Data

Chapter 1

CONCRETE BRIDGES1.1 Introduction

Bridge is a structure that allows the movement of highway and railway traffic over natural or artificial gaps in the topology of the area such as canals,rivers,gap between hills and difference of level in crossing roads etc.

“A structure that spans an opening or gap, 6m or larger, such as: a water way (river, canal, etc) a valley, another roadway or railway lines are called bridge. Further the term bridge is used for the structure built to continue the traffic load, pedestrian traffic or utility lines across a gap in a road way

1.2SELECTION OF A BRIDGE

Selection of type of bridge mainly depends upon following factors

Local condition Availability and cost of materials Volume of traffic Site requirement Geographical Condition0 Aesthetics Expected economic return

1.3 DESIGN DIFFERENCE

Bridges are different to building design in following ways

Bridges are designed for heavy and concentrated moving loads whereas buildings are designed for static distributed loads

Impact of moving load is Considerable as with residential and official buildings Fatigue may become a problem and hence may reduce the strength due to large

number of loading cycles. Greater part of structure is exposed to atmosphere. Controlling specifications for bridges are by AASHTO while for building ACI

and AISC codes are used.

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1 Concrete Bridges

The bridges are broadly classified depending upon their use, in following categories:

i) Foot or pedestrian bridgesii) Highway bridgesiii) Railway bridgesiv) Combined railway and highway bridgesv) Over-bridge (enable one form of land communication to other).

Deck of-Bridge: A deck is the actual carriageway of the bridge consisting of concrete or orthotropic slab and wearing surface; longitudinal and transverse beams may also be present for larger deck in addition to the slab.

Deck Bridge: A deck bridge is a bridge built at or near the top level of the main supporting members of the superstructure, which hang below the deck and are not visible from the bridge.

Through Bridge: In this case the carriage way supported at the bottom of the main supporting member that are visible while traveling on the bridge.

Figure 1-A Typical deck with longitudinal reinforced concrete beams.

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1 Concrete Bridges

1.4PARTS OF A CONCRETE BRIDGE

Super-Structure: The structure of bridge above the bearings. It include slabs,beams,wearing surfaces,expansion joints,and guardrails.

Sub-Structure: It includes the bridge bearing and all the components below the bearing is used to support the super-structure. It includes piers,abutments,piles,pile-cape and caissons.

Abutment: This is the bridge support provided at the end of bridge, where the opening starts. The abutment simultaneously acts as a retaining wall to retain material at end of the gap. It typically consists of breast wall, wing wall and footing.

Wing Wall

Breast Wall

Footing

Approach Road: A road constructed at two ends of the bridge for smooth flow of traffic between the bridges and to protect the bridge structure from accidental damages.

Bridge deck: Bridge deck that supports vehicular traffic including slabs,beams,guardrails and wearing surfaces.

Stringers: Longitudinal beams directly supporting the bridge deck slab are called stringers. Their orientation is parallel to the traffic flow.

Floors Beams: Transverse beam that supports stringers and transfer load to side trusses, plate girders or stiffening girders of suspension cables.

Wearing surface: Wearing surfaces is a layer of concrete or asphalt material provided over decks.

Diaphragm: A short beam used between adjacent parallel stringers to provide them lateral stability and to distribute loads among them.

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Figure 1-BAbutment diagram

1 Concrete Bridges

Figure 1-CLongitudinal Section of a slab beam bridge

Figure 1-D Cross Section of slab beam bridge-Model

Piers: Intermediate supports provides to bridges between the abutments are called piers.

Cession: This type of bridge foundation consists of a hollow shell that is sunk into position to carry the foundation to a considerable depth in order to reach a suitable bearing stratum.

Piles: These are columns that transfer the super-structure load to a greater soil depth.

Pile cap: This is a rigid flexible member provided above the ground to connect a group of pile together. Its function is to make the pile stable.

Transom: This is a transverse beam provided over the piers to support the load from the longitudinal girders from one or from both sides.

Scour depth: This is the depth up to which the foundation material may be eroded due to flowing water.

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1 Concrete Bridges

D (in meter) =0.473(Q/f) 1/3

1.5 Bridge Bearing

The bridge bearing must be designed to allow length changes due to temperature variation. Usually one end is made hinged while the other end slides. For span greater than 15m, provision must be made at the bearing to allow rotation due to vertical bending of the girders.

For span less than 15m, expansion support may be provided only by steel plates sliding against one another. For larger span, rotation and sliding may be provided by the sophisticated arrangement of pier, rollers, rockers and curved bearing plates.

TFE surface is made to slide against a stainless steel surface and the assembly reduces the friction against sliding. The rotation is provided by simultaneous presence of elastomeric pads, curved surfaces, or hinges.

Figure 1-ETypical of Elastomeric pad

1.6TYPES OF CONCRETE BRIDGES

Bridges are classified based on following characteristics.

i) Material of constructionii) Length of spaniii) Structural formsiv) Type of spanv) Load pathsvi) Usagevii)Position

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1 Concrete Bridges

1.6.1 BASED ON THE CONSTRUCTION MATERIAL

Following are the main types of bridges according to the material of construction

a. Steel bridgesb. Reinforced concrete bridgesc. Pre-stressed concrete bridgesd. Timber bridgese. Advanced composite materials

1.6.2 BASED ON SPAN LENGTH

i) Short span bridges 6-38mii) Medium span bridges 38-125miii) Large span bridges >125m

1.6.3 BASED ON STRUCTURAL FORMS

a. Slab Bridges: This is the simplest type of bridge where the deck slab serves as a main load carrying member. The slab is supported directly on embankment or substructure.

