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1.1 Introduction
This section covers the following topics.
Basic Concept
Early Attempts of Prestressing
Brief History
Development of Building Materials
1.1.1 Basic Concept
A prestressed concrete structure is different from a conventional reinforced concrete
structure due to the application of an initial load on the structure prior to its use.
The initial load or prestress is applied to enable the structure to counteract the stresses
arising during its service period.
The prestressing of a structure is not the only instance of prestressing. The concept of
prestressing existed before the applications in concrete. Two examples of prestressing
before the development of prestressed concrete are provided.
Force-fitting of metal bands on wooden barrels
The metal bands induce a state of initial hoop compression, to counteract the hoop
tension caused by filling of liquid in the barrels.
Metal bandsMetal bands
Figure 1-1.1 Force-fitting of metal bands on wooden barrels
Pre-tensioning the spokes in a bicycle wheel
The pre-tension of a spoke in a bicycle wheel is applied to such an extent that there will
always be a residual tension in the spoke.
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SpokesSpokes
Figure 1-1.2 Pre-tensioning the spokes in a bicycle wheel
For concrete, internal stresses are induced (usually, by means of tensioned steel) for
the following reasons.
The tensile strength of concrete is only about 8% to 14% of its compressive
strength.
Cracks tend to develop at early stages of loading in flexural members such as
beams and slabs.
To prevent such cracks, compressive force can be suitably applied in the
perpendicular direction.
Prestressing enhances the bending, shear and torsional capacities of the flexural
members.
In pipes and liquid storage tanks, the hoop tensile stresses can be effectively
counteracted by circular prestressing.
1.1.2 Early Attempts of Prestressing
Prestressing of structures was introduced in late nineteenth century. The following
sketch explains the application of prestress.
Place and stretch mild steel rods, prior to concreting
Release the tension and cut the rods after concreting
Place and stretch mild steel rods, prior to concreting
Release the tension and cut the rods after concreting
Figure 1-1.3 Prestressing of concrete beams by mild steel rods
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Mild steel rods are stretched and concrete is poured around them. After hardening of
concrete, the tension in the rods is released. The rods will try to regain their original
length, but this is prevented by the surrounding concrete to which the steel is bonded.
Thus, the concrete is now effectively in a state of pre-compression. It is capable of
counteracting tensile stress, such as arising from the load shown in the following sketch.
Figure 1-1.4 A prestressed beam under an external load
But, the early attempts of prestressing were not completely successful. It was observed
that the effect of prestress reduced with time. The load resisting capacities of the
members were limited. Under sustained loads, the members were found to fail. This
was due to the following reason.
Concrete shrinks with time. Moreover under sustained load, the strain in concrete
increases with increase in time. This is known as creep strain. The reduction in length
due to creep and shrinkage is also applicable to the embedded steel, resulting in
significant loss in the tensile strain.
In the early applications, the strength of the mild steel and the strain during prestressing
were less. The residual strain and hence, the residual prestress was only about 10% of
the initial value. The following sketches explain the phenomena.
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Original length of steel rod (L1)
Original length of concrete beam (L2
)
Original length of steel rod (L1)
Original length of concrete beam (L2
)
a) Beam before applying prestress
Reduced length of concrete beam (L3)Reduced length of concrete beam (L3)
b) Beam at transfer of prestress
Final length of prestressed beam (L4)Final length of prestressed beam (L4)
c) Beam after long-term losses of prestress
Figure 1-1.5 Variation of length in a prestressed beam
The residual strain in steel = original tensile strain in steel compressive strainscorresponding to short-term and long-term losses.
Original tensile strain in steel = (L2 L1)/L1
Compressive strain due to elastic shortening of beam = (L2 L3)/L1
(short-term loss in prestress)
Compressive strain due to creep and shrinkage = (L3 L4)/L1
(long-term losses in prestress)
Therefore, residual strain in steel = (L4 L1)/L1
The maximum original tensile strain in mild steel = Allowable stress / elastic
modulus
= 140 MPa / 2105 MPa
= 0.0007
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The total loss in strain due to elastic shortening, creep and shrinkage was also close to
0.0007. Thus, the residual strain was negligible.
The solution to increase the residual strain and the effective prestress are as follows.
Adopt high st rength steel with much higher original strain. This leads to the
scope of high prestressing force. Adopt high strength concrete to withstand the high prestressing force.
1.1.3 Brief History
Before the development of prestressed concrete, two significant developments of
reinforced concrete are the invention of Portland cement and introduction of steel in
concrete. These are also mentioned as the part of the history. The key developments
are mentioned next to the corresponding year.
1824 Aspdin, J ., (England)
Obtained a patent for the manufacture of Portland cement.
1857 Monier, J ., (France)
Introduced steel wires in concrete to make flower pots, pipes, arches and slabs.
The following events were significant in the development of prestressed concrete.
1886 J ackson, P. H., (USA)
Introduced the concept of tightening steel tie rods in artificial stone and concrete
arches.
Figure 1-1.6 Steel tie rods in arches
1888 Doehring, C. E. W., (Germany)
Manufactured concrete slabs and small beams with embedded tensioned steel.
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1908 Stainer, C. R., (USA)
Recognised losses due to shrinkage and creep, and suggested retightening the
rods to recover lost prestress.
1923 Emperger, F., (Austria)
Developed a method of winding and pre- tensioning high tensile steel wiresaround concrete pipes.
1924 Hewett, W. H., (USA)
Introduced hoop-stressed horizontal reinforcement around walls of concrete
tanks through the use of turnbuckles.
Thousands of liquid storage tanks and concrete pipes were built in the two decades to
follow.
1925 Dill, R. H., (USA)
Used high strength unbonded steel rods. The rods were tensioned and anchored
after hardening of the concrete.
Figure 1-1.7 Portrait of Eugene Freyssinet
(Reference: Collins, M. P. and Mitchell, D.,Prestressed Concrete Structures)
1926 Eugene Freyssinet (France)
Used high tensile steel wires, with ultimate strength as high as 1725 MPa and
yield stress over 1240 MPa. In 1939, he developed conical wedges for end
anchorages for post-tensioning and developed double-acting jacks. He is often
referred to as the Father of Prestressed concrete.
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1938 Hoyer, E., (Germany)
Developed long line pre-tensioning method.
1940 Magnel, G., (Belgium)
Developed an anchoring system for post-tensioning, using flat wedges.
During the Second World War, applications of prestressed and precast concrete
increased rapidly. The names of a few persons involved in developing prestressed
concrete are mentioned. Guyon, Y., (France) built numerous prestressed concrete
bridges in western and central Europe. Abeles, P. W., (England) introduced the
concept of partial prestressing. Leonhardt, F., (Germany), Mikhailor, V., (Russia) and
Lin, T. Y., (USA) are famous in the field of prestressed concrete.
The International Federation for Prestressing (FIP), a professional organisation in
Europe was established in 1952. The Precast/Prestressed Concrete Institute (PCI) was
established in USA in 1954.
Prestressed concrete was started to be used in building frames, parking structures,
stadiums, railway sleepers, transmission line poles and other types of structures and
elements.
In India, the applications of prestressed concrete diversified over the years. The first
prestressed concrete bridge was built in 1948 under the Assam Rail Link Project.
Among bridges, the Pamban Road Bridge at Rameshwaram, Tamilnadu, remains a
classic example of the use of prestressed concrete girders.
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Figure 1-1.8 Pamban Road Bridge at Rameshwaram, Tamilnadu
(Reference: http://www.ramnad.tn.nic.in)
1.1.4 Development of Building Materials
The development of prestressed concrete can be studied in the perspective of
traditional building materials. In the ancient period, stones and bricks were extensively
used. These materials are strong in compression, but weak in tension. For tension,
bamboos and coir ropes were used in bridges. Subsequently iron and steel bars were
used to resist tension. These members tend to buckle under compression. Wood and
structural steel members were effective both in tension and compression.
In reinforced concrete, concrete and steel are combined such that concrete resists
compression and steel resists tension. This is a passive combination of the two
materials. In prestressed concrete high strength concrete and high strength steel are
combined such that the full section is effective in resisting tension and compression.
This is an active combination of the two materials. The following sketch shows the use
of the different materials with the progress of time.
