figure 5.4: Plan of position of class AA tracked loading in longitudinal direction
Figure 5.5: Reaction on longitudinal girder due to class AA tracked vehicle
Figure 5.6: Position of class AA wheeled loading in longitudinal direction
Figure 5.7: Plan of position of class AA wheeled loading in longitudinal direction
Figure 5.8: Reaction on longitudinal girder due to class AA wheeled loading
Figure 5.9: Position of class AA wheeled loading in longitudinal direction
Figure 5.10: Reaction on longitudinal girder due to class A loading
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FIgure 5.11: Reinforcement Details of Cross Girder
1
1 Introduction
1.1 General
A bridge is a structure that crosses over a river, bay, or other obstruction, permitting the smooth and safe passage of vehicles, trains, and pedestrians. An elevation view of a typical bridge is A bridge structure is divided into an upper part (the superstructure), which consists of the slab, the floor system, and the main truss or girders, and a lower part (the substructure), which are columns, piers, towers, footings, piles, and abutments. The superstructure provides horizontal spans such as deck and girders and carries traffic loads directly. The substructure supports the horizontal spans, elevating above the ground surface.
1.2 Classification of Bridges
1.2.1 Classification by Materials Steel Bridges steel bridge may use a wide variety of structural steel components and systems: girders, frames, trusses, arches, and suspension cables. Concrete Bridges: There are two primary types of concrete bridges: reinforced and pre-stressed. Timber Bridges: Wooden bridges are used when the span is relatively short. Metal Alloy Bridges: Metal alloys such as aluminum alloy and stainless steel are also used in bridge construction. Composite Bridges: Bridges using both steel and concrete as structural materials.
1.2.2 Classification by Objectives Highway Bridges: Bridges on highways.
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Railway Bridges: Bridges on railroads. Combined Bridges: Bridges carrying vehicles and trains. Pedestrian Bridges : Bridges carrying pedestrian traffic. Aqueduct Bridges: Bridges supporting pipes with channeled water flow. Bridges can alternatively be classified into movable (for ships to pass the river) or fixed and permanent or temporary categories.
1.2.3 Classification by Structural System (Superstructures)
Plate Girder Bridges: The main girders consist of a plate assemblage of upper and lower flanges and a web. H or I-cross-sections effectively resist bending and shear. Box Girder Bridges: The single (or multiple) main girder consists of a box beam fabricated from steel plates or formed from concrete, which resists not only bending and shear but also torsion effectively. T-Beam Bridges: A number of reinforced concrete T-beams are placed side by side to support the live load. Composite Girder Bridges: The concrete deck slab works in conjunction with the steel girders to support loads as a united beam. The steel girder takes mainly tension, while the concrete slab takes the compression component of the bending moment. Grillage Girder Bridges: The main girders are connected transversely by floor
beams to form a grid pattern which shares the loads with the main girders.
Truss Bridges: Truss bar members are theoretically considered to be connected with pins at their ends to form triangles. Each member resists an axial force, either in compression or tension.
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Arch Bridges: The arch is a structure that resists load mainly in axial compression. In ancient times stone was the most common material used to construct magnificent arch bridges. Cable-Stayed Bridges: The girders are supported by highly strengthened cables (often composed of tightly bound steel strands) which stem directly from the tower. These are most suited to bridge long distances. Suspension Bridges: The girders are suspended by hangers tied to the main cables which hang from the towers. The load is transmitted mainly by tension in cable
1.2.4 Classification by Design Life
Permanent Bridges
Temporary Bridges
1.2.5 Classification by Span Length
Culverts: Bridges having length less than 8 m. Minor Bridges: Bridges having length 8-30 m. Major bridges: Bridges having length greater than 30 m. Long span bridges: Bridges having length greater than 120 m.
1.3 T-Beam Bridges
Beam and slab bridges are probably the most common form of concrete bridge in the UK today, thanks to the success of standard precast prestressed concrete beams developed originally by the Prestressed Concrete Development Group (Cement & Concrete Association) supplemented later by alternative designs by
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others, culminating in the Y-beam introduced by the Prestressed Concrete Association in the late 1980s.
They have the virtue of simplicity, economy, wide availability of the standard sections, and speed of erection.
The precast beams are placed on the supporting piers or abutments, usually on rubber bearings which are maintenance free. An in-situ reinforced concrete deck slab is then cast on permanent shuttering which spans between the beams.
The precast beams can be joined together at the supports to form continuous beams which are structurally more efficient. However, this is not normally done because the costs involved are not justified by the increased efficiency.