This type of construction is considered suitable for culverts and small bridges up to span of about 8m.Although the thickness of slab is considerable the construction of this type of bridge works out to be economical because of simple arrangement and less expensive formwork.

Figure 1-FSlab bridge diagram

b. Pre-Stressed pre-cast Girder Bridge: Where the erection of temporary form-work is prohibited and working periods are limited, pre-cast concrete can be used

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1 Concrete Bridges

with advantages. The piers and abutments are constructed first and pre-cast concrete beam (or in some case pre-cast concrete arch ribs) which are generally I-beams are erected upon these. These I-beams are lifted by the help of heavy cranes.

Figure 1-GDiagram of precast girder bridge

c. Truss Bridges: The truss is a simple skeletal structure. In design theory, the individual members of a simple truss are only subjected to tension and compression forces and not bending moment forces. Thus for the most part, all beams in a truss bridge are straight. Trusses are comprised of many small beams that together can support a large amount of weight and span great distances. In most cases the design, fabrication, and erection of trusses is relatively simple. However, once assembled trusses take up a greater amount of space in more complex structures.

d. Rigid Frames Bridges: This type of bridge consists of number of parallel longitudinal girders (or solid slab) which is rigidly connected to the supporting columns or piers. The decking and the supporting substructure are normally cast together monolithically.

Generally this type of bridge is not found economical for span less then 10m, upto 20m span it can be used.

Figure 1-HRigid frame bridge

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1 Concrete Bridges

e. Arch Bridge: For this type of bridge abutment should be strong enough to resist the thrust of the bridge arch. This type of construction offers advantage of large head rooms for navigation and is considered to be an aesthetically pleasing bridge form. For very large span the use of Girder Bridge becomes uneconomical and arch bridges can be economically used. This bridge can be economically used up to span of about 200m.

Figure 1-IArch bridge

f. Cable Stayed Bridges: This type of bridge considered suitable for span varying from 200m to 600m.

The main components of bridge are: Towers A number of high tensile steel cables Deck made out of concrete or steel spanning across the stiffened bridges.

In this type of bridge the deck is supported by a number of cable (provided in two parallel planes) connected to the towers. The aim of using multiple cables is to provide support to deck at closer interval thereby resulting in closer spacing of deck girder and hence achieving reduced depth of the decking. The cable can be arranged to meet in the form of bunch at tower or they may meet tower at different levels.

Since the cables supporting the deck are provided above the deck, this type of bridge needs no intermediate piers to support the decks. Thus this bridge provides obstruction free large spans and high clearances permitting navigation of large ships. Generally the ratio is taken 0.2.

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1 Concrete Bridges

Figure 1-JCable stayed bridge

g. Suspension Bridge: This type of bridge is considered to be most suitable for span varying between 400m to 1200m. The main components of suspension bridge are:

Towers High tensile steel flexible cable Anchorage Suspenders made up high steel wires Deck of concrete or steel spanning across the stiffened girders.

In these types of bridges the cable are supported on towers and each cable is anchored to anchorage blocks at both ends. The deck is attached to steel suspenders which transfer the load from the deck to the cable supported on towers, when the bridge is completed ;the cable acquire more or less parabolic shape.

Figure 1-KSuspension bridge

h. Box Girder Bridges: This type of bridge constructed for long span where the use of ordinary pre-stressed concrete girders results in an excessive depth and the area of the main reinforcement becomes so large that it can become difficult to accommodate the bars in main girder. Depending upon the width of carriage way and the loading conditions, the bridge can have a single box girder or two or more box girders.

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1 Concrete Bridges

Figure 1-LBox girder bridge

1.6.4 BASED ON SPAN TYPE

With respect to span type bridges may be classified as:

Simple span Bridges Continuous span Bridges

1.6.5 BASED ON LOAD TYPE

Bridges, according to this classification system, may be of following types:

One dimensional system Tow dimensional system

1.6.6 BASED ON USAGE

These are the bridges which are constructed for airport, runways, pipelines and conveyors.

1.6.7 BASED ON POSITION

Moveable bridges are used for road where the bridge level is not sufficiently higher than the water level to allow navigation through the water course. There are three types of moveable bridges.

Bascule Bridge Lift Bridge Swing Bridge

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Chapter 2

Prestressed Concrete2.1 Pre-stressing

Modern structural engineering tends to progress toward more economical structures through gradually improved methods of design and the use of higher strength materials. This result in a reduction of cross-sectional dimensions and consequent weight savings. Such developments are particularly important in the field of reinforced concrete, where the dead load represents a substantial part of the total load.

Significant savings can be achieved by using high strength concrete and steel in conjunction with present-day design methods. The use of high strength materials is further limited by deflection considerations, particularly when refined analysis is used. The slender members that result may permit deflections that are functionally or visually unacceptable. This is further aggravated by cracking, which reduces the flexural stiffness of members.

