Introduction to Prestressed Concrete
2nd Part of Reinforced Concrete II
LB3 Civil Engineering ITS
Fakultas Teknik Sipil dan Perencanaan
Institut Teknologi Sepuluh Nopember Surabaya
Last Edited Feb-2015
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References
Design of Prestressed Concrete Structures, T.Y. Lin, Ned H.
Burns, John Wiley & Sons, 1982.
Prestressed Concrete, a Fundamental Approach, Edward G.
Nawy, 5th Ed, Prentice Hall, 2006.
Prestressed Concrete Analysis and Design, Fundamentals,
Antoine E. Naaman, 2nd Ed, Tecno Press 3000, 2004.
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Objectives
Upon completion of this topic, student will be able to:
Understand basic concept of prestressed concrete.
Understand the effect of low strength steel and high strength steel
to prestressing.
Distinguish three principle of prestressed concrete.
Understand the advantages and disadvantages of prestressed
concrete.
Understand the loading stages of prestressing.
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Introduction
Developement of prestressed concrete.
General principle of prestressed concrete.
Classification and Types.
Stages of Loading.
Reinforced vs. Prestressed vs. Partial Prestressed Concrete.
Design Codes for Prestressed Concrete.
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Definitions:
Leonhard F.
The basic idea of prestressing is that the concrete should,before
external loading is applied, be put under compression in all parts
where the loading produces tensile stresses, so that on the tensile side
these compressive prestresses will first have to be cancelled before any
tension actually occurs in the concrete.
Naaman A.E.
Prestressing is the deliberate creation of permanent internal stresses in
a structure or system in order to improve its performance. Such
stresses are designed to counteract those induced by external loading.
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Definitions:(cont.)
Abeles,P.W. ;Bardhan-Roy,B.K; Turner,F.H.
Prestressing may be defined as the purposeful creation and controlled
creation of permanent stresses in a structures member, before the full
dead and live loads are opplied, so as to counteract all of part of these
loads. It serves two main purposes: to inprove the resistence of the
member to the dead load and live loads(service load) and to modify
the behavior of the members or structure in such a way as to make it
more suitable for its intended purpose.
Guyon Y from Freyssinet
Precontraindre est une construction, c’est y créer artificiellement avant
application des charges exterieures ou simultanement avec celle-ci, des
contraintes permanentes tellque composes avec les conterintes due
aux charge exterieur les contraint totales restent en tout point, et pour
tous les cas envisage de compris entre les limites au contraintes que la
matiere peut uporter infinement.
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Concept
Basic Concept
Prestressed concrete is basically concrete in which internal stresses of a
suitable magnitude and distribution are introduced so that the stresses
resulting from the external loads are counteracted to a desired degree.
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History
The application of pre-stressing in concrete structures is not the only
instance. There were some earlier attempts made.Two of the instances
are provided below
Force-fitting of metal bands on wooden
barrels.
The metal bands around the barrel induce a
state of initial hoop compression to
counteract the hoop tension caused by filling
of liquid in the barrels.
Pre-tensioning of spokes in a bicycle wheel.
The pre-tension is applied in the spoke to
such an extent that there will always be a
residual tension in the spoke
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Prestressed History
1886
1888
1908
1923
1924
Jackson, P. H., (USA)
Introduced the concept of tightening steel tie rods in artificial stone and concrete arches.
Doehring, C. E. W., (Germany)
Manufactured concrete slabs and small beams with embedded tensioned steel.
Stainer, C. R., (USA)
Recognised losses due to shrinkage and creep, and suggested retightening the rods to recover lost prestress.
Emperger, F., (Austria)
Developed a method of winding and pre- tensioning high
tensile steel wires around concrete pipes.
Hewett, W. H., (USA)
Introduced hoop-stressed horizontal reinforcement around
walls of concrete tanks through the use of turnbuckles.
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1925
1926
1938
1940
Dill, R. H., (USA)
Used high strength unbonded steel rods. The rods were
tensioned and anchored after hardening of the concrete.
Eugene Freyssinet (France)
Used high tensile steel wires, with ultimate strength as high
as 1725 MPa and yield stress over 1240 MPa. In 1939,
he developed conical wedges for end anchorages for posttensioning and developed double-acting jacks. He is often
referred to as the Father of Prestressed concrete.
