CASE STUDY TO DETERMINE THE CAMBER OF
POST-TENSIONED ‘ I ’ BEAM
LEE POH HUAT
UNIVERSITI TEKNOLOGI MALAYSIA
CASE STUDY TO DETERMINE THE CAMBER OF
POST- TENSIONED ‘I’ BEAM
LEE POH HUAT
A project report submitted in partial fulfilment of the
requirements for the award of the degree of
Master of Engineering ( Civil-Structure )
Faculty of Civil Engineering
Universiti Teknologi Malaysia
MARCH 2005
iii
To Elissa and Bryan
for your companionship, understanding and
continuous encouragement over the years.
iv
ACKNOWLEDGEMENT
I would like to thank Assoc. Prof. Dr. Wahid Omar for his guidance and advice
towards making this project a success. My sincere appreciation also goes to his
research team for their assistance in laboratory testing.
v
ABSTRACT
A common problem that most contractors faced in beam bridge construction
was to predict the actual camber of pre-tensioned or post-tensioned beams due to
prestressing in order to achieve bridge design finished levels without any unforeseen
additional construction cost. Four numbers of full scale 36m long post-tensioned “I”
beam with overall height of 1.98m was used to measure the actual beam camber on
site by means of checking the differences of beam’s top levels while design
estimation carried out is based on design code of practice for structural use of
concrete BS 8110 by taken into consideration initial prestress losses due to friction
and anchorage draw-in of tendons.
Comparison between these two methods of
evaluation reveals a significant difference. The results shows actual beam cambers
measured on site are much larger compare to design prediction. The immediate
camber occurred after prestressing is greater by 10.8% and continue to increase to
54.5% over 15 days with a sharp increase focused on the first 3 days after
prestressing. From the findings, it’s therefore concluded that deflection of posttensioned beam cannot be predicted accurately due to many field factors which may
possibly influence loss of prestress force in post-tensioned cables and behaviour of
beam cambering process.
However, design calculation can be used as an
approximate estimation or as a guide for construction purposes
vi
ABSTRAK
Suatu masalah umum yang sering dihadapi oleh kontraktor dalam kerja-kerja
pembinaan jambatan jenis rasuk pra-tegang atau pasca-tegang ialah usaha untuk
membuat anggaran nilai camber rasuk akibat daya mampatan dari tendon supaya
aras rekabentuk jambatan dapat dicapai tanpa perbelanjaan lebihan yang tidak
dijangka. Empat batang rasuk ‘I’ dengan panjang 36m serta tinggi 1.98m telah
digunakan dalam kajian ini bagi menentukan nilai camber sebenar di tapak secara
mengukur perbezaan aras atas rasuk. Pengiraan camber rasuk dibuat dengan
merujuk kepada BS 8110 dan mengambil kira nilai kehilangan daya tegangan akibat
geseran dan gelinciran tambat yang berlaku pada tendon.
Perbandingan yang
dijalankan ke atas kedua-dua jenis cara penilaian ini menunjukkan suatu perbezaan
yang ketara dimana nilai camber sebenar yang diperolehi dari tapak mempunyai
nilai yang lebih besar berbanding dengan hasil dari pengiraan. Camber awal yang
diperolehi dari tapak mempunyai nilai lebihan sebanyak 10.8% pada permulaan dan
meningkat kepada 54.5% dalam masa 15 hari selepas rasuk ditegang. Peningkatan
nilai camber ini tertumpu kepada 3 hari yang pertama dengan nilai penambahan
yang besar. Dari keputusan kajian ini, dapat disimpulkan bahawa nilai camber tidak
dapat dianggarkan dengan mudah dan tepat disebabkan oleh beberapa faktor yang
wujud di tapak yang berkemungkinan dapat mempengaruhi hilangan daya tegangan
pada tendon serta proses pembentukan camber rasuk.
Walau bagaimanapun,
pengiraan camber rasuk masih boleh digunakan sebagai anggaran kasar serta
panduan bagi tujuan pembinaan.
vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
Introduction
1
1.1 General
1
1.2
Problem Statement
2
1.3 Objective of Study
4
1.4 Scope of Study
4
Literature Review
6
2.1
6
Introduction
2.2 Materials for Prestressed Concrete
7
2.2.1 Concrete
7
2.2.2 Prestressing Reinforcement
8
2.2.3 Anchorage System and Equipment
9
2.3 Properties of Material for Prestressed Concrete
12
2.4
2.3.1 Strength of Concrete
12
2.3.2 Modulus of Elasticity of Concrete
13
2.3.3 Creep and Shrinkage of Concrete
14
2.3.4 Relaxation of Prestressing Steel
14
2.3.5 Corrosion and Deterioration of Strands
15
Prestressed Concrete
15
2.4.1 Advantage and Disadvantage of Prestressed Concrete 16
2.4.2 Prestressing System
17
viii
2.5
Partial Loss of Prestress Force
21
2.5.1 Elastic Shortening of Concrete
22
2.5.2 Friction Losses
23
2.5.3 Anchorage Draw-in
24
2.5.4 Concrete Shrinkage
26
2.5.5 Concrete Creep
27
2.5.6 Steel Relaxation
28
2.5.7 Total Prestress Losses
29
2.6 Deflection of Prestressed Concrete
29
2.6.1 Short-term Deflection of Uncracked Member
30
2.6.2 Long-term Deflection
32
2.6.3 Deflection of Cracked Member
33
2.7 Method of Construction for Post-tensioned Beam
3
4
35
2.7.1 Preparation of Base Form
35
2.7.2 Fixing of Reinforcement and Tendon
37
2.7.3 Erection of Steel Mould
38
2.7.4 Concreting of Beam
39
2.7.5 Stripping of Mould and Curing Concrete
41
2.7.6 Stressing and Grouting of Beam
41
Methodology
43
3.1
43
Introduction
3.2 Method of Measurement for Actual Beam Camber
44
3.3 Design Estimation for Beam Camber
47
3.4 Collection of Concrete Specimens
48
Results and Discussion
51
4.1
51
Introduction
4.2 Comparison of Beam Camber
4.3
52
Factors that Influence Beam Camber and
Prevention Method
54
ix
5
Conclusions and Recommendations
56
5.1
56
Conclusion
5.2 Recommendations for Future Study
References
Appendixes A - D
57
58
59 - 80
x
LIST OF TABLE
TABLE NO.
TITLE
2.1
Comprehensive strength for prestressed concrete
3.1
Beam’s top levels surveyed from site
PAGE
7
46
xi
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Schematic illustration of beam camber for a 3 spans bridge
3
1.2
Typical detail for 36m post-tensioned beam
5
2.1
Types of anchorage system
11
2.2
Tangent and secant modulus of concrete
13
2.3
Pre-tensioning method
18
2.4
Post-tensioning method
20
2.5
Draw-in loss : Variation in applied prestress
force with friction
2.6
26
Relationship between tendon eccentricity and
prestress moment diagram
31
2.7
Coefficient K for various type of bending moment diagram 34
3.1
Timber base form & metal side form
37
3.2
Installation of reinforcement and tendon
38
xii
3.3
Erection of steel mould in progress
39
3.4
Concreting of beam carried out by crane
40
3.5
Compaction of fresh concrete by means of
vibrating poker and external vibrator
41
3.6
Post- tensioning and grouting are in progress
43
3.7
Illustration of survey reference point on
post-tensioned beam
44
3.8
Preparation of concrete cylinder’s specimens
49
3.9
Curing of concrete specimens
50
4.1
Beam camber measured immediate after prestressing
52
4.2
Beam camber measured 15 days after prestressing
53
xiii
LIST OF SYMBOLS
ı co
-
stress in concrete at the level of tendon
ı pi
-
initial stress in tendon
Ac
-
the cross sectional area of concrete
Aps
-
cross sectional area of tendon
m
-
modular ratio for steel and concrete
r
-
radius of gyration
M ie
-
additional tensile stress at the level of tendon
e
-
eccentricity of tendon
e(x)
-
eccentricity at section x
Px
-
prestress force at distance x from jack
Po
-
jacking force
Pi
-
prestress force at distance i from jack
¨Pd
-
prestress loss due to anchorage draw-in
¨Psh
-
prestress loss due to shrinkage
¨Pcr
-
prestress loss due to creep
¨Pr
-
prestress loss due to relaxation of steel
L
-
length of tendon
Ld
-
extend of draw-in losses
Li
-
distance from jack to section i
Ec
-
modulus elasticity of concrete
Es
-
Young’s modulus of strand
Ec.eff
-
effective modulus of elasticity
Ect
-
instantaneous modulus of elasticity
Ic
xiv
İsh
-
shrinkage strain
İcr
-
creep strain
Nj
-
coefficient of friction
Ԧ
-
angle deviation of tendon
K
-
wobble factor
s
-
anchorage draw-in length
ij
-
creep coefficient
D
-
initial prestress losses
E
-
total prestress losses
ymax
-
maximum deflection at mid span
K
-
bending moment diagram’s shape constant
1/ rb
-
curvature at mid span or support for a cantilever
į
-
deflection of beam
Ic
-
moment of inertia of section
Ȗc
-
density of concrete
xv
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Calculation of design estimation
59
B
Beam camber measured on site
69
C
Beam camber profile after prestressing
76
D
Formation of beam camber against time
79
CHAPTER 1
INTRODUCTION
1.1
General
A bridge is a structure that spans a divide such as stream, river, ravine,
valley, railway track, roadway and waterway. The traffic that uses a bridge may
include pedestrian or cycle traffic, vehicular or rail traffic, water or gas pipes or a
combination of all the above. Bridges can generally be classified according to their
function, materials of construction, form of superstructure, span and type of service.
