Steel used for Prestressing

PRESTRESSED CONCRETE STRUCTURES There are three basic types of high-strength steel commonly used as
tendons in modern prestressed concrete construction
1. (Cold-drawn, stress-relieved ) round wires
2. (Stress-relieved ) strand
3. High-strength alloy steel bars

Dr.Mohamed Ali Round wires

Available sizes of wires vary from country to country, with diameters of 5-7
ali.mohamed@adelaide.edu.au mm being the most often used. The ASTM specification A421 specifies
School of CEME minimum yield strength for wire at 1% extension (strain).

Engg North N234 For design purposes, the yield strength of stress-relieved wires may be taken
as 0.85 times the minimum tensile strength (i.e. 0.85 fp) and the modulus of
LECTURE SLIDES - Loss of Prestress
elasticity of the wires may be taken as Ep= 200 Gpa.
Note: In recent years, the use of wires in prestressed concrete construction
has declined, with 7-wire strand being preferred in most applications.

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Strands Bars
Stress-relieved strand is the most commonly used
prestressing steel. Strand is fabricated from a The high strength of alloy steel bars is also used as prestressing steel. In the USA,
number of prestressing wires, usually seven. both plain and deformed bars are available in two grades (ultimate stress fp= 1000
Seven wire strand consists of six wires tightly and 1100 MPa) with diameters range from 12.7 (1/2 in) mm to 33 mm (1 3/8 in).
wound around a seventh, slightly large diameter,
central wire.

Seven-wire strand is generally available in two

grades, normal and super grade (Grades 250 and
270 in the USA). Diameters ranging from 7.9 to
15.2 mm are typical. Note: The mechanical
properties of the strand
For design purposes, the yield strength of are slightly different from
stress-relieved strand may be taken as 0.85 those of the wire from
times the minimum tensile strength (i.e. 0.85 which it is made. This is
fp) and the modulus of elasticity of the strand because the stranded The elastic modulus for bars is generally lower than those for strand and wire. For
may be taken as Ep= 195 GPa. wires tend to straighten design purposes Ep may be taken to be 170 Gpa and the yield stress (0.2% offset)
slightly when subjected to may be taken to be 0.85 fp.
tension. 3 4
 Losses of Prestress Losses of Prestress (contd.)
Immediate losses Time-dependent losses
Time-dependent losses
Pj Pi Pe Pi Pe
Prestressing force
Jacking Prestressing force
immediately after
force immediately after
transfer
transfer
Time-dependent loss: The gradual loss of prestress that takes place with
Immediate Loss: The difference between the time is called the time-dependent or deferred loss. If Pe is the force in the
prestressing fore imposed at the jack, Pj, and prestressing tendon after all losses, then
the force in the steel immediately after
transfer at a particular section , Pi, is the
Time - dependent loss = Pi − Pe
immediate loss. It is given by
Immediate loss = Pj − Pi CAUSE:
Gradual shortening of the concrete at the steel level due to creep and shrinkage
CAUSES: and by relaxation of the steel itself.
Elastic deformation of the concrete as the prestress is transferred;
Friction along the draped tendon in a post-tensioned member; and
Slip at the anchorage.
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Post-tensioned members:
the most important immediate losses are due to Elastic deformation losses
(a) elastic compression of the concrete during stressing of the
tendons
Pre-tensioned members
(b) friction along the length of the member, between tendon and
duct, during the stressing of the tendon Immediately after transfer, the change in strain in the prestressing steel ∆ε p caused
(c) movement in the grips as the ends of the tendons are anchored by elastic shortening of the concrete is equal to the strain in concrete at the
steel level, εcp. Thus
Pretensioned construction:
duct friction & anchorage slip do not occur σ cp ∆σ p
ε cp= = ∆ε p =
the main immediate loss is due to elastic compression of the Ec Ep
concrete greater than in post-tensioned construction as The loss of stress in steel, ∆σ p , is therefore
transfer takes place at an earlier age. σ cp
deferred losses due to creep and shrinkage : tend to be larger in ∆σ p = ∆ε p E p ⇒ ∆σ p = Ep
Ec
pretensioned members due to early age at transfer.
Ep
⇒ ∆σ p = σ cp
Ec
where σ cp is the concrete stress at the steel level immediately after transfer.
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 POST-TENSIONED MEMBERS
For post-tensioned members with one cable or with two or more cables stressed
simultaneously, the elastic deformation of the concrete occurs during the
stressing operation before the tendons are anchored. In this case, elastic
shortening losses are zero.

In a member containing more than one tendon and where the tendons are
stressed sequentially, the elastic deformation losses vary from tendon to tendon
and are a maximum in the tendon stressed first and a minimum (zero) in the
tendon stressed last.

