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METHODS AND SYSTEMS OF PRESTRESSING

INTRODUCTION

Prestressed concrete is a concrete that has had internal stresses introduced to counteract the

tensile stresses that will be imposed due to action of service loads. The stress is usually

imposed by tendons of individual hard-drawn wires, cables of hard-drawn wires, or bars of

high strength alloy steel. Prestressing may be achieved either by pretensioning or by post-

tensioning.

PRETENSION CONCRETE

In Pretension concrete the steel is first tensioned in a frame or between anchorages

external to the member. The concrete is then cast around it. After the concrete has developed

sufficient strength, the tension is slowly released from the frame or anchorage to transfer the

stress in to the concrete to which the tendons have by that time become bonded. The force is

transmitted to the concrete over a certain distance from each end of a member known as the

transfer length.

PRE-TENSIONING SYSTEMS

There are general guidelines of prestressing in Section 12 of IS: 1343 – 1980. In pre-

tensioning system, the high strength steel tendons are pulled between two end abutments

(also called bulkheads) prior to the casting of the concrete. The abutments are fixed at the

ends of a prestressing bed. Once the casted concrete attains the desired strength for the

transfer of prestress, the tendons are cut loose from the abutments.

For the pre tensioned members, the prestress is transferred to the concrete from the

tendons, due to the bond at their interface. During the transfer of prestress, the member

undergoes elastic shortening. If the tendons are located eccentrically, the member is likely to

bend and deflect upwards, which is called camber. The prestress is transferred from the steel

to the concrete by the bond at their interface over a certain length, which is called the

transmission length at the ends of the prestressed members.

STAGES OF PRE-TENSIONING OPERATION

The various stages of the pre-tensioning operation are summarized as follows:

1. Anchoring of tendons against the end abutments.

2. Placing of the jacks at the end abutments.

3. Applying tension to the tendons.

4. Casting of the concrete.

5. Curing of Concrete.

6. Cutting the tendons .

ADVANTAGES OF PRETENSIONED CONCRETE

1. Pre-tensioning operation is suitable for precast members produced in bulk where mass

production is necessary.

2. The second advantage is that the pre-tensioning does not need too much of anchorage

device which means that there is an absence of large anchorage device, which is present in

the post-tensioning system.

DISADVANTAGES OF PRE-TENSIONING IN CONCRETE

1. Requirement of prestressing bed.

2. Waiting period in the prestressing bed, before concrete attains sufficient strength.

3.Pre-tensioning requires good bond between the concrete and the steel, to transfer the

prestress from the steel to the concrete.

ESSENTIAL DEVICES USED FOR PRE-TENSIONING

1. Prestressing bed with end abutments

2. The mould or the shuttering

3. The jack

4. The anchoring device

5. The harping device, which can be optional.

HOYER SYSTEM

` An extension of the prestressing 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. As a result there is a increase in the production of the pre-

tensioned members. Shuttering is provided at the sides and between the members. This

system is also called the Long Line Method.

The transfer of prestress to concrete is usually achieved by large hydraulic or screw

jacks by which all the wires arc simultaneously released after the concrete attains the

requisite compressive strength. Generally, strands of up to 18 mm diameter and high-tensile

wires of up to 7 mm diameter anchor themselves satisfactorily with the help of the surface

bond.

The bond of prestressing wires may be considerably improved by forming surface

indentations and by helical crimping of the wires. Strands have considerably better bond

characteristics than plain wires of equal cross-sectional area. Supplementary anchoring

devices are required when single wires of larger diameter (exceeding 7 mm) are used in the

pretensioned units. The most commonly used devices arc the 'Weinberg clip' developed in

France` and the Vorland clip' developed in the United States. These clips are clamped on to

the tensioned wires close to the end diaphragms of the units before concreting operations.

POST TENSION CONCRETE

Post-tensioning is the one where the tension is applied to the tendons after hardening

of the concrete. This is different from pre-tensioning. In pre-tensioning, the tension is applied

first and then the concrete is cast.