Simply supported concrete beams and slab bridges are now giving way to integral bridges which offer the advantages of less cost and lower maintenance due to the elimination of expansion joints and bearings.
1.4 Background
Nearly 590,000 roadway bridges span waterways, dry land depressions, other roads, and railroads throughout the United States. The most dramatic bridges use complex systems like arches, cables, or triangle-filled trusses to carry the roadway between majestic columns or towers. However, the work-horse of the highway bridge system is the relatively simple and inexpensive concrete beam bridge.
Also known as a girder bridge, a beam bridge consists of a horizontal slab supported at each end. Because all of the weight of the slab (and any objects on the slab) is transferred vertically to the support columns, the columns can be less massive than supports for arch or suspension bridges, which transfer part of the weight horizontally.
A simple beam bridge is generally used to span a distance of 250 ft (76.2 m) or less. Longer distances can be spanned by connecting a series of simple beam bridges into what is known as a continuous span. In fact, the world's longest bridge, the Lake Pontchartrain Causeway in Louisiana, is a pair of parallel, two-lane continuous span bridges almost 24 mi (38.4 km) long. The first of the two bridges was completed in 1956 and consists of more than 2,000 individual spans. The sister bridge (now carrying the north-bound traffic) was completed 13 years later; although it is 228 ft longer than the first bridge, it contains only 1,500 spans.
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A bridge has three main elements. First, the substructure (foundation) transfers the loaded weight of the bridge to the ground; it consists of components such as columns (also called piers) and abutments. An abutment is the connection between the end of the bridge and the earth; it provides support for the end sections of the bridge. Second, the superstructure of the bridge is the horizontal platform that spans the space between columns. Finally, the deck of the bridge is the traffic-carrying surface added to the superstructure.
1.5 History
Prehistoric man began building bridges by imitating nature. Finding it useful to walk on a tree that had fallen across a stream, he started to place tree trunks or stone slabs where he wanted to cross streams. When he wanted to bridge a wider stream, he figured out how to pile stones in the water and lay beams of wood or stone between these columns and the bank.
The first bridge to be documented was described by Herodotus in 484 B.C. It consisted of timbers supported by stone columns, and it had been built across the Euphrates River some 300 years earlier.
Most famous for their arch bridges of stone and concrete, the Romans also built beam bridges. In fact, the earliest known Roman bridge, constructed across the Tiber River in 620 B.C. , was called the Pons Sublicius because it was made of wooden beams (sublicae). Roman bridge building techniques included the use of cofferdams while constructing columns. They did this by driving a circular arrangement of wooden poles into the ground around the intended column location. After lining the wooden ring with clay to make it watertight, they pumped the water out of the enclosure. This allowed them to pour the concrete for the column base.
Bridge building began the transition from art to science in 1717 when French engineer Hubert Gautier wrote a treatise on bridge building. In 1847, an American named Squire Whipple wrote A Work on Bridge Building, which contained the first analytical methods for calculating the stresses and strains in a bridge. "Consulting bridge engineering" was established as a specialty within civil engineering in the 1880s.
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Further advances in beam bridge construction would come primarily from improvements in building materials.
1.6 Construction Materials and Their Development
Most highway beam bridges are built of concrete and steel. The Romans used concrete made of lime and pozzalana (a red, volcanic powder) in their bridges. This material set quickly, even under water, and it was strong and waterproof. During the Middle Ages in Europe, lime mortar was used instead, but it was water soluble. Today's popular Portland cement, a particular mixture of limestone and clay, was invented in 1824 by an English bricklayer named Joseph Aspdin, but it was not widely used as a foundation material until the early 1900s.
Concrete has good strength to withstand compression (pressing force), but is not as strong under tension (pulling force). There were several attempts in Europe and the United States during the nineteenth century to strengthen concrete by embedding tension-resisting iron in it. A superior version was developed in France during the 1880s by Francois Hennebique, who used reinforcing bars made of steel. The first significant use of reinforced concrete in a bridge in the United States was in the Alvord Lake Bridge in San Francisco's Golden Gate Park; completed in 1889 and still in use today, it was built with reinforcing bars of twisted steel devised by designer Ernest L. Ransome.
The next significant advance in concrete construction was the development of prestressing. A concrete beam is prestressed by pulling on steel rods running through the beam and then anchoring the ends of the rods to the ends of the beam. This exerts a compressive force on the concrete, offsetting tensile forces that are exerted on the beam when a load is placed on it. (A weight pressing down on a horizontal beam tends to bend the beam downward in the middle, creating compressive forces along the top of the beam and tensile forces along the bottom of the beam.)