It is relatively simple to calculate the elastic deformation losses in any tendon

provided the stressing sequence is known. However, these losses are usually
Multi-stage post-tensioning small and , for practical purposes, the average elastic shortening loss is often
taken as half the value obtained from equation:
Ep
∆σ p = 0.5 σ cp
Ec
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Friction along the tendon − µ (α t + β p L pa )

Pa = Pj e
In post-tensioned members, friction losses occur along the tendon during the where
stressing operation. Friction between the tendon and the duct causes a gradual
Pa is the force in the tendon at any point L pa (in meters) from the jacking end.
reduction in prestress with the distance along the tendon Lpa from the jacking
end. Pj is the force in the tendon at the jacking end.
µ is a friction curvature coefficient which depends on the type of duct. Higher values
The magnitude of the friction loss depends on:
should be used if either the tendon or the duct are rusted.
The total angular change of the tendon;
The distance from the jacking point; and αt is the sum in radians of the absolute values of all successive angular deviations of the tendon
The size and type of the sheathing containing the tendons. over the length L pa .
β p is an angular deviation or wobble terms and depends on the sheath (or duct) diameter.
A reliable estimate of friction losses may be obtained from following equation:

− µ (α t + β p L pa )
Pa = Pj e

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 Anchorage Losses
Problem At B : Pa = P j e
− µ (α t + β p L pa )
= Pj e −0.2 ( 0.105+ 0.01×9 ) = 0.962 Pj For most systems of post-tensioning, when a tendon is tensioned to its
Calculate the friction loss in the cable ⇒ i.e. 3.8% losses full value, the jack is released and the prestress is transferred to the
in the end-span of the post-tensioned
At C : Pa = Pj e −0.2 ( 0.210+ 0.01×18) = 0.925Pj anchorage. The anchorage fixtures that are subject to stresses at this
girder shown below. For this cable,
assume µ = 0.2; β p = 0.01 ⇒ i.e.7.5% losses transfer will tend to deform, thus allowing the tendon to slacken
At D : Pa = Pj e −0.2 ( 0.315+ 0.01×25) = 0.893Pj
⇒ i.e.10.7% losses
slightly.
C
A D A general formula for computing the loss of
B
prestress due to anchorage deformation ∆ a is
∆a Ep
9m 9m 7m ∆σ p =
L
Slope, θ: 0.105 0 -0.105 0
αt : 0 0.105 0.210 0.315 Since this loss of prestress is caused by a fixed total amount of
Lpa : 0 9m 18 m 25 m shortening the percentage of loss is higher for short wires than for
long ones. Refer to manufacturer’s specifications.
13 Generally this loss is counterbalanced by slight overstressing. 14

Deferred losses
Loss of prestress due to Relaxation of steel
The loss of stress in the tendon due to relaxation depends on the
sustained stress in the steel. Owing to creep and shrinkage in the
concrete, the stress in the tendon decreases with time at a faster
rate than would occur due to relaxation alone.
Stress relaxation of prestressing tendons
•All prestressing tendons suffer some loss of stress due to
relaxation when held at constant strain over an extended period
of time.
•Some relaxation thus occurs in all tensioned tendons in any
prestressed construction
•it is necessary to estimate the long-term losses and take them
into account in the design calculations.
•Values commonly quoted for relaxation loss are between 2 and
2.5 per cent.
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AS/NZS 4672.1 distinguishes to two grades of materials; Relax 1, at time j days after stressing
formerly referred as normal-relaxation and Relax 2, formally
referred as low-relaxation. The relaxation requirements prestressing
steel to meet the standard are given in Table 2.2 of Warner’s book.
Basic relaxation of a tendon, Rb, measured to occur at a
temperature of 20oC after 1000 hours of a sustained stress of 0.8 of
the characteristic minimum breaking stress, fpb, for strand and 0.7fpb
for stress-relieved wire and steel-alloy (stress) bars.

The design relaxation for low-relaxation wire, low-relaxation

strand, and alloy-steel bars, R, is calculated as:

k4, k5 & k6 -coefficients related to the time over which the

prestressing force acts, the level of stress in the tendon, and the
mean temperature

Creep losses
Time-dependent losses of Prestress
Creep strain in the concrete at the level of the tendon depends on the stress in the
concrete at that level. Because the concrete stress varies with time, a reliable
Shrinkage Losses: estimate of creep losses requires a detailed time analysis. An approximate and
The loss of stress in a tendon due to shrinkage of concrete may be approximated conservative estimate can be made by assuming that the concrete stress at the
by tendon level remains constant with time and equal to its initial (usually high) value,
εcc (caused by Pi and the permanent part of the load)
∆σ p = ε cs E p
With this assumption, the creep strain at any time t after transfer (at age t0 )
where ε cs is the free shrinkage strain at the time under consideration (AS3600). may be calculated from following expression :

Free shrinkage strain in the concrete at any time t after casting can be estimated from
the design shrinkage strain (AS 3600 ). If the tendon is bonded to the concrete, the change of steel
actual field shrinkage will be less than the free shrinkage if any physical restraints act strain caused by creep is equal to ε cc ( t ) and the creep loss in the tendon is
on the concrete such as reinforcing bars and the modified loss as per AS3600 is

Refer Example 9.1 from book

for further lecture.

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