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Compression (C) Tension (T) C and T
Stones, Bricks Bamboo, Ropes Timber
Structural steelSteel bars, wires
Reinforced
Concrete
Prestressed
Concrete
Passive combination
High StrengthSteel
High StrengthConcrete
Active combination
Concrete
Compression (C) Tension (T) C and T
Stones, Bricks Bamboo, Ropes Timber
Structural steelSteel bars, wires
Reinforced
Concrete
Prestressed
Concrete
Passive combination
High StrengthSteel
High StrengthConcrete
Active combination
Concrete
Figure 1-1.9 Development of building materials
(Reference: Lin, T. Y. and Burns, N. H.,
Design of Prestressed Concrete Structures)
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1.2 Advantages and Types of Prestressing
This section covers the following topics.
Definitions
Advantages of Prestressing
Limitations of Prestressing
Types of Prestressing
1.2.1 Definitions
The terms commonly used in prestressed concrete are explained. The terms are placed
in groups as per usage.
Forms of Prestressing Steel
Wires
Prestressing wire is a single unit made of steel.
Strands
Two, three or seven wires are wound to form a prestressing strand.
Tendon
A group of strands or wires are wound to form a prestressing tendon.
Cable
A group of tendons form a prestressing cable.
Bars
A tendon can be made up of a single steel bar. The diameter of a bar is much
larger than that of a wire.
The different types of prestressing steel are further explained in Section 1.7,
Prestressing Steel.
Nature of Concrete-Steel Interface
Bonded tendon
When there is adequate bond between the prestressing tendon and concrete, it is called
a bonded tendon. Pre-tensioned and grouted post-tensioned tendons are bonded
tendons.
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Unbonded tendon
When there is no bond between the prestressing tendon and concrete, it is called
unbonded tendon. When grout is not applied after post-tensioning, the tendon is an
unbonded tendon.
Stages of LoadingThe analysis of prestressed members can be different for the different stages of loading.
The stages of loading are as follows.
1) Initial : It can be subdivided into two stages.
a) During tensioning of steel
b) At transfer of prestress to concrete.
2) Intermediate : This includes the loads during transportation of the
prestressed members.
3) Final : It can be subdivided into two stages.
a) At service, during operation.
b) At ultimate, during extreme events.
1.2.2 Advantages of Prestressing
The prestressing of concrete has several advantages as compared to traditional
reinforced concrete (RC) without prestressing. A fully prestressed concrete member is
usually subjected to compression during service life. This rectifies several deficiencies
of concrete.
The following text broadly mentions the advantages of a prestressed concrete member
with an equivalent RC member. For each effect, the benefits are listed.
1) Section remains uncracked under service loads
Reduction of steel corrosion
Increase in durability.
Full section is utilised Higher moment of inertia (higher stiffness)
Less deformations (improved serviceability).
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Increase in shear capacity.
Suitable for use in pressure vessels, liquid retaining structures.
Improved performance (resilience) under dynamic and fatigue loading.
2) High span-to-depth ratios
Larger spans possible with prestressing (bridges, buildings with large column-free
spaces)Typical values of span-to-depth ratios in slabs are given below.
Non-prestressed slab 28:1
Prestressed slab 45:1
For the same span, less depth compared to RC member.
Reduction in self weight
More aesthetic appeal due to slender sections
More economical sections.
3) Suitable for precast construction
The advantages of precast construction are as follows.
Rapid construction
Better quality control
Reduced maintenance
Suitable for repetitive construction
Multiple use of formwork
Reduction of formwork
Availability of standard shapes.
The following figure shows the common types of precast sections.
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Double T-sectionT-section
Hollow core Piles
Double T-sectionDouble T-sectionT-sectionT-section
Hollow core Piles
L-section Inverted T-section I-girdersL-section Inverted T-section I-girders
Figure 1-2.1 Typical precast members
1.2.3 Limi tations 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.
1.2.4 Types of Prestressing
Prestressing of concrete can be classified in several ways. The following classifications
are discussed.
Source of prestressing force
This classification is based on the method by which the prestressing force is generated.
There are four sources of prestressing force: Mechanical, hydraulic, electrical and
chemical.
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External or internal prestressing
This classification is based on the location of the prestressing tendon with respect to the
concrete section.
Pre-tensioning or post-tensioning
This is the most important classification and is based on the sequence of casting theconcrete and applying tension to the tendons.
Linear or circular prestressing
This classification is based on the shape of the member prestressed.
Full, limited or partial prestressing
Based on the amount of prestressing force, three types of prestressing are defined.
Uniaxial, biaxial or multi-axial prestressing
As the names suggest, the classification is based on the directions of prestressing a
member.
The individual types of prestressing are explained next.
Source of Prestressing Force
Hydraulic Prestressing
This is the simplest type of prestressing, producing large prestressing forces. The
hydraulic jack used for the tensioning of tendons, comprises of calibrated pressure
gauges which directly indicate the magnitude of force developed during the tensioning.
Mechanical Prestressing
In this type of prestressing, the devices includes weights with or without lever
transmission, geared transmission in conjunction with pulley blocks, screw jacks with or
without gear drives and wire-winding machines. This type of prestressing is adopted for
mass scale production.
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Figure 1-2.3 Internal prestressing of a box girder
(Courtesy: Cochin Port Trust, Kerala)
Pre-tensioning or Post-tensioning
Pre-tensioning
The tension is applied to the tendons before casting of the concrete. The pre-
compression is transmitted from steel to concrete through bond over the transmission
length near the ends. The following figure shows manufactured pre-tensioned electric
poles.
Figure 1-2.4 Pre-tensioned electric poles
(Courtesy: The Concrete Products and Construction Company, COPCO, Chennai)
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Post-tensioning
The tension is applied to the tendons (located in a duct) after hardening of the concrete.
The pre-compression is transmitted from steel to concrete by the anchorage device (at
the end blocks). The following figure shows a post-tensioned box girder of a bridge.
Figure 1-2.5 Post-tensioning of a box girder
(Courtesy: Cochin Port Trust, Kerala)
The details of pre-tensioning and post-tensioning are covered under Section 1.3, Pre-
tensioning Systems and Devices, and Section 1.4, Post-tensioning Systems and
Devices, respectively.
Linear or Circular Prestressing
Linear Prestressing
When the prestressed members are straight or flat, in the direction of prestressing, the
prestressing is called linear prestressing. For example, prestressing of beams, piles,
poles and slabs. The profile of the prestressing tendon may be curved. The following
figure shows linearly prestressed railway sleepers.
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Figure 1-2.6 Linearly prestressed railway sleepers
(Courtesy: The Concrete Products and Construction Company, COPCO, Chennai)
Circular Prestressing
When the prestressed members are curved, in the direction of prestressing, the
prestressing is called circular prestressing. For example, circumferential prestressing of
tanks, silos, pipes and similar structures. The following figure shows the containment
structure for a nuclear reactor which is circularly prestressed.
Figure 1-2.7 Circularly prestressed containment structure, Kaiga Atomic PowerStation, Karnataka
(Reference: Larsen & Toubro Ltd, ECC Division, 60 Landmark Years)
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Full, Limited or Partial Prestressing
Full Prestressing
When the level of prestressing is such that no tensile stress is allowed in concrete under
service loads, it is called Full Prestressing (Type 1, as per IS:1343 - 1980).
Limited PrestressingWhen the level of prestressing is such that the tensile stress under service loads is
within the cracking stress of concrete, it is called Limited Prestressing (Type 2).
Partial Prestressing
When the level of prestressing is such that under tensile stresses due to service loads,
the crack width is within the allowable limit, it is called Partial Prestressing (Type 3).
Uniaxial, Biaxial or Multiaxial Prestressing
Uniaxial Prestressing
When the prestressing tendons are parallel to one axis, it is called Uniaxial Prestressing.
For example, longitudinal prestressing of beams.
Biaxial Prestressing
When there are prestressing tendons parallel to two axes, it is called Biaxial
Prestressing. The following figure shows the biaxial prestressing of slabs.
Duct forprestressingtendon
Non-prestressed reinforcement
Duct forprestressingtendon
Non-prestressed reinforcement
Figure 1-2.8 Biaxial prestressing of a slab
(Courtesy: VSL India Pvt. Ltd., Chennai)
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Multiaxial Prestressing
When the prestressing tendons are parallel to more than two axes, it is called Multiaxial
Prestressing. For example, prestressing of domes.
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1.3 Pre-tensioning Systems and Devices
This section covers the following topics.
Introduction
Stages of Pre-tensioning
Advantages of Pre-tensioning
Disadvantages of Pre-tensioning
Devices
Manufacturing of Pre-tensioned Railway Sleepers
1.3.1 Introduct ion
Prestressing systems have developed over the years and various companies have
patented their products. Detailed information of the systems is given in the product
catalogues and brochures published by companies. There are general guidelines of
prestressing in Section 12 ofIS:1343 - 1980. The information given in this section is
introductory in nature, with emphasis on the basic concepts of the systems.