PRINCIPLE POST TENSIONING SYSTEMS

In post-tensioning systems, the tendons are placed in ducts after the casting of

concrete. The duct prevents the bond between the concrete and the tendons during the

tensioning operation. This is very essential because, during the tensioning operation if any

resistance is present, then the tension will not be applied properly. The duct ensures that there

is no bond between the concrete and the steel during the tensioning process. In pre-

tensioning, the jacks need an end abutment to get the reaction; but in post-tensioning, no need

of such an end abutment because, the jacks are placed against the concrete member itself

from which it gets the reaction.

After the tensioning operation, if the ducts are grouted then it is known as bonded

post-tensioning. Grout is a neat cement paste or a sand cement mortar containing suitable

admixtures. The grouting is done to prevent the steel tendons from corrosion. After the

grouting, there is a contact between the concrete and the steel through the hardened grout.

Unbonded post-tensioning the ducts are not grouted and the tendon is held in tension

solely by the end anchorages. The purpose of unbonded post-tensioning is that it avoids the

process of grouting. It is usually used for slabs where grouting may be difficult in the small

duct holes.

Post-tensioning systems

The duct can have a curved form, based on the design of the profile of the tendon. The

tendons are attached in one end by some anchorage system and then on the other side, the

tendons are pulled by the jacks.

STAGES OF PRE-TENSIONING OPERATION

The various stages of the post-tensioning operation are 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.

ADVANTAGES OF POST-TENSIONING

The relative advantages of post-tensioning as compared to pre-tensioning are as follows.

1) Post-tensioning is suitable for heavy cast-in-place members.

2) The waiting period in the casting bed is less.

3) The transfer of prestress is independent of transmission length.

DISADVANTAGES OF POST-TENSIONING

The relative disadvantage of post-tensioning as compared to pre-tensioning is the requirement

of anchorage device and grouting equipment. Transporting this anchorage device and the

grouting equipment supply may be a hindrance for a project which is in a remote area.

ESSENTIAL DEVICES USED FOR POST-TENSIONING

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).

ANCHORING DEVICES

Most of the commercially patented prestressing systems are based on the following principles

of anchoring the tendons:

1. Wedge action producing a frictional grip on the wires.

2. Direct bearing from rivet or bolt heads formed at the end of the wires.

3. Looping the wires around the concrete.

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.

Freyssinet System

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.

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.

FREYSSINET SYSTEM OF POST-TENSIONING

The post-tensioning systems based on wedge-action include the Freyssinet, Gifford—

Udall, Anderson and Magnel - Blaton anchorages. The Freyssinet anchorage system, which is

widely used in Europe and India, consists of a cylinder with a conical interior through which

the high-tensile wires pass and against the walls of which the wires are wedged by a conical

plug lined longitudinally with grooves to house the wires.

The main advantage of the Freyssinet system is that a large number of wires or

strands can be simultaneously tensioned using the double-acting hydraulic jack.

GIFFORD-UDALL (C.C.L) SYSTEM

The Gifford-Udall (C.C.L) system developed in U.K. consists of steel split-cone and

cylindrical female-cone anchorages to house the high-tensile wires bearing against steel

plates.

Gifford-Udall system

Each wire is tensioned separately and anchored by forcing a sleeve wedge into a

cylindrical grip resting against a bearing plate. The ducts are generally formed by metal

sheaths cast into the concrete member.

Lee—McCall system

Lee—McCall system

In the Lee—McCall system, the tendons comprise high-tensile bars of diameter

varying from 12 to 40 mm which are threaded at the ends. After tensioning, each bar is

anchored by screwing a nut and washer tightly against the end plates. In this system the

forces are transmitted by the bearing at the end blocks: While the system eliminates the loss

of stress due to anchorage slip, it has a disadvantage in that curved tendons cannot be used.

MAGNEL—BLATON POST-TENSIONING SYSTEM

The Magnel—Blaton post-tensioning system adopts metallic sandwich plates, flat

wedges, and a distribution plate for anchoring the wires. Each sandwich plate can house up to

four pairs of wires. The distribution plate may be cast into the member at the desired location.

