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Prestressed Concrete Structures

Module 1

Introduction, Prestressing Systems and Material Properties

Prepared by:Amlan K Sengupta

Devdas Menon

Indian Institute of Technology Madras

Prestressing SteelIntroduction Forms

Module 1-g (7th Hour)

Forms Types

Properties of Prestressing SteelStrength and StiffnessStress-Strain Curves

Relaxation of SteelFatigue Durability

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Introduction

The development of prestressed concrete was

Material Properties

The development of prestressed concrete was influenced by the invention of high strength steel. It is an alloy of iron, carbon, manganese and optional materials. The following material describes the types and properties of prestressing steel.

Th ti f t l f t dThe properties of steel for non-prestressedreinforcement is not covered.

Forms of Prestressing Steel

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Wires Prestressing wire is a single unit made of

Material Properties

Wires Prestressing wire is a single unit made of steel. The nominal diameters of the wires are 2.5, 3.0, 4.0, 5.0, 7.0 and 8.0 mm.

The different types of wires are as follows.

1) Plain wire: No indentations on the surface.

2) Indented wire: There are circular or elliptical indentations on the surface.

Material Properties

Pitch


Elliptical indentations

Circular indentations

Examples of indented wires

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Strands A few wires are spun together in a helical form

Material Properties

to form a prestressing strand. The different types of strands are as follows.

1) Two-wire strand:

2) Three wire strand:2) Three-wire strand:

3) Seven-wire strand: The central wire

is larger than the six wires which are spun

around it.


Tendons A group of strands or wires are placed

Material Properties

Tendons A group of strands or wires are placed together to form a prestressing tendon.

Duct

Grout

Fig 1g-1 Cross-section of a tendon

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Material Properties

Cables A group of tendons form a prestressingcable.

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 Bars are available in thethan that of a wire. Bars are available in the

following sizes: 10, 12, 16, 20, 22, 25, 28 and

32 mm.

Reinforcing barsPrestressing wire, strands and bar

Fig 1g-1 Forms of reinforcing and prestressing steel

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Indented wire

Fig 1g-1 Forms of reinforcing and prestressing steel (contd.)

Types of Prestressing Steel

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Material Properties


The steel is treated to achieve the desired properties. The following are the treatment processes.

Cold working (cold drawing)

This process is done by rolling the bars through a p y g gseries of dyes. It re-aligns the crystals and increases the strength.

Material Properties


Stress relievingStress relieving

This process is done by heating the strand to about 350º C and cooling slowly.

Strain tempering for low relaxationThis process is done by heating the strand to aboutThis process is done by heating the strand to about 350º C while it is under tension.

The last two processes improve the stress-strain behaviour of the steel.

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IS 1343: 2012 specifies the material properties in

Material Properties

p p pSection 5.6. The following types of steel are allowed.

Plain cold drawn stress relieved wire conforming to IS:1785, Part 1

Indented cold drawn wire conforming to IS:6003 High tensile steel bar conforming to IS:2090 High tensile steel bar conforming to IS:2090 Uncoated stress relieved strand conforming to IS:6006 Uncoated stress relieved low-relaxation strand

conforming to IS:14268.

Properties of Prestressing Steel

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Properties of Prestressing Steel

The prestressing steel requires the following properties

Material Properties

The prestressing steel requires the following properties.

High strength and high elastic range

Adequate ductility

Bendability, required at harping points and at ends

High bond required for pre-tensioned members High bond, required for pre-tensioned members

Low relaxation to reduce losses

Minimum corrosion

Good resistance to fatigue.

Strength of Prestressing Steel

The tensile strength of prestressing steel is given in

Material Properties

The tensile strength of prestressing steel is given in terms of the characteristic tensile strength ( fpk ).

The characteristic strength is defined as the ultimatetensile strength of the coupon specimens below which not more than 5% of the test results are expected to fall.

The ultimate tensile strength of a coupon specimen is determined by a testing machine according to IS:1608. The following figure shows a test setup.

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Wedge grips

Extensometer

Coupon specimen

Fig 1g-2 Tensile strength testing for prestressing strand (Courtesy: Indian Institute of Technology Madras)

Fig 1g-3 Failure of a prestressing strand(Courtesy: Indian Institute of Technology Madras)

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Material Properties

Nominal Diameter (mm)

2.50 3.00 4.00 5.00 7.00 8.00

Minimum Tensile Strength

2010 1865 1715 1570 1470 1375

Table 1g-1 Cold Drawn Stress-Relieved Wires (IS: 1785 Part 1)

Tensile Strength fpk (N/mm2)

The proof stress (defined later) should not be less than 85% of the specified tensile strength.