The prestressing systems and devices are described for the two types of prestressing,
pre-tensioning and post-tensioning, separately. This section covers pre-tensioning.
Section 1.4, Post-tensioning Systems and Devices, covers post-tensioning. In pre-
tensioning, the tension is applied to the tendons before casting of the concrete. The
stages of pre-tensioning are described next.
1.3.2 Stages of Pre-tensioning
In pre-tensioning system, the high-strength steel tendons are pulled between two end
abutments (also called bulkheads) prior to the casting of concrete. The abutments are
fixed at the ends of a prestressing bed.
Once the concrete attains the desired strength for prestressing, the tendons are cut
loose from the abutments.
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The prestress is transferred to the concrete from the tendons, due to the bond between
them. During the transfer of prestress, the member undergoes elastic shortening. If the
tendons are located eccentrically, the member is likely to bend and deflect (camber).
The various stages of the pre-tensioning operation are summarised as follows.
1) Anchoring of tendons against the end abutments
2) Placing of jacks3) Applying tension to the tendons
4) Casting of concrete
5) Cutting of the tendons.
During the cutting of the tendons, the prestress is transferred to the concrete with elastic
shortening and camber of the member.
The stages are shown schematically in the following figures.
Prestressing bed
Steel tendon
Endabutment
Jack
Prestressing bed
Steel tendon
Endabutment
Jack
(a) Applying tension to tendons
(b) Casting of concrete
Cutting of tendonCutting of tendon
(c) Transferring of prestress
Figure1-3.1 Stages of pre-tensioning
1.3.3 Advantages of Pre-tensioning
The relative advantages of pre-tensioning as compared to post-tensioning are as
follows.
Pre-tensioning is suitable for precast members produced in bulk.
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In pre-tensioning large anchorage device is not present.
1.3.4Disadvantages of Pre-tensioning
The relative disadvantages are as follows.
A prestressing bed is required for the pre-tensioning operation. There is a waiting period in the prestressing bed, before the concrete attains
sufficient strength.
There should be good bond between concrete and steel over the transmission
length.
1.3.5 Devices
The essential devices for pre-tensioning are as follows.
Prestressing bed
End abutments
Shuttering / mould
J ack
Anchoring device
Harping device (optional)
Prestressing Bed, End Abutments and Mould
The following figure shows the devices.
Prestressing bed
Mould
Endabutment
Jack
Anchoringdevice
Prestressing bed
Mould
Endabutment
Jack
Anchoringdevice
Prestressing bed
Mould
Endabutment
Jack
Anchoringdevice
Figure1-3.2 Prestressing bed, end abutment and mould
An extension of the previous system is the Hoyer system. This system is generally
used for mass production. The end abutments are kept sufficient distance apart, and
several members are cast in a single line. The shuttering is provided at the sides and
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between the members. This system is also called the Long Line Method. The
following figure is a schematic representation of the Hoyer system
Prestressing bed
A series of moulds
Prestressing bed
A series of moulds
Figure 1-3.3 Schematic representation of Hoyer system
The end abutments have to be sufficiently stiff and have good foundations. This is
usually an expensive proposition, particularly when large prestressing forces are
required. The necessity of stiff and strong foundation can be bypassed by a simpler
solution which can also be a cheaper option. It is possible to avoid transmitting the
heavy loads to foundations, by adopting self-equilibrating systems. This is a common
solution in load-testing. Typically, this is done by means of a tension frame. The
following figure shows the basic components of a tension frame. The jack and the
specimen tend to push the end members. But the end members are kept in place by
members under tension such as high strength steel rods.
P
Free bodiesPlan or Elevation
TestspecimenHigh
strengthsteel rods
Loading
jack
P
Free bodies
P
Free bodiesPlan or Elevation
TestspecimenHigh
strengthsteel rods
Loading
jack
Plan or Elevation
TestspecimenHigh
strengthsteel rods
Loading
jack
Figure 1-3.4 A tension frame
The frame that is generally adopted in a pre-tensioning system is called a stress bench.
The concrete mould is placed within the frame and the tendons are stretched and
anchored on the booms of the frame. The following figures show the components of astress bench.
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Jack
Threaded rodElevation
Plan
Mould Strands
Jack
Threaded rodElevation
Jack
Threaded rodElevation
Plan
Mould Strands
Plan
Mould Strands
Figure 1-3.5 Stress bench Self straining frame
The following figure shows the free body diagram by replacing the jacks with the applied
forces.
Plan
Load by jack
Tension instrands
Plan
Load by jack
Tension instrands
Figure 1-3.6 Free body diagram of stress bench
The following figure shows the stress bench after casting of the concrete.
Elevation
Plan
Elevation
Plan
Figure 1-3.7 The stress bench after casting concrete
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Jacks
The jacks are used to apply tension to the tendons. Hydraulic jacks are commonly used.
These jacks work on oil pressure generated by a pump. The principle behind the design
of jacks is Pascals law. The load applied by a jack is measured by the pressure
reading from a gauge attached to the oil inflow or by a separate load cell. The following
figure shows a double acting hydraulic jack with a load cell.
Figure 1-3.8 A double acting hydraulic jack with a load cell
Anchor ing Devices
Anchoring devices are often made on the wedge and friction principle. In pre-tensioned
members, the tendons are to be held in tension during the casting and hardening of
concrete. Here simple and cheap quick-release grips are generally adopted. The
following figure provides some examples of anchoring devices.
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Figure 1-3.9 Chuck assembly for anchoring tendons
(Reference: Lin, T. Y. and Burns, N. H.,
Design of Prestressed Concrete Structures)
Harping Devices
The tendons are frequently bent, except in cases of slabs-on-grade, poles, piles etc.
The tendons are bent (harped) in between the supports with a shallow sag as shown
below.
Harping point Hold up device
a) Before casting of concrete
Harping point Hold up device
a) Before casting of concretea) Before casting of concrete
b) After casting of concreteb) After casting of concrete
Figure 1-3.10 Harping of tendons
The tendons are harped using special hold-down devices as shown in the following
figure.
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Figure 1-3.11 Hold-down anchor for harping of tendons
(Reference: Nawy, E. G., Prestressed Concrete: A Fundamental Approach)
1.3.6 Manufacturing of Pre-tensioned Railway Sleepers
The following photos show the sequence of manufacturing of pre-tensioned railway
sleepers (Courtesy: The Concrete Products and Construction Company, COPCO,
Chennai). The steel strands are stretched in a stress bench that can be moved on
rollers. The stress bench can hold four moulds in a line. The anchoring device holds
the strands at one end of the stress bench. In the other end, two hydraulic jacks push a
plate where the strands are anchored. The movement of the rams of the jacks and the
oil pressure are monitored by a scale and gauges, respectively. Note that after the
extension of the rams, the gap between the end plate and the adjacent mould has
increased. This shows the stretching of the strands.
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Meanwhile the coarse and fine aggregates are batched, mixed with cement, water and
additives in a concrete mixer. The stress bench is moved beneath the concrete mixer.
The concrete is poured through a hopper and the moulds are vibrated. After the
finishing of the surface, the stress bench is placed in a steam curing chamber for a few
hours till the concrete attains a minimum strength.
The stress bench is taken out from the chamber and the strands are cut. The sleepers
are removed from the moulds and stacked for curing in water. After the complete curing,
the sleepers are ready for dispatching.
(a) Travelling pre-tensioning stress bench
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Wedge andcylinderassembly atthe dead end
Wedge andcylinderassembly atthe dead end
(b) Anchoring of strands
Hydraulic jack atstretching end
Initial gap
Endplate
Hydraulic jack atstretching end
Initial gap
Endplate
(c) Stretching of strands
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Automatedbatchingby weight
Automatedbatchingby weight
(f) Batching of materials
Hopper belowconcrete mixerHopper belowconcrete mixer
(g) Pouring of concrete
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(h) Concrete after vibration of mould
(i) Steam curing chamber
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(j) Cutting of strands
(k) Demoulding of sleeper
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(l) Stacking of sleeper
(m) Water curing
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(n) Storage and dispatching of sleepers
Figure 1-3.12 Manufacturing of pre-tensioned railway sleepers
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1.4 Post-tensioning Systems and Devices
This section covers the following topics
Introduction
Stages of Post-tensioning
Advantages of Post-tensioning
Disadvantages of Post-tensioning
Devices
Manufacturing of a Post-tensioned Bridge Girder
1.4.1 Introduction
Prestressing systems have developed over the years and various companies have
patented their products. Detailed information of the systems is given in the product
catalogues and brochures published by companies. There are general guidelines of
prestressing in Section 12 ofIS 1343: 1980. The information given in this section is
introductory in nature, with emphasis on the basic concepts of the systems.