Prestressing can be applied to a concrete beam that is precast at a factory, brought to the construction site, and lifted into place by a crane; or it can be applied to cast-in-place concrete that is poured in the beam's final location. Tension can be applied to the steel wires or rods before the concrete is poured (pretensioning), or the concrete can be poured around tubes containing
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untensioned steel to which tension is applied after the concrete has hardened (postensioning).
1.7 Design
Each bridge must be designed individually before it is built. The designer must take into account a number of factors, including the local topography, water currents, river ice formation possibilities, wind patterns, earthquake potential, soil conditions, projected traffic volumes, esthetics, and cost limitations.
Figure 1.1: Cutaway view of a typical concrete beam bridge.
In addition, the bridge must be designed to be structurally sound. This involves analyzing the forces that will act on each component of the completed bridge. Three types of loads contribute to these forces. Dead load refers to the weight of the bridge itself. Live load refers to the weight of the traffic the bridge will carry. Environmental load refers to other external forces such as wind, possible earthquake action, and potential traffic collisions with bridge supports. The analysis is carried out for the static (stationary) forces of the dead load and the dynamic (moving) forces of the live and environmental loads.
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Since the late 1960s, the value of redundancy in design has been widely accepted. This means that a bridge is designed so the failure of any one member will not cause an immediate collapse of the entire structure. This is accomplished by making other members strong enough to compensate for a damaged member.
1.8 Construction Procedure
Because each bridge is uniquely designed for a specific site and function, the construction process also varies from one bridge to another. The process described below represents the major steps in constructing a fairly typical reinforced concrete bridge spanning a shallow river, with intermediate concrete column supports located in the river.
Example sizes for many of the bridge components are included in the following description as an aid to visualization. Some have been taken from suppliers' brochures or industry standard specifications. Others are details of a freeway bridge that was built across the Rio Grande in Albuquerque, New Mexico, in 1993. The 1,245-ft long, 10-lane wide bridge is supported by 88 columns. It contains 11,456 cubic yards of concrete in the structure and an additional 8,000 cubic yards in the pavement. It also contains 6.2 million pounds of reinforcing steel.
1.8.1 Substructure
1 A cofferdam is constructed around each column location in the riverbed, and the water is pumped from inside the enclosure. One method of setting the foundation is to drill shafts through the riverbed, down to bedrock. As an auger brings soil up from the shaft, a clay slurry is pumped into the hole to replace the soil and keep the shaft from collapsing. When the proper depth is reached (e.g., about 80 ft or 24.4 m), a cylindrical cage of reinforcing steel (rebar) is lowered into the slurry-filled shaft (e.g., 72 in or 2 m in diameter). Concrete is pumped to the bottom of the shaft. As the
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shaft fills with concrete, the slurry is forced out of the top of the shaft, where it is collected and cleaned so it can be reused. The aboveground portion of each column can either be formed and cast in place, or be precast and lifted into place and attached to the foundation.
2 Bridge abutments are prepared on the riverbank where the bridge end will rest. A concrete backwall is formed and poured between the top of the bank and the riverbed; this is a retaining wall for the soil beyond the end of the bridge. A ledge (seat) for the bridge end to rest on is formed in the top of the backwall. Wing walls may also be needed, extending outward from the back-wall along the riverbank to retain fill dirt for the bridge approaches.
1.8.2 Superstructure
4 A crane is used to set steel or prestressed concrete girders between consecutive sets of columns throughout the length of the bridge. The girders are bolted to the column caps. For the Albuquerque freeway bridge, each girder is 6 ft (1.8 m) tall and up to 130 ft (40 m) long, weighing as much as 54 tons.
5 Steel panels or precast concrete slabs are laid across the girders to form a solid platform, completing the bridge superstructure. One manufacturer offers a 4.5 in (11.43 cm) deep corrugated panel of heavy (7-or 9-gauge) steel, for example. Another alternative is a stay-in-place steel form for the concrete deck that will be poured later.
1.8.3 Deck
6 A moisture barrier is placed atop the superstructure platform. Hot-applied polymer-modified asphalt might be used, for example.
7 A grid of reinforcing steel bars is constructed atop the moisture barrier; this grid will subsequently be encased in a concrete slab. The grid is three-dimensional, with a layer of rebar near the bottom of the slab and another near the top.
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8 Concrete pavement is poured. A thickness of 8-12 in (20.32-30.5 cm) of concrete pavement is appropriate for a highway. If stay-in-place forms were used as the superstructure platform, concrete is poured into them. If forms were not used, the concrete can be applied with a slipform paving machine that spreads, consolidates, and smooths the concrete in one continuous operation. In either case, a skid-resistant texture is placed on the fresh concrete slab by manually or mechanically scoring the surface with a brush or rough material like burlap. Lateral joints are provided approximately every 15 ft (5 m) to discourage cracking of the pavement; these are either added to the forms before pouring concrete or cut after a slipformed slab has hardened. A flexible sealant is used to seal the joint.
