Losses of Prestress
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Losses of Prestress
Transcript of Losses of Prestress
Losses of Prestress
Introduction
The force applied to the tendon is measured by the pressure
gauge mounted on the hydraulic jack and is known as the
jacking force, Pi.
However, this force cannot entirely be transmitted to the
concrete because some losses of prestress occur duirng the
process of stretching and anchoring the tendons.
There are several factors which cause the force in prestressing
tendons to fall from the initial force imparted by the jacking
system
Introduction
The fraction of the jacking force that is eventually transferred
to the concrete after releasing the temporary anchor of
withdrawal of the hydraulic jack is the Pi.
This force also keeps on decreasing with time due to time-
dependent response of constituent materials; steel and
concrete and reduced to a final value known as effective
prestressing force, Pi.
Prestress
losses Short term
(immediate)
e.g. elastic
shortening,
anchorage draw
in, friction
Long term
(time
dependent ) e.g.
concrete
shrinkage &
creep, steel
relaxation
Types of losses
Pretensioning Post-tensioning
1. Elastic shortening
Short term losses
1. No loss due to elastic
shortening if all the
wires are
simultaneously
tensioned. If the wires
are successively
tensioned in stages
there will be loss of
prestress due to
elastic shortening
2. Anchorage slip
3. Friction
2. Creep of concrete
3. Shrinkage of concrete
4. Relaxation of stress in
steel
Long term losses
4. Creep of concrete
5. Shrinkage of concrete
6. Relaxation of stress in
steel
Losses in pre-tensioning
During the process of anchoring, the stressed tendon tends to slip before the full grip is established, thus losing some of its imposed strain or in other words, induced stress. This is known as loss due to anchorage draw-in
From the time the tendons are anchored until transferof prestressing force to the concrte, the tendons are held between the two abutments at a constant length. The stretched tendons during this time interval will lose some of its induced stress due to the phenomenon known as relaxation of steel.
As soon as the tendons are cut, the stretched tendons tend to go back to their original state, but are prevented from doing so by the interfacial bond developed between the concreye and the tendons.
Losses in pre-tensioning
The concrete will therefore be subjected to a compressive force, which results in an instantaneous shortening of the member. Since the tendons are bonded to the concrete, they will lose an equal amount of deformation, meaning a reduction of induced stress. This is known as loss due to elastic deformation.
Subsequent to the transfer of prestress, concrete keeps on shrinking due to the loss of free water and continues shortening under sustained stress, thus resulting in a loss of tension in the embedded tendon. These are known as loss due to shrinkage and loss due to creep respectively.
Also, loss due to relaxation of steel continues
After a long period a final value is reached i.e. Pe = Pi
Losses in pre-tensioning
Losses in post-tensioning
The tendons are located inside ducts, and the hydraulic jackis
held directly against the member.During stressing operation,
the tendons tend to get straightened and slide against the duct,
thus resulting in the development of a frictional resistance. As
a result, the stress in the tendon at a distance away from the
jacking end will be smaller than that indicated by the pressure
gauge mounted on the jack. This is known as loss due to
friction.
With regard to elastic shortening, there will be no loss of
prestress if all the tendons are stressed simultaneously because
the prestress gauge records the applied stress after the
shortening has taken place.
Losses in post-tensioning
However, if they are tensioned one after another in sequence,
all tendons except the last one, will lose stress due to elastic
shortening of concrete caused by forces in the subsequent
tendons.
Once the stressed tendons are anchored, the time-dependent
losses caused by shrinkage and creep of concrete and
relaxation of steel begin.
Losses in post-tensioning
Loss due to elastic shortening
The loss of elastic shortening depends on the stress in
concrete at the level of tendon, σcg and modular ratio, m
The loss of prestress due to elastic shortening, σp is
reduction of stress in the tendons due to elastic shortening of
the concrete to which they are bonded
For a post tensioned member the change in strain in the
tendons just after transfer can be assumed to be equal to the
strain in the concrete at the same level even though the ducts
have not been grouted and there is no bond between steel
and concrete.
The loss due to elastic shortening is given by expression below:
where
σp = loss of prestress due to elastic shortening m = modular ratio
σcg = stress in concrete at the level of tendon
σpo = initial stress in the tendons
e = eccentricity of tendon
MD = bending moment due to selfweight
r = radius of gyration of section
Ac = area of concrete cross section
Ap = area of steel tendon
Since MD and e
varies along the
span, so σcg also
varies
Use average σcg
For a post-tensioned member, where all the tendons are
stressed simultaneously , σp = 0
For a post-tensioned member, where the tendons are
stressed sequentially, σp = 0.5mσcg
For pre-tensioned member, σp = mσcg
Example Determine the loss of prestress force due to elastic shortening
for a simply supported post-tensioned prestressed (the tendons
are stressed sequentially)beam with the following information:
Span, L = 20m
Selfweight, Wsw = 9.97 kN/m
Ac = 4.23x105 mm2
Ic = 9.36 x 1010mm4
m = 7.5
σpo = 1239 N/mm2
Ap = 2850 mm2
e at mid span = 580 mm
e at supports = 0 mm
Solution
At midspan :
At the supports
No bending moment at the supports and e = 0, so
Since the structure is postensioned member with tendons are
stressed sequentially, therefore;
Loss of prestress =
Friction
In post-tensioned members there is friction between the
prestressing tendons and the ducts during tensioning.
