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Page 1
PRESTRESSED CONCRETE
? Prestressed concrete is basically a concrete in which internal stress of suitable magnitude and
distribution are introduced so that the stresses resulting from external load are counteracted to a
desired degree.
? A prestressed concrete is different from a conventional RCC structure due to the application of an
initial load on the structure prior to its use.
A. LOSSES IN PRESTRESS
Pre-tensioning Post-tensioning
1. Elastic deformation of concrete 1. No loss due to elastic shortening when all bars
are simultaneously tensioned. If however, wires
are successively tensioned there would 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. Frictional losses
6. Anchorage slip
1. LOSS OF PRESTRESS DUE TO FRICTION
? The friction generated at the interface of concrete and steel during the stretching of a curved
tendon in a post-tensioned member, leads to a drop in the prestress along the member from the
stretching end.
? The loss due to friction does not occur in pre-tensioned members because there is no concrete
during the stretching of the tendons.
? Force in cable at a distance x from jacking end, after frictional loss – Px
Page 2
PRESTRESSED CONCRETE
? Prestressed concrete is basically a concrete in which internal stress of suitable magnitude and
distribution are introduced so that the stresses resulting from external load are counteracted to a
desired degree.
? A prestressed concrete is different from a conventional RCC structure due to the application of an
initial load on the structure prior to its use.
A. LOSSES IN PRESTRESS
Pre-tensioning Post-tensioning
1. Elastic deformation of concrete 1. No loss due to elastic shortening when all bars
are simultaneously tensioned. If however, wires
are successively tensioned there would 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. Frictional losses
6. Anchorage slip
1. LOSS OF PRESTRESS DUE TO FRICTION
? The friction generated at the interface of concrete and steel during the stretching of a curved
tendon in a post-tensioned member, leads to a drop in the prestress along the member from the
stretching end.
? The loss due to friction does not occur in pre-tensioned members because there is no concrete
during the stretching of the tendons.
? Force in cable at a distance x from jacking end, after frictional loss – Px
Px = Poe
-(µa + kx)
Where Px = Prestressing force at a distance x from jacking end.
P0 = Prestressing force at jacking end.
k = coefficient called wobble correction factor
µ = Coefficient for friction in curve
a = Cumulative angle in radian through which the tangent to the cable profile turned between any
two point under consideration.
? For small values of µa + kx, the above expression can be simplified by the Taylor series
expansion.
Px = Po [1-( µa + kx)]
2. LOSS OF PRESTRESSE DUE ANCHORAGE SLIP
? In a post-tensioned member, when the prestress is transferred to the concrete, the wedges slip
through a little distance before they get properly seated in the conical space.
? This loss due to anchorage slip =
s
E
L
?
?
s
E
L
? ??
=
??
??
Es = Young modulus of steel in N/mm
2
? = Anchorage slip in mm
L = Length of cable in mm
Table:- Typical values of anchorage slip
Anchorage system Anchorage slip (?)
Freyssinet 4 mm
12-5 mm ? strands 6 mm
12-8 mm ? strands 8 mm
Magnet 1 mm
3. LOSS OF PRESTRESS DUE TO CREEP OF CONCRETE
? Creep is the property of concrete by which it continues to deform with time under sustained
loading.
Page 3
PRESTRESSED CONCRETE
? Prestressed concrete is basically a concrete in which internal stress of suitable magnitude and
distribution are introduced so that the stresses resulting from external load are counteracted to a
desired degree.
? A prestressed concrete is different from a conventional RCC structure due to the application of an
initial load on the structure prior to its use.
A. LOSSES IN PRESTRESS
Pre-tensioning Post-tensioning
1. Elastic deformation of concrete 1. No loss due to elastic shortening when all bars
are simultaneously tensioned. If however, wires
are successively tensioned there would 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. Frictional losses
6. Anchorage slip
1. LOSS OF PRESTRESS DUE TO FRICTION
? The friction generated at the interface of concrete and steel during the stretching of a curved
tendon in a post-tensioned member, leads to a drop in the prestress along the member from the
stretching end.
? The loss due to friction does not occur in pre-tensioned members because there is no concrete
during the stretching of the tendons.
? Force in cable at a distance x from jacking end, after frictional loss – Px
Px = Poe
-(µa + kx)
Where Px = Prestressing force at a distance x from jacking end.
P0 = Prestressing force at jacking end.
k = coefficient called wobble correction factor
µ = Coefficient for friction in curve
a = Cumulative angle in radian through which the tangent to the cable profile turned between any
two point under consideration.
? For small values of µa + kx, the above expression can be simplified by the Taylor series
expansion.
Px = Po [1-( µa + kx)]
2. LOSS OF PRESTRESSE DUE ANCHORAGE SLIP
? In a post-tensioned member, when the prestress is transferred to the concrete, the wedges slip
through a little distance before they get properly seated in the conical space.
