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Prestressed concrete

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					Prestressed concrete
INTRODUCTION
In ordinary reinforced concrete, consisting of concrete and mild steel as basic
components,the compressive stresses are borne by concrete while tensile stresses are
borne entirely by steel. The concrete surrounding steel reinforcement does not take part in
resisting the external forces/moments since concrete is considered weak in tension. It
simply acts as a bonding material. Thus only that portion of concrete, which lies above
the neutral axis•, is considered to be useful in resisting the external forces. This results in
heavy sections. In the case of prestressed concrete, comprising of concrete and high
tensile steel as basic components, both steel and concrete are stressed prior to the
application of external loads. If such induced pre-stress in concrete is of compressive
nature, it will balance the tensile stress produced in concrete surrounding steel due to
external loads in which there have been introduced internal stresses of such magnitude
and distribution that the stresses resulting from given external loadings are counteracted
to a desired degree. In reinforced concrete member, the prestress is commonly introduced
by tensioning the steel reinforcement. Thus, prestressing is the intentional creation of
permanent stresses in a structure or assembly, for the purpose of improving its behaviour
and strength under various serviceconditions
In prestressed concrete, compression is induced prior to~loading in the zones where
external loads would normally cause tensile stresses. Simple" reinforced concrete has two
major disadvantages. (1) It has weak crack-resistance in consequence of the low tensile
strength-all the reinforced concrete beams and other bending members have c~acks at
working loads. Due to this, corrosion of both the reinforcement and concrete takes place.
(2) It is impossible to use high tensile steel as reinforcement for simple reinforced
concrete. If high tensile steel is used, the high stresses in the tensile reinforcement will
result in such wide cracks in the tensile zone of concrete that the load carrying capacity
of the members will practically be lost. A prestressed concrete construction on the other
hand, has no cracks at working loads and has offered the possibility of employing high-
tensile steel as reinforcement.
The earlier attempts of prestressing were made immediately after the development of
reinforced concrete. P. Jackson (1886) of U.S.A. obtained patents for pretensioning steel
tie rods in artificial stones and concrete arches to serve as floor slabs. K. Doring (1888)
of Germany suggested pretensioning of wires in reinforced concrete floor structures.
However, in all the earlier attempts, low tensile steel was used as prestressing material
with the result that low pretension was lost in shrinkage and creep in concrete. If an
ordinary mild steel bar is prestressed to a working stress of 140 N/ mm2
, the resulting strain in it will be
٤ =140 =   0.00066
  2.1 x 105
.The permanent negative strain due to both. shrinkage and creep is of order of the
0.0008. Since this permanent strain is greater than the initial strain in the mild steel'
caused by tensioning it, the prestress induced in mild steel would soon disappear, leaving
the member simply reinforced.

The permanent negative strain due to both. shrinkage and creep is of order of the
0.0008. Since this permanent strain is greater than the initial strain in the mild steel'
caused by tensioning it, the prestress induced in mild steel would soon disappear, leaving
the member
simply reinforced.
To avoid this trouble, C.R. Steiner (1908) of U.S.A. reco~ended the tightening
of reinforcing rods afte~ some shrinkage and creep of concrete had taken place. R.E. Dill
(1925) of -Nebraska used high strength steel bars coated to prevent bond with concrete.
The bars were tensioned and anchored to concrete by means of nuts, after the concrete
had set. For economical reasons, these methods could not be applied to an appreciable
extent. It was E. Freyssinet (1928) of France who made the first specific contribution of
prestressing as it is today .He used high strength steel wires for prestressing. These wires
has an ultimate strength in tension of 1750 N/mm2 and yield point of about 1260 N/mm2
• If these are prestressed to 1050 N/mm2
, the resulting strain will be
٤ =1050 = 0.005
   2.1 x 105
According to Freyssinet, to prestress a structure is artificially to create either prior
to or simultaneously with the application of external loads such permanent stresses that
in combination with the stress due to external load, total stresses will every where and
for all states of loads envisaged, be within limits of stress that the material cari support
indefinitely. In his earlier attempts, he tried pretensioning in which steel was bonded to
concrete without end anchorages. However, in 1939, he developed conical wedges for
end anchorages and designed double acting jacks which tensioned the wires and then
thrust the male cones into the female cones for anchoring them. After this successful
work, prestressed concrete was very widely developed in many countries and many
famous workers like Guyon, Kani, Leonhardt, Magnel and others, started working on
this. G. Magnel (1940) of Belgium developed the Magnel system, wherein two wires
were stretched at a time and anchored with a simple metal wedge at each end. In the
U.S.S.R., investigations on prestressed concrete were initiated by V.V. Michailov and
then by A.A. Gvosdev, S.A. Dmitriev and others.
As stated earlier, prestressing is the initial application of stresses, controlled in
magnitude and direction, to a structural member to counteract the undesirable stresses
due to working loads. Prestressing is commonly introduced by tensioning the steel
reinforcement. According to Lin, three different concepts may be applied to explain and
analyse the basic behaviour of prestressed concrete. These concepts are as follows : (I)
Stress concept, (2) Strength concept and (3) Balanced load concept.
1. Stress concept : Prestressing to transfonn concrete into an elastic material.
This concept is credited to Eugene Freyssinet who visualised prestressed concrete as
essentially concrete which is transformed from a
brittle material into an elastic one byrecompression given to it. If an