Hoyer, E., (Germany)
Developed ’long line’ pre-tensioning method.
Magnel, G., (Belgium)
Developed an anchoring system for post-tensioning, using
flat wedges.
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Development of Building Materials ∗
MATERIAL
RESISTING
COMPRESSION
MATERIAL
RESISTING
TENSION
STONES
BRICKS
BAMBOOS
ROPES
CONCRETE
IRON BAR
STEEL WIRE
STRUCTURAL
STEEL
CONCRETE
HIGH
STRENGTH
STEEL
ACTIVE
COMBINATION
∗ Reference:
TIMBER
REINFORCED
PASSIVE
COMBINATION
HIGH
STRENGTH
CONCRETE
MATERIAL
RESISTING TENSION
AND COMPRESSION
PRESTRESSED
CONCRETE
Lin, T. Y. and Burns, N. H., Design of Prestressed Concrete Structures
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First Patent
Original Length of Steel = L
Steel is Prestressed
δ
lengthening of steel
= 0.00062L
Prestressed is Lost
Shrinkage and creep
of concrete
= -0.00062L
The first patented method were not
successful because the low tensile
prestress in the steel was soon lost
as result of the shrinkage and creep
of concrete.
Consider an ordinary steel bar
prestressed to a working stress of
124 MPa. If modulus of elasticity of
steel approximately 200 × 103 MPa,
the unit lengthening of the bar is
given by:
124
f
=
= 0.00062
E
200000
Shrinkage and creep of concrete induce comparable amount of
shortening in concrete.
δ=
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Modern Prestressed
Original Length of Steel = L
Steel is Prestressed
lengthening of steel
= 0.0050L
Using high strength steel wire for
prestressing. Such wire, with
ultimate strength as high as 1725
MPa, and yield point over 1240
MPa, are prestressed to about 1000
MPa, creating strain of:
100
f
=
= 0.005
E
200000
Assuming the total lost due to shrinkage and creep is 0.0008, the net
strain of 0.0050-0.0008=0.0042 would still be left in the wires, which is
equaivalent to a stress of:
Prestressed is Lost
Shrinkage and creep
of concrete = -0.0008L
effective strain in
steel = 0.0042L
δ=
f = Eδ = 200000 × 0.0042 = 840 MPa
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General Principles
Three different concepts may be applied to explain and analyze the
basic behavior of prestressed concrete.
Prestressed to transform concrete into an Elastic Material.
Prestressing for combination of High-strength Steel with Concrete.
Prestressing to archive Load Balancing.
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General Principles: Elastic Material
First concept – Prestressing to transform concrete into elastic
material.
concentric tendon
(Force F )
Beam Prestressed and Loaded
F
A
My
I
F
A
F
A
Mc
I
±
+
Mc
I
Mc
I
F
A
−
Mc
I
The stress distribution is given by:
f =
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F
My
±
A
I
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Example : First Concept
A beam of 200x300mm with the span of 8m, prestress with force
F = 240 kN placed at c.g of beam, Concrete weight= 25 kN/m3 , the
distributed dead load qDL = 1.5 kN/m
1
Moment at mid span MDL,mid = qDL L2 = 12 kN.m
8
3
Moment at 1/4 span MDL,L/4 =
qDL L2 = 9 kN.m
32
Stresses:
caused by Compression force:
240000
F
=
= 4 MPa
A
200 × 300
caused by moment at mid span:
12 × 106 × 150
MDL c
=
= 4 MPa, (3 MPa ,for L/4)
1
I
× 200 × 3003
12
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concentric tendon
(Force F )
Beam Prestressed and Loaded
8
4
Stress at mid section
4
-4
0
7
Stress at L/4 section
4
Stress due to F
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-3
1
Stress due to M
Stress combination
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Example : First Concept, add excentricity
Put the prestressed 100mm below concrete center of gravity (c.g.c), the
stresses are:
c.g.c
F
F
c.g.s
h = 300
e = 100
b = 200
Beam Prestressed and Loaded
Stress at mid section
-8
4
stress at any section
0
f=
F
A
± FIey ± MI y
capable of additional load :
4
8
F
A
F ey
I
-4
MDL y
I
1
8
f=
F
A
±
F ey
I
±
My
I
Stress at L/4 section
-8
3
MLL = f yI = 8 12
200×3003
150
MLL = 24kN.m or
-1
qLL = 3 kN/m
4
8
F
A
F ey
I
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-3
MDL y
I
7
f=
F
A
±
F ey
I
Reinforced Concrete II
±
My
I
there is tension (-1 MPa)
at top fiber on 14 L section
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Parabolic tendon
The ideal tendon geometry is the same shape of the moment diagram,
which is:
1
1
1
Mx =
qL x − qx2 or Mx = q(l − x2 )
2
2
2
The ideal curve set by parabolic equation:
y = ax2 + bx + c
by finding a, b, and c we get:
y=
4fh(l − x)
l2
where h is depth of parabola. (our case f = e = 100)
by putting x = 41 l = 2000mm will get:
y=
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4 × 100 × 2000(8000 − 2000)
= 75mm
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the y = 75 mm is excentricity of prestressed at 14 l of the section.