There are two basic mechanism which produce friction:
a) Curvature friction – the curvature of the tendons to achieve
a desire profile (occur due to intended curvature of the
cable path)
b) Wobble friction – inevitable, due to unintentional deviation
between the centre lines of the tendon and the ducts.
The expression for the force in a tendon due to both curvature and wobble effects is given by :
Where
x = distance from start of curvature
Po = initial force in tendons
P(x) = tendon force at distance x from the start of curvature
= coefficient of friction ( Clause 4.9.4.3)
rps = the radius of curvature (for parabolic curve = L2/8)
k = profile coefficient (Clause 4.9.3.3)
Example
Determine the loss of prestress due to friction at centre and the
right hand end if prestress force is applied at the left hand end.
Given the following information:
Span, L = 20m
= 0.25
k = 17 x 10-4 per metre
σpo = 1239 N/mm2
Aps = 2850 mm2
e at both ends = 0
e at mid span = 558 mm
Solution
rps = L2/8 >>>> for parabolic curve
= 202/8(558)
= 89.61 m
Po = σpo x Aps
= (1239 ) (2850)
= 3531.15 kN
At mid span, (x = 10m from support)
P(10) =
loss of presstress = Po – P(10) = 3531.15 – 3376.2 = 155kN
= 155/3531.15 x 100 = 4.4%
= yms - ys
At the right end ( x = 20m)
P(20) =
= 3228.9 kN
Loss of prestress = 3531.15 – 3228.9
= 302.3 kN
= 302.3/3531.15 x 100
= 8.6%
Anchorage Draw In
Anchorage draw in – a small contraction during the process of transferring the tensioning force from the jack to the anchorage
The exact amount of anchorage draw-in (ad) depends on the type of anchorage used and is usually specified by the manufacturer of the anchorage. A typical value would be 5mm.
For a pre-tensioned member, it can be compensated easily by initially over-extending the tendons by the calculated amount of the anchorage draw-in.
Since the anchorage draw-in is a fixed amount which is dependent only on the type of anchorage used, the effect is much greater on a short prestressed concrete member than on a long one.
Anchorage Draw-in
Anchorage draw in is refer to the situation where a
prestressing tendon may undergo a small contraction during
the process of transfering the tensioning force from the jack to
the anchorage.
The value of anchorage draw is depend on the anchorage
system used. A typical value = 5mm
Since the anchorage draw-in is a fixed amount which is
dependent only on the type of anchorage used the effect is
much greater on a short prestressed concrete member than on
a long one.
Variation of Initial Prestress Force Along a Post-tensioned
Member
To look at how the prestress force varies along the length of a
post-tensioned member immediately after transfer of the
prestress force (ignoring elastic shortening)
Prestress
Force
Example
Determine the initial prestress force distribution along the
beam if the anchorage draw-in is 5mm. Given the following:
Span = 20m
= 0.25 & K = 17 x 10-4 per metre
σpo = 1239 N/mm2 , Aps = 2850 mm2
e at both ends = 0
e at mid span = 558mm
Es = 195 kN/mm2
Solution
The friction loss per unit length near the anchorage is given by :
The loss of prestress force at the left hand end is given by:
Prestress force at :
Left end = Pi - PA = 3531.2 – 419.3 = 3111.9 kN
At midspan = Pi - PA + friction effect = 3531.2 – 419.3 – (15.82x10)=3270.1kN
At right end = Pi – friction effect = 3531.2 – (15.82x20) = 3214.8 kN
Pi after losses (due to ad + friction) = (3111.9 + 3270.1 +3214.8)/3 = 3198.9 kN
Long Term Losses
1. Loss due to shrinkage
Ɛsh = shrinkage strain ( estimated value : 300-800x10-6)
Loss of stress, σp = Ɛsh x Es
Amount of shrinkage depending whether it pretension or post
tension.
Values of shrinkage bigger in pretension compared to post
tension.
2. Loss due to creep
Creep strain, ɛcreep = ɛc = σc/Eci
Loss of stress, σp = ɛcreep X Es
= (σc/Eci) Es
Where, = creep coefficient
Eci = elastic modulus of concrete at transfer
Estimation for creep coefficient, = 1.5 – 3.0
3. Loss due to relaxation of steel
Loss of stress, σp = RF X RV X σpi
Where, RF = relaxation factor
RV = relaxation value
σpi = initial stress in tendon