The number of wires in the Magnel cable varies from 2 to 64.

Magnel—Blaton post-tensioning system

B.B.R.V. POST-TENSIONING SYSTEM

The B.B.R.V. post-tensioning system was developed in 1949 by four Swiss engineers

Birkenmeier, Brandestini, Ros and Vogt. This system is well suited for transmitting large

forces. B.B.R.V. tendon consists of several parallel lengths of high-tensile wires, with each

end terminating in a cold-formed button head with a machined anchorage fixture. In the case

of tendons formed by strands, they are anchored to the machined fixture by split-cone

sleeves. At present, tendons capable of developing forces up to 12000 kN are available under

this system. For heavy constructions, such as long-span bridges and nuclear containment

vessels, tendons comprising 90 to 170 wires arc commonly used. The B.B.R.V. system

provides for the simultaneous stressing of all the wires in a tendon. After the desired

extension of the tendon is reached, a threaded nut is screwed to the anchor-head, which

transmits the forces by bearing against the end-plate.

FILL IN THE BLANKS

MULTIPLE CHOICE

KEY

FILL IN THE BLANKS

1. Prestressing of concrete

2. Pretensioning

3. Strength

4. Transmission length

5. Tension; Compression

6. Cracking Load

7. Rings

8. Freyssinet

9. Tendon

10. Thermoelectric prestressing

MULTIPLE CHOICE

1) a 2) c 3) c 4)b 5)a

6)b 7)c 8)d 9)b 10)c

UNIT II

LOSSES OF PRESTRESS

2.1 INTRODUCTION

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 initial prestress in concrete undergoes a gradual reduction with time from fix

stage of transfer due to various causes. This is generally referred to as "loss of prestress' . A

reasonably good estimate of the magnitude of loss of prestress is necessary from the point of

view of design.

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.

The different types of losses encountered in the pre-tensioning and post-tensioning systems

are as follows:

Table 2.1 Types of losses of prestress

S.NO PRETENSIONING S.NO POST-TENSIONING

1 Elastic deformation of

concrete 1

No loss due to elastic deformation if all the wires are

simultaneously tensioned. If the wires are

successively tensioned, there will be loss of prestress

due to elastic deformation of concrete

2 Relaxation of stress in

steel 2 Relaxation of stress in steel

3 Shrinkage of concrete 3 Shrinkage of concrete

4 Creep of concrete 4 Creep of concrete

5 Friction

6 Anchorage slip

In addition to the above, there may be losses of prestress due to sudden changes in

temperature, especially in steam curing of pretensioned units. The rise in temperature causes a partial

transfer of prestress (due to the elongation of the tendons between adjacent units in the long-line

process) which may cause a large amount of creep if the concrete is not properly cured. If there is a

possibility of a change of temperature between the times of tensioning and transfer, the corresponding

loss should be allowed for in the design.

2.2 LOSS DUE TO ELASTIC SHORTENING

In pretensioned 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.

In 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 loss of prestress due to elastic deformation of concrete depends on the modular ratio and

the avenge stress in concrete at the level of steel.

fc = Prestress in concrete at the level of steel

Es = Modulus of elasticity of steel.

Ec = Modulus of elasticity of Concrete.

αe = 𝐸𝑠

𝐸𝑐 = Modular ratio

Strain in concrete at the level of steel = fc/ Ec

Stress in steel corresponding to this strain = (fc/ Ec) Es

Loss of stress in Steel = αe fc

If the initial stress in steel is known, the percentage loss of stress in steel due to the elastic

deformation of concrete can be computed.