A bridge should be designed such that it is safe, aesthetically pleasing, and
economical.
In the construction of pre-tensioned or post-tensioned beam bridges, a very
common problem that most contractors faced was to determine and estimate the
actual upward deflection or camber of pre-tensioned or post-tensioned beams due to
prestressing. In order to achieve the design bridge finished levels without any
unforeseen additional construction cost, camber of beams shall be accurately
estimated. If it’s under estimated, then the finished design levels will not be able to
achieve without reducing the thickness of deck slab or bituminous wearing course.
2
While in the case of over estimated, the finished design levels can only be attained
by increasing the deck slab or wearing course thickness and this is certainly will
incurred additional construction cost.
1.2
Problem Statement
One of the important criteria in bridge design and construction is to produce
a smooth driving surface for a comfortable driving experience by the road user. In
order to achieve the design bridge surface finished levels without compromising on
the deck slab or bituminous wearing course thickness, camber on bridge surface
needs to be estimated and accounted for when the riding surface is established. If
camber of beam is not accounted for by designer and ignored by the contractor in a
multi span bridge construction, it may leads to an undulating or “roller coaster”
riding surface and potential hazard to travelling public especially on a superelevated
bridge deck.
To overcome this problem, camber of pre-tensioned or post-tensioned beams
shall be identified, and adjustment has to be made on the finished levels of beam
seats, abutment walls and piers based on the estimated beam cambers accordingly
and subsequently increase the thickness of deck slab at both ends of each span of
bridge to compensate the adjusted levels in order to produce a smooth bridge deck
surface. ( Figure 1.1 )
3
Beam camber for a 3 spans bridge
An undulating bridge surface due to fixed deck thickness
Thickening deck slab to overcome beam camber’s problem
Figure 1.1 : Schematic illustration of beam camber for a 3 spans bridge
4
1.3
Objective of Study
The purpose of this study is to determine the actual camber of post-tensioned
“I” beam. Among the objectives are :-
x
To determine the actual beam camber on site for post-tensioned “ I ” beam.
x
Compare beam camber between design estimation based on BS 8110 and
actual site data.
x
And, to identify various factors that can possibly influence the deflection of
post-tensioned beam.
1.4
Scope of Study
The scope of this study will be focused on full scale 36m long post-tensioned
“I” beam with overall height of 1.98m.( Figure 1.2 ) Field data for actual beam
camber will be measured base on differences of survey levels before and after
prestressing of post-tensioned cables, while design estimation is based on BS 8110.
The possible criteria that may affect deflection of post-tensioned beam such
as strength of concrete, modulus of elasticity, creep and shrinkage of concrete will
be monitored.
Insitu concrete specimens such as concrete cubes and concrete
cylinders will be collected and laboratory testing will also be carried out.
Figure 1.2 : Typical detail for 36m post-tensioned beam
5
CHAPTER II
Literature Review
2.1
Introduction
The precasting industry for prestressed concrete has in recent years become a
well-established entity.
Efficient management and outstanding quality control
procedures have awarded the industry a highly competitive position in the
construction market. Prestressed concrete superstructures generally eliminate the
need for construction falsework which has always been economically advantageous.
Like ordinary reinforced concrete, prestressed concrete consists of concrete
resisting compression and reinforcement resisting tension. Based on the concept that
reinforced concrete’s tensile strength is limited while its compressive strength is
extensive, consequently, prestressing become essential in many applications in order
to fully utilise the compressive strength of reinforced concrete and through proper
design, elimination or control of cracking and deflection can be achieved.
7
2.2
Materials for Prestressed Concrete
2.21
Concrete
Concrete, particularly high-strength concrete, is a major constituent of all
prestressed concrete elements. Strength and endurance are two major qualities that
are particularly important in prestressed concrete structures. Long-term detrimental
effects can rapidly reduce the prestressing forces and could result in unexpected
failure. Hence, measures have to be taken to ensure strict quality control and quality
assurance at the various stages of production.
The mechanical properties of hardened concrete can be classified into two
categories: short-term or instantaneous properties and long-term properties. The
short-term properties are strength in compression, tension, and shear; and stiffness,
as measured by the modulus of elasticity. The long-term properties can be classified
in terms of creep and shrinkage. The range of concrete strength normally used for
prestressed concrete is shown in Table 2.1
Table 2.1 : Comprehensive strength for prestressed concrete
Compressive strength at
Specified standard
initial prestress (N/mm²)
strength (N/mm²)
Post-tensioning system
More than 20
More than 24
Pre-tensioning system
More than 30
More than 35
8
In the pre-tensioning system, the anchorage of the prestressed concrete steel is
required to have enough bond strength as in the bond between steel and concrete.
So, higher values of specified standard strength are adopted compared to those of the
post-tensioning system where a lower value in strength is used as there is no
necessity for high bond strength due to the anchorage method.
2.22
Prestressing Reinforcement
Due to the high creep and shrinkage losses in concrete, effective prestressing
can be achieved by using very high-strength steel in prestressed concrete. Such highstressed steels are able to counterbalance these losses in the surrounding concrete
and have adequate leftover stress levels to sustain the required prestressing force.
Prestressing reinforcement used in prestressed concrete can be in the form of single
wire, strand or high strength bars covered by respective British Standards as follows:
i)
wire, (BS5896 : 1980)
ii)
strand, (BS5896: 1980)
iii)
bars,
(BS4486: 1980)
High strength steel wire came in a range of diameter from 3 to 7mm with
carbon content of 0.7-0.85%. For pre-tensioned concrete members, the prestress
force is transferred to the concrete by bond between the steel and concrete. This
bond is substantially increased if indentations are made on the wire surface such as
crimped and undulating instead of a straight.
Strand is produced by spinning several individual wires around a central core
wire for most prestressing application since single wire generally does not have
sufficient strength. Modern strands comprise of seven wires with overall diameters
ranging from 8 to 18mm are widely used in prestressing industry. Hot-rolled alloy-
9
steel bars are varying in diameter from 20 to 40mm, and are stretched once they
have cooled in order to improve their mechanical properties. They may be ribbed, to
provide a continuous thread, or smooth with threads at the ends of the bars. In both
cases the threads are used to anchor the bars or to provide a coupling between
adjacent bars.
The use of solid high-yield bars is generally limited as they do not have the
flexibility to be profiled along the length of the member. High tensile steel wire is
by far the more widely used material for both pre-tensioning and post-tensioning. In
post-tensioned concrete, it is common to group many strands together to form a
cable or tendon. A complete prestressing tendon can be made up of as many strands
as are needed to carry the required tension, will all the strands enclosed in a single
duct.
In addition, large structures may have many individual tendons running
parallel to each other along the length of the member.
An important point to consider with all the types of steel described above is
that their high strength is produce by essentially a cold-working process. Thus,
during storage and construction care must be taken not to expose the steel to heat
from causes such as welding.
2.23
Anchorage System and Equipment
For both pre-tensioning and post-tensioning of concrete members, specialist
equipment is required for stressing the steel and anchoring the stressed steel to the
concrete. A wide variety of systems has been developed for these purposes, many of
which are patented by their manufacturers. The tensioning of the steel is usually
achieved by mechanical jacking using hydraulic jacks. In pre-tensioning, the jacks
pull the steel against the supports of the casting beds. The strands in pre-tensioned
10
members are often stressed individually using small jacks. In post-tensioning, the
jacks pull the steel against the hardening concrete member itself. As the strands are
usually grouped in tendons, large multi-strand jacks are often used to tension all the
strands in the tendon simultaneously.
In pre-tensioning, before the prestress is transferred to the concrete a
temporary anchor are required to hold the ends of the strands while they are being
tensioned. One of the most popular methods of anchoring the ends of the strands in
the casting bed is the wedge grip of a tendon and to hold the strands permanently in
the tendon anchor. The bearing plate on the anchor transmits the force in the strands
to the main body of the assembly which in turn transmits the force to the
surrounding concrete. Some anchorage system and their devices are shown in
Figure 2.1
11
Figure 2.1 : Types of anchorage system
12
2.3
Properties of Material for Prestressed Concrete
2.31
Strength of Concrete
The strength of concrete is primarily affected by the water/cement ratio
where lower the water/cement ratio will gives higher concrete strength. A major
factor affecting strength is the amount of voids left in the concrete after compaction.
The more air contained in the concrete, the more compressible it becomes and gives
less strength. It is thus important that the concrete is compacted as fully as possible.
It is often the case that the concrete at the top of a horizontally cast member is s well
compacted than at the bottom and leading to lower strength. Another property of
concrete affected by poor compaction is the bond developed between the concrete
and any steel placed within it. This is particularly important for pre-tensioned
members, where reliance is made on this bond to transfer the prestress force to the
concrete.
The strength of concrete increases with age, but the rate at which it increases
is greatly affected by the curing conditions. Ideally, the concrete should be kept in a
moist condition to allow as much hydration of the cement as possible to take place.
Most concrete members are cured for the first few days under moist covering and
then cured in air. The usual range of concrete design strengths used in prestressed
concrete is 25-50 N/mm²,ȱwith values at the lower end of the range used for slabs,
and those at the upper end used for beams.