the stress at 41 l section is:
f =
Fec
240 × 103 × 75 × 150
=
= 6 MPa.
1
3
I
12 × 200 × 300
Stress at L/4 section
-6
4
6
F
A
F ey
I
3
1
-3
MDL y
I
7
f=
F
A
±
F ey
I
±
My
I
the advantages of parabola curve that there is no tension at any section
of the beam.
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General Principles: C-line Method
Second Concept – Prestressing for Combination of High-Strength
Steel with Concrete.
This concept consider prestressed concrete as a combination of
steel and concrete, similar to reinforced concrete. with steel taking
tension and concrete taking compression so that the two materials
form a resisting couple against external moment.
From figure it is evident that the C-line is varying distance a from
the T-line. The moment given by:
M = Ca = Ta
while excentricity e is known, so e0 = a − e, since C = T, a = M/T
e0 =
M
−e
T
from figure:
ft =
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Ce0 ct
C
Ce0 ct
C
+
and fb =
−
Ac
Ic
Ac
Ic
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w=0
w=0
C=0
a
e
T =p C=p
T =0
l/2
l/2
(a)
a=0
(b)
w = w1
w = w1
C = C1
C=p
a
a = a1 = e
T =p
T = T1
l/2
w=w
l/2
(c)
w=w
(d)
C = C2
C=p
0
e
e
a
T =p
T = T2
l/2
l/2
(e)
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a
(f)
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Example: C-line Method
From previous parabolic tendon with excentrivity 100mm, at midle
section M = 12 kN.m , T = C = 240 kN
M
12 × 106
=
= 50 mm
T
240 × 103
e0 = a − e = 50 − 100 = −50 mm below cgc
a=
ft =
fb =
Fe0 ct
240 × 103
240 × 103 × 50 × 150
F
=
−
−
=0
1
3
A
Ic
200 × 300
×
200
×
300
12
F
Fe0 cb
240 × 103
240 × 103 × 50 × 150
+
=
+
=8
1
3
A
Ic
200 × 300
12 × 200 × 300
We get similar result compared to previous example.
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General Principles: Load Balancing Method
This technique is based on utilizing the vertical force of the draped or
harped prestressing tendon to counteract or balance the imposed
gravity loading to which a beam is subjected. Hence, it is applicable to
nonstraight prestressing tendons.
w
w
F
R
θ
F
wb
θ
(b)
(a)
Parabolic Tendon Profile.:
Let the parabolic function
y = Ax2 + Bx + C
represent the tendon drape; the force F denotes the pull to which the
tendon is subjected.
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Then for x = 0, we have.
y = 0,
dy
= 0,
dx
C=0
B=0
for x = l/2,
y = a,
A=
4a
l2
But from calculus, the load intensity is
q=F
∂2 y
∂x2
This will yield:
4a
8Fa
×2 = 2
2
l
l
Hence, if the tendon has a parabolic profile in the prestressed beam
and the prestressing force is denoted by F, the balanced-load intensity
q=F
wb =
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8Fa
l2
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Example: Load Balancing Method
As previous example, calculate balancing load:
wb =
8Fa
8 × 240 × 0.1
=
= 3 kN/m
l2
82
This upward balancing load will hold the dead load from structure,
the balancing load it self have twice the value of dead load (1.5kN/m).
