Bridge Engineering Lecture Note.pdf

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ETHIOPIAN CIVIL SURVICE UNIVERSITY INSTITUTE OF URBAN DEVELOPMENT STUDY

URBAN ENGINEERING DEPARTMENT FUNDAMENTALS OF BRIDGE DESIGN (UE 575)

Course: Fundamental of Bridge design (UE575)

Prerequisite: UE 452 -Design of RC Structures II, & UE 342 - Theory of Structures II Credit Hours: 3 (2 Lecture hours and 3 Tutorial hours) Targeted group: Year 5th Academic Year: 2016/17/semester I Instructor name: Yonas A.

COURSE OUTLINE 1. Introduction

2. Investigation for Bridges - Site Selection

- Data Collection, Span Determination

3. Types of Bridges and their Selection - Types of Bridges

- Selection of Bridges

4. Bridge Loading - Types of Loads

- Distribution of Loads According to AASHTO

5. Superstructure

- Reinforced Concrete Superstructures - Steel Superstructures

- Composite Superstructures - Arches, Cable stayed, Suspension 6. Substructures

- Piers - Abutments - Wing Walls - Scour Protection 7. Bearings and Railings

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References:1. ERA Bridge Design Manual, 2002 2. AASHTO LRFD Bridge Design Manual

3. Bridge Engineering-Superstructure (Downloaded from Digital Engineering Library @ McGraw-Hill

(www.digitalengineeringlibrary.com)

4. Bridge Engineering Handbook, Wai-Fah Chen and Lian Duan. (2000) 5. Structural Engineering Handbook, Gaylord, E.H (1997)

6. Bridge Engineering, Ponnuswamy, S( 1999)

7. Design of Modern Concrete Highway Bridges, Heins and Lawrie (1984)

Evaluation:

Attendance and Class Activity………10% (90% attendance for all student) Project………...40% [Min./Max.5 &6 Group] Mid Exam……….20%

Final Exam………...30%

“Everything should be made as simple as possible.

But not simpler!”

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Fundamental of Bridge Design 1

1. Introduction

Bridges are important structures to pass obstacles, such as rivers, gorges, roads and railways. They are not seen or understand in the same way by everyone. For instance: A simple bridge over a small river will be viewed differently by different people because the eyes each one sees it with are unique to that individual.

- Some one travelling over the bridge everyday while going to work may only realize a bridge is there because the road way has posts and railing on either side.

- Others may remember a time before the bridge was built how far they had to travel to visit friends and to get the children to school.

- Civic leaders see the bridge as a link between neighborhoods and a way to provide fire and police protection and access to hospital.

- In business community, the bridge is seen as opening up new markets and expanding commerce.

- An artist will consider the bridge and its setting as a possible subject for a future painting. - A theologian may see the bridge as symbolic of making a connection between God and

human beings.

- While a boater on the river, looking up when passing underneath the bridge, will have a completely different perspective.

Bridges affect people. People use them and engineers design them and later build and maintain them. Bridges must be planned and engineered before they can be constructed. Bridge engineering is one of the fascinating fields in civil engineering calling for expertise in many areas: structural analysis and design, geotechniques, traffic projection, surveying, runoff calculation and methods of construction.

Mankind takes lessons from nature to construct bridges

• Tree fallen accidentally across a stream was the earliest example of a beam type bridge. • Similarly, the natural rock arch formed by erosion of the loose soil below was the earliest

forebear of arch bridges.

• Creeper hanging from tree to tree allowing monkeys to cross from one bank to the other was the forerunners of suspension bridges.

Transportation System and Bridges

Transportation system which is implemented on land needs bridges. Basically in Road Transportation System Bridge is mandatory for two reasons.

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2. To facilitate the transportation system. This is to say in larges cities there is traffic jam when two or more roads meet at a point. For such cases bridges, called interchanges are provided. E.g. Gotera interchange, Addis Ababa

A bridge controls the capacity of the transportation system. For instance: If the strength of the bridge is unable to carry heavy trucks, loads limits will be posted and heavy trucks will be rerouted.

Bridges are expensive structures. The cost per meter of a bridge is high in comparison to the road.

If the bridge fails, the transportation system will not be in a position to give function. Therefore, bridge designer has control over the

• capacity, • cost and • Safety.

2. Investigation for Bridges

Bridge Site Selection

In locating a bridge crossing the following considerations come in to picture.

• The reach of the river should be straight. Especially this has to hold on upstream side of the crossing. This is necessary so that the approach flow is not angular and the obstructions caused by piers, etc have minimum disturbance effect on the flow.

• The river in the reach should have a regime flow free of excess of currents.

If this is present, it will be aggravated by the piers that have to be put up and will result in excessive scour which endanger the foundation.

• The channel in the reach should be well defined. • The crossing site should be as narrow as possible.

• The crossing site should have firm high banks which are fairly inerodable. In this case the river flow will be defined and confined and any excessive velocity will not cause erosion. • The site on a meandering river should be a nodal point. A nodal point is defined as the location where the river regime does not normally shift and the location serves as a fulcrum about which river channel swing laterally ( both upstream and down stream) • The site should have suitable strata at reasonable and workable depth for founding piers

and abutments.

• The site should allow for constructing approach road. • The site should be selected where skewness can be avoided.

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For a river crossing it is important to identify the type of river to be crossed. There are two types of rivers namely alluvial and incised.

Alluvial rivers are winding and they erode their banks and scour their beds; they have flood

plains on either side of the channel and the flow regularly overtops the channel banks to spread across the flood plain. They are continually active, scouring and depositing materials on the banks and transporting sediments.

Incised rivers have a relatively stable banks and arc generally narrower and deeper than alluvial

rivers.

Bridge crossing over alluvial rivers nearly always require training works to stabilize the channel flow with in tile bridge waterway opening.

Data Collection

Once the engineer has identified a likely site for the bridge, he/she needs to obtain field information on the catchment area and run off, local terrain conditions and water levels, navigational (like Baro River) and other clearance requirements.

Field reviews shall be made by the designer in order to become familiar with the site. The most complete survey data cannot adequately depict all site conditions or substitute for personal inspection by someone experienced in bridge design.

• River Survey

Information required by the designer for analysis and design should include all features that can affect the magnitude and the frequency of the flood flow which will pass the site under study. These are: Climatologically characteristics, land runoff characteristics, stream gauging records, high water marks and size and performance of existing structures in the vicinity.

High water marks can be obtained from gauges or from local people. In addition, they can be

identified from small debris, such as grass or twigs caught in tree branches, elephant grass or similar matted down, mud lines on stones or bridges, are all high water indicators.

The hydrologic characteristics of the basin or watershed of the stream under study are

needed for any predictive methods used to forecast flood flows. Although many of these characteristics can be found from office studies, some are better found by a field survey of the basin. The size and configuration of the watershed, the geometry of the stream network, storage volumes of ponds, lakes, reservoirs, and flood plains, and the general geology and soils of the basin can be found from maps.