13
2.32
Modulus of Elasticity of Concrete
The modulus of elasticity of concrete is important, not only in estimating
deflections of prestressed concrete members but also because some of the losses of
prestress force are influenced by it. From the stress-strain curve of concrete shown
in Figure 2.2, the initial slope of the tangent to the curve is defined as the initial
tangent modulus, and it is also possible to construct a tangent modulus at any point
of the curve. The slope of the straight line that connects the origin to a given stress
at about 0.4f’c determines the secant modulus of elasticity of concrete. This value,
termed in design calculation the modulus of elasticity, satisfies the practical
assumption that strains occurring during loading can be considered basically elastic
or completely recoverable on unloading, and that any subsequent strain due to the
load is regarded as creep.
Figure 2.2 : Tangent and secant modulus of concrete
The values of secant modulus for concretes of varying strengths may be
used for determining the short-term deflections of prestressed concrete members and
the initial losses of prestress force due to elastic shortening.
For long-term
deflections, the time dependent effects of creep and shrinkage should be taken into
account.
14
2.33
Creep and Shrinkage of Concrete
Creep and shrinkage of concrete are time-dependent deformations. Creep of
concrete is the phenomenon in which the deformation continues with time under
constant load. Creep is particularly important in concrete, and affects both the longterm deflections and loss of prestress force in prestressed concrete member. The
basic mechanism of creep in concrete is that of gradual loss of moisture, causing
contraction in the structure of the cement paste in the concrete. The effects of creep
in prestressed concrete members are more pronounced than reinforced concrete due
to its greater proportion of the cross-section of the member is in compression.
Shrinkage is defined as decrease in the volume of concrete with respect to
time when surplus water that has not been used to hydrate the cement evaporated.
The amount of shrinkage is dependent on the environmental conditions surrounding
the concrete, and is independent of the external load on the member. If the concrete
is in a dry windy climate, the loss of moisture will be much greater than if the
concrete is kept in a moist condition.
2.34
Relaxation of Prestressing Steel
Relaxation of steel stress is similar to creep in concrete in that it is timedependent deformation under constant load except that creep is a change in strains
whereas steel relaxation is a loss in steel stresses. The amount of relaxation depends
on time, temperature and level of stress. The standard test for relaxation determines
the value of maximum relaxation in percentage after 1000 hours at 20° C. Two
classes of relaxation are specified in BS5896, Class 1 corresponding to stressrelieved, or normal-relaxation, wires, and Class 2 corresponding to stabilized, or
low-relaxation, wires.
15
2.35
Corrosion and Deterioration of Strands
Protection against corrosion of prestressing steel is more critical than in the
case of non-prestressed steel. Such precaution is necessary since the strength of the
prestressed concrete element is a function of the prestressing force, which in turn is a
function of the prestressing tendon area. Reduction of the prestressing steel area due
to corrosion can drastically reduce the nominal moment strength of the prestressed
section, which can lead to premature failure of the structural system.
In pre-tensioned members, protection against corrosion is provided by the
concrete surrounding the tendon, provided that adequate concrete cover is available.
In post-tensioned members, protection can be obtained by full grouting of the ducts
after prestressing is completed or by greasing. Another form of wire or strand
deterioration is stress corrosion, which is characterised by the formation of
microscopic cracks in the steel which lead to brittleness and failure. This type of
reduction in strength can occur only under very high stress, although it’s infrequent
but it’s difficult to prevent.
2.4
Prestressed Concrete
Precast and prestressed concrete is the most recent major form of
construction introduced in the structural engineering.
It has become a well
established method of construction where its technology is available in most
developed and in many developing countries. Today, prestressed concrete are used
in buildings, underground structures, communication towers, floating storage and
offshore structures, power stations, nuclear reactor vessels, and numerous types of
bridge systems including segmental and cable-stayed bridges.
16
In the field of bridge engineering, the introduction of prestressed concrete
has aided the construction of long-span concrete bridges. These often comprise
precast units, lifted into position and then tensioned against the units already in
place, the process being continued until the span is complete. For smaller bridges,
the use of simply supported precast prestressed concrete beams has proved an
economical form of construction, particularly where there is restricted access
beneath the bridge for construction. The introduction of ranges of standard beam
section has also simplified the design and construction of bridges.
The normal design procedures for precast and prestressed concrete beams are
to design for allowable working stresses and to check initial stresses and ultimate
moment capacity.
Camber of beams need to be estimated during design and
accounted for when the riding surface is established. For some low volume, low
speed or single span structure, camber is sometimes ignored. However, if camber of
beam is not accounted for in multi spans bridge structures, the undulating riding
surface produced may be potentially hazard to the travelling public.
2.4.1
Advantage and Disadvantage of Prestressed Concrete
One of the advantages of prestressed concrete over reinforced concrete is
that, for a given span and loading, a smaller prestressed concrete member is
required. Another important advantage of prestressed concrete is that by a suitable
prestressing, the structure can be rendered crack-free and this is an important
implication for durability, especially for liquid-retaining structures. By preventing
tensile cracking, it also means increasing the resistance of steel to corrosion. A third
advantage is that prestressing offers a means of controlling deflections where with a
suitable choice of prestress force, the deflections under applied load can be reduced
or eliminated entirely. In addition, prestressed concrete also increases the overall
stiffness of the member and can be fabricated in-situ or as precast units.
17
However, due to concrete cross section for perstressed concrete is in
compression under all load conditions, it means that any inherent problems due to
long-term creep movements will be increased. From construction point of view,
production of prestressed concrete required high level of quality control for both
materials and workmanship. Besides that, prestressed concrete also required certain
technology and equipment for prestressing works which may not be available in
many developing countries.
2.4.2 Prestressing System
Prestress is normally applied to members by steel strands tensioned using
hydraulic jacks at one or both ends of the member. The tensioning operation can be
performed either before the concrete is cast, in which case the member is classed as
pre-tensioned or after the concrete is cast, in which case the member is classed as
post-tensioned.
2.4.2.1 Pre-tensioning
The pre-tensioning process involves three basic stages, each of which is
illustrated in Figure 2.3. In the first stage, the steel strands are placed in a casting
bed, stressed to the required level and anchored between two supports. The concrete
is then cast around the strands and allowed to set. During this curing stage, the
strands bond to the surrounding concrete.
When the concrete has developed
sufficient compressive strength, the strands are release from the supports.
Immediately after the release, the strands attempt to contract. Owing to their bond
with the concrete this prestress contraction force is transferred to the concrete, thus
18
forcing the concrete into compression. Pre-tensioning is most commonly employed
where many similar precast members are required. It is generally only carried out
off site at precasting factories which have permanent casting beds. Therefore, the
size and weight of pre-tensioned members are limited by the transportation
requirements.
( a ) Stage 1 : Steel strands are tensioned
( b ) Stage 2 : Concrete is cast
( c ) Stage 3 : Strands are cut
Figure 2.3 : Pre-tensioning method
19
2.4.2.2 Post-tensioning
The post-tensioning process also involves three fundamental stages, which
are illustrated in Figure 2.4 for a simple beam. In the first stage of the process, the
concrete is cast around a hollow duct. After the concrete has set, a tendon consisting
of a number of strands is pushed through the duct or alternatively, the tendon can be
placed in the duct before casting. Thus, unlike in pre-tensioned members, the tendon
in post-tensioned members can be fixed in any desired linear or curved profile. By
varying the eccentricity of the tendon from the centroid, the maximum effectiveness
of a constant prestressing force can be utilized by applying the prestress only where
it is required. Once the concrete has achieved sufficient strength in compression, the
tendon is jacked from one or both ends using hydraulic jacks, thus putting the
concrete into compression. When the required level of prestress is achieved, the
tendon is anchored at the ends of the member.
After anchorage, the ducts are usually filled with grout under pressure. The
grout is provided mainly to prevent corrosion of the tendon but it also forms a bond
between the tendon and the concrete which reduces the dependence of the beam on
the integrity of the anchor and hence improves it robustness. Post-tensioning is the
most common method of prestressing in situ because it does not require a casting
bed. However, the technique is also used off site to make large purpose-built
individual precast units.
An important different between pre-tensioned and post-tensioned systems is
that it is easy to incorporate curved tendons in the post-tensioned system. The
flexible ducts can be held to a curved shape while the concrete is poured around
them while for pre-tensioned member, it would be extremely difficult to arrange for
a pre-tensioned curved tendon, although it is possible to have a sharp change of
direction. Other advantage of post-tensioning over pre-tensioning is that the
tensioning can be carried out in stages, for all tendons in a member, or for some of
them. This can be useful where the load is applied in well-defined stages.
20
( a ) Concrete is cast around hollow duct
( b ) Tendons is jacked from one end when concrete achieved sufficient strength
Figure 2.4 : Post-tensioning method
21
2.5
Partial Loss of Prestress Force
The design of a prestressed member involves checking the stresses in the
concrete at transfer and service due to the combination of applied loads and
prestressing. Owing to losses of force which occur in prestressing strands and
tendons, the effective prestress force which is transferred to the concrete is not
generally equal to the applied jacking force, nor is it constant along the length of the
member. Therefore, in order to determine the effective stress due to prestress at
transfer and service, the losses in prestress must first be calculated at each design
section. Essentially, the reduction in the prestressing force can be grouped into two
categories :
x
Immediate elastic loss during the fabrication or construction process, including
elastic shortening of the concrete, anchorage losses, and frictional losses.
x
Time-dependent losses such as creep, shrinkage, and steel relaxation, all of
which are determinable at the service-load limit state of stress in the
prestressed concrete element.