ordinary
concrete, whether plain or reinforced,is subjected to only compressive stresses,
it behaves as a perfect elastic material ecause no tension cracks are there. But
if it is subjected to flexural stresses,some portion of it will be in tension
resulting in tension cracks ; the materialunder such circumstance no longer remains
elastic. In prestressed concrete, on theother hand, concrete is visualised as being FIG.
45.1. CONCENTRICALLY PRESTRESSED SECTION.subjected to two system of
forces: internal prestress, which is compressive and external load causing tensile stresses.
The tensile stresses caused due to external load are counterbalanced by the compressive
stress due to prestress, with the result that final stress in the extreme fibre is either
compressive or zero. Due to absence of final tensile stress, no tension cracks would be
there in concrete, and it will thus be transformed from brittle to elasic material. To
elaborate this point, let us consider two cases: (a) concentric tendon (steel reinforcement)
and (b) eccentric tendon.
Fig.shows a concentrically prestressed concrete beam. Due to prestress force
T in tendon, a uniform compressive stress = T/ A will be induced in concrete. If the beam




is subjected to a moment M due to
external load,' inclusive of its own weight, the stress at any point will be ~ Y where y is
the distance of the point from the· centriodal axis and MII is the moment of inertia of the
section. The final stress at any point section. The final stress at any point
is given by f=T/A.+My/A
Fig. shows an eccentrically prestressed beam with external loading. Due to prestress
force T in tendon, applied eccentrically, the moment produced due to prestress will be
T.e. Hence the stress l' due to prestress at any point will be
F’ = T/A + Tey/I

2. Strength concept: Prestressing for combination of high strength steel and concrete
In reinforced concrete, steel takes tension while concrete takes compression and the
couple formed by the resultant compressive force C and tensile force T (where C = T )
resists the external moment




The same concept can be applied for a prestressed concrete section. The prestressed
concrete is considered as a combination of steel and concrete, with steel taking T
(passing through the tendon) and concrete taking compression C [passing through the C.
G. of the stress distribution c shown shaded in Fig. 45.3(a)], so thatthe two materials
form a resisting couple to resist the external moment. This concept has been well utilised
to determine the ultimate strength of prestressed concrete beams.




Thus, the parabolic cable supports a uniformly distributed load p given by the above
equations. If the external U.D.L. w is equal to p, transverse load on the beam is balanced
and the beam is subjected to only the axial force T, which produces uniform stress in
concrete =f = T/ A. If the external load w is greater than p, the mid-span moment M
for the remaining force (w - p) can be computed and fibre stresses due to that moment
would be T My M y / /. The resulting stresses will then be equal to A ± -/-.
Fig. 45.5(a) shows a beam with bent tendon while Fig. 45.5(b) shows the freebody
          of concrete with tendon replaced by forces. In the figure, C.G.c. stands for centre
of




          The uniform compressive stress in beam is given by


While this 'load balancing concept' often represents the simplest approach to prestressed
design and analysis, its advantage over the other two concepts is not significant for
statically determinate structures. However, the method offers tremendous advantages
when dealing with statically indeterminate structures.
Example 1
. Stress concept. : A simply supported prestressed concrete beam of
rectangular cross-section 400 mm x 600 mm, is loaded with a total uniformly distributed
load of 256 kN over a span of 6 m. Sketch the distribution of stresses at mid-span and
end sections if the prestressing force is 1920 kN and the tendon is (a) concentric, (b)
         eccentric, located at 200 mm above the bottom fibre.