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Having determined these basin characteristics, runoff times, infiltration values, storage values, and runoff coefficients can be found and used in calculating flood flow values using different methods . Like: Reve’s formula, rational formula, Area-Velocity formula

Soil Investigation

Once at the site it is easy and of great value to sample for soil, rock, stone, water, etc. in cooperation with the soil investigators.

Soil investigation is required to get soil profile, engineering property of the foundation material and foundation level of the abutments and piers for design of the foundation.

This information is obtained by analyzing samples taken from boreholes, test pits or geophysical surveying.

Samples of at least 2Kg each should be collected marking station number and river name where the crossing site is fixed.

Field Sketching and Photos

It has proved very practical to make a simple sketch of the bridge site with approximate water shores, existing structures, scour holes, main stream location, etc including very rough dimensions with approximate measurements

As a minimum, photos shall be taken looking upstream and downstream from the site as well as along the contemplated highway centerline in both directions. Details of the streambed and banks should also be photographed along with any existing structures in the vicinity both upstream and downstream. Close-up photographs complete with a scale or grid shall be taken to facilitate estimates of the stream bed gradation.

Check List of Site Investigation

A form or checklist that can be used by the field investigator/designer in identifying and cataloging field information is shown on .A checklist for Inspection of existing bridges is shown below.

FIELD VISIT INVESTIGATION FORM

• PROJECT:…………...………...……… Date: …...………. Inv. by ………...………...… Site Situated @ STA: ...……….

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High Water Mark:... ... Level: +...Side Slopes: ...degrees: ... Diversions/ Flow concentration / Flood Hazards year, level: ... % Grade of Stream: ... Channel, Base: ……(m) Height of Banks:…... (m) Manning's Value n=... Crossing angle (estimated): …………degrees Meandering: ………(show figure below) Bottom/Base material... Material on channel side: ... n=... Up or Downstream Restriction (debris/sedimentation/scour/soil mtrl.): ... ...

• STRUCTURES : Bridges/ Buildings upstream and downstream: ... @ M up/down:... Type: ...Piers: Type: ... Abutment Types: ...Width: ...(m) Size of Spans: ... Clear Height: ……(m) @...; ...m@...; ...m@ ...; Total water width at HWL:...(m); (Overflow? Year? Level: +...) ...

• MISC. Land Uses upstream and downstream: ... Vegetation (Location, Type, Name): ... Wildlife (Paths, Traces, Type, Name): ...

• Soil Conditions: ... at Roadway STA: ... Sample no: ... @ STA: ...; Sample no: ... @ STN: ...; Sample no: ... @ STA: ...;

• Photos no:...@STN:... Shows: ... Photos no:...@STA:... Shows: ... Photos no:...@STN:... Shows: ... Photos no:...@STN:... Shows: ...

• REMARKS: ... ... ... ... (please, make simple plan sketch incl. water shores/Road alignment and continue the text on back side of this page, if needed) Economical Span

Span determination is usually dictated by the hydraulic requirement. However, there are conditions where lengthen spans are chosen for the sake of road alignment.

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For a given span the most economical span is the length at which superstructure cost equals to substructure cost.

Hydraulic Requirements

Bridges are designed to accommodate design discharge at design flood. When a river has a wide flood plain, the economical solution may be using short span bridge with proper scour and erosion protection for the embankment, abutments and piers.

Piers should be located in such a manner that they can provide the required lineal waterway and navigational clearance.

The alignment of piers and abutments should, if possible, be set parallel to the direction of flow during maximum flood.

Free Board

The waterway below the superstructure must be designed to pass the design flood and the floating debris carried on it.

The free board allows for uncertainty in determining DFL also. The minimum free board above the design water level is given in table below unless refined hydraulic analyses have been made.

Table: Free Board

Discharge (m3/s) Vertical Clearance/Free board (m)

0 to 3.0 0.3

3.0 to 30.0 0.6

30.0 to 300 0.9

> 300 1.2

These clearance measurements should be increased for backwater effects when the flow is restricted by short span bridge or when the river has history of unusual large floating items or in case of navigational requirements.

Grade Requirements

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climb, vertical curve and sight distance. These requirements may increase the span beyond the hydraulic requirement.

3. Types of Bridges and their Selection

3.1 Types of Bridges

Bridges can be classified in different ways

(a) Traffic type/functionality

- Road bridge - Railway bridge - Pedestrian bridge - Aqueduct - Viaduct - Equipment bridge (b) Life Span - Temporary bridges - Permanent bridges - Semi-permanent bridges (c) Horizontal Arrangement - Straight/Normal bridge - Skewed bridge - Curved bridge (d) Vertical Arrangement

- Horizontal/ Flat/ Normal - Inclined

(e) Span

- L ≤ 6m (Culvert)

- 7m < L ≤ 15m (Small span bridges) - 16 ≤ L ≤ 50m (Medium span Bridges) - 50 ≤ L≤ 150m (Large Span Bridges) - L≥150m (Extra Large Span Bridges)

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(f) Construction Materials

- Timber Bridges - Masonry Bridges

- Reinforced Concrete Bridges - Prestressed Concrete Bridges - Steel Bridges - Composite Bridges (g) Span Arrangement - Simply Supported - Continuous - Cantilever (h) Structural Arrangement - Slab Bridges

- Girder (Deck girder Bridges) - Box Girder

- Portal Frame Bridges - Arch Bridges

- Truss Bridges - Plate Girder Bridges - Cable Stayed Bridges - Suspension Bridges - Box Cell/ Box culvert

(i) Movements

- Movable Bridges - Fixed Bridges

3.2 Selection of Bridge Type

In selection of a bridge type, there is no unique answer. For each span length range there is more than one bridge type that will satisfy the design criteria. Generally the following factors should be considered.

• Geometric Condition of the Site: The type of bridge selected will often depend on the horizontal and vertical alignment of the highway route and on the clearances above and below the road way. E.g. If the alignment is on a curve, box and slab type bridges are best options.

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• Subsurface Conditions of the Site: The foundation soils at a site will determine whether abutments and piers can be founded on spread footings, driven piles and etc.

The potential for seismic activity at a site should be a part of the subsurface investigation because this will change details of the substructure. E.g. an inclined leg rigid frame bridge requires strong foundation

• Functional Requirements: Bridge should serve the present and future traffic.

E.g. If future widening or replacement of bridge decks is a concern girder type bridge is best option.

• Aesthetics: It is necessary to understand what qualities and features of a bridge tend to make that aesthetics statement a good one. This understanding requires training and time.

- When a bridge is placed across a relatively shallow valley, the most pleasing appearance occurs when there are an odd number of spans with span lengths that decrease going up the side of the valley.

- Harmony between the whole structure and its surrounding needed to be addressed. - Repeating similar spans too many times can become monotonous, just as hearing the

same music with a heavy beat that is repeated over and over again can be uncomfortable.