Table 1g-2 Indented wire (IS: 6003)

Material Properties

Nominal Diameter (mm)

3.00 4.00 5.00

Minimum Tensile Strength fpk

(N/mm2)

1865 1715 1570

(N/mm2)

The proof stress should not be less than 85% of the specified tensile strength.

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Material Properties

High Tensile Steel Bars (IS: 2090)

The minimum tensile strength is 980 N/mm2. The proof stress should not be less than 80% of the specified tensile strength.

Stiffness of Prestressing Steel

The stiffness of prestressing steel is given by the initial

Material Properties

modulus of elasticity. The modulus of elasticity depends on the form of prestressing steel (wires or strands or bars).

fpfp

Ep

εp

εp

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Allowable Stress in Prestressing Steel

Material Properties

As per Clause 18.5.1, the maximum tensile stress during prestressing (fpi) shall not exceed 76% of the characteristic strength.

pkpi ff 0.76 (1g-1)

There is no upper limit for the stress at transfer (after short term losses) or for the effective prestress (after long term losses).

Stress-Strain Curves for Prestressing Steel

Material Properties

The stress versus strain behaviour of prestressingsteel under uniaxial tension is initially linear (stress is proportional to strain) and elastic (strain is recovered at unloading).

Beyond about 70% of the ultimate strength the behaviour becomes nonlinear and inelastic. There is no defined yield point.

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The yield point is defined in terms of the proof stress or a

Material Properties

specified yield strain. IS 1343:2012 recommends the yield point at 0.2% proof stress. This stress corresponds to an inelastic strain of 0.002.

Proof

fp

0.002

stress

εp


The characteristic stress-strain curve is given in Figure 5of IS 1343:2012. The stress corresponding to a strain can be found out by using this curve

Material Properties

be found out by using this curve.

0.95fpk

0.9fpk

fp

0.002 0.005 εpStress relievedstrands and bars

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The stress-strain curves are influenced by the treatment

Material Properties

processes. The following figure shows the variation in the 0.2% proof stress for wires under different treatment processes.

Low relaxation

Stress relieved

fp

Stress relievedAs-drawn(untreated)

εp


The design stress-strain curves are calculated by

Material Properties

The design stress strain curves are calculated by dividing the stress beyond 0.8fpk by a material safety factor m = 1.15.

0.8f k

fp

Characteristic curve

0.8fpk

εp

Design curve

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A generalised equation uses the RambergOsgood

Material Properties

function.

(1g-2)

A1

fp

AEp

k

CCp

ppp

f

Bε

AAεEf

1

1

1

p

AE

B

1-( )

Ep

εp

p

Governed by C

pkf


Material Properties

For low relaxation strands A = 0 025 B = 118 C = 10For low-relaxation strands, A = 0.025, B = 118, C = 10For stress-relieved strands, A = 0.03, B = 121, C = 6

Reference: Collins, M. P. and Mitchell, D.,

Prestressed Concrete Structures

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Relaxation of Steel

Relaxation of Steel

Material Properties

Relaxation of steel is defined as the decrease in stress with time under constant strain. Due to the relaxation of steel, the prestress in the tendon is reduced with time. Hence, the study of relaxation is important in prestressed concrete to calculate the loss in prestress.

The relaxation depends on the type of steel, initial prestress and the temperature.

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Relaxation of Steel

Material Properties

fp

Fast loading

With sustained loadingEffect of relaxation

εp

Relaxation of Steel

The following figure shows the variation of stress with time for different levels of prestressing.

Material Properties

p g

100

90

80

70

fp

fpi

py

pi

f

f0.60.70.80 9

60

5010 100 1000 10,000 100,000

Time (hours)

0.9

Reference: Collins, M. P. and Mitchell, D., Prestressed Concrete Structures

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Relaxation of Steel

Material Properties

It can be observed that there is significant relaxation loss when the applied stress is more than 70% of the characteristic tensile strength.

Load cell

Specimen

Fig 1g-4 Relaxation test of a single wire strand(Courtesy: Indian Institute of Technology Madras)

Load cell

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Specimen

Fig 1g-5 Relaxation test of a seven-wire strand(Courtesy: Indian Institute of Technology Madras)

Relaxation of Steel

The upper limits of relaxation loss are specified as follows.