? This loss due to anchorage slip =
s
E
L
?
?
s
E
L
? ??
=
??
??
Es = Young modulus of steel in N/mm
2
? = Anchorage slip in mm
L = Length of cable in mm
Table:- Typical values of anchorage slip
Anchorage system Anchorage slip (?)
Freyssinet 4 mm
12-5 mm ? strands 6 mm
12-8 mm ? strands 8 mm
Magnet 1 mm
3. LOSS OF PRESTRESS DUE TO CREEP OF CONCRETE
? Creep is the property of concrete by which it continues to deform with time under sustained
loading.
? Creep coefficient is defined as
cp
c
creep strain
elasticstrain
?
? = =
?
? Loss of stress = m ?fc
? Note that elastic shorting loss multiplied by creep co-efficient is equal to loss due to creep.
Age at loading Creep co-efficient
7 days 2.2
28 days 1.6
1 year 1.1
4. LOSS DUE TO SHRINKAGE OF CONCRETE
? The loss of stress in steel due to the shrinkage of concrete is estimated as, Loss of stress = ?cs ×
Es
Where Es = modulus of elasticity of steel.
? ?cs = total residual shrinkage strain having values of 3 × 10
–4
for pre tensioning and ?cs = [(2 ×
10
–4
)/log10(t + 2)] for post-tensioning
Where, t = age of concrete at transfer in days.
5. LOSSS OF PRESTRESS DUE TO RELAXATION OF STEEL
6. Initial Stress (1) Relaxation Loss N/mm
2
0.5 fp 0
0.6 fp 35
0.7 fp 70
0.8 fp 90
Note:
fp is the characteristic strength of prestressing steel.
Final conclusion of above discussions:
Sr. No. Type of loss Equation
1 Wobble & curvature effect (µa + kx)P0
2 Anchorage slip Es ?/L
3 Shrinkage loss ?sc Es
4 Creep of concrete m ? fc
5 Elastic shortening of concrete mfc
6 Relaxation in steel 2 to 5% for initial stress in steel
Type of loss Pretensioned (%) Post tensioned (%)
Elastic shorting of conc. 3 1
Shrinkage 7 6
Creep 6 5
Page 4
PRESTRESSED CONCRETE
? Prestressed concrete is basically a concrete in which internal stress of suitable magnitude and
distribution are introduced so that the stresses resulting from external load are counteracted to a
desired degree.
? A prestressed concrete is different from a conventional RCC structure due to the application of an
initial load on the structure prior to its use.
A. LOSSES IN PRESTRESS
Pre-tensioning Post-tensioning
1. Elastic deformation of concrete 1. No loss due to elastic shortening when all bars
are simultaneously tensioned. If however, wires
are successively tensioned there would 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. Frictional losses
6. Anchorage slip
1. LOSS OF PRESTRESS DUE TO FRICTION
? The friction generated at the interface of concrete and steel during the stretching of a curved
tendon in a post-tensioned member, leads to a drop in the prestress along the member from the
stretching end.
? The loss due to friction does not occur in pre-tensioned members because there is no concrete
during the stretching of the tendons.
? Force in cable at a distance x from jacking end, after frictional loss – Px
Px = Poe
-(µa + kx)
Where Px = Prestressing force at a distance x from jacking end.
P0 = Prestressing force at jacking end.
k = coefficient called wobble correction factor
µ = Coefficient for friction in curve
a = Cumulative angle in radian through which the tangent to the cable profile turned between any
two point under consideration.
? For small values of µa + kx, the above expression can be simplified by the Taylor series
expansion.
Px = Po [1-( µa + kx)]
2. LOSS OF PRESTRESSE DUE ANCHORAGE SLIP
? In a post-tensioned member, when the prestress is transferred to the concrete, the wedges slip
through a little distance before they get properly seated in the conical space.
? This loss due to anchorage slip =
s
E
L
?
?
s
E
L
? ??
=
??
??
Es = Young modulus of steel in N/mm
2
? = Anchorage slip in mm
L = Length of cable in mm
Table:- Typical values of anchorage slip
Anchorage system Anchorage slip (?)
Freyssinet 4 mm
12-5 mm ? strands 6 mm
12-8 mm ? strands 8 mm
Magnet 1 mm
3. LOSS OF PRESTRESS DUE TO CREEP OF CONCRETE
? Creep is the property of concrete by which it continues to deform with time under sustained
loading.
? Creep coefficient is defined as
cp
c
creep strain
elasticstrain
?
? = =
?
? Loss of stress = m ?fc
? Note that elastic shorting loss multiplied by creep co-efficient is equal to loss due to creep.