These limiting features of ordinary reinforced concrete have been largely over-come by the development of prestressed concrete. A prestressed concrete member can be defined as one in which there have been introduced internal stresses of such magnitude and distribution that the stresses resulting from the given external loading are counteracted to a desired degree. Concrete is basically a compressive material, with its strength in tension being relatively low.

Deflection and crack control, achieved through prestressing, permit the engineer to make use of efficient and economical high strength steels in the form of strands, wires, or bars, in conjunction with concrete of much higher strength than normal. Thus, pre-stressing results in the overall improvement in performance of structural concrete used for ordinary loads.

2.2 Effects of prestressing

There are three ways to look t the prestressing of concrete:

a. Concrete stress controlb. Equivalent loadsc. Special variation of reinforced concrete

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Each of these are useful in the analysis and design of prestressed concrete structure.

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2 Prestressed Concrete

a. Concrete stress control

Now conside an identical beam in which a longitudinal axial force P is introduced prior to the vertical loading. The longitudinal prestressing force will produce a uniform axial compression fc = P/Ac, where Ac is the cross-sctioal area of the concrete. The force can be adjusted in magnitude so that, when the transverse load Q is applied, the superposition of stress due to P and Q will result in zero tensile stress at the beam. Tensile stress in the concrete may be eliminated in this way or reduced to specified amount.

fr

fcfc2fc

fcft=fc

2fc 2fc

2fc 2ft=2fc

2fc 2fc

2fc2ft=2fc

fcfcfc

2fc fc

fcfc

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Figure 2-MAlternative schemes for prestressing a rectangular concrete beams


Some important conclusions can be drawn from these examples are:

i. Prestressing can control or even eliminate concrete tensile stress for specified loads.

ii. Eccentric prestress is usually much more efficient than concrete prestress.iii. Variable eccentricity is usually preferable to constant eccentricity, from

the view point of both stress control and deflection control.

b. Equivalent loads

The effect of a change in the vertical alignment of a prestreeing tendon is to produce a vertical force on the concrete beam. That force, together with the prestressing force acting at the ends of the beam through the tendon anchorages, can be looked upon as a system of external loads.

Figure 2-B Equivalent loads and moments produced by prestressing tendons

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It may be evident that for any arrangement of applied loads, a tendon profile can be selected so that the equivalent loads acting on the beam from the tendon are just equal and opposite to the applied load. An advantage of the equivalent load concept is that it leads the designer to select to select what is probably the best tendon profile for a particular loading.

c. Prestressed concrete as a variation of reinforced concrete

It is implied that the prestress force remained constant as the vertical load was introduced, that the concrete responded elastically, and that no concrete cracking occurred. These conditions may prevail up to about the service load level, but if the loads should be increased much beyond that, flexural tensile stresses will eventually exceed the modulus of rupture and cracks will form.

The behavior at this stage is almost identical to that of an ordinary reinforce concrete beam at overload. The main difference is that the very high strength steel used must be prestrained before loads are applied to the beam, otherwise the high steel stresses would produce excessive concrete cracking and large beam deflections.

2.3 Advantages of prestressed concrete

a. Less depth compared to RC member. i. Reduction in self weightii. More aesthetic appeal due to slender sections iii. More economical sections.

b. Section remains uncracked under service loadsi. Reduction of steel corrosionii. Increase in durability.iii. Less deformations (improved serviceability).iv. Increase in shear capacity.

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v. Improved performance (resilience) under dynamic and fatigue loading.c. Larger spans possible with prestressing (bridges, buildings with large column-free

spaces) d. Tension in the cross-section is either reduced or is completely eliminated.e. Better quality control because The quality of the materials is tested during the

prestressing.f. The prestressing produces negative moments in simply supported beams causing

upward camber, the service loads first balance these upward deflection and then cause reduced downward deformations.

g. Deflection can be limited to an acceptable value.h. A crack free prestressed member behaves as a homogenous and elastic material.i. Suitable for precast construction

i. Rapid construction ii. Reduced maintenance and have longer life.iii. Reduction of formwork iv. Availability of standard shapes.

2.4 Limitations of Prestressing Although prestressing has advantages, some aspects need to be carefully addressed. Prestressing needs skilled technology. Hence, it is not as common as reinforced

concrete. The use of high strength materials is costly. There is additional cost in auxiliary equipments. There is need for quality control and inspection.

2.5 Sources of prestress force Prestress can be applied to a concrete member in many ways. Post-tensioning by jacking against abutments Post-tensioning with jacks reacting against beams Pretensioning with tendon stressed between fixed external anchorages

2.6 Methods of presstressing

a. Pre-tensioned

Pre-tensioned concrete is cast around already tensioned tendons. This method produces a good bond between the tendon and concrete, which both protects the tendon from corrosion and allows for direct transfer of tension. The cured concrete adheres and bonds to the bars and when the tension is released it is transferred to the concrete as compression by static friction. However, it requires stout anchoring points between which the tendon is to be stretched and the tendons are usually in a straight

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http://en.wikipedia.org/wiki/Friction


line. Thus, most pretensioned concrete elements are prefabricated in a factory and must be transported to the construction site, which limits their size. Pre-tensioned elements may be balcony elements, lintels, floor slabs, beams or foundation piles.

b. Bonded post-tensioned

Bonded post-tensioned concrete is the descriptive term for a method of applying compression after pouring concrete and the curing process (in situ). The concrete is cast around plastic, steel or aluminum curved duct, to follow the area where otherwise tension would occur in the concrete element. A set of tendons are fished through the duct and the concrete is poured. Once the concrete has hardened, the tendons are tensioned by hydraulic jacks that react (push) against the concrete member itself. When the tendons have stretched sufficiently, according to the design specifications (see Hooke's law); they are wedged in position and maintain tension after the jacks are removed, transferring pressure to the concrete. The duct is then grouted to protect the tendons from corrosion. Post-tensioning is also used in the construction of various bridges.