Moreover, contrast and texture, light and shadow are additional aesthetic parameter in bridge design.

• Economics and ease of maintenance: In comparison of the economics of different bridge types, the construction cost and maintenance cost should be taken together. A general rule is that the bridge with minimum number of spans, fewest deck joints and widest spacing of girders will be the most economical. By reducing the number of spans, the construction cost of one pier is eliminated.

Deck joints are a high maintenance cost item, so minimizing their number will reduce the life cycle cost of the bridge,

Generally, concrete structures require less maintenance than steel structures.

• Construction and erection considerations: The selection of the bridge type to be built is often governed by construction and erection considerations. In general, the larger the prefabricated or precast member, the shorter the construction time. However, the larger the members, the more difficult they are to transport and lift into place.

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The availability of skilled labor and specified materials will also influence the choice of a particular bridge type.

• Legal Considerations: Applicable laws like environmental laws also govern the type of bridge.

4. Bridge Loadings

4.1 Types of loads

The following permanent and transient loads and forces shall be considered for design of bridges where applicable. The load provisions may also be applied to the structural evaluation of existing bridges.

• Permanent Loads

DC = dead load of structural components and nonstructural attachments DD = down drag

DW = dead load of wearing surfaces and utilities EH = horizontal earth pressure load

EL = accumulated locked-in effects resulting from the construction process ES = earth surcharge load

EV = vertical pressure from dead load of earth fill • Transient Loads

BR = vehicular braking force CE = vehicular centrifugal force CR = creep

CT = vehicular collision force EQ = earthquake

FR = friction

IM = vehicular dynamic load allowance LL = vehicular live load

LS = live load surcharge PL = pedestrian live load SE = settlement

SH = shrinkage

TG = temperature gradient TU = uniform temperature

WA = water load and stream pressure WL = wind on live load

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WS = wind load on structure

4.2 Dead Loads

Dead load shall include the weight of all components of the structure, appurtenances and utilities attached thereto, earth cover, wearing surface, future overlays, and planned widening.

In the absence of more precise information, the densities, specified in table below, shall be used for dead loads.

Densities and Force Effects of Different Materials

MATERIAL DENSITY (kg/m3) Force effect (kN/m3)

Bituminous Wearing Surfaces 2250 22.5

Cast Iron 7200 72

Cinder (volcanic stone) Filling 960 9.6

Compacted Sand, silt, or Clay 1925 19.3

Concrete Normal 2400 24

Loose Sand, Silt, or Gravel 1800 18

Soft Clay 1700 17

Rolled Gravel or Ballast 2250 22.5

Steel 7850 79 Stone Masonry 2725 27.3 Wood Hard 960 9.6 Soft 800 8 Water Fresh 1000 10

4.3 Live Loads

Number of Design Lanes: Generally, the number of design lanes should be determined by

taking the integer part of the ratio w/3600, where w is the clear roadway width in mm between curbs and/or barriers.

Multiple Presence of Live Load: The provisions of this subchapter shall not be applied to the

fatigue limit state for which one design truck is used, regardless of the number of design lanes. Trucks will be present in adjacent lanes on roadways with multiple design lanes but this is unlikely that all adjacent lanes will be loaded simultaneously. This will be considered by the multiple presence factors.

Number of Loaded Lanes 1 2 3 >3

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When the loading condition includes the pedestrian loads combined with one or more lanes of the vehicular live load, the pedestrian loads shall be taken to be one loaded lane.

4.3.1 Vehicular Live Loads

Vehicular live loading on the roadways of bridges structures, designated HL-93, and shall consist of a combination of the:

• Design truck or design tandem, and • Design lane load

• Design truck: The weights and spacing of axles and wheels for the design truck shall be as specified in Figure below.

Fig. Characteristics of the Design Truck

• Design Tandem: The design tandem used for Strategic Bridges shall consist of a pair of 110

kN axles spaced 1.2 m apart. The transverse spacing of wheels shall be taken as 1.8 m. See below.

Fig. Design Tandem Load 3.000 mm

4.3 m

4.3 –9.0 m

1.8 m

Plan of Design Truck Load showing tire contact areas

110 kN

1.2 m

1.8 m 110 kN

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• Design Lane Load: The design lane load shall consist of a load of 9.3 kN/m, uniformly distributed in the longitudinal direction. Transversely, the design lane load shall be assumed to be uniformly distributed over a 3.0-m width. The force effects from the design lane load shall not be subject to a dynamic load allowance.

4.3.2 Dynamic Load Allowance

Ø (IM = Vehicular Dynamic Load Allowance): Dynamic effects due to moving vehicles shall be attributed to two sources:

1- Hammering effect is the dynamic response of the wheel assembly to riding surface discontinuities, such as deck joints, cracks, potholes, and delaminations, and

2- Dynamic response of the bridge as a whole to passing vehicles, which shall be due to long undulations in the roadway pavement, such as those caused by settlement of fill, or to resonant excitation as a result of similar frequencies of vibration between bridge and vehicle. The frequency of vibration of any bridge should not exceed 3 Hz.

Dynamic load allowance need not be applied to:

• Retaining walls not subject to vertical reactions from the superstructure, and • Foundation components that are entirely below ground level.

The dynamic load allowance shall not be applied to pedestrian loads or to the design lane load. The factor to be applied to the static load shall be taken as: (1 + IM/100).

Component IM

Deck Joints – All Limit States 75% All Other Components

• Fatigue and Fracture Limit State • All Other Limit States

15% 33%

Table

Dynamic Load Allowance, IM

The dynamic load allowance for culverts and other buried structures, in %, shall be taken as: IM = 33 (1.0 - 4.l*10-4 DE) > 0%

Where:

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4.3.3

Centrifugal forces

(CE= Vehicular Centrifugal Force):

Centrifugal force is due to inertia force of vehicles on curved bridges at speed. Centrifugal forces shall be applied horizontally at a distance 1.8 m above the roadway surface.

Centrifugal forces shall be taken as the product of the axle weights of the design truck or tandem and the factor C, taken as:

C = 4 v2 3 g*R

where: v = highway design speed (m/s)

g = gravitational acceleration: 9.81 (m/s2) R = radius of curvature of traffic lane (m)

4.3.4

Breaking Force

(BR= Vehicular Braking Force):

From AASHTO Commentary 3.6.4 Based on energy principles, and assuming uniform deceleration (retardation), the braking force determined as a fraction "b" of vehicle weight is: b = v2

2ga

Where a = the length of uniform deceleration.

From AASHTO Article 3.6.4 Braking forces shall be taken as 25 % of the axle weights of the design truck or tandem per lane placed in all design lanes headed in the same direction.

These forces shall be assumed to act horizontally at a distance of 1800 mm above the roadway surface in either longitudinal direction to cause extreme force effects.