                                   Solution 1+8+1
(a) Concentric tendon
A = 400 x 600 = 240000 mm2
I=1 (400) (600)3= 72 x 108 mm 4
     12

fl due to prestressing force
= 1920 x 1000 = 8 N/ mm2
  240000
At the end section, B.M. is zero, and hence the section will be subjected to uniform
compressive stress of 8 N/mm2 throughout its depth.
Mid span moment=WL= 256 x 6
                 8      8
= 192kN-m
Extreme fibre stress = fb = + 8 N/mm2
Hence final stress
F= ft + fb = 16 or 0.
(b) Eccentric tendon. Eccentricity ; e = 300 - 200 = 100 mm.
The stresses due to eccentric prestress force is
F= T/A + T.e y
            I




F’= f1+ f2
F1= 8 N/mm2
F2= + 8 N/mm2
By shifting position of tendon the extreme fiber stress in concrete is reduced from 16 to 8
N/mm 2.
Post-Tensioned Beams : In the case of post tensioned beam with a single concentric
tendon, as the tendon is stretched and anchored against concrete, all the elastic strain has
occurred in concrete when the jacking force is reached in tendon. Since the force in the
cable is measured after the elastic shortening of the concrete nas taken place, no loss
in prestress due to this need be accounted for. However, in actual practice there are more
than one tendon. If the tendons are stressed in succession, the prestress is applied
gradually.
Due to this, the tendon that is stressed first will suffer the maximum loss while the one
that is tensioned last will not suffer any loss. Accurate calculation for losses is
complicated, but for all practical purposes, it may be assumed that average loss of each
cable is equal to half the loss in first cable. In order to counteract elastic loss all the
tendons are anchord at an overstress equal to the average elastic loss in practice.. The
average loss in post-tensioned beam may be
of the order 40%.
2. Loss due to creep of concrete:
Creep in concrete is defined as its time-dependent
deformation resulting from the presence of stress. It is the plastic flow of concrete under
compression. Creep strain varies with the intensity of stress, and is about two to three
times the elastic strain. The rate of creep is high ~tially, and then decreases as time
increases. The creep increases with higher water-cement ratio and with a lower aggregate
cement ratio. It varies inversely with strength of concrete. It also depends upon the
humidity of surrounding atmosphere and the strength at the time of loading. It is known
that the failure of early efforts at prestressing was attributed 1<irgelyto the lack of
knowledge concerning creep in concrete. It is still one of the main source of loss, and a
serious one, if the prestress in the steel is low and the compression in concrete is high.
Pre-tensioned members have more loss than post-tensioned ones, because transfer of'
prestress usually takes place earlier in pre-tensioned members.
conditions. Creep strain (ter) is given by
ter = (Ce - 1) tel where tel = elastic strain in concrete.
3. Loss due to shrinkage of concrete : Shrinkage in concrete is its contraction
due to drying and chemical changes. It depends upon the quantity of water, type of
aggregates used in the mix and surrounding atmospheric conditions. If minimum
shrinkage is desired, the water cement ratio and the proportion of cement paste should be
kept to a minimum. Aggregates of larger size, well graded for minimum void, need a
smaller amount of cement paste, and shrinkage. will be smaller. Harder and denser
aggregates of low absorptions and high modulus of elasticity will exhibit small shrinkage.
Shrinkage is relatively small for cements high in tricalcium silicate and low in the
alkalies and the. oxides of sodium and potassium. Shrinkage is also time dependent,
though bulk of the shrinkage takes place in the early days of the hardening of concrete. In
pre-tensioned work, wires are subjected to some compression due to creep of concrete,
before the release of wires.
The concrete around the wires is subjected to tension as the anchored wires are not free to
shorten its length. The concrete thus tends to slip in the early stages and develop fine
cracks.
When the wires are released, these cracks close, causing a loss of prestress. After that,
the time dependent shrinkage continue to shorten the length of member, though at a much
reduced rate. In post-tensioning work, shrinkage takes place unhampered and hence loss
of shrinkage is relatively small.

				
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