Among the advantages of this system over unbounded post-tensioning are:

Large reduction in traditional reinforcement requirements as tendons cannot distress in accidents.

Tendons can be easily "woven" allowing a more efficient design approach. Higher ultimate strength due to bond generated between the strand and concrete. No long term issues with maintaining the integrity of the anchor/dead end.

c. Unbounded post-tensioned

Unbounded post-tensioned concrete differs from bonded post-tensioning by providing each individual cable permanent freedom of movement relative to the concrete. To achieve this, each individual tendon is coated with grease and covered by a plastic sheathing formed in an extrusion process. The transfer of tension to the concrete is achieved by the steel cable acting against steel anchors embedded in the perimeter of the slab. The main disadvantage over bonded post-tensioning is the fact that a cable can distress itself and burst out of the slab if damaged (such as during repair on the slab). The advantages of this system over bonded post-tensioning are:

1. The ability to individually adjust cables based on poor field conditions (For example: shifting a group of 4 cables around an opening by placing 2 to either side).

2. The procedure of post-stress grouting is eliminated.3. The ability to de-stress the tendons before attempting repair work.

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http://en.wikipedia.org/wiki/Deep_foundation

http://en.wikipedia.org/wiki/Lintel

http://en.wikipedia.org/wiki/Balcony

http://en.wikipedia.org/wiki/Prefabrication


Advantages of Post Tensioning Concrete

1. Reduction in depth of slab (common depth/span ratios of 1:40)2. Reduction of depth of beams (common depth/span ratio of 1:20)3. Controlled cracking – beneficial in car parks.4. Very economic and structurally efficient over 6m spans5. Flexibility in planning & design6. Deflection can be controlled and is reduced compared to r.c.7. Smaller quantities of reinforcement required8. A prestressed structure is ‘pre-tested’ since a significant load is applied during

post tensioning.

2.7 Stages of Loading The analysis of prestressed members can be different for the different stages of loading. The stages of loading are as follows.

i. Initial During tensioning of steel At transfer of prestress to concrete.

ii. Intermediate This includes the loads during transportation of the prestressed members.

iii. Final At service, during operation. At ultimate, during extreme events.

2.8 Loss of prestress

In prestressed concrete the most important parameter is the prestressing force. If the prestressing force reduces with time, prestresses also get reduced.

Even at the time of the transfer of prestress to the concrete member, there is a drop of the prestressing force from the recorded value in the jack gauge. Various reductions of the prestressing force are termed as the losses in prestress.

A loss of prestress will affect the stress distribution on a section of the member. It is therefore necessary to estimate the probable loss of prestress that may be incurred in a prestressed member. Total loss of prestress consists of those losses which are instantaneous at the transfer stage as well as those which are time dependent.

i. Instantaneous lossesii. Time dependent losses

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Instantaneous losses

These losses take place immediately after the application of jacking force. These losses are:

ΔfPE = Loss of Prestress Due to Elastic ShorteningΔfPF = Loss of Prestress during the Tensioning Process Due to FrictionΔfPA = Loss of Prestress Due to Anchorage Slip

Time dependent losses

These losses occure after the concrete has gained its specified cylindrical compressive stress (fc’)

ΔfPCR = Loss of Prestress Due to Creep of ConcreteΔfPSR = Loss of Prestess Due to Shrinkage of ConcreteΔfPR = Loss of Prestress Due to Relaxation of Steel

2.9 Prestress Loss Prediction MethodsSeveral loss prediction methods have been developed over the years, but simple

practical solutions for accurate estimation of prestress loss have proved difficult. The accurate estimation of losses requires more precise knowledge of material properties as well as the interaction between creep, shrinkage of concrete and the relaxation of steel. The current methods for the prediction of losses can be classified according to their approach for the calculation of losses. They are listed according to their descending order of perceived accuracy:

i) Time-Step methodsii) Refined methodsiii) Lump-Sum methods

2.10 Stresses on Different Stages

STRESSES AT STAGE-1

(a) Only Pi Is Acting:

The prestress force (Pi) acting at an eccentricity (e) from the centroid of the section is equivalent to a concentric force Pi and a moment Pi x e. The force Pi

produces a uniform compression and the moment Pi x e produces tension at the top and compression at the bottom for beam of fig………….The result may be smaller tension at the top and larger compression at the bottom.

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- PiA

+PieC 1Ar . r

f1

- PieC 1Ar . r

f2

f1= - PiA +

PieC 1Ar . r = -

PiA [1− eC1

r . r ]f2= -

PiA –

PieC 2Ar . r = -

PiA [1+ eC 2

r . r ]

(b) Prestress Pi and self weight are acting:

The self-weight moment modifies the above stress diagram and is given in fig.