4.3.5

Vehicular Collision

(CT= Vehicular Collision Force):

Unless protections are provided a horizontal force of 1800KN applied at 1.2m above the ground should be considered.

4.3.6 Pedestrian Loads

A pedestrian load of 3.6 kPa (kN/m2) shall be applied to all sidewalks wider than 0.6 m and considered simultaneously with the vehicular design live load.

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4.3.7

Water Loads

(WA= Water Load and Stream Pressure)

• Static Pressure: Static pressure of water shall be assumed to act perpendicular to the surface that is retaining the water. Pressure shall be calculated as the product of height of water above the point of consideration, the density of water, and "g" (the acceleration of gravity = 9.81 m/s2).

p = γ * g * z * 10-9

Where p = static pressure (Mpa) γ = density of water (kg/m3)

z = height of water above the point of consideration (mm) g = Gravitational acceleration (m/s2)

4.3.8

Buoyancy

: Buoyancy shall be considered an uplift force, taken as the sum of

the vertical components of static pressures, acting on all components below design water level.

4.3.9

Stream Pressure

Longitudinal: The longitudinal drag force shall be taken as the product of longitudinal stream pressure and the projected surface exposed thereto.

p = 5.14*10-4 CDV2

Where: p = pressure of flowing water (MPa)

CD = drag coefficient for piers as specified in Table below

V = design velocity in m/s of water for the design flood in strength and service limit states and for the check flood in the extreme event limit state

Type CD

Semicircular-nosed pier 0.7

Square-ended pier 1.4

Debris lodged against the pier 1.4

Wedged-nosed pier with nose angle 90o or less 0.8 Table. Drag Coefficient

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Lateral: The lateral, uniformly distributed pressure on substructure due to water flowing at an angle, θ, to the longitudinal axis of the pier (see Figure below) shall be taken as:

PL = 5.14 x 10-4CLV2

Where: PL = lateral pressure (MPa)

CL = lateral drag coefficient specified in Table below.

Plan View of Pier Showing Stream Flow Pressure

Angle, θ, between direction of flow and longitudinal axis of the pier

CL 0o 0.0 1o 0.5 10o 0.7 20o 0.9 ≥30o 1.0

Table. Lateral Drag Coefficient

The lateral drag force shall be taken as the product of the lateral stream pressure and the surface exposed thereto.

4.3.10

Wind Loads

(WL= Wind on Live load; WS= Wind load on Structure)

§ Wind Pressure on Structures, (WS): For small and medium sized concrete bridges below 50m length the wind load on structures shall be neglected.

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Fundamental of Bridge Design 17 2       = B DZ B D V V P P

Where PB = base wind pressure specified in Table below:

VDZ = design velocity of wind at design elevation, Z (Km/hr) VB= Base wind velocity (Km/hr)

STRUCTURAL COMPONENT WINDWARD LOAD, kPa LEEWARD LOAD, kPa

Trusses, Columns, and Arches 2.4 1.2

Beams 2.4 Not applicable

Large Flat Surfaces 1.9 Not applicable

Table 3-12 Base Pressures, PB Corresponding to VB = 160 km/h (45 m/s)

The wind loading shall not be taken less than 4.4 kN/m2 in the plane of a windward chord and 2.2 kN/m2 in the plane of a leeward chord on truss and arch components, and not less than 4.4 kN/m2 on beam or girder components.

§ Wind Pressure on Vehicles, (WL): When vehicles are present, the design wind pressure shall be applied to both structure and vehicles. Wind pressure on vehicles shall be represented by an interruptible, moving force of 1.46 kN/m acting normal to, and 1.8 m above, the roadway and shall be transmitted to the structure

§ Aeroelastic Instability: Many bridges, decks, or individual structural components have been shown to be aeroelastically insensitive if their length-to-width or length-to-depth ratios are under about 30.0. Wind tunnel testing of bridges and other civil engineering structures is a highly developed technology, which shall be used to study the wind response characteristics of a structural model or to verify the results of analysis. This is especially applicable to long spans.

4.3.11 Earthquake Effects (EQ= Earthquake)

Earthquake loads are given by the product of the elastic seismic response coefficient Csm and

the equivalent weight of the superstructure. These are inertia forces due to mass of the bridge when a sudden shaking of the ground occurs. Minimum seat width requirements shall be at least 500 mm at each abutment.

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Fundamental of Bridge Design 18 Seismic Zone Single-Span Bridges Multispan Bridges

Other Bridges Essential Bridges Critical Bridges Regular Irregular Regular Irregular Regular Irregular 1-3 4 No Seismic Analysis Seismic Analysis * SM/UL * SM * SM/UL * MM * MM * MM

Minimum Analysis Requirements for Seismic Effects

In which:

* = no seismic analysis required (Zone 1-3) UL = uniform load elastic method

SM = single-mode elastic method MM = multimode elastic method

The selection of the method of analysis depends on seismic zone, regularity, and importance of the bridge.

Essential bridges are generally those that should, as a minimum, be open to emergency vehicles and for security/defense purposes immediately after the design earthquake, i.e., a 475-year return period event. However, some bridges must remain open to all traffic after the design earthquake and be usable by emergency vehicles and for security/defense purposes immediately after a large earthquake, e.g., a 2500 year return period event. These bridges should be regarded as critical structures.

4.3.12

Earth Pressure

(EH = Horizontal Earth Pressure; ES = Earth Surcharge;

LS = Live Load Surcharge; DD = Down drag) Earth pressure shall be considered as a function of the:

• Type and density of earth, • Water content,

• Soil creep characteristics, • Degree of compaction

• Location of groundwater table, • Earth-structure interaction, • Amount of surcharge, and • Earthquake effects.

Walls that can tolerate little or no movement should be designed for at-rest earth pressure. Walls that can move away from the soil mass should be designed for pressures between active and at-rest conditions, depending on the magnitude of the tolerable movements. Movement required to reach the minimum active pressure or the maximum passive pressure is a function of the wall height and the soil type. Some typical values of these mobilizing movements, relative to wall height, are given in Table below:

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Approximate Values of Relative Movements Required to Reach Minimum Active or Maximum Passive Earth Pressure Conditions

Type of Backfill Values of ∆/H Active Passive Dense sand 0.001 0.01 Medium-dense sand 0.002 0.02 Loose sand 0.004 0.04 Compacted silt 0.002 0.02

Compacted lean clay 0.010 0.05

Compacted fat clay 0.010 0.05

Where:

∆ = movement of top of wall required to reach minimum active or maximum passive pressure by tilting or lateral translation (mm)

H = height of wall (mm)

For walls that are backfilled with cohesive materials, the effects of soil creep should be taken into consideration in estimating the design earth pressures.

Where activity by mechanical compaction equipment is anticipated within a distance of one-half the height of the wall, taken as the difference in elevation between the point where finished grade intersects the back of the wall and the base of the wall, the effect of additional earth pressure that shall be induced by compaction shall be taken into account.

