Losses of Pre-stress:
In pre-stressed concrete application, the most
important variable is the Pre-stressing Force. In the early days, it was
observed that the pre-stressing force does not stay constant, but reduces with
time. Even during pre-stressing of the tendons and the transfer of pre-stress
to the concrete member, there is a drop of the pre-stressing force from the
recorded value in the jack gauge. The various reductions of the Pre-stressing
Force are termed as the Losses in Pre-stress.
Classification of Losses of Pre-stress:
The Losses of Pre-stress Force are broadly
classified into two groups,
------Immediate
Losses of Pre-stress,
------Time-dependent
Losses of Pre-stress.
Immediate Losses of Pre-stress:
The immediate losses occur during pre-stressing of the
tendons and the transfer of pre-stress to the concrete 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
Time-Dependent Losses of Pre-stress:
The time-dependent losses occur during the service life
of the pre-stressed member. The losses due to the shrinkage and creep of the
concrete and relaxation of the steel are the time-dependent losses.
Figure-01
indicates the Classification of Losses of Pre-stress,
Figure-01: Classification of Losses of Pre-stress
Generally
the following types of Losses of Pre-stress are used in everywhere in the
world, these are,
------Elastic
shortening of concrete,
------Losses
due to creep of concrete,
------Losses
due to shrinkage of concrete,
------Losses
due to Steel Relaxation,
------Losses
due to anchorage take-up,
------Frictional
Loss,
------Losses
due to bending moment of the member,
Significances of Losses of Pre-stress:
The
total analysis and design of a pre-stressed concrete tendon at each significant
stages of loading gather with appropriate material properties for that one in
the life history of the structure. The most common stages are as follows,
Immediately
following transfer of pre-stress force to the concrete section stresses are
evaluated from a measure of behavior.
At
service load after all losses of pre-stress have occurred and a long-term
effective pre-stress level has been reached, stresses are checked again as a
measure of behavior and sometimes of strength.
Why do we estimate effective pre-stress force of pre-stressed concrete?
The
effective pre-stress is the initial losses of pre-stressing force. Now while
the initial pre-stress can be measured and applied accurately- the losses that
we assumed, since it is difficult to generalize the amount of loss of
pre-stress, because it is dependent on so many factors, the properties of
steel, curing & moisture conditions, magnitude and time of application of
pre-stressing force, the process of pre-stressing etc. Each of these factors
are themselves variable and there is no definite method to accurately express
them, besides other types of losses can occur too. Hence the effective
pre-stress is estimated based on practical data & experiments.
Importance of Loss Estimation of Pre-stressed Concrete:
All
the pre-stressing design is made considering the effective pre-stress (which is
the initial losses of the pre-stressing force) during preparing the span. So it
is very essential to estimate the magnitude of the total losses of pre-stress.
Since it leads to the value of effective pre-stressing force needed for
designing.
The
accurate determination of losses is more important for some structures than
other. The more accurate and detailed the technique of predicting losses, the
more specific is the input information needed.
The
percentage of loss in case of Post-tensioned beam increase, if the number of
tendon is increased:
If
there is only a single tendon in a Post-tensioned member, the concrete shortens
as that tendon is jacked against the concrete. But if there is more than one
tendon and the tendons are stressed one by one, then the pre-stress is
gradually applied to the concrete. As a result the tendon that is first
tensioned would suffer the maximum amount of loss due to the shortening of
concrete by the application of pre-stress from all other tendons.
Formulas:
Losses
of Pre-stressing Force in case of Pre-tensioned Pre-stress beam:
Losses
due to Elastic Shortening, Δfs = nfc ,
Losses
due to Creep, Δfs = (Cc-1)nfc ,
Losses
due to Shrinkage, Δfs = Esδs ,
Losses
due to Steel Relaxation, Δfs = 5% of fi ,
Losses
of Pre-stressing Force in case of Post-tensioned Pre-stress beam:
Losses
due to Elastic Shortening, Δfs = 0.5nfc ,
Losses
due to Creep, Δfs = (Cc-1)nfc ,
Losses
due to Shrinkage, Δfs = Esδs ,
Losses
due to Anchor Slip, Δfs = (Δa Es)/L ,
Losses
due Friction, Δfs = (f2-f1) = (fi-f1) ,
Losses
due to Steel Relaxation, Δfs = 5% of fi ,
Now, Using the above formulas, I am going to present two examples about Losses of Pre-stress to all of my viewers.
The basic question of these two examples are same but One example is for Pre-tensioned Pre-stress Concrete Beam and the Other one is for Post-tensioned Concrete Beam.
So that, by the mathematical example here we will try to calculate the amount of Losses in case of both Pre-tensioned and Post-tensioned Concrete.
At first the basic question is,
A Pre-stress Beam of rectangular cross-section of 23 cm X 47 cm is tensioned with a cable of 20 wires of 7 mm diameter. The cable of circular cross section in with an eccentricity 16 cm at the mid span and zero at the supports. The total span is 20 m long. The wires are initially stressed to 850 N/sq. mm.
Find the corresponding Losses of Pre-stress if this Pre-stress Beam is Pre-tensioned or Post-tensioned.
At first, we will solve this above mathematical problem in case of Pre-tensioned Pre-stressed Concrete Structures,
Already we know the required formulas for losses of pre-tensioned pre-stressed concrete which is,
Losses due to Elastic Shortening, Δfs = nfc ,
Losses due to Creep, Δfs = (Cc-1)nfc ,
Losses due to Shrinkage, Δfs = Esδs ,
Losses due to Steel Relaxation, Δfs = 5% of fi ,
So lets start,
The following Page-01 to Page-05 indicates the solution of the above mathematical problem when the structure is Pre-tensioned Pre-stressed Concrete Structure,
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| Page-01: Pre-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-02: Pre-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-03: Pre-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-04: Pre-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-05: Pre-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
Losses due to Elastic Shortening, Δfs = 0.5nfc ,
Losses due to Creep, Δfs = (Cc-1)nfc ,
Losses due to Shrinkage, Δfs = Esδs ,
Losses due to Anchor Slip, Δfs = (Δa Es)/L ,
Losses due Friction, Δfs = (f2-f1) = (fi-f1) ,
Losses due to Steel Relaxation, Δfs = 5% of fi ,
So lets start,
The following Page-01 to Page-07 indicates the solution of the above mathematical problem when the structure is Post-tensioned Pre-stressed Concrete Structure,
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| Page-01: Post-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-02: Post-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-03: Post-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-04: Post-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-05: Post-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-06: Post-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
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| Page-07: Post-tensioned Pre-stressed Concrete Structures, seasoft022.blogspot.com |
Discussion:
The amount of Losses reduces in case of Post-tensioned Pre-stressed Concrete Beam than Pre-tensioned Pre-stressed Concrete Beam.
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