The prestressing systems and devices are described for the two types of prestressing,
pre-tensioning and post-tensioning, separately. This section covers post-tensioning.
Section 1.3, Pre-tensioning Systems and Devices, covers pre-tensioning. In post-
tensioning, the tension is applied to the tendons after hardening of the concrete. The
stages of post-tensioning are described next.
1.4.2 Stages of Post-tensioning
In post-tensioning systems, the ducts for the tendons (or strands) are placed along with
the reinforcement before the casting of concrete. The tendons are placed in the ducts
after the casting of concrete. The duct prevents contact between concrete and the
tendons during the tensioning operation.
Unlike pre-tensioning, the tendons are pulled with the reaction acting against the
hardened concrete.
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If the ducts are filled with grout, then it is known as bonded post-tensioning. The grout
is a neat cement paste or a sand-cement mortar containing suitable admixture. The
grouting operation is discussed later in the section. The properties of grout are
discussed in Section 1.6, Concrete (Part-II).
In unbonded post-tensioning, as the name suggests, the ducts are never grouted andthe tendon is held in tension solely by the end anchorages. The following sketch shows
a schematic representation of a grouted post-tensioned member. The profile of the duct
depends on the support conditions. For a simply supported member, the duct has a
sagging profile between the ends. For a continuous member, the duct sags in the span
and hogs over the support.
Figure 1-4.1 Post-tensioning (Reference: VSL International Ltd.)
Among the following figures, the first photograph shows the placement of ducts in a box
girder of a simply supported bridge. The second photograph shows the end of the box
girder after the post-tensioning of some tendons.
Figure 1-4.2 Post-tensioning ducts in a box girder
(Courtesy: Cochin Port Trust, Kerala)
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Figure 1-4.3 Post-tensioning of a box girder
(Courtesy: Cochin Port Trust, Kerala)
The various stages of the post-tensioning operation are summarised as follows.
1) Casting of concrete.
2) Placement of the tendons.
3) Placement of the anchorage block and jack.
4) Applying tension to the tendons.
5) Seating of the wedges.
6) Cutting of the tendons.
The stages are shown schematically in the following figures. After anchoring a tendon
at one end, the tension is applied at the other end by a jack. The tensioning of tendons
and pre-compression of concrete occur simultaneously. A system of self-equilibrating
forces develops after the stretching of the tendons.
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Casting bed
Duct
Side viewCasting bed
Duct
Side view
(a) Casting of concrete
JackJack
(b) Tensioning of tendons
AnchorAnchor
(c)Anchoring the tendon at the stretching end
Figure 1-4.4 Stages of post-tensioning (shown in elevation)
1.4.3 Advantages of Post-tensioning
The relative advantages of post-tensioning as compared to pre-tensioning are as
follows.
Post-tensioning is suitable for heavy cast-in-place members.
The waiting period in the casting bed is less.
The transfer of prestress is independent of transmission length.
1.4.4 Disadvantage of Post-tensioning
The relative disadvantage of post-tensioning as compared to pre-tensioning is the
requirement of anchorage device and grouting equipment.
1.4.5 Devices
The essential devices for post-tensioning are as follows.
1) Casting bed
2) Mould/Shuttering
3) Ducts
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4) Anchoring devices
5) J acks
6) Couplers (optional)
7) Grouting equipment (optional).
Casting Bed, Mould and DuctsThe following figure shows the devices.
Casting bed
Mould
Duct
Casting bed
Mould
Duct
Figure 1-4.5 Casting bed, mould and duct
Anchor ing Devices
In post-tensioned members the anchoring devices transfer the prestress to the concrete.
The devices are based on the following principles of anchoring the tendons.
1) Wedge action
2) Direct bearing
3) Looping the wires
Wedge action
The anchoring device based on wedge action consists of an anchorage block and
wedges. The strands are held by frictional grip of the wedges in the anchorage block.
Some examples of systems based on the wedge-action are Freyssinet, Gifford-Udall,
Anderson and Magnel-Blaton anchorages. The following figures show some patented
anchoring devices.
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Figure 1-4.6 Freyssinet T system anchorage cones
(Reference: Lin, T. Y. and Burns, N. H., Design of Prestressed Concrete Structures)
Figure 1-4.7 Anchoring devices
(Reference: Collins, M. P. and Mitchell, D., Prestressed Concrete Structures)
Figure 1-4.8 Anchoring devices (Reference: VSL International Ltd)
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Direct bearing
The rivet or bolt heads or button heads formed at the end of the wires directly bear
against a block. The B.B.R.V post-tensioning system and the Prescon system are
based on this principle. The following figure shows the anchoring by direct bearing.
Figure 1-4.9 Anchoring with button heads
(Reference: Collins, M. P. and Mitchell, D., Prestressed Concrete Structures)
Looping the wires
The Baur-Leonhardt system, Leoba system and also the Dwidag single-bar anchorage
system, work on this principle where the wires are looped around the concrete. The
wires are looped to make a bulb. The following photo shows the anchorage by looping
of the wires in a post-tensioned slab.
Figure 1-4.10 Anchorage by looping the wires in a slab
(Courtesy : VSL India Pvt. Ltd.)
The anchoring devices are tested to calculate their strength. The following photo shows
the testing of an anchorage block.
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Figure 1-4.11 Testing of an anchorage device
Sequence of Anchoring
The following figures show the sequence of stressing and anchoring the strands. The
photo of an anchoring device is also provided.
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Figure 1-4.12 Sequence of anchoring
(Reference: VSL International Ltd.)
Figure 1-4.13 Final form of an anchoring device
(Reference: VSL International Ltd)
JacksThe working of a jack and measuring the load were discussed in Section 1.3, Pre-
tensioning Systems and Devices. The following figure shows an extruded sketch of the
anchoring devices.
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Figure 1-4.14 J acking and anchoring with wedges
(Reference: Collins, M. P. and Mitchell, D., Prestressed Concrete Structures)
Couplers
The couplers are used to connect strands or bars. They are located at the junction of
the members, for example at or near columns in post-tensioned slabs, on piers in post-
tensioned bridge decks.
The couplers are tested to transmit the full capacity of the strands or bars. A few types
of couplers are shown.
Figure 1-4.15 Coupler for strands
(Reference: VSL International Ltd)
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Figure 1-4.16 Couplers for strands
(Reference: Dywidag Systems International)
Figure 1-4.17 Couplers for strands
(Reference: Dywidag Systems International)
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GroutingGrouting can be defined as the filling of duct, with a material that provides an anti-
corrosive alkaline environment to the prestressing steel and also a strong bond between
the tendon and the surrounding grout.
The major part of grout comprises of water and cement, with a water-to-cement ratio ofabout 0.5, together with some water-reducing admixtures, expansion agent and
pozzolans. The properties of grout are discussed in Section 1.6, Concrete (Part-II).
The following figure shows a grouting equipment, where the ingredients are mixed and
the grout is pumped.
Figure 1-4.18 Grouting equipment
(Reference: Williams Form Engineering Corp.)
1.4.6 Manufacturing of Post-tensioned Bridge Girders
The following photographs show some steps in the manufacturing of a post-tensioned I-
girder for a bridge (Courtesy: Larsen & Toubro). The first photo shows the fabricated
steel reinforcement with the ducts for the tendons placed inside. Note the parabolic
profiles of the duct for the simply supported girder. After the concrete is cast and cured
to gain sufficient strength, the tendons are passed through the ducts, as shown in the
second photo. The tendons are anchored at one end and stretched at the other end by
a hydraulic jack. This can be observed from the third photo.
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(a) Fabrication of reinforcement
(b) Placement of tendons
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(c) Stretching and anchoring of tendons
Figure 1-4.19 Manufacturing of a post-tensioned bridge I-girder
The following photos show the construction of post-tensioned box girders for a bridge
(Courtesy: Cochin Port Trust). The first photo shows the fabricated steel reinforcement
with the ducts for the tendons placed inside. The top flange will be constructed later.
The second photo shows the formwork in the pre-casting yard. The formwork for the
inner sides of the webs and the flanges is yet to be placed. In the third photo a girder is
being post-tensioned after adequate curing. The next photo shows a crane on a barge
that transports a girder to the bridge site. The completed bridge can be seen in the last
photo.