Wherever possible, the development of hydrostatic water pressure on walls should be eliminated through use of free-draining (rapid-draining) backfill material and/or the use of weep holes and crushed rock, pipe drains, gravel drains, perforated drains, or geofabric drains that provide drainage.

Where soils are subject to both saturation and seismic or other cyclic/instantaneous loads, special consideration should be given to addressing the possibility of soil liquefaction.

• EH = Horizontal Earth Pressure

There are two earth pressure theories used. These are Rankin and Coulomb Earth Pressure Theories.

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Coulomb theory is recommended by AASHTO for masonry and RC abutment since this theory holds better for the actual situation.

Basic earth pressure (p, in MPa) shall be assumed to be linearly proportional to the depth of earth and taken as:

p = kh*γs*g*z *10-9

Where: kh = coefficient of lateral earth pressure taken as ko, from table below for walls that do

not deflect or move,

Soil type Coefficient of Lateral Earth Pressure, ko

OCR = 1 OCR = 2 OCR = 5 OCR = 10

Loose sand 0.45 0.65 1.10 1.60

Medium Sand 0.40 0.60 1.05 1.55

Dense Sand 0.35 0.55 1.00 1.50

Silt (ML) 0.50 0.70 1.10 1.60

Lean Clay (CL) 0.60 0.80 1.20 1.65

Highly Plastic Clay (CH) 0.65 0.80 1.10 1.40

Or ka, specified in Equations below, walls that deflect

ka = sin2 (θ + ϕ/) Γ* sin2θ sin (θ - δ) In which: 2 Γ = 1 + sin (ϕ/ + δ) sin (ϕ/ - β) sin (θ - δ) sin (θ + β)

Where: δ = friction angle between fill and wall β = angle of fill to the horizontal

θ = angle of backfill of wall to the vertical ϕ/ = effective angle of internal friction (°)

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Notations γs = density of soil (kg/m

3

)

z = depth below the surface of earth (mm) g = Gravitational acceleration (m/s2)

• ES = Earth Surcharge; LS = Live Load Surcharge

Where a uniform surcharge is present, a constant horizontal earth pressure, ∆p (MPa), shall be

added to the basic earth pressure. This constant earth pressure shall be taken as: ∆p = ks qs

Where: ks = coefficient of earth pressure due to surcharge

qs = uniform surcharge applied to the upper surface of the active earth wedge (MPa)

live load surcharge shall be applied where vehicular load is expected to act on the surface of the backfill within a distance equal to the wall height behind the back face of the wall.

The increase in horizontal pressure due to live load surcharge shall be estimated as: ∆p = k*γs*g*heq *10-9

where: ∆p = constant horizontal earth pressure due to uniform surcharge (MPa)

γs = density of soil (kg /m3)

k = coefficient of earth pressure

heq = equivalent height of soil for the design truck (mm)

Equivalent heights of soil, heq, for highway loadings shall be taken from Table below. Linear

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The “Wall Height” shall be taken as the distance between the surface of the backfill and the bottom of the footing.

Wall Height (mm)

_h

_eq_(mm)

≤1500 1700

3000 1200

6000 760

≥9000 610

Equivalent Height of Soil, heq for Different Wall Heights Due to Vehicular Loading

N.B If the vehicular loading is transmitted through a structural slab, which is also supported by means other than earth, an appropriate reduction in the surcharge loads shall be permitted.

• Down Drag (DD):

When soil surrounding piles settle, it applies a downward force. In this case, the force should be considered.

4.3.13 Force Effects Due to Superimposed Deformations: TU, TG, SH, CR, SE

- Uniform temperature, (TU): Bridge materials expend and contract in response to rise and fall of temperature. The difference between the lowest or the highest temperature and the base construction temperature assumed in design shall be used to calculate thermal deformation effects.

- Temperature Gradient, (TG): Temperature rise can differ on the top and bottom surfaces of abridge because the top surface is subjected to direct solar radiation. - Differential Shrinkage, (SH): Where appropriate, differential shrinkage strains

between concretes of different age and composition, and between concrete and steel or wood, shall be determined. The designer may specify timing and sequence of construction in order to minimize stresses due to differential shrinkage between components.

- Creep, (CR): In determining force effects and deformations due to creep, dependence on time and changes in compressive stresses shall be taken into account. - Settlement, (SE): This will cause internal forces in continues structures. Force effects

due to extreme values of differential settlements among substructures and within individual substructure units shall be considered.

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4.4 Design Philosophy

In engineering design the general principle is that the resistance of a cross section has to exceed the effects come from the applied loads. That is

Resistance ≥Effect of Loads

When a particular loading condition reaches and just exceeds the resistance capacity of the provided section failure is the result. Such a condition is referred to as a Limit State.

A limit state is a condition beyond which a bridge system or bridge component ceases to full fill the function for which it is designed.

Preventing a limit state from being reached is the central goal of design of bridges. In addition to this function, appearance and economy must get due attention.

Safety is achieved by using reasonable margin of safety factors. These factors are results of collective experience and judgment of qualified group of engineers and officials.

In Highway Bridge design AASHTO LRFD provision is used for bridge design. The resistance side of the inequality of Equation above is multiplied by a statistically based resistance factor, whose value is usually less than one, and the load side is multiplied by a statistically based load factor, whose value is usually greater than one.

The load effect at a particular limit state involves a combination of a different load types (Qi) that have different degrees of predictability. Due to this reason the load effect side is written in a summation form. The equation is

Φ∗Rn≥

∑

γi∗Qi

And this equation involves both load factors and resistance factor due to this the design method is called load and resistance factor design method. In AASHTO LRFD bridge design specification the equation is given by

η∗

∑

γi∗Qi≤Φ∗Rn

The additional parameter η is known as load modifier which is incorporated to consider ductility, redundancy and operational importance of the bridge.

Under the umbrella of the LRFD the strength limit state, extreme event limit state, service limit state and fatigue and fracture limit state exist.

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The total factored force effect shall be taken as:

Q =

Ση

iγi

Q

i

Where:

ηi= load modifier

Qi = force effects from loads specified herein

γi = load factors specified in Tables B and C below

Rn= is resistance

Components and connections of a bridge shall satisfy the above equation for the applicable combinations of factored extreme force effects as specified at each of the limit states presented in Table A:

Table A Limit States

STRENGTH I

Basic load combination relating to the normal vehicular use of the bridge without wind. A reduced value of 0.50, applicable to all strength load combinations, specified for uniform temperature (TU), creep (CR), and shrinkage (SH), used when calculating force effects other than displacements at the strength limit state, represents an expected reduction of these force effects in conjunction with the inelastic response of the structure. The calculation of displacements for these loads utilizes a factor greater than 1.0 to avoid undersized joints and bearings.

STRENGTH II

Load combination relating to the use of the bridge by ERA-specified special design or permit vehicles, without wind.