An exact determination of the magnitude of these losses, particularly the time
dependent ones is not feasible, since they depend on a multiplicity of interrelated
factors. Empirical methods for estimating losses differ with the different codes of
practice or recommendations.
22
2.5.1
Elastic Shortening of Concrete ( Clause 4.8.3, BS8110 )
As the prestress is transfer to the concrete, an elastic shortening of the
member occurs. This movement is accompanied by an equal reduction in length of
the prestressing steel resulting in loss in prestress force. For pre-tensioned beam,
loss in prestress force is m ı co where,
ı pi
ı co =
m +
Ac
Aps ( 1 + e² / r² )
If the tendons are closely grouped in the tensile zone, the loss due to elastic
shortening may be found by taking ı co as the stress in concrete at the level of the
centroid of the tendons. For post-tensioned beam, the elastic shortening loss varies
from zero if all tendons are jacked simultaneously to half the value calculated in the
pre-tensioned case. Loss in prestress force is 1/2mıco where,
ı pi
ı co =
m+
Ac
Mi e
Ic
Aps ( 1 + e² / r² )
The value of ı co will vary along the member, since generally both e and Mi will
vary. In this case, an average value of ı co should be assumed.
23
For a post-tensioned member with a single tendon, or with several tendons
tensioned simultaneously, there is no elastic shortening loss since jacking will
proceed until the desired prestress force is reached.
In the more usual and
economical case where the tendons are tensioned sequentially, after the first tendon
the tensioning of any subsequent tendon will reduce the force in those already
anchored, with the exception of the last tendon, which will suffer no loss.
While it is possible to determine the resulting forces in a group of tendons
for a given sequence of tensioning, the amount of work involved may be large. An
acceptable approximation is to assume that the loss in each tendon is equal to the
average loss in all the tendons. The loss for the first tendon is approximately equal
to mıco, and the loss for the last tendon is zero, so that the average loss is 1/2mıco.
2.5.2
Friction Losses ( Clause 4.9, BS8110 )
Loss of prestressing occurs in post-tensioning members due to friction
between the prestressing tendons and the inner surface of the ducts during
tensioning. There are basically four causes which produce frictions. First is the
curvature of the tendons to achieve a desired profile. Second is the inevitable, and
unintentional, deviation between the centrelines of the tendons and the ducts, known
as ‘wobble’ of the duct. This loss is described by a ‘wobble factor’ K which varies
with the rigidity of the duct, the frequency and the strength of the duct supports.
The combined effect of curvature and wobble gives the variation in prestress force
Px at a distance of x from the jack. Where,
Px = Po exp [ -(NjԦ + Kx)]
24
For a parabolic cable profile, since Ԧ represents the change in slope it is a
linear function of x. Thus, prestress force Po from the jack decreases linearly with
distance. For a circular arc, Ԧ = L/R is the change in slope or ‘angle consumed’
The third cause takes place as the tendons pass through the anchorages. This
effect is small, of the order of 2%, and is usually covered by the calculated duct
friction losses, which tend to be conservative. The fourth is also a small amount of
friction within the jack itself between the piston and the jack casing, which causes
the load applied to the tendon to be smaller than indicated by the hydraulic pressure
within the jack. This is usually determined by the jack manufacturer and
compensation made in the pressure gauge reading.
In pre-tensioned members there is some loss if the tendons are tensioned
against deflectors caused by friction between the tendon and the deflector. The
magnitude of this loss will depend upon the details of the deflector, and will usually
be determined from tests on the particular deflection system being used.
2.5.3
Anchorage Draw-in ( Clause 4.8.6, BS8110 )
In prestressed concrete, tendon may undergo a small contraction during the
process of transferring the tensioning force from the jack to the anchorage, this is
known as anchorage ‘draw-in’. The exact amount of this contraction depends on the
type of anchorage used and is usually specified by the manufacturer of the
anchorage. In the case of pre-tensioning, it can be compensated easily by initially
over-extending the tendons by the calculated amount of the anchorage drawn-in.
25
For post-tensioning, many anchorage systems use wedges to grip the tendon
and transfer the tendon force to a solid steel anchorage set in the concrete. There is
some deformation of the solid anchorage itself, but this is very small and most of the
contraction in the length of the tendon takes places as a result of slip between the
tendon and the wedges. This loss of prestressed does not extend very far from the
region of the anchor in most cases particularly in longer member. Since the
anchorage draw-in 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. However,
the effect is greatly reduced in post-tensioned members by the friction that exists
between the tendons and the ducts as the tendons move back due to the draw-in.
Losses in prestress due to anchorage draw-in, ¨Pd is given as :
Loss in Prestress Force, ¨Pd = ( s / L )(Es) Aps
And, the extend of draw-in losses around the anchor region as illustrated in
Figure 2.5 are given as :
½
Extend of Draw-in Losses, Ld = { s Es Aps Li / ( Po – Pi ) }
26
Tendon
jacking P
force
Po
¨Pd
Friction loss
Draw-in loss
Friction Loss Line
Ld
Pi
Distance from jack, x
Li
Figure 2.5 : Draw-in loss : Variation in applied prestress force with friction
2.5.4
Concrete Shrinkage ( Clause 4.8.4, BS8110 )
The magnitude of the shrinkage of concrete is affected by several factors.
They include mixture proportions, type of aggregate, type of cement, curing time,
time between the end of external curing and the application of prestressing, size of
the member, and the environmental conditions. Size and shape of the member also
effect shrinkage.
27
The loss of prestress in the tendons is obtained as the product of the
shrinkage per unit length of the concrete and the modulus of elasticity of the
tendons. The shrinkage strain İsh is taken as 300x10-6 for pre-tensioned work and
200x10-6 for post-tensioned concrete where stressing is assumed to take places 2-3
weeks after concreting. Normally, half the total shrinkage takes place in the first
month after transfer and ¾ of the total in the first 6 month.
Loss in Prestress Force Due to Shrinkage, ¨Psh = İsh (Es) Aps
2.5.5
Concrete Creep ( Clause 4.8.5, BS8110 )
The deformation or strain resulting from this time-dependent behaviour is a
function of the magnitude of the applied load, its duration, the properties of the
concrete including its mixture proportions, curing conditions, the age of the element
at first loading, and environmental conditions. Creep is essentially the same as that
of relaxation. The distinction is that relaxation refers to the loss of stress under
constant strain while creep is the increase of strain which occurs at constant stress.
For the purposes of prestressed concrete, relaxation occurs in the steel while
creep occurs in the concrete. Creep of concrete is unpredictable and can be quite
substantial in prestressed members where the stress is kept constant for the design
life of the structure.
Loss of Prestress due to Creep, ¨Pcr = İcr (Es) Aps
28
The creep strain used for calculating creep loss is given as, İsh = (ij ı c) / Ec
Where, ij is creep coefficient equal to 1.8 for transfer at 3 to 7 days and 1.4 for
transfer after 28 days.
2.5.6
Steel Relaxation ( Clause 4.8.2, BS8110 )
The long-term relaxation loss is specified in BS8110 as the 1000-hour
relaxation test values given by the tendon manufacturer multiply by factor given in
table 4.6 of BS8110. The initial force should be taken as the value immediately after
stressing for pre-tensioning and immediately after transfer for post-tensioning. The
relaxation factors given in table 4.6 include allowances for the effect of strain
reductions due to creep and shrinkage of the concrete and in the case of pretensioning, due to the elastic deformation of the concrete at transfer.
Loss of Prestress, ¨Pr = Relaxation Factors
Table 4.6 (BS8110)
x
1000 hour Test Value
(Clause 4.8.2.2 BS8110)
29
2.5.7
Total Prestress Losses
If the initial prestress force applied to a member is Po, then the effective
prestress force at transfers is DPo, while that at service load is EPo. The value of D
reflects the short term losses due to elastic shortening, anchorage draw-in and
friction while the total loss coefficient E accounts for the short term and long term
time dependent losses due to concrete shrinkage and creep and steel relaxation.
Although there are many factors which affect the total loss of prestress force,
as described in the preceding sections, it is very useful at the initial design stage to
have an approximate figure for the prestress loss. This can be refined later in the
design process, when more details of the prestressing steel are available. For both
pre-tensioned and post-tensioned members, the approximate values of D and E may
be taken as 0.9 and 0.75 respectively.
2.6
Deflection of Prestressed Concrete
In prestressed concrete member, deflections under a given load can be
eliminated entirely.
This is achieved by the use of a suitable arrangement of
prestressing. The deflection in prestressed concrete usually occurs with no applied
load; this is known as camber and is generally an upward deflection.
The effect of deflections in particular structures varies according to the use
of the structure. For bridge, excessive deflection may lead to the creation of pools of
water on road surface. It is recommended that for structures where the sag of a
member would be noticeable, the deflection under quasi-permanent load be limited
30
to L / 250, where L is the span of a beam or the length of a cantilever. This limit
may also be taken to apply to the initial upward camber for prestressed concrete
members.
The difficulty in predicting very accurately the total long term prestress
losses makes it more difficult to give a precise estimate of the magnitude of
expected camber. Concrete it self does not have a linear stress-strain curve, and the
load-deflection characteristics of concrete beams, reinforced or prestressed are nonlinear in general. Therefore, the method of calculation should be regarded as giving
only estimates of the deflections. For most structures, the best that can be said is
that the deflections lie within certain bounds.