(a) Reinforcement cage for box girder
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(b) Formwork for box girder
(c) Post-tensioning of box girder
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(d) Transporting of box girder
(e) Completed bridge
Figure 1-4.20 Manufacturing of post-tensioned bridge box girders
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1.5 Concrete (Part I)
This section covers the following topics.
Constituents of Concrete
Properties ofHardened Concrete (Part I)
1.5.1 Const ituents of Concrete
Introduction
Concrete is a composite material composed of gravels or crushed stones (coarse
aggregate), sand (fine aggregate) and hydrated cement (binder). It is expected that the
student of this course is familiar with the basics of concrete technology. Only the
information pertinent to prestressed concrete design is presented here.
The following figure shows a petrographic section of concrete. Note the scattered
coarse aggregates and the matrix surrounding them. The matrix consists of sand,
hydrated cement and tiny voids.
Figure 1-5.1 Petrographic section of hardened concrete
(Reference: Portland Cement Association, Design and Control of Concrete Mixtures)
Aggregate
The coarse aggregate are granular materials obtained from rocks and crushed stones.
They may be also obtained from synthetic material like slag, shale, fly ash and clay for
use in light-weight concrete.
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The sand obtained from river beds or quarries is used as fine aggregate. The fine
aggregate along with the hydrated cement paste fill the space between the coarse
aggregate.
The important properties of aggregate are as follows.
1) Shape and texture2) Size gradation
3) Moisture content
4) Specific gravity
5) Unit weight
6) Durability and absence of deleterious materials.
The requirements of aggregate is covered in Section 4.2 of IS:1343 - 1980.
The nominal maximum coarse aggregate size is limited by the lowest of the following
quantities.
1) 1/4 times the minimum thickness of the member
2) Spacing between the tendons/strands minus 5 mm
3) 40 mm.
The deleterious substances that should be limited in aggregate are clay lumps, wood,coal, chert, silt, rock dust (material finer than 75 microns), organic material, unsound
and friable particles.
Cement
In present day concrete, cement is a mixture of lime stone and clay heated in a kiln to
1400 - 1600C. The types of cement permitted by IS:1343 - 1980 (Clause 4.1) for
prestressed applications are the following. The information is revised as per IS:456 -
2000, Plain and Reinforced Concrete Code of Practice.
1) Ordinary Portland cement confirming to IS:269 - 1989, Ordinary Portland Cement,
33 Grade Specification.
2) Portland slag cement confirming to IS:455 - 1989, Portland Slag Cement
Specification, but with not more than 50% slag content.
3) Rapid-hardening Portland cement confirming to IS:8041 - 1990, Rapid Hardening
Portland Cement Specification.
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WaterThe water should satisfy the requirements ofSection 5.4 ofIS:456 - 2000.
Water used for mixing and curing shall be clean and free from injurious amounts of oils,
acids, alkalis, salts, sugar, organic materials or other substances that may be
deleterious to concrete and steel.
Admixtures
IS:1343 - 1980 allows to use admixtures that conform to IS:9103 - 1999, Concrete
Admixtures Specification. The admixtures can be broadly divided into two types:
chemical admixtures and mineral admixtures. The common chemical admixtures are as
follows.
1) Air-entraining admixtures
2) Water reducing admixtures
3) Set retarding admixtures
4) Set accelerating admixtures
5) Water reducing and set retarding admixtures
6) Water reducing and set accelerating admixtures.
The common mineral admixtures are as follows.
1) Fly ash2) Ground granulated blast-furnace slag
3) Silica fumes
4) Rice husk ash
5) Metakoline
These are cementitious and pozzolanic materials.
1.5.2 Propert ies of Hardened Concrete (Part I)
The concrete in prestressed applications has to be of good quality. It requires the
following attributes.
1) High strength with low water-to-cement ratio
2) Durability with low permeability, minimum cement content and proper mixing,
compaction and curing
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3) Minimum shrinkage and creep by limiting the cement content.
The following topics are discussed.
1) Strength of concrete
2) Stiffness of concrete
3) Durability of concrete
4) High performance concrete5) Allowable stresses in concrete.
Strength of Concrete
The following sections describe the properties with reference to IS:1343 - 1980. The
strength of concrete is required to calculate the strength of the members. For
prestressed concrete applications, high strength concrete is required for the following
reasons.
1) To sustain the high stresses at anchorage regions.
2) To have higher resistance in compression, tension, shear and bond.
3) To have higher stiffness for reduced deflection.
4) To have reduced shrinkage cracks.
Compressive Strength
The compressive strength of concrete is given in terms of the characteristic
compressive strength of 150 mm size cubes tested at 28 days (fck). The characteristic
strength is defined as the strength of the concrete below which not more than 5% of thetest results are expected to fall. This concept assumes a normal distribution of the
strengths of the samples of concrete.
The following sketch shows an idealised distribution of the values of compressive
strength for a sizeable number of test cubes. The horizontal axis represents the values
of compressive strength. The vertical axis represents the number of test samples for a
particular compressive strength. This is also termed as frequency. The average of the
values of compressive strength (mean strength) is represented as fcm. The characteristic
strength (fck) is the value in the x-axis below which 5% of the total area under the curve
falls. The value offck is lower than fcm by 1.65, where is the standard deviation of the
normal distribution.
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fck fcm
1.65
Frequency
28 day cube compressive strength
5% area fck fcm
1.65
Frequency
28 day cube compressive strength
5% area
Figure 1-5.2 Idealised normal distribution of concrete strength
(Reference: Pillai, S. U., and Menon, D., Reinforced Concrete Design)
The sampling and strength test of concrete are as per Section 15 of IS:1343 - 1980.The grades of concrete are explained in Table 1 of the Code.
The minimum grades of concrete for prestressed applications are as follows.
30 MPa for post-tensioned members
40 MPa for pre-tensioned members.
The maximum grade of concrete is 60 MPa.
Since at the time of publication of IS:1343 in 1980, the properties of higher strength
concrete were not adequately documented, a limit was imposed on the maximum
strength. It is expected that higher strength concrete may be used after proper testing.
The increase in strength with age as given in IS:1343 - 1980, is not observed in present
day concrete that gains substantial strength in 28 days. Hence, the age factor given in
Clause 5.2.1 should not be used. It has been removed from IS:456 - 2000.
Tensile Strength
The tensile strength of concrete can be expressed as follows.
1) Flexural tensile strength: It is measured by testing beams under 2 point loading
(also called 4 point loading including the reactions).
2) Splitting tensile strength: It is measured by testing cylinders under diametral
compression.
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3) Direct tensile strength: It is measured by testing rectangular specimens under
direct tension.
In absence of test results, the Code recommends to use an estimate of the flexural
tensile strength from the compressive strength by the following equation.
cr ck f = f0.7 (1-5.1)
Here,
fcr = flexural tensile strength in N/mm2
fck = characteristic compressive strength of cubes in N/mm2.
Stiffness of Concrete
The stiffness of concrete is required to estimate the deflection of members. The
stiffness is given by the modulus of elasticity. For a non-linear stress (fc) versus strain
(c) behaviour of concrete the modulus can be initial, tangential or secant modulus.
IS:1343 - 1980 recommends a secant modulus at a stress level of about 0.3fck. The
modulus is expressed in terms of the characteristic compressive strength and not the
design compressive strength. The following figure shows the secant modulus in the
compressive stress-strain curve for concrete.
c
fc
fck
Ec
fc
c
fc
fck
Ecc
fc
fck
Ec
fcfc
Figure 1-5.3 a) Concrete cube under compression, b) Compressive stress-strain
curve for concrete
The modulus of elasticity for short term loading (neglecting the effect of creep) is given
by the following equation.
c cE = f5000 k (1-5.2)
Here,
Ec = short-term static modulus of elasticity in N/mm2
fck = characteristic compressive strength of cubes in N/mm2.
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Table 10 provides the values for the above quantities for concrete exposed to sulphate
attack.
To limit the creep and shrinkage, IS:1343 - 1980 specifies a maximum cement content
of 530 kg per m3 of concrete (Clause 8.1.1).
High Performance Concrete
With the advancement of concrete technology, high performance concrete is getting
popular in prestressed applications. The attributes of high performance concrete are as
follows.
1) High strength
2) Minimum shrinkage and creep
3) High durability
4) Easy to cast
5) Cost effective.