The permit vehicle should not be assumed to be the only vehicle on the bridge unless so assured by traffic control. Otherwise, the other lanes should be assumed to be occupied by the vehicular live load as specified herein. For bridges longer than the permit vehicle, the presence of the design lane load, preceding and following the permit load in its lane, should be considered.

STRENGTH III

Load combination relating to the bridge exposed to wind velocity exceeding 90 km/h. Vehicles become unstable at higher wind velocities. Therefore, high winds prevent the presence of significant live load on the bridge.

STRENGTH IV

Load combination relating to very high dead load to live load force effect ratios.

The standard calibration process for the strength limit state consists of trying out various combinations of load and resistance factors on a number of bridges and their components. Combinations that yield a safety index close to the target value of β = 3.5 are retained for potential application. From these are selected constant load factors γ and corresponding resistance factors ϕ for each type of structural component reflecting its use.

This calibration process had been carried out for a large number of bridges with spans not exceeding 60 m. For the primary components of large bridges, the ratio of dead and

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live load force effects is rather high, and could result in a set of resistance factors different from those found acceptable for small- and medium-span bridges. It is believed to be more practical to investigate one additional load case than to require the use of two sets of resistance factors with the load factors provided in Strength Load Combination I, depending on other permanent loads present. For bridges with up to 180 m spans, Load Combination IV will govern where the dead load to live load force effect ratio exceeds 7.0.

STRENGTH V

Load combination relating to normal vehicular use of the bridge with wind of 90 km/h (25 m/s) velocity

EXTREME EVENT I

Load combination including earthquake

This limit state includes water loads, WA. The probability of a major flood and an earthquake occurring at the same time is very small. Therefore, consideration of basing water loads and scour depths on mean discharges shall be warranted. Live load coincident with an earthquake is discussed elsewhere in this chapter.

SERVICE I Load combination relating to the normal operational use of the bridge with a 90 km/h (25 m/s) wind and all loads taken at their nominal values. Also related to deflection control in buried metal structures, tunnel liner plate, and thermoplastic pipe and to control crack width in reinforced concrete structures. This load combination should also be used for the investigation of slope stability.

Compression in prestressed concrete components is investigated using this load combination. Service III is used to investigate tensile stresses in prestressed concrete components.

SERVICE II Load combination intended to control yielding of steel structures and slip of slip critical connections due to vehicular live load.

This load combination corresponds to the overload provision for steel structures, and it is applicable only to steel structures. From the point of view of load level, this combination is approximately halfway between that used for Service I and Strength I Limit States.

SERVICE III Load combination relating only to tension in prestressed concrete structures with the objective of crack control.

The live load specified in these Specifications reflects, among other things, exclusion weight limits. The statistical significance of the 0.80 factor on live load is that the event is expected to occur about once a year for bridges with two traffic lanes, less often for bridges with more than two traffic lanes, and about once a day for bridges with a single traffic lane.

FATIGUE Fatigue and fracture load combination relating to repetitive gravitational vehicular live load and dynamic responses under a single design truck having a constant axle spacing of 9.0 m between 145 kN axles.

The load factor, applied to a single design truck, reflects a load level found to be representative of the truck population with respect to a large number of return cycles of stresses and to their cumulative effects in steel elements, components, and connections.

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The load factors for various loads comprising a design load combination shall be taken as specified in Table B. All relevant subsets of the load combinations shall be investigated. For each load combination, every load that is indicated to be taken into account and that is germane to the component being designed, including all significant effects due to distortion, shall be multiplied by the appropriate load factor and multiple presence factor specified in, if applicable.. The factors shall be selected to produce the total extreme factored force effect. For each load combination, both positive and negative extremes shall be investigated.

In load combinations where one force effect decreases another effect, the minimum value shall be applied to the load reducing the force effect. For permanent force effects, the load factor that produces the more critical combination shall be selected from Table C.

Where the permanent load increases the stability or load-carrying capacity of a component or bridge, the minimum value of the load factor for that permanent load shall also be investigated. The larger of the two values provided for load factors of Uniform Temperature (TU), Creep (CR), and Shrinkage (SH) shall be used for deformations and the smaller values for all other effects.

Table B - Load Combinations and Load Factors Load Combination Limit State DC DD DW EH EV ES LL IM CE BR PL LS EL WA WS WL FR TU CR SH TG SE Use one of these at a time EQ CT STRENGTH 1 (Unless noted) γp 1.75 1.00 - - 1.00 0.50/1.20 γTG γSE - - STRENGTH II γp 1.35 1.00 - - 1.00 0.50/1.20 γTG γSE - - STRENGTH III γp - 1.00 1.40 - 1.00 0.50/1.20 γTG γSE - - STRENGTH IV

EH, EV, ES, DW DC ONLY γp 1.5 - 1.00 - - 1.00 0.50/1.20 - - - - STRENGTH V γp 1.35 1.00 0.50 1.0 1.00 0.50/1.20 γTG γSE - - EXTREME EVENT I γp γEQ 1.00 - - 1.00 - - - 1.0 0 - SERVICE I 1.00 1.00 1.00 0.30 1.0 1.00 1.00/1.20 γTG γSE - - SERVICE II 1.00 1.30 1.00 - - 1.00 1.00/1.20 - - - - SERVICE III 1.00 0.80 1.00 - - 1.00 1.00/1.20 γTG γSE - - FATIGUE LL, IM and CE ONLY - 0.75 - - - -

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Where (see following text):

BR = vehicular braking force CE = vehicular centrifugal force CR = creep

CT = vehicular collision force

DC = dead load of structural components DD = downdrag

DW = dead load of wearing surfaces and utilities EH = horizontal earth pressure load

EL = accumulated locked-in effects resulting from the construction process

EQ = earthquake load ES = earth surcharge load

EV = vertical pressure from dead load of earth fill

FR = friction

IM = vehicular dynamic load allowance LL = vehicular live load

LS = live load surcharge PL = pedestrian live load SE = settlement

SH = shrinkage

TG = temperature gradient TU = uniform temperature

WA = water load and stream

pressure

WL = wind on live load WS = wind load on structure

Table C - Load Factors for Permanent Loads, γp

Type of Load Load Factor (γp)

Maximum Minimum

DC: Component and Attachments 1.25 0.90

DD: Downdrag 1.80 0.45

DW: Wearing Surfaces and Utilities 1.50 0.65

EH: Horizontal Earth Pressure • Active • At-Rest 1.50 1.35 0.90 0.90

EL: Locked-in Erection Stresses 1.0 1.0

EV: Vertical Earth Pressure • Overall Stability • Retaining Structure • Rigid Buried Structure • Rigid Frames

• Flexible Buried Structures other than Metal Box Culvert

• Flexible Metal Box Culverts

1.35 1.35 1.30 1.35 1.95 1.50 N/A 1.00 0.90 0.90 0.90 0.90

ES: Earth Surcharge 1.50 0.75

For example, at Strength I Limit State where the permanent load reaction is positive and live load can cause a negative reaction, the load combination would be:

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If both reactions were negative, the load combination would be: 1.25DC + 1.50DW + 1.75(LL+IM).