-PiA [1− eC1

r . r ]– MgC1I

f1

Pi * e

-PiA [1− eC1

r . r ] + MgC1I

f2

f1= -PiA [1− eC1

r . r ] – MgC1I

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f2= -PiA [1+ eC 2

r . r ] + MgC2I

STRESSES AT STAGE-2( Pe + Self weight)

The shapes of stress diagrams are the same as those of stage-1b but the ordinates are changed due to replacement of Pi with Pe. The top and bottom stresses are given as under:

f1= -PeA [1−eC 1

r .r ] – MgC1I

f2= -PeA [1+ eC 2

r . r ] + MgC2I

STRESSES AT STAGE-3 (Pe + Self weight + Service load)

Producing larger tensile stresses at the bottom and compressive stresses at the top, as shown in fig.

- C1(Md+Ml)

If1

Pe * e

+ C2(Md+Ml)

If2

The resultant stresses at this stage of loading are given by the following expressions:

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f1= -PeA [1−eC 1

r .r ] – C1(Mg+Md+Ml)

I

f2= -PeA [1+ eC 2

r . r ] + C2(Mg+Md+Ml)

I

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Chapter 3

PRESTRESSING MATERIALS3.1 Concrete for prestressed construction

Higher strength concrete , having fc ‘ > 35 MPa , is usually used for prestressed members for quick and efficient construction with lesser loss of prestressing force due to elastic shortening, creep and shrinkage. The advantages of high strength concrete in prestressed construction are as follows:

a) With larger compressive strength of concrete, its modulus of elasticity is increased reducing the elastic shortening due to prestress force. Further, long term deformations due to creep and shrinkage are also reduced. Hence, by the use of high strength concrete, the prestress losses are significantly reduced increasing the efficiency of such construction.

b) The concrete gains high early strength and hence the prestress may be applied to the concrete earlier. The speed of construction is increased when high strength concrete is used.

c) Bearing strength is better for high strength concrete. This makes it easy to transfer the prestress forces at the anchorages, which may require lesser contact area of anchorage fittings.

d) The bond between steel and concrete is improved when high strength concrete is used.

e) Higher strengthare easy to achieve in case of prestressed precast construction in factories where batching, mixing, placing and curing is carried out under controlled conditions.

Following notation is used to specify strength of concrete for prestressed construction:

Fc’ = the specified minimum 28-day cylinder compressive strength of concrete.Fcl’ = the minimum cylinder compressive strength of concrete at the time of initial transfer of prestressing force

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3 Prestressing Materials

3.2 ACI PERMISSIBLE CONCRETE STRESSES

The allowable stresses in concrete are different at various stages of loading and for different categories of flexural members. Prestressed flexural members are classified into three classes depending upon their behavior.

Class U Members

These members behave as uncracked members and computed extreme fiber tensile stress at service loads (ft) is lesser than or equal to 0.62 √ fc 'Prestressed two-way slab systems are also considered in this category.

Class T Members

These are transition members between uncracked and cracked cases. The computed extreme fiber stress is within the limits: 0.62√ fc '<ft ≤ 1.0 √ fc ' . For this class, the stresses at service loads are allowed to be computed using the uncracked section as for class U. Deflections are calculated by bilinear curve for cracked section.

Class C Members

These are cracked members whose behavior at service loads must be studied using cracked section. The computed extreme fiber stress, f t, is greater than 1.0√ fc ' . Deflections are to be calculated by bilinear curve for cracked section.

3.3 Prestress Forces

Jacking force (Pj)It is the force required to pull the tendon to required stress level.

Initial prestress force (Pi)It is the force after transfer and is equal to jacking force reduced due to the

instantaneous shortening of the concrete.

Effective prestress force (Pe)It is the amount of prestress force left after instantaneous and time

dependant losses.

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Effectiveness ratio (R)The effectiveness ratio (R) is defined as the ratio of effective prestress to

the initial prestress.R=Pe/Pi

A usually conservative value of R=0.85 may be used in place of detailed actual calculations.

3.4 Prestressing steel

In prestressing, high strength steels are used, the losses in terms of strains remain nearly the same and very high effective strains and stresses are left within the member.

Type Nominal Diameter (mm)

Nominal Area (mm2)

Nominal Weight (kg/m)

Seven Wire strands(Grade 1725)

6035 23.22 0.01827.94 37.42 0.2949.53 51.61 0.405

11.11 69.68 0.54812.70 92.90 0.73015.24 139.35 1.094

Seven Wire strands(Grade 1860)

9.53 54.84 0.43211.11 74.19 0.58212.70 98.71 0.77515.24 140.00 1.102

Prestressing Wire(Grade 1620,1655,1725)

4.88 18.7 0.1464.98 19.4 0.1496.35 32 0.2537.1 39 0.298

Prestressing Bars, Plain(Grade 1035, 1100)

19 284 2.2322 387 3.0425 503 3.9729 639 5.0332 794 6.2135 955 7.52

Prestressing Bars, Deformed(Grade 1035, 1100)

15 181 1.4620 271 2.2226 548 4.4832 806 6.5436 1019 8.28

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The prestressing steel may be in the form of smaller diameter wires, relatively large diameter alloy steel bars or in the form of strands. The term strand is used for a group of wires helically wounded. A seven-wire strand is shown in fig……..The term tendon is used for one group of reinforcement consisting of a single wire, a strand or a group of strands used together.