EXAMPLE 2.2.1

A pretensioned concrete beam, 100 mm wide and 300 mm deep, is prestressed by straight

wires carrying an initial force of 150kN at an eccentricity of 50 mm. The modulus of

elasticity of steel and concrete are 210 and 35 kN/mm2 respectively. Estimate the percentage

loss of stress in steel due to elastic deformation of concrete if the area of steel wires is

188 mm2

EXAMPLE 2.2.2

A rectangular concrete beam, 300 mm deep and 150 mm wide, is prestressed by means of

eight 7 mm diameter high tensile wires located at 100mm mm from the soffit of the beam. If

the wires are initially tensioned to a stress of 1100 N/mm2, calculate the percentage loss of

stress in steel due to elastic deformation of concrete. Assume modulus of elasticity of

concrete and steel as 31.5 and 210 kN/mm2.

EXAMPLE 2.2.3

A post-tensioned concrete beam, l00 mm wide and 300 mm deep, is prestressed by three

cables, each with a cross-sectional area of 50 rnm2 and with an initial stress of 1200N/mm2.

All the three cables are straight and located 100 mm from the soffit of the beam. If the

modular ratio is 6, calculate the loss of stress in the three cables due to elastic deformation of

concrete for only the following cases:

(a) Simultaneous tensioning and anchoring of all the three cables; and

(b) Successive tensioning of the three cables, one at a time.

2.2.1 LOSS OF STRESS DUE TO SUCCESSIVE TENSIONING OF CURVED

CABLES

In most bridge girders, the cables are curved with maximum eccentricity at the centre

of the span. In such cases the loss of stress due to the elastic deformation of concrete is

estimated by considering the average stress in concrete at the level of steel. Consider a beam

shown below, which is post-tensioned by 3 parabolic cables. The stress distribution in

concrete at the level of cable 1 is also shown in the figure when cable 2 is tensioned. For

computing the loss of stress, the average stress (shown in figure) is considered. When cable 3

is tensioned, there will be losses of stress in both cables 1 and 2. This is illustrated in the

following example

.

Fig 2.1 Successive tensioning of curved cables

2.3 LOSS DUE TO SHRINKAGE OF CONCRETE

The shrinkage of concrete in prestressed members results in a shortening of tensioned

wires and hence contributes to the loss of stress. The shrinkage of concrete is influenced by

the type of cement and aggregates and the method of curing used. Use of high-strength

concrete with low water cement ratios results in a reduction in shrinkage and consequent loss

of prestress. The rate of shrinkage is higher at the surface of the members. The differential

shrinkage between the interior and surface of large members may result in strain gradients

leading to surface cracking. Hence, proper curing is essential to prevent shrinkage cracks in

prestressed members.

In the case of pre-tensioned members, generally moist curing is resorted to in order to

prevent shrinkage until the time of transfer. Consequently, the total residual shrinkage strain

will be larger in pretensioned members in comparison with post-tensioned members.This

aspect has been considered in the recommendations made by the Indian standard code (IS:

1343) for the loss of pre-stress due to the shrinkage of concrete and is detailed below.

εcs= total residual shrinkage strain having values of 300 x 106 for pretensioning and

for post tensioning 200𝑋10−6

log10(𝑡+2)

where, t = age of concrete at transfer in days.

This value may be increased by 50 per cent in dry atmospheric conditions, subject to a

maximum value of 300 x 104 units.

The loss of stress in steel due to the shrinkage of concrete is estimated as,

Loss of stress = εcs x Es.

when Es = modulus of elasticity of steel.

EXAMPLE 2.3.1

A concrete beam is prestressed by a cable carrying an initial prestressing force of 300kN. The

cross-sectional area of the wires in the cable is 300 mm2. Calculate the percentage loss of

stress in the cable only due to shrinkage of concrete using IS: 1343 recommendations

assuming the beam to be, (a) pre-tensioned and (b) post-tensioned. Assume Es= 210 kN/mm2

and age of concrete at transfer = 8 days.

2.4 LOSS DUE TO CREEP OF CONCRETE

The sustained prestress in the concrete of a prestressed member results in creep of

concrete which effectively reduces the stress in high-tensile steel.

The various factors influencing creep of concrete are relative humidity, stress level,

strength of the concrete, age of the concrete at loading, duration of stress, water/cement ratio

and the type of cement and aggregate in the concrete. The loss of stress in steel due to creep

of concrete can be estimated if the magnitude of ultimate creep strain or creep coefficient is

known.