Load Modifiers, ηi = ηDηRηI :

ηD = a factor relating to ductility, as specified below

ηR = a factor relating to redundancy as specified below

ηI = a factor relating to operational importance as specified below

Ductility, redundancy, and operational importance are significant aspects affecting the margin of safety of bridges.

• Ductility: The structural system of a bridge shall be proportioned and detailed to ensure the development of significant and visible inelastic deformations at the strength and extreme event limit states prior to failure.

For the strength limit state:

ηD ≥ 1.05 for non-ductile components and connections

ηD = 1.00 for conventional designs and details complying with these Specifications

ηD ≥ 0.95 for components and connections for which additional ductility-enhancing

measures have been specified beyond those required by these Specifications For all other limit states:

ηD = 1.00

• Redundancy: Multiple load-path structures should be used unless there are compelling reasons not to use them.

For the strength limit state:

ηR≥1.05 for nonredundant members

=1.00 for conventional levels of redundancy ≤0.95 For exceptional levels of redundancy For all other limit states:

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• Operational importance: This definition shall apply to the strength and extreme event limit

states only. Some bridges or structural components and connections shall be declared to be of operational importance.

Such classification should be based on social/survival and/or security/defense requirements. For the strength limit state:

ηl ≥ 1.05 for important bridges

= 1.00 for typical bridges

≤ 0.95 For relatively less important bridges For all other limit states:

ηl = 1.00

For Conventional Construction, Resistance Factors Ф shall be taken as

For flexure and tension of RC = 0.9 For flexure and tension of PSC = 1.0 For shear and torsion = 0.9 For bearing on concrete = 0.7 For compression in strut-and-tie model = 0.7 For compression in anchorage zones = 0.8 For tension in steel in anchorage zones = 1.0 For resistance during pile driving = 1.0

5. Superstructure Types

An efficient design of bridge superstructure is essential to achieve overall economy in the whole bridge structure in that the superstructure dead weight may form a significant portion of the gravity load the bridge must sustain and transmit to the foundation. A light superstructure is economical not _only material requirements of the superstructure but also requires smaller size for substructure and foundations. A clear understanding of the structural behavior of structural behavior under loads is essential for efficient design.

A bridge superstructure is an integrated body of various members of reinforced concrete, prestressed concrete, steel, composite, diaphragms, trusses, arches, etc. Determination of' forces in theses components is essential for design purposes.

The following types of bridges are discussed as follows.

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Reinforced concrete bridges:

Steel and concrete are construction materials.

Reinforced concrete bridges possess several advantages over steel bridges. - adaptability of concrete wide variety of structural shapes - Low maintenance cost

- Long life and better resistance to temporary overloads and dynamic loads than steel bridges.

- Cast-in-place Reinforced concrete structures are continuous and monolithic, attributes, which translate into easy construction, low cost and good seismic resistance. They can also be given the desired aesthetic appearance.

The disadvantage

- large dead weight - difficulty to widen - longer construction time

- requires formwork and false work

Bridge live loads occupy partial area of the decks unlike live loads in buildings which is taken uniformly distributed all over the floor area. Live load on bridges can occupy random positions both longitudinally and transversely, and this affects the live load shared by various beams. This aspect of live load distribution is one of the primary concerns in the analysis of bridge decks. Influence lines will be used to determine load position for maximum effect and the magnitude of these effects.

The following RC bridges will be discussed. Slab bridge

T-girder bridge Box girder bridge Continuous RC bridge RC rigid frame bridges

Slab Bridge:

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Uniform thickness

Voided slab

Slab Bridge normally requires more concrete and reinforced steel than Girder Bridge of the same span but the formwork is simpler and less expressive, hence they are economical when these cast factor balance favorably.

The structural configuration of bridge is shown below.

Typical Cross-section of Slab Bridge

Slab bridges are most commonly used to span short spans up to 12 meters. The load carrying mechanism is by plate action, i.e., by bending and twisting due to continuity in all directions. Application of a load on the portion make the slab deflect into a dish shape locally, causing a two-dimensional system of bending and twisting moments, the mechanism through which the load is transferred to the adjacent elements of the deck, which are less severely loaded.

Slab Notch

Edge beam Post & raining

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Where: Z is the downward deflection of the plate q is intensity of uniform load

D is flexural rigidity of tile plate

In the absence of closed form solution to the above equation, approximate methods are developed.

One method is the method of influence surfaces, which uses design charts. These charts have been prepared by Pucher or slabs of various shapes and support conditions (1964),and by Rusch and Heregnroder (1961) and Dalas and Hanuska (1964) for simply supported skew slabs.

Grillage method is also used for analysis and softwares are available for this. Another method that AASHTO recommends is the Strip Method.

Load distributions:

The equivalent width of longitudinal strips per lane for both shear and moment with one lane, i.e., two lines of wheels, loaded shall be determined as:

The equivalent width, E of longitudinal strips per lane for both shear and moment with more than one lane loaded shall be determined as:

Where: E = equivalent width (mm)

L1 = modified span length taken ≤ of the actual span or 18,000 (mm)

W1 = modified edge-to-edge width of bridge taken to be ≤ of the actual width or

18,000 mm for multilane loading, or 9,000 mm for single-lane loading (mm) W = physical edge-to-edge width of bridge (mm)

NL = number of design lanes as specified

Where decks span primarily in the direction of traffic, the effective width of a strip, with or without an edge beam, shall be taken as the sum of the distance between the edge of the deck and the inside face of the barrier, plus 300 mm, plus one-half of the strip width. The effective width shall not exceed either the full strip width or 1800 mm.

T-girder Bridge:

T- Girders are used for bridges spanning from about 10meters-25 meters. These usually consist of equal1y spaced beams (generally with spacing of 1.8-3.6m) spanning longitudinally between

1 1W L 42 . 0 250 E= + L 1 1 N W W L 12 . 0 2100 E= + ≤

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supports. The slab is structural1y continuous across the top. The slab serves dual purpose of supporting the live load on the bridge and acting as the top flange of the longitudinal beams. Diaphragms are provided transversely between the beams over the supports and depending on the span, at midspan and other intermediate locations. The purpose of providing diaphragms is to ensure lateral distribution of live loads to various adjacent stringers, the magnitude of the share of each stringer depends on the stiffness of the diaphragms relative to the stringers and on the method of connectivity.

Design of T- girder bridges consists of deck slab analysis and design, and the T-girder analysis and design.