Various types of available prestressing steel are given in table……….and the following standards are used to check the prestressing steel requirements:

1. ASTM A421-Standard specification for uncoated stress-relieved steel wire for prestressed concrete.2. ASTM A416-Standard specification for steel strand (uncoated seven wire stress-relieved) for prestressed concrete.3. ASTM A722-Standard specification for uncoated high-strength steel bar for prestressed concrete.

3.5Maximum Permissible Prestressing Steel Stresses

S. No. Description Maximum Stress level1. Stress due to jacking force. It should not exceed a stress smaller of

0.80fpu and 0.94fpy.2. Stress immediately after prestress

transfer.It should not exceed a stress smaller of 0.74fpu and 0.82fpy.

3. At anchorage device for post tensioning tendons, immediately after anchorage.

0.70fpu

Loading Stages

Tendon typeStress Relived

Strand and Plain High Strength bars

Low Relaxation Strand

Deformed High Strength Bars

At Jacking (fpj):i) Pre-tenioningii) Post-tensioning

0.72 fpu

0.76 fpu

0.78 fpu

0.80 fpu

-0.75 fpu

After transfer (fpt):i) Pre-tenioningii) Post-tensioning, generaliii) Post-tensioning at

anchorages and couplers immediately after anchor set

0.70 fpu

0.70 fpu

0.70 fpu

0.74 fpu

0.70 fpu

0.74 fpu

-0.66 fpu

0.66 fpu

At Service State (fpe):i) After losses 0.80 fpy 0.80 fpy 0.80 fpy

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3.6 DIFFERENCE BETWEEN BEHAVIOR OF PRESTRESSED AND ORDINARY REINFORCED CONCRETES

The external bending moment in a beam is resisted by a couple formed by internal tensile force in steel and compressive force in concrete. In ordinary reinforced concrete beam, the increase in lever arm by the increase of loading is lesser and the resisting moment basically increases by the increase in steel tensile force and compression in the concrete. The situation is reverse in case of prestressed concrete beam where the forces in steel and concrete remain nearly constant and the resisting moment increases by the increase in lever arm.

After the development of tensile stresses in concrete due to increase of load on prestressed beam, its behavior is almost similar to ordinary reinforced concrete beams.

3.7 TENDON PROFILES

The path of prestressing tendon along the length of prestressed member is called Tendon profile and it is decided based on the shape of bending moment.

Positive moment requires prestressing force below the section centroid, negative moment requires it above the centroid and desired eccentricity of prestressing force increases with the increase of applied bending moment. Curved tendon profiles approximately following the shape of bending moment diagram are better and are easy to be placed in case of post-tensioning. However, in case of pre-tensioning especially for large prestressing beds having a number of units to be cast together, straight tendons are easy to be placed.

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Chapter 4

LOADINGS OF HIGHWAYS

4.1 Classical Deformations Method of Analysis: In this method stiffness equations of components of a structure are separately formulated and equilibrium and compatibility conditions are satisfied at the interfaces to get the complete section.

4.2 Classical Force Method of Analysis: In this method the structure is sub divided into statically determinate element and equilibrium of the interface force is than satisfied to get the complete solution.

4.3 TRAFFIC LOADINGS:

The traffic loading is considered in this project work are given in the following sections. Before discussing the traffic loading for high way bridges, there are some basic definitions which are necessary to highlight in context with the traffic loadings.

Deck: Deck is the bridge slab supporting the load directly or through the wearing surface.

End Zone: It is the part of the structure where, due to the structural or load discontinuity, normal beam theory does not apply.

Equivalent Strip: It is defined as an isolated predefined width of the deck in the longitudinal or transverse direction which when designed individually represents the full design of the deck and the same design is used throughout.

Foot Print: It is the specified wheel contact area over the roadway.

Force Effect: It is defined as a deformation, stress or stress resultant caused by the applied loads, imposed deformation or volumetric changes.

Frame Action: It is said to be in large bridges.

Lever Rule: It means the statically summation of moments about any point to calculate the reaction at some other point.

Skew Angle: It is defined as the angle between the centerline of a bridge support and a line normal to the roadway centerline.

Tandem: Two closely spaced and interconnected axles of equal weight are together called Tandems.

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4 Loadings of Highways

4.4 DESIGN LANE

The design lane has a width equal to the lesser of 3600 mm or width of the traffic lane. Roadway width from 6000 to 7200 mm has two design lanes each equal to one-half the roadway width. The number of design lane is taken as the integer part of the result when the clear roadway width in mm between the curb is divided by 3600mm.

The load shall occupy a width of 3000 mm transversely within a design lane and all design lanes must be loaded simultaneously by a truck or tandem and the lane loads (without any gap for the truck except when such gap increases the force effect)

If the lanes are more than one, reduction factor of table is applied on the live load force effect called MULTIPLE PRESENCE FACTOR denoted by (m).

Number of loadedLanes

Multiple presenceFactor(m)

1 1.20

2 1.00

3 0.65

>3 0.65

Multiple Presence factor Table

4.5 AASHTO STANDARD

AASHTO Highway Loading (HL-93) Considered for analysis of bridge super structures consists of following three types of loads.

HL-93 Truck Loading Tandem Loading Lane Loading

4.6 DESIGN TRUCK

A standard truck consists of front axle of 35kn,rear axle of 145kn at 4.3 m spacing from the front axle and trailer axel of 145 KN having a variable spacing of 4.3 to 9 m from the truck rear axle (the spacing producing the maximum force effect must be used). The axle load and transverse clearances are shown in the fig.