Traditionally high performance concrete implied high strength concrete with higher
cement content and low water-to-cement ratio. But higher cement content leads to
autogenous and plastic shrinkage cracking and thermal cracking. At present durability
is also given importance along with strength.
Some special types of high performance concrete are as follows.1) High strength concrete
2) High workability concrete
3) Self-compacting concrete
4) Reactive powder concrete
5) High volume fly ash concrete
6) Fibre reinforced concrete
In a post-tensioned member, the concrete next to the anchorage blocks (referred to as
end block) is subjected to high stress concentration. The type of concrete at the end
blocks may be different from that at the rest of the member. Fibre reinforced concrete is
used to check the cracking due to the bursting forces.
The following photo shows that the end blocks were cast separately with high strength
concrete.
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Figure 1-5.4 End-blocks in a bridge deck
(Courtesy: Cochin Port Trust, Kerala)
Al lowable Stresses in Concrete
The allowable stresses are used to analyse and design members under service loads.
IS:1343 - 1980 specifies the maximum allowable compressive stresses for different
grades of concrete under different loading conditions in Section 22.8.
Allowable Compressive Stresses under Flexure
The following sketch shows the variation of allowable compressive stresses for different
grades of concrete at transfer. The cube strength at transfer is denoted as fci.
M30 M60 M40 M60
0.51fci0.44fci
0.54fci0.37fci
Post-tension Pre-tension
M30 M60 M40 M60
0.51fci0.44fci
0.54fci0.37fci
Post-tension Pre-tension
Figure 1-5.5 Variation of allowable compressive stresses at transfer
The following sketch shows the variation of allowable compressive stresses for different
grades of concrete at service loads.
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0.34fck
0.41fck
0.27fck
0.35fck
M 30 M 60
Zone I
Zone II
Figure 1-5.6 Variation of allowable compressive stresses at service loads
Here, Zone I represents the locations where the compressive stresses are not likely to
increase. Zone II represents the locations where the compressive stresses are likely to
increase, such as due to transient loads from vehicles in bridge decks.
Allowable Compressive Stresses under Direct Compression
For direct compression, except in the parts immediately behind the anchorage, the
maximum stress is equal to 0.8 times the maximum compressive stress under flexure.
Allowable Tensile Stresses under Flexure
The prestressed members are classified into three different types based on the
allowable tensile stresses. The amount of prestressing varies in the three types. The
allowable tensile stresses for the three types of members are specified in Section 22.7.
The values are reproduced below.
Table 1-5.2 Allowable tensile stresses (IS:1343 - 1980)
Type 1 No tensile stress
Type 23 N/mm2.
This value can be increased to 4.5 N/mm2 for temporary loads.
Type 3 Table 8 provides hypothetical values of allowable tensile stresses.
The purpose of providing hypothetical values is to use the elastic analysis method for
Type 3 members even after cracking of concrete.
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1.6 Concrete (Part II)
This section covers the following topics.
Properties ofHardened Concrete (Part II)
Properties of Grout
Codal Provisions of Concrete
1.6.1 Propert ies of Hardened Concrete (Part II)
The properties that are discussed are as follows.
1) Stress-strain curves for concrete
2) Creep of concrete
3) Shrinkage of concrete
Stress-strain Curves for Concrete
Curve under uniaxial compression
The stress versus strain behaviour of concrete under uniaxial compression is initially
linear (stress is proportional to strain) and elastic (strain is recovered at unloading). With
the generation of micro-cracks, the behaviour becomes nonlinear and inelastic. After the
specimen reaches the peak stress, the resisting stress decreases with increase in strain.
IS:1343 - 1980 recommends a parabolic characteristic stress-strain curve, proposed by
Hognestad, for concrete under uniaxial compression (Figure 3 in the Code).
c0 cu
fc
fck
fc
c0 cu
fc
fck
c0 cu
fc
fck
fcfc
Figure 1-6.1 a) Concrete cube under compression, b) Design stress-strain curve for
concrete under compression due to flexure
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The equation for the design curve under compression due to flexure is as follows.
Forc0
c cck ck
f = f -
2
0 0
2 (1-6.1)
Forc< ccu
fc= fck (1-6.2)Here,
fc = compressive stress
fck = characteristic compressive strength of cubes
c = compressive strain
0 = strain corresponding to fck= 0.002
cu = ultimate compressive strain = 0.0035
For concrete under compression due to axial load, the ultimate strain is restricted to
0.002. From the characteristic curve, the design curve is defined by multiplying the
stress with a size factor of 0.67 and dividing the stress by a material safety factor of m =
1.5. The design curve is used in the calculation of ultimate strength. The following
sketch shows the two curves.
0 cu c
fc
fck
0.447 fck
Characteristic curve
Design curve
0 cu c
fc
fck
0.447 fck
Characteristic curve
Design curve
Figure 1-6.2 Stress-strain curves for concrete under compression due to flexure
In the calculation of deflection at service loads, a linear stress-strain curve is assumed
up to the allowable stress. This curve is given by the following equation.
fc= Ecc (1-6.3)
Note that, the size factor and the material safety factor are not used in the elastic
modulus Ec.
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For high strength concrete (say M100 grade of concrete and above) under uniaxial
compression, the ascending and descending branches are steep.
0 c
fcfck
Es
Eci
0 c
fcfck
Es
Eci
Figure 1-6.3 Stress-strain curves for high strength concrete under compression
The equation proposed by Thorenfeldt, Tomaxzewicz and Jensen is appropriate for high
strength concrete.
c
c ck nk
c
n
f = f
n - +
0
0
1
(1-6.4)
The variables in the previous equation are as follows.
fc = compressive stress
fck = characteristic compressive strength of cubes in N/mm2
c = compressive strain
0 = strain corresponding to fck
k = 1 forc0
= 0.67 + (fck / 77.5) forc>0. The value ofkshould be greater than 1.
n = Eci / (Eci Es)
Eci = initial modulus
Es = secant modulus at fck= fck /0.
The previous equation is applicable for both the ascending and descending branches of
the curve. Also, the parameter k models the slope of the descending branch, which
increases with the characteristic strength fck. To be precise, the value of 0 can be
considered to vary with the compressive strength of concrete.
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Curve under uniaxial tension
The stress versus strain behaviour of concrete under uniaxial tension is linear elastic
initially. Close to cracking nonlinear behaviour is observed.
fc
c
fcfc
c
fc
c
fcfc
(a) (b)
Figure 1-6.4 a) Concrete panel under tension, b) Stress-strain curve for concrete
under tension
In calculation of deflections of flexural members at service loads, the nonlinearity is
neglected and a linear elastic behaviourfc= Ecc is assumed. In the analysis of ultimate
strength, the tensile strength of concrete is usually neglected.
Creep of Concrete
Creep of concrete is defined as the increase in deformation with time under constant
load. Due to the creep of concrete, the prestress in the tendon is reduced with time.
Hence, the study of creep is important in prestressed concrete to calculate the loss in
prestress.
The creep occurs due to two causes.
1. Rearrangement of hydrated cement paste (especially the layered products)
2. Expulsion of water from voids under load
If a concrete specimen is subjected to slow compressive loading, the stress versus
strain curve is elongated along the strain axis as compared to the curve for fast loading.
This can be explained in terms of creep. If the load is sustained at a level, the increase
in strain due to creep will lead to a shift from the fast loading curve to the slow loading
curve (Figure 1-6.5).
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c
fcFast loading
Slow loading
Effect of creep
c
fcFast loading
Slow loading
Effect of creep
Figure 1-6.5 Stress-strain curves for concrete under compression
Creep is quantified in terms of the strain that occurs in addition to the elastic strain due
to the applied loads. If the applied loads are close to the service loads, the creep strain
increases at a decreasing rate with time. The ultimate creep strain is found to be
proportional to the elastic strain. The ratio of the ultimate creep strain to the elastic
strain is called the creep coefficient.
For stress in concrete less than about one-third of the characteristic strength, the
ultimate creep strain is given as follows.
cr,ult el = (1-6.5)
The variation of strain with time, under constant axial compressive stress, is
represented in the following figure.
strain
Time (linear scale)
cr, ult= ultimate creep strain
el= elastic strainstrain
Time (linear scale)
cr, ult= ultimate creep strain
el= elastic strain
Figure 1-6.6 Variation of strain with time for concrete under compression
If the load is removed, the elastic strain is immediately recovered. However the
recovered elastic strain is less than the initial elastic strain, as the elastic modulus
increases with age.
There is reduction of strain due to creep recovery which is less than the creep strain.