In the case where if the exact
deflection of a particular structure is very important to know, the only reliable
method is to carry out test on a model of the structure by using similar materials.
As a general guideline, for beams carrying heavy loads, such as bridge
beams, a span:depth ratio in the range 20-26 for uncracked members would be
suitable, while for cracked floor of roof beams, a span:depth ratio in the range 26-30
would give a good initial estimate of section size.
2.6.1 Short-term Deflection of Uncracked Member
Short-term deflection in prestressed concrete member is calculated on the
assumption that the sections are homogeneous, isotropic and elastic.
Such an
assumption is an approximation of actual behaviour, particularly that the modulus of
concrete varies with age of the concrete and the moment of inertia varies with the
stage of loading. The prediction of deflection for uncracked prestressed concrete
members is more straightforward than reinforced concrete members, since the
ordinary strength-of-materials method for finding deflections are applicable. There
31
are several such methods and one of which is based on the principle of virtual work.
The principle of virtual work states that the work done by the external applied load,
W moving through the displacement, į given by the arbitrary deflected shape is
equal to the internal work done along the beam during that displacement. This work
is usually considered as that due to bending only. Thus,
L
Wį = œ
M(x)dø
0
where, M(x) is the bending moment at a section x induced by the applied load and ø
is the rotation of the member at that section due to the arbitrary displacement.
In order to determine the deflections of simply supported members under
prestress force only, use is made of the fact that the moment in the member at any
section x is equal to Pe(x) where e(x) is the eccentricity at that section. The prestress
moment diagram is thus proportional to the area between the member centroid and
the location of the resultant prestressing force. ( Figure 2.6 )
Moment diagram
Figure 2.6 : Relationship between tendon eccentricity and prestress moment diagram
32
2.6.2 Long-term Deflection
The deflections of prestressed concrete members determined above have
been short-term deflections caused by elastic deformation of the concrete in
response to loading. However, long term shrinkage and creep movements will cause
the deflection of concrete members to increase with time. The effects of creep may
be estimated by using a method given in BS8110 whereby an effective modulus of
elasticity Ec.eff is given by :
Ec.eff = Ect /( 1+ij )
Where, Ect is the instantaneous modulus of elasticity at the age considered and ij is
the creep coefficient. The value of Ect may be estimated from Clause 7.2 BS8110 :
Part 2.
When a concrete beam shrinks, it does not usually do so uniformly across the
section since it is restrained by the present of steel. The concentration of which is
usually greater on the tension face than the compression face, and this will gives rise
to an extra component of deflection. However, shrinkage effect can be taken into
account if necessary by increasing the long-term deflections caused by loading and
creep by approximately 20%.
33
In the case where only a proportion of the service load is permanent, the
long-term curvature of a section may be determined by using the following
procedure :
x
Determine the short-term curvature ( a ) under the permanent load
x
Determine the short-term curvature ( b ) under the total load
x
Determine the long-term curvature ( c ) under the permanent load
Total Long-term Curvature = Curvature (c ) + Curvature (b) – Curvature (a)
2.6.3 Deflection of Cracked Member
The ordinary strength-of-materials approach to the calculation of deflection
may be used for members uncracked in tensioned, but for cracked members, account
must be taken of the loss in stiffness of the section after cracking has occurred. The
general relationship between the curvature 1/ r at a point x along a member and the
corresponding deflection y is given by :
1 / r = d2y / dx2
34
A simplified method of finding the maximum deflection of concrete members is
outlined in BS8110 and is suitable for Class 3 members with low percentages of
prestressing steel. In this case, the maximum deflection ymax is given by ymax =
KL2/rb where L is the effective span, 1/ rb is the curvature at mid span or at the
support for a cantilever and K is a constant which depends on the shape of the
bending moment diagram. ( Figure 2.7 )
Figure 2.7 : Coefficient K for various type of bending moment diagram
CHAPTER III
Methodology
3.1
Introduction
This chapter discussed the method statements for construction of posttensioned beam and the method used to measure the actual beam camber on site.
Design estimation for beam camber was then carried out based on design code of
practice for structural use of concrete, BS 8110. The methods and procedures used
for preparation of concrete specimens was presented and it will be tested in
laboratory by other researchers from UTM to identify the properties of concrete used
such as compressive strength of hardened concrete, modulus of elasticity, creep of
concrete in compression and shrinkage of concrete.
The methodology for this case study to determine the camber of posttensioned beam can generally be classified into four sections as follows:
x
Method of construction for post-tensioned beam
x
Method of measurement for actual beam camber
x
Design estimation for beam camber
x
Collection of concrete specimens
36
3.2
Method of Construction for Post-tensioned Beam
3.2.1
Preparation of Base Formwork
The post-tensioned I-beam was casted on a timber base formwork, where it’s
rested on a well compacted earth platform. The base form is made of 2”x 3”, 3”x
6”, 6”x 6” hardwood timber and a 12mm thick tegofilm plywood. Between the
timber base and earth platform, sand bedding was used for levelling purposes.
( Figure 3.1 )
37
Figure 3.1 : Timber base form & metal side form
38
3.2.2
Fixing of Reinforcement and Tendon
Fixing of steel reinforcement as per approved bar bending schedule on top of
base formwork were carried out soon after completion of the timber bed.
In
conjunction to this, post-tensioned cables were installed accordingly to the height
and alignment of cable profiles as stated in the construction drawings. The end
plates of the beam and stressing anchor blockheads were then installed into position.
( Figure 3.2 )
Figure 3.2 : Installation of reinforcement and tendon
39
3.2.3
Erection of Steel Mould
Prior to erection, steel moulds for beam was applied with form release agent
in the inner face to ease the stripping process later. Then, it was erected on the base
formwork from one end to the other until the whole beam was fully covered. Angle
top guides were used to secure at the top portion of beam while M25 tie bars is used
at the bottom. Steel turn buckles was then installed to prop the side forms in order
to check the verticality and alignment of the beam. ( Figure 3.3 )
Figure 3.3 : Erection of steel mould in progress
40
3.2.4
Concreting of Beam
Upon completion of mould installation a final joint inspection were carried
out. Then, the concreting operation will proceed by using mobile crane and concrete
bucket. The concreting process was carried out in one operation (one casting) by
using grade 50 concrete and placed into steel mould in 4 horizontal layers. The
fresh concrete were then carefully compacted by using vibrator pokers from inside
and form ( external ) vibrator from outside. ( Figure 3.4 & 3.5 )
Figure 3.4 : Concreting of beam carried out by crane
41
Figure 3.5 : Compaction of fresh concrete by means of vibrating poker and
external vibrator
42
3.2.5
Stripping of Steel Mould & Curing Concrete
On the next day after concreting, steel moulds or side forms of beam were
removed. Soon after removal of formwork, curing of concrete was proceeded by
spraying curing compound to all bare concrete surfaces of the whole beam.
3.2.6
Stressing and Grouting of Beam
7 days after concreting, the concrete strength will be checked by crushing
test cubes.
When the minimum required concrete strength as manifested by
compressive cube strength results is achieved, the prestressing work can be
preceded. Stressing of post-tensioned cables were carried out by using a high
capacity multistrand jack and assisted by a high pressure hydraulic pump. Upon
completion, all cables were grouted as soon as possible to prevent it from any
corrosion by using pressure grout system. ( Figure 3.6 )
43
Figure 3.6 : Post- tensioning and grouting are in progress
44
3.3 Method of Measurement for Actual Beam Camber
The method of measurement carried out to identify beam camber on site was
based on differences of beam’s top levels before and after prestressing of posttensioned cables. Four numbers of 36m nominal length ‘I’ beam with height of
1.98m was used in this study where each of them was cast on site at consecutively
with one day interval.
In order to fulfil the purpose of this study to identify the maximum beam
camber at mid span, it was therefore the levelling reference points on top of beam
chosen to be 5 points with equal distance of 8.95m between each other. Thus, the
difference of levels between point No.3 and average of point No.1 and 5 will
represent the maximum beam camber. (Figure 3.7)
8850
Point 1
8850
Point 2
8850
Point 3
8850
Point 4
Point 5
Precast Post-tensioned ‘ I ’ Beam
35700
Figure 3.7 : Illustration of survey reference point on post-tensioned beam
45
The beam’s top levels were measured by using a survey dumpy level. A
datum reference was established to counter check for any vertical movement or
settlement of beam after prestressing. For this purpose, the top levels of base form
at both ends of beam was recorded and compared to the next session of levels taken.
Since the method of measurement are comparative in nature, the sequence of
reading taken are based on the same manner where one reading was taken before
prestressing while the other were recorded immediately after prestressing operation.
In order to observe the process of beam cambering due to time-dependent factors as
discussed in chapter 2, 5 continuous sets of readings was taken for the following 15
days after prestressing with 3 days interval for each set of reading. However, the
scope of this study is limited to comparison or determination of beam camber due to
initial prestress loss at the stage of transfer only.
Level readings recorded were then tabulated to ease the subsequence
calculation and data correction as given in Table 3.1. From these survey data, it’s
clearly shown that the beam’s top levels were uneven and ground settlement has
taken place at both ends of beams. Therefore, data correction was necessary in this
case. To overcome the problem of ground settlement, correction of survey data to
each reference point was made by adjusting the survey data for point No.2 to 4
based on apportioned difference of levels between point No.1 and 5 for each set of
reading taken. Then, correction due to beam’s surface unevenness was carried out
by determining difference of levels among all reference points before prestressing
and made adjustment accordingly. Hence, difference of beam levels between mid
span ( point No.3 ) and end of beam ( point No 1&5 ) are then can be considered as
actual beam camber.