Age at loading Creep co-efficient
7 days 2.2
28 days 1.6
1 year 1.1
4. LOSS DUE TO SHRINKAGE OF CONCRETE
? The loss of stress in steel due to the shrinkage of concrete is estimated as, Loss of stress = ?cs ×
Es
Where Es = modulus of elasticity of steel.
? ?cs = total residual shrinkage strain having values of 3 × 10
–4
for pre tensioning and ?cs = [(2 ×
10
–4
)/log10(t + 2)] for post-tensioning
Where, t = age of concrete at transfer in days.
5. LOSSS OF PRESTRESS DUE TO RELAXATION OF STEEL
6. Initial Stress (1) Relaxation Loss N/mm
2
0.5 fp 0
0.6 fp 35
0.7 fp 70
0.8 fp 90
Note:
fp is the characteristic strength of prestressing steel.
Final conclusion of above discussions:
Sr. No. Type of loss Equation
1 Wobble & curvature effect (µa + kx)P0
2 Anchorage slip Es ?/L
3 Shrinkage loss ?sc Es
4 Creep of concrete m ? fc
5 Elastic shortening of concrete mfc
6 Relaxation in steel 2 to 5% for initial stress in steel
Type of loss Pretensioned (%) Post tensioned (%)
Elastic shorting of conc. 3 1
Shrinkage 7 6
Creep 6 5
Relaxation 2 3
Total Loss 18% 15%
Losses Pretensioning Post tensioning
Length effect No Yes
Curvature effect No Yes
Anchorage slip No Yes
Shrinkage of concrete Yes Yes
Creep of concrete Yes Yes
Elastic deformation or
shortening of concrete
Yes No (If all wires are simultaneously tensioned) Yes
(If wires are successively tensioned)
B. DEFLECTION OF PRESTRESSED BEAM
I. Effect of tendon profile on deflection
1. Straight tendons:
Figure below shows a beam with a straight tendon at a uniform eccentricity below the centroidal
axis, if upward deflection are considered as negative and,
P = effective prestressing force
E = eccentricity
L = length of the beam
a = -(Pe/2)L(L/4)/(EI) = -(PeL
2
/8EI)
2. Trapezoidal tendons:
A draped tendon with a trapezoidal profile is shown in Fig. Considering the B.M.D., the deflection at
the centre of the beam is obtained by taking the moment of area of the B.M.D. over one - half of the
span. Thus,
a = -
Pe
EI
??
??
??
[L2 (L1 + L2/2) + (L1/2)(2/3L1)]
Page 5
PRESTRESSED CONCRETE
? Prestressed concrete is basically a concrete in which internal stress of suitable magnitude and
distribution are introduced so that the stresses resulting from external load are counteracted to a
desired degree.
? A prestressed concrete is different from a conventional RCC structure due to the application of an
initial load on the structure prior to its use.
A. LOSSES IN PRESTRESS
Pre-tensioning Post-tensioning
1. Elastic deformation of concrete 1. No loss due to elastic shortening when all bars
are simultaneously tensioned. If however, wires
are successively tensioned there would 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. Frictional losses
6. Anchorage slip
1. LOSS OF PRESTRESS DUE TO FRICTION
? The friction generated at the interface of concrete and steel during the stretching of a curved
tendon in a post-tensioned member, leads to a drop in the prestress along the member from the
stretching end.
? The loss due to friction does not occur in pre-tensioned members because there is no concrete
during the stretching of the tendons.
? Force in cable at a distance x from jacking end, after frictional loss – Px
Px = Poe
-(µa + kx)
Where Px = Prestressing force at a distance x from jacking end.
P0 = Prestressing force at jacking end.
k = coefficient called wobble correction factor
µ = Coefficient for friction in curve
a = Cumulative angle in radian through which the tangent to the cable profile turned between any
two point under consideration.
? For small values of µa + kx, the above expression can be simplified by the Taylor series
expansion.
Px = Po [1-( µa + kx)]
2. LOSS OF PRESTRESSE DUE ANCHORAGE SLIP
? In a post-tensioned member, when the prestress is transferred to the concrete, the wedges slip
through a little distance before they get properly seated in the conical space.
? This loss due to anchorage slip =
s
E
L
?
?
s
E
L
? ??
=
??
??
Es = Young modulus of steel in N/mm
2
? = Anchorage slip in mm
L = Length of cable in mm
Table:- Typical values of anchorage slip
Anchorage system Anchorage slip (?)
Freyssinet 4 mm
12-5 mm ? strands 6 mm
12-8 mm ? strands 8 mm
Magnet 1 mm
3. LOSS OF PRESTRESS DUE TO CREEP OF CONCRETE
? Creep is the property of concrete by which it continues to deform with time under sustained
loading.
? Creep coefficient is defined as
cp
c
creep strain
elasticstrain
?
? = =
?
? Loss of stress = m ?fc
? Note that elastic shorting loss multiplied by creep co-efficient is equal to loss due to creep.