Structural analysis of the deck slab involves taking a continuous strip perpendicular to the girders (AASHTO Art.9.6.1) and analyzing by moment distribution or using design aid given by AASHTO, ILS for critical position of loads. Extreme positive moment at any point will be taken to apply to all positive moment regions (Art 4.6.2.1.1). The width of equivalent interior transverse strip over which the wheel loads can be considered distributed longitudinally in cast - in - place concrete decks is given as [Table Art. 4.6.2. I .3-1]

• overhang, 11401-0.83lX • positive moment, 660+0.55S • negative moment, 1220+0.25S

Where X is the distance from the wheel load to centerline of support and S is the spacing of' the T-beams.

In the design of overhang deck slab design forces acting on the post and railings or barrier should be considered.

Load Distribution Factors for the Girders:

For moment:

- Interior girders: The live load flexural moment for interior beams with concrete decks shall be determined by applying the lane fraction specified in Table below

Type of Beams Applicable

Cross-section from Figure

13-2

Distribution Factors Range of

Applicability

Concrete Deck on Wood Beams

l One Design Lane Loaded: S/3700

Two or More Design Lanes Loaded: S/3000

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Type of Beams Applicable

Cross-section from Figure

13-2

Distribution Factors Range of

Applicability

Concrete Deck, Filled Grid, or Partially Filled Grid on Steel or Concrete Beams; Concrete T-Beams, T-and Double T- Sections a, e, k and also i, j if sufficiently connected to act as a unit

One Design Lane Loaded: 0.06 + S 0.4 S 0.3 Kg 0.1

4300 L Lts3

Two or More Design Lanes Loaded: 0.075 + S 0.6 S 0.2 Kg 0.1 4300 L Lts 3 1100≤ S≤4900 110 ≤ ts ≤ 300 6000≤L≤73000 Nb≥ 4

Use lesser of the values obtained from the equation above with Nb = 3 or the

lever rule

Nb = 3

Multicell Concrete Box Beam

d One Design Lane Loaded:

1.75 + S 300 0.35 1 0.45 1100 L Nc

Two or More Design Lanes Loaded: 13 0.3 S 1 0.25 Nc 430 L 2100≤S≤4000 18 000 ≤ L ≤ 73000 Nc≥ 3 If Nc>8 use Nc=8

Steel Grids on Steel Beams

a One Design Lane Loaded:

S/2300 If tg < 100 mm

S/3050 If tg≥ 100 mm

Two or More Design Lanes Loaded: S/2400 If tg < 100 mm

S/3050 If tg≥ 100 mm

S ≤ 1800 mm

S ≤ 3200 mm

Table Distribution of Live Load per Lane for Moment in Interior Beam

- Exterior girders: The live load flexural moment for exterior beams shall be determined by applying the lane fraction, g, specified in Table below

Type of Superstructure Applicable Cross-section from Figure 13-2 One Design Lane Loaded Two or More Design Lanes Loaded Range of Applicability

Wood Deck on Wood or Steel Beam

a, l Lever Rule Lever Rule N/A

Concrete Deck on Wood Beams

L Lever Rule Lever Rule N/A

Concrete Deck, filled Grid, or Partially Filled Grid on Steel or Concrete Beams:

a, e, k and also i, j if sufficiently connected to act as

Lever Rule g = e ginterior

e = 0.77 + de

2800

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Concrete T-Beams. T and Double T Sections

a unit Use lesser of the

values obtained from the equation above with Nb = 3

or the lever rule

Nb = 3

Table. Distribution of Live Loads per Lane for Moment in Exterior Longitudinal Beams

For shear:

- Interior girders: The live load shear for interior beams shall be determined by applying the lane fractions specified in Table

Type of Superstructure Applicable Cross-section from Figure 13-2 One Design Lane Loaded Two or More Design Lanes Loaded Range of Applicability Concrete Deck on Wood Beams

l Lever Rule Lever Rule N/A

Concrete Deck, Filled Grid, or Partially Filled Grid on Steel or Concrete Beams: Concrete T-Beams. T and Double T Sections

a, e, k and also i, j if sufficiently connected to act as a unit 0.36 + S 7600 0.2 + S - S 2.0 3600 10700 1100 ≤ S ≤4900 6000 ≤ L ≤ 73000 110 ≤ ts≤ 300 4x109≤ kg≤ 3x10 12 Nb≥ 4

Lever Rule Lever Rule Nb = 3

Multi-cell Concrete Box Beams, Box Sections d S 0.6 d 0.1 2900 L S 0.9 d 0.1 2200 L 1800 ≤ S ≤ 4900 6000 ≤ L ≤ 73000 890 ≤ d ≤ 2800 Nc≥ 3

Table -Distribution of Live Load per Lane for Shear in Interior Beams

- Exterior girders: The live load shear for exterior beams shall be determined by applying the lane fractions specified in Table

Type of Superstructure Applicable Cross-section from Figure 13-2 One Design Lane Loaded Two or More Design Lanes Loaded Range of Applicability

Wood Deck on Wood or steel Beams

a, l Lever Rule Lever Rule N/A

Concrete Deck, Filled Grid, or Partially Filled Grid on Steel or Concrete Beams; Concrete T-Beams, T- and Double T-Beams

a, e, k and also i, j if sufficiently connected to act

as a unit

Lever Rule g = e ginterior θ = 0.6 + de .

3000

-300 ≤ de≤ 1700

Lever Rule Nb = 3

Multi-cell Concrete Box Beams, Box Sections

d Lever Rule g = e ginterior

θ = 0.64 + de .

3800

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Fundamental of Bridge Design 36 Type of Superstructure Applicable Cross-section from Figure 13-2 One Design Lane Loaded Two or More Design Lanes Loaded Range of Applicability

Steel Grid Deck on Steel Beams

a Lever Rule Lever Rule N/A

Table Distribution of Live Load Per Lane for Shear in Exterior Beams

Where: S = spacing between girders (mm) L = Length of Girder (mm) ts = thickness of slab (mm)

The lever rule involves summing moments about one support to find the reaction at another

support by assuming that the supported component is hinged at interior supports.

When using the lever rule on a three-girder bridge, the notional model should be taken as shown in Figure 13-1. Moments should be taken about the assumed, or notional, hinge in the deck over the middle girder to find the reaction on the exterior girder.

Figure 13-1 Notional Model for Applying Lever Rule to Three-Girder Bridges

Multiple presence factors shall not be used with the approximate load assignment methods other than statical moment or lever arm methods because these factors are already incorporated in the distribution factors.

Box Girder Bridge:

Concrete box girder bridges are economical for spans of above 25 to 45m. They can be reinforced concrete or prestressed concrete. Longer span than 45m will have to be prestressed. They are similar to T-beams in configuration except the webs of T-beams are all interconnected by a common flange resulting in a cellular superstructure. The top slab, webs and bottom slab are built monolithically to act as a unit, which means that full shear transfer must be provided between all parts of the section.

Reinforced concrete box girders have high torsional resistance due to their closed shape and are particularly suitable for structures with significant curvature. This construction also lends itself to aesthetic treatment.