46
Table 3.1 : Beam’s top levels surveyed from site
Beam No.
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
Reference Points
Beam’s Top Levels, ( mm )
1
1343
1338
1340
1484
1485
1480
1
136
1
1346
1340
1598
16
16
1594
1
1210
1194
1190
1447
146
5
1443
1
1233
1217
1213
146
9
1487
146
5
1
156
2
1545
1538
1802
1818
1796
1
1594
1577
1570
1834
1850
1829
1
16
30
16
10
16
03
186
9
1880
1858
2
1345
1335
1342
1472
1472
146
8
2
1329
1299
1313
1555
156
5
1558
2
116
9
1140
1157
1401
1412
1404
2
1189
1158
1180
1420
1434
1423
2
1518
1487
1505
1750
176
2
1753
2
1549
1516
1537
1778
1793
1784
2
1582
1550
156
9
1813
1825
1815
3
1347
1336
1342
146
6
146
3
146
3
3
1323
1289
1301
1533
1551
1544
3
116
1
1128
1142
1374
1395
1386
3
1180
1149
116
5
1394
1415
1403
3
1510
1478
1491
1724
1742
1730
3
1540
1507
1521
1751
1773
176
3
3
1573
1540
1553
1785
1805
1794
4
1348
1339
1345
146
5
146
0
1457
4
1344
1316
1329
1542
1545
1539
4
1188
116
1
1178
1385
1385
1380
4
1209
1182
1201
1404
1406
1400
4
1539
1512
1528
1733
1735
1730
4
1570
1541
1558
176
5
176
8
176
2
4
16
02
1574
1590
1799
1801
1793
5
1346
1338
1339
1456
1445
1445
5
136
9
1350
1346
1550
156
4
1554
5
1217
1208
1200
1402
1421
1405
5
1239
1231
1225
1425
1443
1425
5
156
9
156
2
1553
1755
1770
1755
5
16
01
1591
1584
1786
1804
1789
5
16
32
16
24
16
16
1820
1840
1822
Remarks
TBM
=
2209
TBM
=
2111
eLvels taken
on 11/1/2005
( Before
prestressing )
eLvels taken on 11/1/2005
( After prestressing )
TBM
=
2229
eLvels taken on 14/1/2005
TBM
=
2078
eLvels taken on 17/1/2005
TBM
=
2100
eLvels taken on 20/1/2005
TBM
=
2433
eLvels taken on 23/1/2005
TBM
=
246
5
eLvels taken on 26/1/2005
TBM
=
2494
47
3.2 Design Estimation for Beam Camber
Design estimation for beam camber was carried out based on design code of
practice for structural use of concrete, BS8110. Design criteria such as properties of
concrete and prestressing reinforcement was taken from construction drawing and
design manual while some assumption made was referred to recommendation from
BS8110. The principal of design estimation or prediction of beam camber applied in
this study is to determine the resultant value of hogging deflections produced by
prestress force from post-tensioned cables minus the sagging deflection caused by
beam’s self weight.
The calculation of initial prestress losses considered in the design estimation
is limited to prestress losses due to friction and anchorage drawn-in only and it’s
focused at the mid span of beam. For this purpose, the angle of deviation of tendon
at mid span, and the extend of anchorage draw-in for each tendons was first
identified. From the total prestress force after initial losses calculated, the upward
deflection of beam was then identified by equivalent weight method where
deflection at mid span of a uniformly loaded simply supported beam is given as :
į
=
5 L2
( Pe )
48EcIc
This equation was also used to calculate the sagging deflection due to self
weight of beam where moment of Pe was substituted by moment due to beam’s dead
load WL²/8. And, the resultant deflection value obtained from the differences between
these two opposite direction’s deflections is defined as estimated beam camber. In
order to plot this estimated beam camber as a parabolic profile for the purpose of
48
comparison with the actual beam camber on site, the coordinates of profile for first
quarter span ( L/4 ) and third quarter span (
3L
/4 ) of the parabolic curve was then
identified from parabolic profile’s equation y = Bx² + C. (The calculations of design
estimation for beam camber were attached in Appendix A).
3.3 Collection of Concrete Specimens
The specified characteristic strength of concrete used for casting of beam in
this study is 50 N/mm² at 28 days with concrete slump of 125 + 25mm. It was
produced in ready mix batching plant and transported to site by transit-mix concrete
truck. 5 trucks of concrete with concrete volume of 5m³ each are required for
casting of one beam and it took about 2 hours for discharging, placing and
compacting.
Two types of concrete specimens were collected for laboratory test. For
every casting of beam, 12 numbers of 150mm concrete cubes were prepared in cast
iron mould where fresh concrete was filled into moulds in 3 layers and compacted
with 25mm square steel punner for 25 strokes for each layer of concrete. On the
other hand, 15 numbers of concrete cylinders with 100mm diameter by 300mm long
were taken with UPVC mould in vertical position, placed in 3 equal layers and
compacted with 10mm diameter round ended tamping rod for 25 strokes each layer.
( Figure 3.8 )
For curing purposes, all concrete specimens prepared were covered with
wetted gunny sacks immediately after it has been finished by means of a float. On
the next day after casting, the mould is stripped and the concrete specimens are
further cured in water for the next 7 days. ( Figure 3.9 )
49
Figure 3.8 : Preparation of concrete cylinder’s specimens
50
Figure 3.9 : Curing of concrete specimens
CHAPTER IV
Results and Discussion
4.1
Introduction
The results from this study revealed that there are huge differences between
actual beam camber on site and design estimation. This shows the importance of
accuracy in predicting actual beam camber when riding surface of bridge is
established during design stage. Besides achieving its objective, the finding also
show the sequence of beam cambering formation and its behaviour after prestress of
post-tensioned cables, where it’s known to be an important criteria in beam bridge
construction.
In establishing the valid relationship between site measurement and design
prediction of beam camber and the cambering formation process against time, all the
collected data as attached in Appendix B and design estimation determined in
Appendix A were then plotted into a same graph as enclosed in Appendix C & D.
52
4.2
Comparison of Beam Camber
From design estimation the maximum beam camber is determined as
42.4mm while the maximum actual beam cambers immediately after prestressing
measured from site are ranging from 37mm to 57mm. This findings show that the
beam camber calculated from design is 10.8% lesser than actual beam camber on
site. (Figures 4.1)
Height of Camber, mm
60
50
40
30
20
10
0
0
8950
17900
26850
35800
Beam Length, mm
Beam 1
Beam 2
Beam 3
Beam 4
Design Profile
Figure 4.1 : Beam Camber Measured Immediate After Prestressing
Moreover, the results observed over 15 days after prestressing also show an
increase in cambering of beams to the range from 56mm to 75mm. This means an
increase of 18.5mm or 39.4% to a total difference of 54.5% if to compare with the
design value. (Figure 4.2)
Height of Camber, mm
53
80
70
60
50
40
30
20
10
0
0
8950
17900
26850
35800
Beam Length, mm
1
2
3
4
Design Profile
Figure 4.2 : Beam Camber Measured 15 days After Prestressing
Nevertheless, from all beam camber profiles plotted in Appendix D, it’s
clearly shows that a sharp increased in beam camber only happened during the first
3 days after prestressing, and after which, it increase steadily with only a small
margin.
Although it’s undeniable the importance of estimating precise beam camber
in bridge design and construction, but the difficulty of predicting very accurately as
discussed in Chapter 2 are proven to be a fact in this study. This can be seen from
the beam camber profile enclosed in Appendix C where the magnitudes of camber
for all beams used in this study are of different values.
54
4.3
Factors that Influence Beam Camber Prevention Method
As discussed in Chapter 2, the magnitude of beam camber due to prestressing
can be influenced by numerous factors such as :
x
Types of material
x
Prestressing system
x
Strength of concrete
x
Modules elasticity of concrete
x
Initial and time-dependent prestress losses
Besides that, other field factors related to method of construction may also
influence beam camber profile if it was not well taken care off during production of
beam.
During installation of post-tensioned cables, the vertical profile and
longitudinal alignment of tendons must be accurately position as per design
requirement because any change in tendon’s profile alignment regardless of vertical
on longitudinal position will change the eccentricity of tendon from the neutral axis
of beam. This will in turn affect the prestress force in tendon and subsequently
change the cambering behaviour of beam profile.
As discussed earlier, the strength of concrete plays an important role in
prestressed concrete particularly for pre-tensioned members. Therefore, the method
and sequence of placing concrete during production of beam can also affect the
pattern and consistency of beam camber profile. This is because not all trucks of
concrete delivered to site give same compressive strength value although they are
made of same materials. Thus, it’s advisable to place concrete into beam’s mould in
few horizontal layers from one end to the others until the whole beam is fully casted.
55
Other factors that may possibly influence beam camber are compaction of
fresh concrete and curing of concreted beam. These two factors are well recognised
facts that can affect strength of concrete and the amount of voids left in the concrete.
To overcome the compaction problem, external form vibrator that attached the beam
mould shall be used at the lower portions of beam as these are the area where hand
vibrator normally unable to work effectively due to the congested reinforcement and
prestressing tendons. As for curing of concrete, it shall be carried out soon after
removal of mould to prevent from excessive lost of water from concrete while it’s
developing strength for a minimum period of 7 days.