The unbalance load (reserved capacity):
wub = 1.5 − 3 = −1.5 kN/m
or equivalent to:
1
1.5 × 82 = 12 kN.m
8
This potentially used to carry live load and supper imposed dead load.
M=
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Classification and Type
Based on method of
prestressing
Based on concreting
In-situ
Precast
pre-tensioning
Post-tensioning
Self stressing
Based on level of prestressing
Full prestressing
Partial prestressing
Based on position of tendons.
External prestressing
Internal prestressing
Based on concrete steel
interface
Based on tendon shapes
Bonded
Unbonded
Linear
Circular
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Advantage of Prestressed Concrete
1
Section remains uncracked under service loads
Reduction of steel corrosion: Increase in durability.
Full section is utilised: Higher moment of inertia, Less
deformations, Increase in shear capacity, Suitable for use in
pressure vessels, Improved performance (resilience) under
dynamic and fatigue loading
2
High span-to-depth ratios
Reduction in self weight.
More aesthetic appeal due to slender sections.
More economical sections.
3
Suitable for precast construction
Rapid construction
Better quality control
Reduced maintenance
Suitable for repetitive construction
Multiple use of formwork
Availability of standard shapes.
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Disadvantage of Prestressed Concrete
1
Prestressing needs skilled technology. Hence, it is not as common
as reinforced concrete.
2
The use of high strength materials is costly.
3
There is additional cost in auxiliary equipments.
4
There is need for quality control and inspection.
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Stages of Loading
Initial stage
Before Prestressing:
Support yield should be prevented,
Controlled curing is important,
Shrinkage crack should be prevented.
At transfer of Prestress:
Maximum tendon stress is limited (0.8fpu or 0.95fpy )
Crushing of concrete at the anchorage is prevented
Decentering and Retensioning:
False work maybe removed after prestressing
The stresses at various stages of tensioning must be studied
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Stages of Loading
Intermediate stage
This is the stage during transportation and erection. It is occur only for
precast member when they are transported to the site and erected in
position. It highly important to ensure
The member are properly supported
The member are properly handled
proper support condition and loading.
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Stages of Loading
Final stage
This is the stage when actual working loads come on stuuctures.
Sustained load
Control of camber and deflection.
Working Load
Check for excessive stresses and strins.
Cracking Load
Investigate the cracking load due to use of structures.
Ultimate Load
For code requirement, ultimate load should be calculated using
load factor and strength reduction factor.
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Reinforced vs Prestressed vs Partial Prestressed
Typical Load
Cracked with
deflection under
deadload and
full service load
Reinforced
Concrete
Reinforcing bar
Dead Load
Prestressed
Concrete
Prestressing Tendon
Uncracked with
likely camber
under dead load
and prestressed
Full Service Load
Dead Load
Partial
Prestressed
Concrete
Uncracked under
dead load
Cracked under
Service Load
Full Service Load
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Design Code for Prestressed Concrete
SNI 2847-2013 or ACI 318-11 already integrate the design of reinforced
and prestressed concrete design.
SNI 2847-2013 or ACI 318-11 already use unified provision, meanings
that there is no difference in strength reduction factors for reinforced
concrete or prestressed concrete.
Prestressed concrete sections shall be classified as either
tension-controlled, transition, or compression-controlled sections, in
accordance with 10.3.3 and 10.3.4. The appropriate strength reduction
factors, φ , from 9.3.2 shall apply.
The provisions of Chapter 18 of SNI/ACI were developed primarily
for structural members such as slabs, beams, and columns that are
commonly used in buildings.
For bridges structures AASHTO-LRFD Bridge Design Specifications
normally used or for indonesia RSNI T12 2004.
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Terminology
Tendon:
stretched element used in a concrete member of structure to
impart prestress to the concrete.
Anchorage:
A device generally used to enable the tendon to impart and
maintain prestress in concrete.
Pretensioning:
A method of prestressing concrete in which the tendons are
tensioned before the concrete is placed. In this method, the
concrete is introduced by bond between steel & concrete.
Post-tensioning:
A method of prestressing concrete by tensioning the tendons
against hardened concrete. In this method, the prestress is
imparted to concrete by bearing.
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Posttensioned Beam
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Pretensioned Beam
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External Prestressing
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Home Work
Find the prestressed structures that you think it is most attractive and
most innovative use of prestressing.
Pictures/ figures/ skets is good.
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