I. Ultimate Creep Strain Method

If εcc = ultimate creep strain for a sustained unit stress

fc = compressive stress in concrete at the level of steel

Es= modulus of elasticity of steel

Then the loss of stress in steel due to creep of concrete = εcc fc Es

II. Creep Coefficient Method

If φ = creep coefficient

εc = creep strain

εe = elastic strain

αe = modular ratio

fc = stress in concrete

Ec = modulus of elasticity of concrete

Es = modulus of elasticity of steel

Creep coefficient = Creep strain

Elastic strain

φ = ε𝑐

ε𝑒

∴ εc= φ εe= φ(fc/ Ec)

Hence, loss of stress in steel = εc Ec φ Es = φ(fc/ Ec)Es= φ fc αe

The magnitude of the creep coefficient, φ varies depending upon the humidity, concrete

quality, duration of applied loading and the age of the concrete when loaded. The general

values recommended for the creep coefficient vary from 1.5 for watery situations to 4.0 for

dry conditions with a relative humidity of 35 per cent.

EXAMPLE 2.4.1

A concrete beam of rectangular section 100 mm wide and 300 mm deep, is prestressed by

five wires of 7 mm diameter located at an eccentricity of 50 mm, the initial stress in the wires

being 1200 N/mm2. Estimate the loss of stress in steel due to creep of concrete using the

ultimate creep strain method and the creep coefficient method (IS: 1343-1980). Use the

following data:

EXAMPLE 2.4.2

A post-tensioned concrete beam of rectangular section 100 mm wide and 300 mm deep, is

stressed by a parabolic cable with zero eccentricity at the supports and an eccentricity of

50mm at the centre of span. The area of the cable is 200mm2 and initial stress in the cable is

1200 N/mm2. If the ultimate creep strain is 30 x 10-6 mm/mm per N/mm2 of stress and

modulus of elasticity of steel is 210 mm2, compute the loss of stress in steel only due to creep

of concrete.

2.5 LOSS DUE TO RELAXATION OF STRESS IN STEEL

Most of the codes provide for the loss of stress due to relaxation of steel as a

percentage of the initial stress in steel. The Indian standard code recommends a value varying

from 0 to 90 N/mm2 for stress in wires varying from 0.5fPu to 0.8fPu . The loss of prestress due

to relaxation of steel recommended in British and Indian codes. Temporary over-stressing by

5-10 percent for a period of 2 min is sometimes used to reduce this loss as in the case of

drawn wires.

2.6 LOSS OF STRESS DUE TO FRICTION

In the case of post-tensioned members, the tendons are housed in ducts preformed in

concrete. The ducts are either straight or follow a curved profile depending upon the design

requirements. Consequently, on tensioning the curved tendons, loss of stress occurs in the

post-tensioned members due to friction between the tendons and the surrounding concrete

ducts. The magnitude of this loss is of the following types:

(a) Loss of stress due to the curvature effect, which depends upon the tendon form or

alignment which generally follows a curved profile along the length of the beam.

(b) Loss of stress due to the wobble effect, which depends upon the local deviations in the

alignment of the cable.

The wobble or wave effect is the result of accidental or unavoidable misalignment, since

ducts or sheath cannot be perfectly located to follow a predetermined profile throughout the

length of the beam.

The magnitude of the prestressing force, Px , at a distance x from the tensioning end follows

an exponential function of the type, Px = P0𝑒−(𝛼𝜇+𝑘𝑥)

Fig 2.2 Loss Of Stress Due To Friction

where P0 = prestressing force at the jacking end

μ = coefficient of friction between cable and duct

α = the cumulative angle in radians through which the tangent to the cable

prank has turned between any two points under consideration

K = friction coefficient for 'wave' effect

e = 2.7183

The Indian standard code recommends the following values for μ and K.