Age at loading Creep co-efficient
7 days 2.2
28 days 1.6
1 year 1.1
4. LOSS DUE TO SHRINKAGE OF CONCRETE
? The loss of stress in steel due to the shrinkage of concrete is estimated as, Loss of stress = ?cs ×
Es
Where Es = modulus of elasticity of steel.
? ?cs = total residual shrinkage strain having values of 3 × 10
–4
for pre tensioning and ?cs = [(2 ×
10
–4
)/log10(t + 2)] for post-tensioning
Where, t = age of concrete at transfer in days.
5. LOSSS OF PRESTRESS DUE TO RELAXATION OF STEEL
6. Initial Stress (1) Relaxation Loss N/mm
2
0.5 fp 0
0.6 fp 35
0.7 fp 70
0.8 fp 90
Note:
fp is the characteristic strength of prestressing steel.
Final conclusion of above discussions:
Sr. No. Type of loss Equation
1 Wobble & curvature effect (µa + kx)P0
2 Anchorage slip Es ?/L
3 Shrinkage loss ?sc Es
4 Creep of concrete m ? fc
5 Elastic shortening of concrete mfc
6 Relaxation in steel 2 to 5% for initial stress in steel
Type of loss Pretensioned (%) Post tensioned (%)
Elastic shorting of conc. 3 1
Shrinkage 7 6
Creep 6 5
Relaxation 2 3
Total Loss 18% 15%
Losses Pretensioning Post tensioning
Length effect No Yes
Curvature effect No Yes
Anchorage slip No Yes
Shrinkage of concrete Yes Yes
Creep of concrete Yes Yes
Elastic deformation or
shortening of concrete
Yes No (If all wires are simultaneously tensioned) Yes
(If wires are successively tensioned)
B. DEFLECTION OF PRESTRESSED BEAM
I. Effect of tendon profile on deflection
1. Straight tendons:
Figure below shows a beam with a straight tendon at a uniform eccentricity below the centroidal
axis, if upward deflection are considered as negative and,
P = effective prestressing force
E = eccentricity
L = length of the beam
a = -(Pe/2)L(L/4)/(EI) = -(PeL
2
/8EI)
2. Trapezoidal tendons:
A draped tendon with a trapezoidal profile is shown in Fig. Considering the B.M.D., the deflection at
the centre of the beam is obtained by taking the moment of area of the B.M.D. over one - half of the
span. Thus,
a = -
Pe
EI
??
??
??
[L2 (L1 + L2/2) + (L1/2)(2/3L1)]
( )
( )
22
1 1 2 2
Pe 6EI 2L 6L L 3L = + +
3. Parabolic tendons (central anchors):
The deflection of a beam with parabolic tendons having an eccentricity e at the centre and zero at
the support is given by,
2
Pe 2 L 5 L 5PeL
EI 3 2 8 2 48 EI
??
??
? = - ? ? ? = -??
??
??
??
??
4. Parabolic tendons (eccentric anchors):
Fig, below shows a beam, with parabolic tendons having an eccentricity e1 at the centre of span and
e2 at the support section.
• The resultant deflection at the centre is obtained as the sum of the upward deflection of a beam
with a parabolic tendon of eccentricity (e1 + e2) at the centre and zero at the supports and the
downward deflection of a beam subjected to a uniform sagging bending
moment of intensity Pe2 throughout the length.
Read More
FAQs on Short Notes: Prestressed Concrete - Short Notes for Civil Engineering - Civil Engineering (CE)
| 1. What is prestressed concrete? |  |
Ans. Prestressed concrete is a type of concrete that has been compressed with internal stresses to improve its tensile strength. This is achieved by placing steel tendons under tension before pouring the concrete, which helps counteract the weak tensile strength of regular concrete.
| 2. How is prestressed concrete different from reinforced concrete? | |
Ans. Prestressed concrete differs from reinforced concrete in that the steel reinforcement in prestressed concrete is placed under tension before the concrete is poured, whereas in reinforced concrete, the steel bars are placed in the concrete after it has hardened.
| 3. What are the advantages of using prestressed concrete? | |
Ans. Some advantages of using prestressed concrete include reduced cracking, increased resistance to impact and fatigue, longer spans without the need for additional support columns, and the ability to create thinner and lighter concrete structures.
| 4. What are some common applications of prestressed concrete? | |
Ans. Prestressed concrete is commonly used in bridges, parking structures, high-rise buildings, nuclear containment structures, and offshore structures due to its ability to span longer distances and resist heavy loads.
| 5. Are there any limitations to using prestressed concrete? | |
Ans. Some limitations of prestressed concrete include higher initial costs due to the need for specialized equipment and expertise, potential corrosion of the prestressing tendons over time, and the complexity of design and construction compared to traditional concrete structures.
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