CHAPTER V
Conclusion and Recommendation
5.1
Conclusions
Computations of short-term deflections in prestressed concrete flexural
members are made with the assumption that the concrete section acts as an elastic
and homogeneous material. This assumption is only approximately correct, as the
elastic modulus for concrete is not a constant value for all stress levels. In addition,
the elastic modulus varies with the age of the concrete and is influenced by other
factors. Furthermore, differences between assumed and actual dimensions of the
concrete cross section and prestressed reinforcements often exist.
As a result,
deflection computations for prestressed concrete are approximations and should not
be considered to have high precision.
From the four post-tensioned beams studied, the results shows the actual
beam cambers measured are much larger than design estimation based on design
code BS 8110. It’s therefore can be concluded that deflection of post-tensioned
beam cannot be predicted accurately due to many field factors which may possibly
influence loss of prestress force in post-tensioned cables and behaviour of beam
57
cambering process. However, design calculation can be used as an approximate
estimation or as a guide for construction purposes.
5.2
Recommendation for Future Study
As the prestressing industry is gaining popular in Malaysia, particularly in
the field of bridge engineering, it would be desirable to recommend to carry out
future studies on this topic by evaluate the effects of creep and shrinkage of
concrete, modulus of elasticity of concrete, and environmental factors. Research is
also recommended to investigate beam camber for :
x
Other types of post-tensioned beam
x
Pre-tensioned beam
The data from such studies would be very helpful to validate the findings of
this study and it would be very useful as reference for future beam bridge
construction.
58
References
1.
Canrad P.Heins; Richard A Lawrie. (1984) “Design of Modern Concrete
Highway Bridges” A Wiley-Interscience Publication, Canada.
2.
M.K. Hurst. (1998) “Prestressed Concrete Design”, Second Edition, E & FN
Spon, London.
3.
Edward G. Nawy, (2000) “Prestressed Concrete (A Fundamental
Approach)”, Third Edition, Prentice Hall, New Jersey.
4.
Neville, A.M. ( 2002 ) “Properties of Concrete”, Fourth Edition, , Prentice
Hall, London.
5.
Eugene J.O’Brien; Andrew S. Dixon, (1995) “Reinforced and Prestressed
Concrete Design”, Longman Scientific & Technical, London.
6.
Shunran Takahashi, (2000) “Basic Design of Prestressed Concrete Structures
For Engineers”. Pelican Printing & Packaging Sdn Bhd, Malaysia.
7.
BS8110: Part 1, (1985) British Standard, Structural use of Concrete, British
Standards Institution, London.
APPENDIX A
Calculation of Design Estimation
Properties of Tendon :
Nominal cross section area, Aps = 98.7mm2/strand
Young’s modulus of strand, Es = 190 KN/mm2
Coefficient of friction, Nj = 0.20/rad
Wobble factor, K = 8x10-4/m
Anchorage draw-in, s = 7mm
No of strand in tendon and jacking force,
T1 = 12 nos (1656 KN)
T2 = 12 nos (1656 KN)
T3 = 19 nos (2622 KN)
T4 = 12 nos (1656 KN)
59
60
61
1.
Prestress Loss Due to Friction
From maximum sagging distance of all tendons, ǻY, value A for each parabolic
profile can be identified as follow:For tendon T1, when distance x = 17900mm, y = 1560mm
?
y = Ax2
A = 1560 / (17900)2
A = 4.868 x 10-6
Tendon
ǻY (mm)
L/2 (mm)
Value A
T4
1560
17900
4.868 x 10-6
T3
910
17900
2.840 x 10-6
T2
260
17900
8.115 x 10-6
T1
260
17900
8.115 x 10-6
62
Angle of deviation (rad) for tendon’s profile at mid span,
Ԧ = 4y / L
Ԧ
Ԧ
2Ԧ
Tendon T4
Deviation angle for tendon T4 at mid span,
Ԧ4 = 4y / L
Ԧ4 = 4 (1560) / 2 (17900)
Ԧ4 = 0.174 rad
Tendon force at mid span after friction losses for T4 ,
Px4 = Po exp [ -(NjԦ + Kx)]
Px4 = (1656) exp -[(0.20)(0.174) + (8x104)(17.9)]
Px4 = 1577 KN
Tendon T3
63
Deviation angle for tendon T3 at mid span,
Ԧ3 = 4y / L
Ԧ3 = 4 (910) / 2 (17900)
Ԧ3 = 0.102 rad
Tendon force at mid span after friction losses for T3 ,
Px3 = Po exp [ -(NjԦ + Kx)]
Px3 = (2622) exp -[(0.20)(0.102) + (8x104)(17.9)]
Px3 = 2533 KN
Tendon T1 & T2
Deviation angle for tendon T1 & T2 at mid span,
Ԧ1 = Ԧ2 = 4y / L
= 4 (260) / 2 (17900)
= 0.029 rad
Tendon force at mid span after friction losses for T1 & T2 ,
Px1 = Px2 = Po exp [ -(NjԦ + Kx)]
= (1656) exp -[(0.20)(0.029) + (8x104)(17.9)]
= 1623 KN
2.
Prestress Loss Due to Draw-in
64
Tendon T4
Extend of draw-in losses,
Ld =
sEsAps
½
(Po-Pi) /Li
Ld4 = (7)(190)(12 x 98.7)
½
(1656-1577) / (17900)
= 18892 mm > 17900 mm
Prestress losses due to anchorage draw-in,
ǻPd4 = (s/L)(Es)(Aps)
= (7 / 17900)(190)(12 x 98.7)
= 88 KN
By interpolation, draw-in loss at mid span = ( 88 / 18892 )( 18892-17900 )
= 4.6 KN
Therefore, tendon force at mid span after friction and draw-in losses,
P4 = 1577 - 4.6 = 1572.4 KN
Tendon T3
65
Extend of draw-in losses,
Ld3 = (7)(190)(19 x 98.7)
½
(2622-2533) / 17900
= 22397mm > 17900 mm
Prestress losses due to draw-in,
ǻPd3 = ( 7 / 17900 )(190)(19 x 98.7)
= 139.3 KN
Therefore, tendon force at mid span after friction and draw-in losses,
P3 = 2533 – (139.3 / 22397)(22397-17900)
= 2505 KN
Tendon T1 and T2
Extend of anchorage draw-in losses,
Ld1 = Ld2 = (7)(190)(12 x 98.7)
(1656-1623) / 17900
= 29231 mm > 17900 mm
Prestress losses due to anchorage draw-in,
½
66
ǻPd1 = ǻPd2 = ( 7 / 17900 )(190)(12 x 98.7)
= 88 KN
Therefore, tendon force at mid span after friction and draw-in losses,
P1 = P2 = 1623 – (88 / 29231)(29231-17900)
= 1589 KN
3.
Beam Camber due to Prestressing
Properties of concrete :
Cross section area of concrete, Ac = 0.628 m²
Density of concrete, Ȗc = 24 KN/m³
Moment of inertia of section, Ixx = 0.275 m4
Elastic modulus of concrete, Ec = 3.4 x 107 KN/m2
Total prestress force after initial prestress losses, P = 7255 KN
Centroid of beam from bottom, yc = 0.862 m
Centre of gravity of tendons from bottom, yt = 0.120 m
Eccentricity of tendons, e = 0.862 - 0.120 = 0.742 m
Camber at mid span,
įH = (5 L2 / 48EcIc)(Pe)
= 5(35.8) 2 (7255)(0.742) x 103
48(3.4 x 107)(0.275)
= 76.9 mm
4.
Beam Sagging due to Self Weight
67
Beam self weight, w = (24)(0.628) = 15.072 KN/m
Beam deflection at mid span,
įs = 5 wL4
384 EcIc
= 5(15.07)(35.8)4
x 103
384 (3.4x107)(0.275)
= 34.5 mm
Resultant beam camber, įR
įR = 76.9 – 34.5
= 42.4 mm
Camber at first quarter, L/4 and third quarter span, 3L/4
From Parabolic profile,
At mid span,
y = Bx² + C
y = 42.4 and x = 17900
B = 42.4
;
(17900)²
= 1.323 x 10-7
Hence,
y = 1.323 x10-7 x2
C=0
68
At
L
/4 and
Therefore,
3L
/4, x = 8950 mm
y = 1.323 x 10-7(8950)²
= 10.6 mm
And, Camber = 42.4 – 10.6
= 31.8 mm
Coordinates for design beam camber profile :
(0, 0); (8950, 31.8); (17900, 42.4); (8950, 31.8); (0, 0)
4
3
2
1
Beam
No.
1
1343
1343
1338
1338
1340
1340
1484
1484
2
1345
1344
1335
1335
1342
1342
1472
1479
3
1347
1346
1336
1336
1342
1343
1466
1480
4
1348
1346
1339
1339
1345
1346
1465
1486
5
1346
1343
1338
1338
1339
1340
1456
1484
Reference Points Survey
Levels, ( mm )
28
1
0
¨1&5
-3
7
0.25
0
±
-0.75
Adjustment
( 1 ) Level taken on 11/1/2005 ( before prestressing )
1470
1340
1338
Average
Levels of
Pt.1 & Pt.5
1345
1
2
0
0
0
-1
0
-14
0
2
-1
-1
3
3
-3
-2
-2
5
3
-3
-3
2
2
-3
-3
4
4
4
-4
-3
-1
-1
-6
-6
5
-2
Beam Camber ( mm )
Beam Camber Measured on Site
APPENDIX B
5
-2
0
0
0
1
0
14
0
Differences due to settlements
Differences due to surface unevenness
Remarks
69
1346
1346
1340
1340
1598
1598
3
4
1
1361
1361
1555
1567
1313
1312
1299
1298
2
1329
1327
1533
1557
1301
1298
1289
1287
3
1323
1319
1542
1578
1329
1325
1316
1313
4
1344
1338
1550
1598
1346
1340
1350
1346
5
1369
1361
Reference Points Survey
Levels, ( mm )
2
1
Beam
No.