There is some residual strain which cannot be recovered (Figure 1-6.7).
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strain
Time (linear scale)
Residual strain
Creep recovery
Elastic recovery
Unloadingstrain
Time (linear scale)
Residual strain
Creep recovery
Elastic recovery
Unloading
Figure 1-6.7 Variation of strain with time showing the effect of unloading
The creep strain depends on several factors. It increases with the increase in the
following variables.
1) Cement content (cement paste to aggregate ratio)
2) Water-to-cement ratio
3) Air entrainment4) Ambient temperature.
The creep strain decreases with the increase in the following variables.
1) Age of concrete at the time of loading.
2) Relative humidity
3) Volume to surface area ratio.
The creep strain also depends on the type of aggregate.
IS:1343 - 1980 gives guidelines to estimate the ultimate creep strain in Section 5.2.5. It
is a simplified estimate where only one factor has been considered. The factor is age of
loading of the prestressed concrete structure. The creep coefficient is provided for
three values of age of loading.
Table 1-6.1 Creep coefficient for three values of age of loading
Age of Loading Creep Coefficient
7 days 2.2
28 days 1.6
1 year 1.1
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It can be observed that if the structure is loaded at 7 days, the creep coefficient is 2.2.
This means that the creep strain is 2.2 times the elastic strain. Thus, the total strain is
more than thrice the elastic strain. Hence, it is necessary to study the effect of creep in
the loss of prestress and deflection of prestressed flexural members. Even if the
structure is loaded at 28 days, the creep strain is substantial. This implies higher loss of
prestress and higher deflection.
Curing the concrete adequately and delaying the application of load provide long term
benefits with regards to durability, loss of prestress and deflection.
In special situations detailed calculations may be necessary to monitor creep strain with
time. Specialised literature or international codes can provide guidelines for such
calculations.
Shrinkage of Concrete
Shrinkage of concrete is defined as the contraction due to loss of moisture. The study of
shrinkage is also important in prestressed concrete to calculate the loss in prestress.
The shrinkage occurs due to two causes.
1. Loss of water from voids
2. Reduction of volume during carbonation
The following figure shows the variation of shrinkage strain with time. Here, t0 is the time
at commencement of drying. The shrinkage strain increases at a decreasing rate with
time. The ultimate shrinkage strain (sh) is estimated to calculate the loss in prestress.
Shrinkage
strain
t0 Time (linear scale)
sh
Shrinkage
strain
t0 Time (linear scale)
sh
Figure 1-6.8 Variation of shrinkage strain with time
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Like creep, shrinkage also depends on several factors. The shrinkage strain increases
with the increase in the following variables.
1) Ambient temperature
2) Temperature gradient in the members
3) Water-to-cement ratio
4) Cement content.
The shrinkage strain decreases with the increase in the following variables.
1) Age of concrete at commencement of drying
2) Relative humidity
3) Volume to surface area ratio.
The shrinkage strain also depends on the type of aggregate.
IS:1343 - 1980 gives guidelines to estimate the shrinkage strain in Section 5.2.4. It is a
simplified estimate of the ultimate shrinkage strain (sh).
For pre-tension
sh = 0.0003 (1-6.6)
For post-tension
(1-6.7)
( )sh =
log t +10
0.0002
2
Here, tis the age at transfer in days. Note that for post-tension, tis the age at transfer
in days which approximates the curing time.
It can be observed that with increasing age at transfer, the shrinkage strain reduces. As
mentioned before, curing the concrete adequately and delaying the application of load
provide long term benefits with regards to durability and loss of prestress.
In special situations detailed calculations may be necessary to monitor shrinkage strain
with time. Specialised literature or international codes can provide guidelines for such
calculations.
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1.6.2 Properties of Grout
Grout is a mixture of water, cement and optional materials like sand, water-reducing
admixtures, expansion agent and pozzolans. The water-to-cement ratio is around 0.5.
Fine sand is used to avoid segregation.
The desirable properties of grout are as follows.
1) Fluidity
2) Minimum bleeding and segregation
3) Low shrinkage
4) Adequate strength after hardening
5) No detrimental compounds
6) Durable.
IS:1343 - 1980 specifies the properties of grout in Sections 12.3.1 and Section 12.3.2.
The following specifications are important.
1) The sand should pass 150 m Indian Standard sieve.
2) The compressive strength of 100 mm cubes of the grout shall not be less than 17
N/mm2 at 7 days.
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1.6.5 Codal Provisions of Concrete
The following topics are covered in IS:1343 - 1980 under the respective sections. These
provisions are not duplicated here.
Table 1-6.2 Topics and sections
Workability of concrete Section 6
Concrete mix proportioning Section 8
Production and control of concrete Section 9
Formwork Section 10
Transporting, placing, compacting Section 13
Concrete under special conditions Section 14
Sampling and strength test of concrete Section 15
Acceptance criteria Section 16
Inspection and testing of structures Section 17
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2.1 Losses in Prestress (Part I)
This section covers the following topics.
Introduction
Elastic Shortening
The relevant notations are explained first.
Notations
Geometric Properties
The commonly used geometric properties of a prestressed member are defined as
follows.
Ac = Area of concrete section
= Net cross-sectional area of concrete excluding the area of
prestressing steel.Ap = Area of prestressing steel
= Total cross-sectional area of the tendons.
A = Area of prestressed member
= Gross cross-sectional area of prestressed member.
=Ac+Ap
At = Transformed area of prestressed member
= Area of the member when steel is substituted by an equivalent
area of concrete.
=Ac+ mAp
=A + (m 1)Ap
Here,
m = the modular ratio = Ep/Ec
Ec = short-term elastic modulus of concrete
Ep = elastic modulus of steel.
The following figure shows the commonly used areas of the prestressed members.
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= +
A Ac Ap At
= +
A Ac Ap At
Figure 2-1.1 Areas for prestressed members
CGC = Centroid of concrete
= Centroid of the gross section. The CGC may lie outside the
concrete (Figure 2-1.2).
CGS = Centroid of prestressing steel
= Centroid of the tendons. The CGS may lie outside the tendons or
the concrete (Figure 2-1.2).
I = Moment of inertia of prestressed member
= Second moment of area of the gross section about the CGC.
It = Moment of inertia of transformed section
= Second moment of area of the transformed section about the
centroid of the transformed section.
e = Eccentricity of CGS with respect to CGC
= Vertical distance between CGC and CGS. If CGS lies below CGC,
e will be considered positive and vice versa (Figure 2-1.2).
CGSCGCe
CGS
CGCe
CGSCGCeCGSCGCCGSCGCe
CGS
CGCe
CGS
CGC
CGS
CGC
CGS
CGCe
Figure 2-1.2 CGC, CGS and eccentricity of typical prestressed members
Load Variables
Pi = Initial prestressing force
= The force which is applied to the tendons by the jack.
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P0 = Prestressing force after immediate losses
= The reduced value of prestressing force after elastic shortening,
anchorage slip and loss due to friction.
Pe = Effective prestressing force after time-dependent losses
= The final value of prestressing force after the occurrence of creep,
shrinkage and relaxation.
2.1.1 Introduction
In prestressed concrete applications, the most important variable is the prestressing
force. In the early days, it was observed that the prestressing force does not stay
constant, but reduces with time. Even during prestressing of the tendons and the
transfer of prestress to the concrete member, there is a drop of the prestressing force
from the recorded value in the jack gauge. The various reductions of the prestressing
force are termed as the losses in prestress.
The losses are broadly classified into two groups, immediate and time-dependent. The
immediate losses occur during prestressing of the tendons and the transfer of prestress
to the concrete member. The time-dependent losses occur during the service life of the
prestressed member. The losses due to elastic shortening of the member, friction at the
tendon-concrete interface and slip of the anchorage are the immediate losses. The
losses due to the shrinkage and creep of the concrete and relaxation of the steel are the
time-dependent losses. The causes of the various losses in prestress are shown in the
following chart.
Losses
Immediate Time dependent
Elasticshortening
Friction Anchorageslip
Creep Shrinkage Relaxation
Figure 2-1.3 Causes of the various losses in prestress
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2.1.2 Elastic Shortening
Pre-tensioned Members
When the tendons are cut and the prestressing force is transferred to the member, the
concrete undergoes immediate shortening due to the prestress. The tendon also
shortens by the same amount, which leads to the loss of prestress.
Post-tensioned Members
If there is only one tendon, there is no loss because the applied prestress is recorded
after the elastic shortening of the member. For more than one tendon, if the tendons
are stretched sequentially, there is loss in a tendon during subsequent stretching of the
other tendons.