Dynamic load allowance of 33℅ is to be applied on these loads. The design truck and tandem shall be placed transversely at 300 mm from the face of curb pr railing for the design of bridge overhang and 600 mm from the edge of the lane for the design of all other components.

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(a) Longitudinal view of truck diagram

(b) Back view of truck

4.7 DESIGN TANDEM: The design tandem consists of a pair of 110 KN at a longitudinal spacing of 1200 mm with the transverse c/c spacing of the wheels being 1800 mm as shown in fig.

Dynamic load allowance of 33 percent is to be applied on these loads. For negative moment and reaction at the interior supports, pair of tandem may be considered at a spacing of 8 to 12m.

4.8 DESIGN LANE LOAD: The design lane load is 9.3 KN/m along the length and having the width of 300 mm as shown in fig.

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The load intensity becomes 3100 N/m2 Dynamic load allowance is not to be applied on lane loading.

(Lane loading)

4.9 Predestrian Loads: A pedestrian load of 3600 N/m2 is used on all sidewalks simultaneously with the vehicular design live load. Separate bridges for pedestrian and bicycle traffic should be designed for a live load of 4100 N/m2 .The dynamic load allowance is not considered for these loads.

4.10Pakistan code of practice for Highway Bridge (1967) loading

The highway loading according to the Pakistan code of Pakistan code of practice for highway bridges consists of Class A, Class Band Class AA loadings. Some local truck loading NLC loadings

Standard Truck/Train Weight of Truck/Tank – W(kN)

Class A 276Class B 166

Military Tank 698

Axle Load Longitude Tire contact Length

BL (mm)

Transverse Tires Contact with

BT (mm)110.4 255 510

66.4 , 69.0 205 38027.6 150 20541.5 150 30516.6 125 180

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Clear Road Width Rw (m) Distance-J for most criticalDesign condition(mm)

5.0 or lass 05.0 to 5.5 800 (Rw-5.0)5.5 to 7.3 400 + 450 (Rw – 5.5)Above 7.3 1210

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Chapter 5

PROXIMATE ANALYSIS OF GIRDER

5.1 CONDITIONS FOR APPROXIMATE METHOD TO BE APPLICABLE

i. Spacing of beams, S, should be between 1.1 and 4.9 m.ii. Thickness of deck slab, ts, should be between 110 and 300 mm.

iii. Length of beam should be 6.0 and 73.0 m.iv. Number of longitudinal beams in the cross-section, Nb, should be greater than

equal to 4.v. The deck cross-section should be one of the standard types given in the AASHTO

specification. The width of deck should be constant.vi. Multiple presence factors are not to be applied when using the given expression.

However, it is always to be considered if the lever rule is used to the fined the force effects.

vii. If beam spacing exceeds 4.9m, the live load on each beam shall be the reaction of the loaded lanes based on thr lever rule.

viii. Beams should be parallel and should have approximately the same stiffness.ix. The roadway part of the overhang, dc, does not exceed 9110mm.x. The curvature in plan is less than the specified AASHTO limits.

xi. The given expressions are only applicable to concrete deck on steel or concrete beams.

5.2 LATERAL DISTRIBUTION FACTORS FOR INTERIOR GIRDER

The distance, de shall be taken as positive if the exterior web is within the roadway and negative if it is outside the roadways.

One Design Lane Loaded

For moment:

g = 0.06 + (S/4300)0.4 (S/L) 0.3 (KG/Lts3)0.1

For shear

g = 0.36 + (S/7600)

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Two or More Design Lane Loaded

For moment

g = 0.075 + (S/2900)0.6(S/L) 0.2 (kg/Lts3)0.1

For shear

g = 0.65x [0.2+(S/3600) – (S/10700)2]

5.3 LATERAL DISTRIBUTION FACTORS FOR EXTERIOR GIRDER

One Design Lane Loaded

For moment: Using lever rule

For shear: Using lever rule

Two or More Design Lanes Loaded

For Moment: g = e* gin where e = 0.77 + de/2800 ≥ 1

For shear: g = e x gint where e = 0.6 + de/3000 ≥ 1

Design of Prestressed Girder

Design a bridge of 3 spans, the length of girder in each span is 13750mm, require data is given below.

GIVEN DATA

L=13.75m

Md=520 kN/m

Ml=700 kN/m

Fc’= 40 MPa

Fci’= 29 MPa

CLASS-U member

Fpu= 1725 MPa

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Fpy= 1550 MPa

R=0.85 for 15% time dependent losses

SOLUTION

MD + ML= 1220 kN-m

Depth of Girder

h ≈ 33√Mmax = 331√1220

h = 1152.64mm

Also

h ≈ L/ 17 = 13.75 x 1000/17

h = 808.8 mm

While

Approximate Self Weight

wg = 0.006 h2 to 0.007h2 N/m

= 0.007 x 11502 /1000

= 9.26 KN/m

Mg = wgl2/8

Mg = 9.26 x 13.752/8 = 218.85 KN-m

For Class U-Member, the stress limits are:

Fci = -0.6 fci’ = -0.6 x 29 = -17.4 MPa

Fti = 0.25 √ f ci’ = 0.25√29 = 1.35 MPa

Fcs = -0.60 fc’ = -0.60 x 40 = -24 MPa

Fts = 0.62√ f c’ = 0.06√40 = 3.92 MPa

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Select Section

S1 ≥ (1−R )Mg+Ml+Md

Rf ti−f cs=

[ (1−0.85 )∗218.85+1220 ]∗106

0.85∗1.35−(−24)

S1 = 49.82 x 106 mm3

S2 ≥(1−R )Mg+Ml+Md

f ts−rf ci=

[ (1−0.85 )∗218.85+1220 ]∗106

3.92−0.85 (−17.4)

S2 = 66.96 x 106 mm3

For symmetrical section, S= 66.96 x 106 mm3

Thickness

t ≈ 0.15 h = 0.15 x 1150

= 172.5 mm ≈ 175mm

b = 6Sh−t(0.93h−2 t)3

h3−(0.93h−2 t)3 =

(6∗66.96∗106∗1150)−175 (0.93∗1150−2∗175)3

11503−(0.93∗1150−2∗175)3

b = 345.56 mm ≈ 350 mm

Check

b/h = 350/1150 = 0.304 (If b/h is in between 0.2 to 0.6 then) OK

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Selected section of Girder

Area of section

Ac = 2(175*350) +4 (0.5*115*87.5) + (800*175)

= 282625 mm2

Actual Self weight = 0.283 *9.8* 2400 kg/m

wg = 6.6562 kN/m

Mg =wgl2/8 = (6.66*13.752)/8

= 157.40 kN-m < Mg AssumedOK

Strands

Fcci= fti – c1/ h (fti - fci) = 1.35 – 0.5 (1.35 + 17.4)

= -8.025 Mpa

Initial prestress force

Pi = Ac * |fcci| = 282625 x 8.025 / 1000

= 2268.066 kN

Allowable steel stress just after transfer, fps

= lesser of 0.74fpu and 0.82fpy

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= lesser of 1276.5 MPa and 1271 MPa

Take

fps =1271 Mpa

Area of Strands

Aps = Pi / fps = 2268.066 x 1000 / 1271

= 1784.5 mm2 ≈ 1785mm2

Area of 12.70 mm diameter strand = 92.90 mm2

Number of strands

Ns= Aps / 92.90 = 1785/92.90

= 19.214 say 20 strands

Initial force in each strand = Pi /Ns

= 2268.066/20

=113.40 KN

Provide 3 Tendons having 21 Strands in each Tendons

“Maximum eccentricity, we need the actual values of S1 and Mg”

I = bh3

12 – (b−t) (0.93h−2t )3

12

350 X11503

12 – (350−175)(0.93∗1150−2∗175 )3

12

= 3892698.63 x 104 mm4

S = I/y = 3892698.63 x 104/575

S = 67699.11 x 103 mm3

Mg = 1/8 x 6.66 x 13.752 = 157.40 kN-m

Eccentricity

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em = (fti - fcci) S1

P i + M g

Pi= (1.35+8.025)

67.7∗106

2268.066∗103 + 157.40∗106

2268.066∗103

em = 346.18 mm < 372.5 mm OK

The detail of the eccentricity is shown in figure.

Location of Tendons

Tendon Profile

Calculations for Tendon Profile

Tendon 1 Tendon 2 Tendon 3X

(mm)Y

(mm)Z

(mm)X

(mm)Y

(mm)Z

(mm)X

(mm)Y

(mm)Z

(mm)0 0 0 0 0 0 0 0 0

1000 3 1 1000 7 0 1000 12 -12000 13 3 2000 30 0 2000 46 -33000 28 6 3000 66 0 3000 105 -64000 50 11 4000 118 0 4000 186 -115000 79 16 5000 185 0 5000 290 -166000 114 23 6000 266 0 6000 418 -23

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6875 149 30 6875 349 0 6875 549 -30

Drawings

1) Plan view of Girder2) Cross-section of Girder: Section A-A and B-B3) Longitudinal view of Girder4) End Block detail of Girder5) Plan view of bridge6) Longitudinal view of bridge (section 1-1)7) Cross-section of bridge (section 2-2)

Design a bridge using AASHTO LRFD Bridge Design Specifications. The AASHTO LRFD Bridge Design Specifications will be adopted by the Department for the design of new bridges and retaining walls. In which we take the factor load of dead and live loads and easy to understand. Factor load resists the maximum expected and make the structure safe.

Design a 3 spans bridge using the HL-93 Loading. The length of girder in each span is 13.75m. There are 7 girders in each span so; the total number of girders is 21. The Bridge Design manual is being updated and will be available to meet the specification. The bridge standard drawings and design data sheets are also being updated.

Use the prestressed girder of high strength materials that make the structure economical by reducing the dead load of structure, in prestressed girder only service used.

This project helps to understand the behavior of prestressed girder and give a detail study and design of prestressed girder bridge for the readers. And drawings show the dimensions of bridge which is easily understandable.

Zahid Ahmad Siddiqi, Concrete Structure, Part-2, Help Civil Engineering Publisher, Lahore, 2009

Arthur H. Nilson, David Darwin, Charles W.Dolan, Design of Concrete Structures, 13th

edition, TATA McGraw-Hill, 2005

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Data

Documents

Transcript of Data