1.9 Problem Statement
A reinforced concrete bridge was to be constructed over a railway line. It was
required to Design the bridge superstructure and to sketch the layout of plan,
elevation and reinforcement details of various components for the following data:
Width of carriage way = 7.5 m
Effective span = 14 m
Centre to centre spacing of longitudinal girders = 3.2 m
Number of longitudinal girders = 3
No. of cross girders = 4
Thickness of wearing coat = 56 mm
Material for construction = M-35 grade concrete and Fe-415 steel conforming to
IS 1786.
Loading = IRC class A-A and IRC class A ,which given worst effect
Footpath = 1.7 m on left hand side of the bridge.
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Total width of road = 10.3 m.
Design the bridge superstructure and sketch the layout of plan, elevation and
reinforcement details of various components.
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2 Deck Slab
2.1 Structural Details
Let us assume slab thickness of 225 mm.
For cantilever slab, thickness at junction = 350 mm and 100 mm at the end.
Providing vehicle crash barriers (for without footpath) on one side of carriage way
and vehicle crash barrier and pedestrian railing on the other side of the
carriageway.
2.2 Effective Span Size of Panel for Bending Moment Calculation
Let us provide longitudinal beam c/c spaced 3.2 m and with rib width 300 mm.
4 cross girders provided with c/c spaced 4.67 m and rib width 250 mm.
Effective depth of slab = 225 - 25 - 8 = 192 mm
Span in transverse direction = 3.2 m
Effective span in transverse direction = 3.2 - 0.3 + 0.192 = 3.092 m 3.1 m
Span in longitudinal direction = 4.67 - 0.25 + 0.192 = 4.6 m
Effective size of panel = 3.1 m x 4.6 m
2.3 Effective Span Size of Panel for Shear Force Calculation
Effective span in transverse direction = 3.2 - 0.3 = 2.9 m
Span in longitudinal direction = 4.67 - 0.25 = 4.42 m
Effective size of panel = 2.9 m x 4.42 m
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Figure 2.1: Plan of Bridge Deck
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Figure 2.2: Section X-X of Bridge Deck Plan
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Figure 2.3: Section Y-Y of Bridge Deck Plan
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2.4 Moment due to Dead Load
Effective size of panel = 3.1m x 4.6 m
Self Wt. of deck slab = 0.225 x 24= 5.4 KN/m2
Wt. of wearing course = 0.056 x 22 = 1.23 KN/m2
Total = 6.63 KN/m2
Ratio K = Short SpanLong Span =
3.14.6 = 0.674
1 K = 1.48
From Pigeaud's curve, we get by interpolation
m1 = 4.8 x 10-2
m2 = 1.9 x 10-2
Total dead wt. = 6.63 x 3.1 x 4.6 = 94.54 KN
Moment along short span = (0.048 + 0.15 x 0.019) x 94.54 = 4.81 KN-m
Moment along long span = (0.019 + 0.15 x 0.048) x 94.54 = 2.38 KN-m
2.5 Moment due to Live Load
2.5.1 Live load BM due to IRC Class AA Tracked Vehicle
Since the effective width of panel is 3.1 m, two possibilities should be considered
for finding maximum bending moment in the panel due to Class AA tracked
vehicle. In the first possibility one of the track of 35t will be placed centrally
(figure 2.4) on the panel. In second possibility both track of 35t each will be
placed symmetrically as shown in figure 2.5.
Case 1: Class AA Track located as in figure 2.4 for Maximum Moment
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Figure 2.4: Class AA Track located for Maximum Moment on Deck Slab
Impact factor = 25%
u = = 0.988m
v = = 3.72m
K = 0.674
uB =
0.9883.1 = 0.319
vL =
3.724.6 = 0.809
From Pigeaud's curve, we get by interpolation
m1 = 10.5 x 10-2
m2 = 4.1 x 10-2
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Total load per track including impact = 1.25 x 350 = 437.5 KN
Moment along short span = (10.5 + 0.15 x 4.1) x 10-2 x 437.5 = 48.63 KN-m
Moment along long span = (4.1 + 0.15 x 10.5) x 10-2 x 437.5 = 24.83 KN-m
Final Moment after applying effect of continuity
MB = 48.63 x 0.8 = 38.9 KN-m
ML = 24.83 x 0.8 = 19.86 KN-m
Case 2: Both track of 35t each symmetrically as shown in figure 2.5.