The elastic shortening loss is quantified by the drop in prestress (fp) in a tendon due to
the change in strain in the tendon (p). It is assumed that the change in strain in the
tendon is equal to the strain in concrete (c) at the level of the tendon due to the
prestressing force. This assumption is called strain compatibility between concrete
and steel. The strain in concrete at the level of the tendon is calculated from the stress
in concrete (fc) at the same level due to the prestressing force. A linear elastic
relationship is used to calculate the strain from the stress.
The quantification of the losses is explained below.
p p p
p c
cp
c
p c
f = E
= E
f= E
E
f = mf (2-1.1)
For simplicity, the loss in all the tendons can be calculated based on the stress inconcrete at the level of CGS. This simplification cannot be used when tendons are
stretched sequentially in a post-tensioned member. The calculation is illustrated for the
following types of members separately.
Pre-tensioned Axial Members
Pre-tensioned Bending Members
Post-tensioned Axial Members
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Post-tensioned Bending Members
Pre-tensioned Axial Members
The following figure shows the changes in length and the prestressing force due to
elastic shortening of a pre-tensioned axial member.
Original length of member at transfer of prestress
Length after elastic shortening
Pi
P0
Original length of member at transfer of prestress
Length after elastic shortening
Pi
P0
Figure 2-1.4 Elastic shortening of a pre-tensioned axial member
The loss can be calculated as per Eqn. (2-1.1) by expressing the stress in concrete in
terms of the prestressing force and area of the section as follows.
(2-1.2)
p c
c
i ip
t
f = mf
P= m
AP P
f = m mA A
0
Note that the stress in concrete due to the prestressing force after immediate losses
(P0/Ac) can be equated to the stress in the transformed section due to the initial
prestress (Pi /At). This is derived below. Further, the transformed area At of the
prestressed member can be approximated to the gross areaA.
The following figure shows that the strain in concrete due to elastic shortening ( c) is the
difference between the initial strain in steel (pi) and the residual strain in steel (p0).
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Pi
P0
Length of tendon before stretchingpi
p0
c
Pi
P0
Length of tendon before stretchingpi
p0
c
Figure 2-1.5 Strain variables in elastic shortening
The following equation relates the strain variables.
c=pi- p0 (2-1.3)
The strains can be expressed in terms of the prestressing forces as follows.
c
c c
P =
A E0
(2-1.4)
ipi
p p
P =
A E
(2-1.5)
p
p p
P =
A E0
0
(2-1.6)
Substituting the expressions of the strains in Eqn. (2-1.3)
i
c c p p p p
i
c c p p p p
i
c p p
i
c p c
P PP= -
A E A E A E
P, P + =
A E A E A E
Pm 1P + =
A A A
P P=
A mA + A
0 0
0
0
0
1 1or
or,
or,
0or i
c t
P P=
A A
(2-1.7)
Thus, the stress in concrete due to the prestressing force after immediate losses (P0/Ac)
can be equated to the stress in the transformed section due to the initial prestress (Pi
/At).
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The following problem illustrates the calculation of loss due to elastic shortening in an
idealised pre-tensioned railway sleeper.
Example 2-1.1
A prest ressed concrete sleeper produced by pre-tension ing method has a
rectangular cross-section of 300mm 250 mm (b h). It is prestressed with 9
numbers of straight 7mm diameter wires at 0.8 times the ultimate strength of 1570
N/mm2. Estimate the percentage loss of stress due to elastic shor tening of
concrete. Considerm = 6.
250
40
300
40
Solution
a) Approximate solution considering gross section
The sectional properties are calculated as follows.
Area of a single wire, Aw = /4 72
= 38.48 mm2
Area of total prestressing steel, Ap = 9 38.48
= 346.32 mm2
Area of concrete section, A = 300 250
= 75 103 mm2
Moment of inertia of section, I = 300 2503/12
= 3.91 108 mm4
Distance of centroid of steel area (CGS) from the soffit,
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( )438.48 250- 40 +538.4840y =
938.48
=115.5 mm
Prestressing force, Pi = 0.8 1570 346.32 N
= 435 kN
Eccentricity of prestressing force,
e = (250/2) 115.5
= 9.5 mm
The stress diagrams due to Piare shown.
Since the wires are distributed above and below the CGC, the losses are calculated for
the top and bottom wires separately.
Stress at level of top wires (y= yt= 125 40)
115.5
e
=+
iP-A
i iP P .e- yA I
iP .e yI
( )
( )3 3
3 8
2
435 10 435 10 9.5= - + 125 - 40
7510 3.9110
= -5.8+0.9
= -4.9 N/mm
i i
c tt
P P .e
f = - + y A I
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Stress at level of bottom wires (y= yb = 125 40),
( )
( )3 3
3 8
2
43510 43510 9.5= - - 125 - 40
7510 3.9110
= -5.8- 0.9
= -6.7 N/mm
i ic bb
P P .ef = - - y
A I
Loss of prestress in top wires = mfcAp
(in terms of force) = 6 4.9 (4 38.48)
= 4525.25 N
Loss of prestress in bottom wires = 6 6.7 (5 38.48)
= 7734.48 N
Total loss of prestress = 4525 + 7735
= 12259.73 N
12.3 kN
Percentage loss = (12.3 / 435) 100%
= 2.83%
b) Accurate solution considering transformed section.
Transformed area of top steel,
A1 = (6 1) 4 38.48
= 769.6 mm2
Transformed area of bottom steel,
A2 = (6 1) 5 38.48
= 962.0 mm2
Total area of transformed section,
AT = A + A1 +A2
= 75000.0 + 769.6 + 962.0
= 76731.6 mm2
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Centroid of the section (CGC)
A + A + A y =
A1 2125 (250 - 40) 40
= 124.8 mm from soffit of beam
Moment of inertia of transformed section,IT = Ig+A(0.2)
2 +A1(210 124.8)2 +A2(124.8 40)
2
= 4.02 108mm4
Eccentricity of prestressing force,
e = 124.8 115.5
= 9.3 mm
Stress at the level of bottom wires,3 3
3 8
2
43510 (43510 9.3)84.8= - -
76.7310 4.0210
= -5.67 - 0.85
= -6.52 N/mm
c b(f )
Stress at the level of top wires,
3 3
3 8
2
43510 (43510 9.3)85.2= - +
76.7310 4.0210= -5.67+0.86
= -4.81 N/mm
c t(f )
Loss of prestress in top wires = 6 4.81 (4 38.48)
= 4442 N
Loss of prestress in bottom wires = 6 6.52 (5 38.48)
= 7527 N
Total loss = 4442 + 7527
= 11969 N
12 kN
Percentage loss = (12 / 435) 100%
= 2.75 %
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It can be observed that the accurate and approximate solutions are close. Hence, the
simpler calculations based onA and Iis acceptable.
Pre-tensioned Bending Members
The following figure shows the changes in length and the prestressing force due to
elastic shortening of a pre-tensioned bending member.Pi
wsw (self-weight)
Pi
wsw (self-weight)
Figure 2-1.6 Elastic shortening of a pre-tensioned bending member
Due to the effect of self-weight, the stress in concrete varies along length (Figure 2-1.6).
The loss can be calculated by Eqn. (2-1.1) with a suitable evaluation of the stress in
concrete. To have a conservative estimate of the loss, the maximum stress at the level
of CGS at the mid-span is considered.
(2-1.8)swi ic
M eP Pe.ef = - - +
A I I
Here, Msw is the moment at mid-span due to self-weight. Precise result usingAtand It in
place of A and I, respectively, is not computationally warranted. In the above
expression, the eccentricity of the CGS (e) was assumed to be constant.
For a large member, the calculation of the loss can be refined by evaluating the strain in
concrete at the level of the CGS accurately from the definition of strain. This is
demonstrated later for post-tensioned bending members.
Post-tensioned Axial Members
For more than one tendon, if the tendons are stretched sequentially, there is loss in a
tendon during subsequent stretching of the other tendons. The loss in each tendon can
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be calculated in progressive sequence. Else, an approximation can be used to
calculate the losses.
The loss in the first tendon is evaluated precisely and half of that value is used as an
average loss for all the tendons.
(2-1.9)
p p
c
ni,j
j=
f = f
mf
P= m
A
1
1
2
1
21
=2
1
2
Here,
Pi,j = initial prestressing force in tendonj
n = number of tendons
The eccentricity of individual tendon is neglected.
Post-tensioned Bending Members
The calculation of loss for tendons