Material Properties

Cold drawn stress-relieved wires

5% of initial prestress

Indented wires 5% of initial

Table 1g-3 Relaxation losses at 1000 hours (IS: 1785, IS: 6003, IS: 6006, IS: 2090)

Indented wires 5% of initial prestress

Stress-relieved strand

5% of initial prestress

Bars 49 N/mm2

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Relaxation of Steel

In absence of test data, IS 1343:2012 recommends the following estimates of relaxation losses For long-term

Material Properties

following estimates of relaxation losses. For long-term loss, the values are multiplied by 3.0.

Initial Stress

Relaxation Loss (%)Regular strands Low relaxation

d

Table 1g-4 Relaxation losses at 1000 hours at 202°C

strands

0.5fpk 0 0

0.6fpk 3.0 1.0

0.7fpk 5.0 2.5

0.8fpk 8.0 4.5

Relaxation of Steel

The following equation provides an estimate of the drop

Material Properties

The following equation provides an estimate of the drop in stress with time under normal temperature.

(1g-3)

0.55

log1

py

pipip f

f

K

tftf

Type KStress-relieved 7Low-relaxation 30

Reference:AASHTO LRFD Bridge Design Specifications

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Relaxation of Steel

The following figure shows the effect of temperature schematically

Material Properties

schematically.

1

0.9

0.8fp

f

Temperature

0.7

0.6

0.5Time

fpi

Fatigue

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Fatigue

Under repeated dynamic loads the strength of a member

Material Properties

Under repeated dynamic loads the strength of a member may reduce with the number of cycles of applied load. The reduction in strength is referred to as fatigue.

Fatigue tests are conducted to develop the stress range (S) versus number of cycles for failure (N) diagram.

Under a limiting value of stress range, the specimen can withstand infinite number of cycles. This limit is known as the endurance limit.

Fatigue

S-N Diagram for prestressing tendons

Material Properties

0 50.5

0.4

0.3

0.2

0.1

fp

fpu

Endurance

0.0103 104 105 106 107

Number of cycles (log scale)

Endurance Limit

Reference: Naaman, A. E., Prestressed Concrete Analysis and Design

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Fatigue

S-N Relationship for prestressing tendons

Material Properties

(1g-4)0.87log0.123 Nf

∆f

pu

p

Reference: Naaman, A. E., Prestressed Concrete Analysis and Design

Fatigue

Material Properties

In prestressed applications, the fatigue is negligible in members that do not crack under service loads. If a member cracks, fatigue may be a concern due to the following reasons.

1) High stress in the steel at the location of cracks1) High stress in the steel at the location of cracks

2) Effect of fretting (wearing due to contact of strands

under motion)

3) Stress corrosion.

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Fatigue

Material Properties

The prestressed member is designed such that the fluctuating stress range in the steel under service loads remain under the specified endurance limit.

Specimens are tested under 2 x 106 cycles of load to observe any effect of fatigueobserve any effect of fatigue.

Fig 1g-6 Fatigue testing setup for railsleeper fastening (Courtesy: Indian Institute of Technology Madras)

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Durability

Durability

Material Properties

Corrosion of bars in concrete structures occurs due to the breakdown of the passive alkaline film, in presence of moisture and oxygen, under the effect of the following.

1) Diffusion of chloride ions1) Diffusion of chloride ions

2) Carbonation of concrete

Pitting corrosion is more severe in prestressed strands because of the smaller diameter.

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Durability

Material Properties

In addition, prestressing steel is susceptible to the following in aggressive environments.

1) Stress corrosion

2) Hydrogen embrittlement

Hence, prestressing strands needs to be adequately protected.

Durability

Material Properties

For bonded post-tensioned tendons, the alkaline environment of the grout provides adequate protection. However, if the grout has voids or develops void with time, then the strands are susceptible to corrosion.

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Durability

Material Properties

For unbonded tendons, corrosion protection is provided by one or more of the following methods (Cl. 12.1.5.1).

1) Epoxy coating of strands

2) Mastic wrap (grease impregnated tape) around strands

3) G l i d d3) Galvanized strands

4) Non-corroding sheathing duct (HDPE or FRP duct)

5) Anchorages covered by casing

6) Encasing of strands in tubes (for external prestressing).

Codal Provisions

Material Properties

The following topics are covered in IS 1343:2012 under the respective sections. These provisions are not duplicated here.

Assembly of prestressing and reinforcing steel: Section 12

SPrestressing: Section 13

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Prestressing SteelIntroduction Forms

Summary

Forms Types

Properties of Prestressing SteelStrength and StiffnessStress-Strain Curves

Relaxation of SteelFatigue Durability

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