CURSO NPTEL - Civil Engineering - Pre-Stressed Concrete Structures

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 bands Metal 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.

Spokes

Spokes

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

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.

Original length of steel rod (

L

Original length of concrete beam (

L

L

Original length of concrete beam (

L

Reduced length of concrete beam (

L

)

Reduced length of concrete beam (

L

)

b) Beam at transfer of prestress Final length of prestressed beam (

L

L

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 strains corresponding 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 / 2×105 MPa = 0.0007

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 strength 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 Jackson, 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)

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 wires around 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.

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.

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.

Compression (C) Tension (T) C and T

Stones, Bricks Bamboo, Ropes Timber

Structural steel Steel bars, wires

Reinforced Concrete Prestressed Concrete Passive combination High Strength Steel High Strength Concrete Active combination Concrete

Compression (C) Tension (T) C and T

Stones, Bricks Bamboo, Ropes Timber

Structural steel Steel bars, wires

Reinforced Concrete Prestressed Concrete Passive combination High Strength Steel High Strength Concrete Active combination Concrete

Figure 1-1.9 Development of building materials (Reference: Lin, T. Y. and Burns, N. H.,

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.

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 Loading

The 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

¾ Reduction of steel corrosion

• Increase in durability.

¾ Full section is utilised

• Higher moment of inertia (higher stiffness)

¾ Increase in shear capacity.

¾ Suitable for use in pressure vessels, liquid retaining structures.

¾ 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.

Double T-section T-section

Hollow core _Piles

Double T-section Double T-section T-section

T-section

Hollow core _Piles

L-section Inverted T-section _I-girders L-section Inverted T-section _I-girders

Figure 1-2.1 Typical precast members

1.2.3 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.

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.

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 the concrete 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.

Electrical Prestressing

In this type of prestressing, the steel wires are electrically heated and anchored before placing concrete in the moulds. This type of prestressing is also known as thermo-electric prestressing.

External or Internal Prestressing External Prestressing

When the prestressing is achieved by elements located outside the concrete, it is called external prestressing. The tendons can lie outside the member (for example in I-girders or walls) or inside the hollow space of a box girder. This technique is adopted in bridges and strengthening of buildings. In the following figure, the box girder of a bridge is prestressed with tendons that lie outside the concrete.

Figure 1-2.2 External prestressing of a box girder (Reference: VSL International Ltd.)

Internal Prestressing

When the prestressing is achieved by elements located inside the concrete member (commonly, by embedded tendons), it is called internal prestressing. Most of the applications of prestressing are internal prestressing. In the following figure, concrete will be cast around the ducts for placing the tendons.

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

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-“Pre-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.

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 Power Station, Karnataka

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 Prestressing

When 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 for prestressing tendon Non-prestressed reinforcement Duct for prestressing tendon Non-prestressed reinforcement

Figure 1-2.8 Biaxial prestressing of a slab (Courtesy: VSL India Pvt. Ltd., Chennai)

Multiaxial Prestressing

When the prestressing tendons are parallel to more than two axes, it is called Multiaxial Prestressing. For example, prestressing of domes.

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 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 of IS: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.

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 jacks

3) 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 End abutment Jack Prestressing bed Steel tendon End abutment Jack

(a) Applying tension to tendons

(b) Casting of concrete

Cutting of tendon Cutting 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.

• In pre-tensioning large anchorage device is not present.

1.3.4 Disadvantages 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

• Jack

• Anchoring device

• Harping device (optional)

Prestressing Bed, End Abutments and Mould

The following figure shows the devices.

Prestressing bed Mould End abutment Jack Anchoring device Prestressing bed Mould End abutment Jack Anchoring device Prestressing bed Mould End abutment Jack Anchoring device

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

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 bodies Plan or Elevation Test specimen High strength steel rods Loading jack P Free bodies P Free bodies Plan or Elevation Test specimen High strength steel rods Loading jack Plan or Elevation Test specimen High strength steel 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 a stress bench.