Figure 2.5: Both Class AA Track located for Maximum Moment on Deck Slab
X = 0.531 m u1 =0.988 m v = 3.72 m
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i) u = 2( u1 +X) = 3.038 m v = 3.72m
u B =
3.038 3.1
vL =
3.724.6 = 0.809
From Pigeaud's curve, we get by interpolation
m1 = 5.5 x 10-2
m2 = 2.5 x 10-2
M1 = (5.5 + 0.15 x 2.5) x 10-2 x 1.519 = 0.0892
M2 = (2.5 + 0.15 x 5.5) x 10-2 x 1.519 = 0.051
ii) u = 2X = 1.062 v =3.72
u B =
1.0623.1 = 0.343
vL =
3.724.6 = 0.809
From Pigeaud's curve, we get by interpolation
m1 = 10.5 x 10-2
m2 = 4.0 x 10-2
M1 = (10.5 + 0.15 x 4.0) x 10-2 x 0.531 = 0.0589
M2 = (4.0 + 0.15 x 10.5) x 10-2 x 0.531 = 0.0296
Final moment applying effect of continuity and impact
MB = (0.0892 - 0.0589) x 2 x 350 x 1.25 x 0.8/0.988 = 21.468 KN-m
ML = (0.051 - 0.0296) x 2 x 350 x 1.25 x 0.8/0.988 = 15.16 KN-m
2.5.2 Live Load BM due to IRC Class AA Wheeled Vehicle
Since the effective width is 3.1 m, all four wheels of the axle can be
accommodated on the panel for finding maximum bending moment in the panel
due to Class AA wheeled vehicle. In the first possibility four loads of 37.5 KN and
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four loads 62.5 KN are placed symmetrical to both the axis as shown in figure 2.6.
In second possibility all four loads of first axle is place symmetrically with all four
wheels of second axle following it as shown in figure 2.7. A third possibility should
also be tried in which four wheel loads of the first axle are so placed that the
middle 62.5KN wheel load is placed centrally, with the four wheel loads of second
axle following it as shown in figure 2.8.
Case 1: All four loads of 37.5 KN and four loads 62.5 KN are placed symmetrical to
both the axis as shown in figure 2.6.
Impact factor = 25%
u1 = = 0.469 m
v1 = = 0.345 m
(A) For Load W1 of Both Axles
X = 0.865 m Y= 0.428 m
i) u = 2(u1 +X) = 2 x 1.335 = 2.67 m
v = 2(v1 + Y) = 2 x 0.773 = 1.546 m
u B =
2.673.1 = 0.861
vL =
1.5464.6 = 0.336
From Pigeaud's curve, we get by interpolation
m1 = 8.5x 10-2
m2= 6.0 x 10-2
M1 = (8.5 + 0.15 x 6.0) x 10-2 x 1.335 x 1.546/2 = 0 .097
M2= (6.0 + 0.15 x 8.5) x 10-2 x 1.335 x 1.546/2 = 0.075
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Figure 2.6: Disposition of Class AA Wheeled Vehicle as Case 1 for Maximum
Moment
ii) u = 2X = 1.73 m v = 2Y = 0.856 m
u B =
1.733.1 = 0.558
vL =
0.8564.6 = 0.186
From Pigeaud's curve, we get by interpolation
m1 = 12.0 x 10-2
m2 = 10.0 x 10-2
M1 = (12.0 + 0.15 x 10.0) x 10-2 x 0.866 x 0.428 = 0.050
M2= (10 + 0.15 x 12.0) x 10-2 x 0.866 x 0.428 = 0.049
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iii) u = 2(u1 +X) = 2.67 m v = 2Y = 0.856 m
u B = 0.861
vL = 0.186
From Pigeaud's curve, we get by interpolation
m1 = 8.5 x 10-2
m2 = 7.5 x 10-2
M1 = (8.5 + 0.15 x 7.5) x 10-2 x 1.335 x 0.428 = 0.055
M2 = (7.5 + 0.15 x 8.5) x 10-2 x 1.335 x 0.428 = 0.050
iv) u = 2X = 1.73 m v = 2(v1+Y) = 1.546 m
= 1.733.1 = 0.558
vL = 0.336
From Pigeaud's curve, we get by interpolation
m1 = 11.5 x 10-2
m2 = 7.5 x 10-2
M1 = (11.5 + 0.15 x 7.5) x 10-2 x 0.866 x 0.773 = 0.0845
M2 = (7.5 + 0.15 x 11.5) x 10-2 x 0.866 x 0.773 = 0.0618