Values for the coefficient of friction μ

0.55 for steel moving on smooth concrete

0.35 for steel moving on steel fixed to duct

0.25 for steel moving on steel fixed to concrete

0.25 for steel moving on lead

0.18-0.30 for multi-layer wire rope cables in rigid rectangular steel sheaths

0.15-0.25 for multi-layer wire rope cables with spacer plates providing lateral separation

These recommendations are based on the experimental work done by Guyon and Cooley.

Values for the friction coefficient for wave effect K

0.15 per 100 m for normal conditions

1.5 per 100 m for thin-walled ducts and where heavy vibrations are encountered and in other

adverse conditions.

The coefficient may be reduced to zero where the clearance between the duct and cable is

sufficiently large to eliminate the 'wave' effect.

Frictional losses can be reduced by several methods, such as

(a) over tensioning the tendons by an amount equal to the maximum frictional loss, and

(b) jacking the tendons from both ends of the beam, generally adopted when the tendons are

long or when the angles of bending are large.

EXAMPLE 2.6.1

A concrete beam of 10 m span, 100 mm wide and 300 mm deep, is prestressed by 3 cables.

The area of each cable is 200 mm2 and the initial stress in the cable is 1200 N/mm2. Cable I is

parabolic with an eccentricity of 50 mm above the centroid at the supports and 50 mm below

at the centre of span. Cable 2 is also parabolic with zero eccentricity at supports and 50 mm

below the centroid at the centre of span. Cable 3 is straight with uniform eccentricity of 50

ram below the centroid. If the cables are tensioned from one end only, estimate the

percentage loss of stress in each cable due to friction. Assume μ= 0.35 and K = 0.0015 per m.

Equation of a parabola is given by:

y = (4e/L2)x(L-x)

EXAMPLE 2.6.2

A cylindrical concrete tank. 40 m external diameter, is to be prestressed circumferentially by

means of a high-strength steel wire (E, = 210 kN/mm2) jacked at 4 points, 90 degrees apart. If

the minimum stress in the wires immediately after tensioning is to be 600 N/mm2 and the

coefficient of friction is 0.5, calculate

(a) the maximum stress to be applied to the wires at the jack, and

(b) the expected extension at the jack.

The prestressing force at the farther end, Px is related to the force at the jacking end, Po by the

expression

2.7 LOSS DUE TO ANCHORAGE SLIP

In most post-tensioning systems, when the cable is tensioned and the jack is released

to transfer prestress to concrete, the friction wedges, employed to grip the wires, slip over a

small distance before the wires are firmly housed between the wedges. The magnitude of slip

depends upon the type of wedge and the stress in the wires. In systems where the tendons are

looped around concrete anchorage blocks, loss of stress may take place due to the wires

biting into the anchorage

The magnitude of the loss of stress due to the slip in anchorage is computed as

follows:

If Δ = slip of anchorage, mm

L = length of the cable, mm

A = cross-sectional area of the cable, mm2

Es = modulus of elasticity of steel, N/mm2

P = Prestressing forte in the cable, N

Then, PL

AEs, = Δ

Loss of stress due to anchorage slip = P

A =

ΔEs

L

Since the loss of stress is caused by a definite total amount of shortening, the percentage loss

is higher for short members than for long ones.

EXAMPLE 2.7.1

A concrete beam is post-tensioned by a cable carrying an initial stress of 1000 N/mm2. The

slip at the jacking end was observed to be 5 mm. The modulus of elasticity of steel is

210 kN/mm2. Estimate the percentage loss of stress due to anchorage slip if the length of the

beam is (a) 30 m (b) 3 m.

FILL IN THE BLANKS

MULTIPLE CHOICE

KEY

FILL IN THE BLANKS

11) Shortening of concrete

12) Shrinkage of concrete

13) Deformation

14) Creep coefficient

15) Relaxation of stress

16) Anchorage slip

17) Post-tensioned

18) Percentage of creep

19) profile of cable

20)Trapezoidal

MULTIPLE CHOICE

11) d 12)c 13)b 14)d 15)c

16)a 17)b 18)c 19)a 20)c