Jack Threaded rod Elevation Plan Mould Strands Jack Threaded rod Elevation Jack Threaded rod Elevation 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 in strands Plan Load by jack Tension in strands

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

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 Pascal’s 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

Anchoring 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.

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 concrete a) Before casting of concrete

b) After casting of concrete b) 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.

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.

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.

Wedge and cylinder assembly at the dead end Wedge and cylinder assembly at the dead end

(b) Anchoring of strands Hydraulic jack at stretching end Initial gap End plate Hydraulic jack at stretching end Initial gap End plate (c) Stretching of strands

Extension of ram Final gap Threaded rod Extension of ram Final gap Threaded rod (d) Stretching of strands Coarse aggregate Fine aggregate Coarse aggregate Fine aggregate

Automated

batching

by weight

Automated

batching

by weight

(h) Concrete after vibration of mould

(j) Cutting of strands

(l) Stacking of sleeper

(n) Storage and dispatching of sleepers

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 of IS 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.

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 and the 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)

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.

Casting bed Duct Side view Casting bed Duct Side view (a) Casting of concrete

Jack

Jack

Anchor

Anchor

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

4) Anchoring devices 5) Jacks

6) Couplers (optional)

7) Grouting equipment (optional).

Casting Bed, Mould and Ducts

The following figure shows the devices.

Casting bed Mould Duct Casting bed Mould Duct

Figure 1-4.5 Casting bed, mould and duct

Anchoring 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.

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)

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.

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.

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)

Jacks

The 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.

Figure 1-4.14 Jacking 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 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)

Figure 1-4.16 Couplers for strands (Reference: Dywidag – Systems International)

Figure 1-4.17 Couplers for strands (Reference: Dywidag – Systems International)

Grouting

Grouting 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 of about 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.

(a) Fabrication of reinforcement

(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.

(b) Formwork for box girder

(d) Transporting of box girder

(e) Completed bridge

1.5 Concrete (Part I)

This section covers the following topics. • Constituents of Concrete

• Properties of Hardened Concrete (Part I)

1.5.1 Constituents 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.

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 texture

2) 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 - 1600ºC. 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.

Water

The water should satisfy the requirements of Section 5.4 of IS: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 ash

2) Ground granulated blast-furnace slag 3) Silica fumes

4) Rice husk ash 5) Metakoline

These are cementitious and pozzolanic materials.

1.5.2 Properties 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

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 concrete 5) 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 the test 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 of fck is lower than fcm by 1.65σ, where σ is the standard deviation of the

f_ck f_cm

1.65σ Frequency

28 day cube compressive strength

5% area fck fcm

1.65σ 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.

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 =0.7 f (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

(εc) 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.

ε_c f_c f_ck E_c f_c ε_c f_c f_ck E_c ε_c f_c f_ck E_c f_c f_c

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 c

E =5000 f_k (1-5.2) Here,

Ec = short-term static modulus of elasticity in N/mm2

The above expression is updated as per IS:456 - 2000.

Durability of Concrete

The durability of concrete is of vital importance regarding the life cycle cost of a structure. The life cycle cost includes not only the initial cost of the materials and labour, but also the cost of maintenance and repair.

In recent years emphasis has been laid on the durability issues of concrete. This is reflected in the enhanced section on durability (Section 8) in IS:456 - 2000. It is expected that the revised version of IS:1343 will also have similar importance on durability.

The durability of concrete is defined as its ability to resist weathering action, chemical attack, abrasion, or any other process of deterioration. The common durability problems in concrete are as follows.

1) Sulphate and other chemical attacks of concrete. 2) Alkali-aggregate reaction.

3) Freezing and thawing damage in cold regions. 4) Corrosion of steel bars or tendons.

The durability of concrete is intrinsically related to its water tightness or permeability. Hence, the concrete should have low permeability and there should be adequate cover to reinforcing bars. The selection of proper materials and good quality control are essential for durability of concrete.