48
-6
-4
¨1&5
-8
12
-1.5
-1
±
-2
Adjustment
1574
1343
1348
Average
Levels of
Pt.1 & Pt.5
1365
( 2 ) Level taken on 11/1/2005 ( immediately after prestressing )
1
4
0
0
2
0
0
3
0
0
-24
0
0
2
36
34
35
49
48
45
30
29
31
19
31
26
3
42
42
45
59
59
57
42
42
45
41
41
37
4
21
23
26
32
33
34
14
16
21
32
20
22
Beam Camber ( mm )
5
-4
0
0
-2
0
0
-3
0
0
24
0
0
Differences due to settlements
Camber after correction due to settlements
Actual beam camber
Remarks
70
1194
1194
1190
1190
1447
1447
3
4
1
1210
1210
1401
1412
1157
1155
1140
1137
2
1169
1167
1374
1397
1142
1137
1128
1121
3
1161
1158
1385
1419
1178
1171
1161
1151
4
1188
1183
1402
1447
1200
1190
1208
1194
5
1217
1210
Reference Points Survey
Levels, ( mm )
2
1
Beam
No.
( 3 ) Level taken on 14/1/2005
45
-10
-14
¨1&5
-7
11.25
-2.5
-3.5
±
-1.75
Adjustment
1425
1195
1201
Average
Levels of
Pt.1 & Pt.5
1214
1
4
0
0
7
0
0
5
0
0
-23
0
0
2
45
43
44
61
58
55
38
36
38
24
35
30
3
53
53
55
73
73
71
53
53
56
51
51
47
4
26
27
30
40
44
45
17
20
25
40
28
30
Beam Camber ( mm )
5
-4
0
0
-7
0
0
-5
0
0
23
0
0
Differences due to settlements
Camber after correction due to settlements
Actual beam camber
Remarks
71
1217
1217
1213
1213
1469
1469
3
4
1
1233
1233
1420
1431
1180
1177
1158
1155
2
1189
1188
1394
1416
1165
1159
1149
1142
3
1180
1177
1404
1437
1201
1192
1182
1172
4
1209
1205
1425
1469
1225
1213
1231
1217
5
1239
1233
Reference Points Survey
Levels, ( mm )
2
1
Beam
No.
( 4 ) Level taken on 17/1/2005
44
-12
-14
¨1&5
-6
11
-3
-3.5
±
-1.5
Adjustment
1447
1219
1224
Average
Levels of
Pt.1 & Pt.5
1236
1
3
0
0
7
0
0
6
0
0
-22
0
0
2
47
46
47
66
63
60
39
36
38
27
38
33
3
56
56
59
75
75
73
54
54
57
53
53
49
4
27
29
31
42
46
47
18
21
27
43
32
34
Beam Camber ( mm )
5
-3
0
0
-7
0
0
-6
0
0
22
0
0
Differences due to settlements
Camber after correction due to settlements
Actual beam camber
Remarks
72
1545
1545
1538
1538
1802
1802
3
4
1
1562
1562
1750
1762
1505
1501
1487
1483
2
1518
1516
1724
1748
1491
1484
1478
1470
3
1510
1507
1733
1768
1528
1517
1512
1499
4
1539
1534
1755
1802
1553
1538
1562
1545
5
1569
1562
Reference Points Survey
Levels, ( mm )
2
1
Beam
No.
( 5 ) Level taken on 20/1/2005
47
-15
-17
¨1&5
-7
11.75
-3.75
-4.25
±
-1.75
Adjustment
1779
1546
1554
Average
Levels of
Pt.1 & Pt.5
1566
1
4
0
0
9
0
0
8
0
0
-24
0
0
2
48
46
47
67
62
59
41
37
39
29
40
35
3
56
56
58
76
76
74
55
55
57
55
55
51
4
27
28
31
42
46
47
18
21
27
46
34
36
Beam Camber ( mm )
5
-4
0
0
-9
0
0
-8
0
0
24
0
0
Differences due to settlements
Camber after correction due to settlements
Actual beam camber
Remarks
73
1577
1577
1570
1570
1834
1834
3
4
1
1594
1594
1778
1790
1537
1534
1516
1513
2
1549
1547
1751
1775
1521
1514
1507
1500
3
1540
1537
1765
1801
1558
1548
1541
1531
4
1570
1565
1786
1834
1584
1570
1591
1577
5
1601
1594
Reference Points Survey
Levels, ( mm )
2
1
Beam
No.
( 6 ) Level taken on 23/1/2005
48
-14
-14
¨1&5
-7
12
-3.5
-3.5
±
-1.75
Adjustment
1810
1577
1584
Average
Levels of
Pt.1 & Pt.5
1598
1
4
0
0
7
0
0
7
0
0
-24
0
0
2
49
47
48
68
65
62
40
37
39
32
44
39
3
58
58
60
77
77
75
56
56
59
59
59
55
4
28
29
32
43
47
48
19
23
28
45
33
35
5
-4
0
0
-7
0
0
-7
0
0
24
0
0
Beam Camber ( mm )
Differences due to settlements
Camber after correction due to settlements
Actual beam camber
Remarks
74
1610
1610
1603
1603
1869
1869
3
4
1
1630
1630
1813
1825
1569
1566
1550
1547
2
1582
1582
1785
1810
1553
1547
1540
1533
3
1573
1572
1799
1836
1590
1580
1574
1564
4
1602
1601
1820
1869
1616
1603
1624
1610
5
1632
1630
Reference Points Survey
Levels, ( mm )
2
1
Beam
No.
( 7 ) Level taken on 26/1/2005
49
-13
-14
¨1&5
-2
12.25
-3.25
-3.5
±
-0.5
Adjustment
1845
1610
1617
Average
Levels of
Pt.1 & Pt.5
1631
1
1
0
0
7
0
0
7
0
0
-25
0
0
2
49
49
50
67
64
61
41
37
40
32
44
39
3
58
58
61
77
77
75
57
57
59
60
60
56
4
29
30
32
43
47
48
20
23
29
46
33
35
Beam Camber ( mm )
5
-1
0
0
-7
0
0
-7
0
0
25
0
0
Differences due to settlements
Camber after correction due to settlements
Actual beam camber
Remarks
75
APPENDIX C
76
Beam Camber Profile After Prestressing
Height of Camber, mm
Beam Camber Profile Immediately After Prestressing
60
50
40
30
20
10
0
0
8950
17900
26850
35800
Beam Length, mm
Beam 1
Beam 2
Beam 3
Beam 4
Design Profile
Height of Camber, mm
Beam Camber Profile 3 Days After Prestressing
80
70
60
50
40
30
20
10
0
0
8950
17900
26850
35800
Beam Length, mm
Beam 1
Beam 2
Beam 3
Beam 4
Design Profile
77
Beam Camber Profile 6 Days After Prestressing
Height of Camber, mm
80
70
60
50
40
30
20
10
0
0
8950
17900
26850
35800
Beam Length, mm
1
2
3
4
Design Profile
Beam Camber Profile 9 Days After Prestressing
Height of Camber, mm
80
70
60
50
40
30
20
10
0
0
8950
17900
26850
35800
Beam Length, mm
1
2
3
4
Design Profile
78
Height of Camber, mm
Beam Camber Profile 12 Days After Prestressing
80
70
60
50
40
30
20
10
0
0
8950
17900
26850
35800
Beam Length, mm
1
2
3
4
Design Profile
Height of Camber, mm
Beam Camber Profile 15 Days After Prestressing
80
70
60
50
40
30
20
10
0
0
8950
17900
26850
35800
Beam Length, mm
1
2
3
4
Design Profile
APPENDIX D
79
Formation of Beam Camber Against Time
Camber Profile for Beam No. 1
Height of Camber, mm
70
60
50
40
30
20
10
0
-10
0
8950
17900
26850
35800
Beam Length, mm
Before prestressing
After prestressing
3 days after prestressing
6 days after prestressing
9 days after prestressing
12 days after prestressing
15 days after prestressing
Design Profile
Camber Profile for Beam No. 2
Height of Camber, mm
70
60
50
40
30
20
10
0
-10
0
8950
17900
26850
35800
Beam Length, mm
Before prestressing
After prestressing
3 days after prestressing
6 days after prestressing
9 days after prestressing
12 days after prestressing
15 days after prestressing
Design Camber
80
Camber Profile for Beam No. 3
Height of Camber, mm
80
70
60
50
40
30
20
10
0
-10 0
8950
17900
26850
35800
Beam Length, mm
Before prestressing
After prestressing
3 days after prestressing
6 days after prestressing
9 days after prestressing
12 days after prestressing
15 days after prestressing
Design Camber
Height of Camber, mm
Camber Profile for Beam No. 4
60
50
40
30
20
10
0
0
8950
17900
26850
-10
35800
Beam Length, mm
Before prestressing
After prestressing
3 days after prestressing
6 days after prestressing
9 days after prestressing
12 days after prestressing
15 days after prestressing
Design Camber