The durability is addressed in IS:1343 - 1980 in Section 7. In Appendix A there are guidelines on durability. Table 9 specifies the maximum water-to-cement (w-c) ratio and the minimum cement content for different exposure conditions. The values for moderate exposure condition are reproduced below.

Table 1-5.1 Maximum water-to-cement (w-c) ratio and the minimum cement content for moderate exposure conditions (IS:1343 - 1980).

Min. cement content : 300 kg per m3 of concrete

Max w-c ratio* : 0.50

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.

Figure 1-5.4 End-blocks in a bridge deck (Courtesy: Cochin Port Trust, Kerala)

Allowable 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 0.51f_ci 0.44f_ci 0.54f_ci 0.37f_ci Post-tension Pre-tension M30 M60 M40 M60 0.51f_ci 0.44f_ci 0.54f_ci 0.37f_ci 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.

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 2

3 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.

1.6 Concrete (Part II)

This section covers the following topics.

• Properties of Hardened Concrete (Part II) • Properties of Grout

• Codal Provisions of Concrete

1.6.1 Properties 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).

ε_c ε₀ ε_cu f_c f_ck f_c ε_c ε₀ ε_cu f_c f_ck ε_c ε₀ ε_cu f_c f_ck f_c f_c

Figure 1-6.1 a) Concrete cube under compression, b) Design stress-strain curve for concrete under compression due to flexure

The equation for the design curve under compression due to flexure is as follows. For εc ≤ ε0 ⎡ _{⎛ ⎞ ⎛ ⎞} ⎤ ⎢ _{⎜ ⎟ ⎜ ⎟} ⎥ ⎝ ⎠ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦ c c ck ck ε ε f = f -ε ε 2 0 0 2 _(1-6.1) For εc < εc ≤ εcu fc = fck (1-6.2) Here, fc = compressive stress

fck = characteristic compressive strength of cubes

εc = compressive strain

ε0 = strain corresponding to fck = 0.002

εcu = 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 γm =

1.5. The design curve is used in the calculation of ultimate strength. The following sketch shows the two curves.

ε₀ ε_cu ε_c f_c f_ck 0.447f_ck Characteristic curve Design curve ε₀ ε_cu ε_c f_c f_ck 0.447f_ck 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 = Ecεc (1-6.3)

Note that, the size factor and the material safety factor are not used in the elastic modulus Ec.

For high strength concrete (say M100 grade of concrete and above) under uniaxial compression, the ascending and descending branches are steep.

ε

ε

f

f

E

E

ε

ε

f

f

E

E

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 ε n ε f = f ε n - + ε 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

εc = compressive strain

ε0 = strain corresponding to fck

k = 1 for εc ≤ ε0

= 0.67 + (fck / 77.5) for εc > ε0. The value of k should be greater than 1. n = Eci / (Eci – Es)

Eci = initial modulus

Es = secant modulus at fck = fck / ε0.

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 ε0 can be

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.

f

ε

f

f

ε

f

ε

f

f

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 behaviour fc = Ecεc 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).

ε_c f_c Fast loading Slow loading Effect of creep ε_c f_c Fast 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 θ.

For stress in concrete less than about one-third of the characteristic strength, the ultimate creep strain is given as follows.

cr,ult el

ε = θε (1-6.5)

The variation of strain with time, under constant axial compressive stress, is represented in the following figure.

st

ra

in

Time (linear scale) ε_{cr, ult}= ultimate creep strain

ε_el= elastic strain

st

ra

in

Time (linear scale) ε_{cr, ult}= ultimate creep strain

ε_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).

strain

Time (linear scale)

Residual strain Creep recovery Elastic recovery Unloading

strain

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 entrainment

4) 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 θ is provided for three values of age of loading.

Table 1-6.1 Creep coefficient θ for three values of age of loading

Age of Loading Creep Coefficient

7 days 2.2

28 days 1.6

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 (εsh) is estimated to calculate the loss in prestress.

Sh

rinkag

e strain

t₀

_{Time (linear scale)}

ε

Sh

rinkag

e strain

t₀

_{Time (linear scale)}

ε