Tính tóan sàn ứng lực
Post tensioned construction has for many years occu, posiltion, especially in the construction of bridges anh storage tanks. The reason for this lies in its decisive techinical and economical advantages.
POST-TENSIONED
SLABS
Fundamentals of the design process
Ultimate limit state
Serviceability limit state
Detailed design aspects
Construction Procedures
Preliminary Design
Execution of the calculations
Completed structures
4.2
VSL REPORT SERIES PUBLISHED BY
VSL INTERNATIONAL LTD.
Authors
Dr. P. Ritz, Civil Engineer ETH
P. Matt, Civil Engineer ETH
Ch. Tellenbach, Civil Engineer ETH
P. Schlub, Civil Engineer ETH
H. U. Aeberhard, Civil Engineer ETH
Copyright
VSL INTERNATIONAL LTD, Berne/Swizerland
All rights reserved
Printed in Switzerland
Foreword
With the publication of this technical report, VSL representatives we offer to interested parties
INTERNATIONAL LTD is pleased to make a throughout the world our assistance end
contribution to the development of Civil support in the planning, design and construction
Engineering. of posttensioned buildings in general and post-
The research work carried out throughout the tensioned slabs in particular.
world in the field of post-tensioned slab I would like to thank the authors and all those
structures and the associated practical who in some way have made a contribution to
experience have been reviewed and analysed the realization of this report for their excellent
in order to etablish the recommendations and work. My special thanks are due to Professor Dr
guidelines set out in this report. The document B. Thürlimann of the Swiss Federal Institute of
is intended primarily for design engineers, Technology (ETH) Zürich and his colleagues,
but we shall be very pleased if it is also of use who were good enough to reed through and
to contractors and clients. Through our critically appraise the manuscript.
Hans Georg Elsaesser
Chairman of the Board and President
Berne, January 1985 If VSLINTERNATIONALLTD
Table of contents
Page Page Page
1. lntroduction 2 5. Detail design aspects 13 9.5. Doubletree Inn, Monterey,
1.1. General 2 5.1. Arrangement of tendons 13 California,USA 30
1.2. Historical review 2 5.2. Joints 9.6. Shopping Centre, Burwood,
1.3. Post-tensioning with or Australia 30
without bonding of tendons 3 9.7. Municipal Construction Office
1.4. Typical applications of 6.Construction procedures 16 Building, Leiden,Netherlands 31
post-tensioned slabs 4 6.1.General 16 9.8.Underground garage for ÖVA
6.2. Fabrication of the tendons 16 Brunswick, FR Germany 32
6.3.Construction procedure for 9.9. Shopping Centre, Oberes Muri-
2. Fundamentals of the design process 6 bonded post-tensioning 16 feld/Wittigkooen, Berne,
2.1. General 6 6.4.Construction procedure for Switzerland 33
2.2. Research 6 unbonded post-tensioning 17 9.10. Underground garage Oed XII,
2.3. Standards 6 Lure, Austria 35
9.11. Multi-storey car park,
7. Preliminary design 19 Seas-Fee, Switzerland 35
9.12. Summary 37
3. Ultimate limit state 6
3 1 Flexure 6
3.2 Punching shear 9 8. Execution of the calculations 20 10. Bibliography 38
8.1. Flow diagram 20
8.2. Calculation example 20
Appendix 1: Symbols/ Definitions/
4. Serviceability limit state 11 Dimensional units/
41 Crack limitation 11 9. Completed structures 26 Signs 39
42. Deflections 12 9.1.Introduction 26
43 Post-tensioning force in 9.2.Orchard Towers, Singapore 26
the tendon 12 9.3. Headquarters of the Ilford Group, Appendix 2: Summary of various
44 Vibrations 13 Basildon, Great Britain 28 standards for unbond-
45 Fire resistance 13 9.4.Centro Empresarial, São Paulo, ed post-tensioning 41
4Z Corrosion protection 13 Brazil 28 1
1. Introduction
1.1. General
Post-tensioned construction has for many
years occupied a very important position,
especially in the construction of bridges and
storage tanks. The reason for this lies in its
decisive technical and economical
advantages.
The most important advantages offered by
post-tensioning may be briefly recalled here:
- By comparison with reinforced concrete, a
considerable saving in concrete and steel
since, due to the working of the entire
concrete cross-section more slender
designs are possible.
- Smaller deflections than with steel and
reinforced concrete.
- Good crack behaviour and therefore
permanent protection of the steel against
corrosion.
- Almost unchanged serviceability even
after considerable overload, since
temporary cracks close again after the
overload has disappeared.
- High fatigue strength, since the amplitude
of the stress changes in the prestressing
steel under alternating loads are quite
small.
For the above reasons post-tensioned
construction has also come to be used in Figure 1. Consumption of prestressing steel in the USA (cumulative curves)
many situations in buildings (see Fig 1).
The objective of the present report is to
summarize the experience available today
in the field of post-tensioning in building
construction and in particular to discuss
the design and construction of post-
tensioned slab structures, especially post-
tensioned flat slabs*. A detailed
explanation will be given of the checksto
be carried out, the aspects to be
considered in the design and the
construction procedures and sequences
of a post-tensioned slab. The execution of
the design will be explained with reference
to an example. In addition, already built
structures will be described. In all the
chapters, both bonded and unbundled
post-tensicmng will be dealt with.
In addition to the already mentioned general
features of post-tensioned construction, the
following advantages of post-tensioned slabs
over reinforced concrete slabs may be listed:
- More economical structures resulting Figure 2: Slab thicknesses as a function of span lengths (recommended limis slendernesses)
from the use of prestressing steels with a
very high tensile strength instead of
normal reinforcing steels.
- larger spans and greater slenderness
(see Fig. 2). The latter results in reduced 1.2. Historical review
dead load, which also has a beneficial
effect upon the columns and foundations Although some post-tensioned slab experiments on post-tensioned plates (see
and reduces the overall height of structures had been constructed in Europe Chapter 2.2). Joint efforts by researchers,
buildings or enables additional floors to quite early on, the real development took design engineers and prestressing firms
be incorporated in buildings of a given place in the USA and Australia. The first post- resulted in corresponding standards and
height. recommendations and assisted in promoting
tensioned slabs were erected in the USA In
- Under permanent load, very good
1955, already using unbonded post- the widespread use of this form of
behavior in respect of deflectons and
tensioning. In the succeeding years construction in the USA and Australia. To
crackIng.
- Higher punching shear strength numerous post-tensioned slabs were date, in the USA alone, more than 50 million
obtainable by appropriate layout of designed and constructed in connection with m2 of slabs have been post tensioned.
tendons the lift slab method. Post-tensionmg enabled In Europe. renewed interest in this form of
- Considerable reduction In construction the lifting weight to be reduced and the construction was again exhibited in the early
time as a result of earlier striking of deflection and cracking performance to be seventies Some constructions were
formwork real slabs. improved. Attempts were made to improve completed at that time in Great Britain, the
knowledge In depth by theoretical studies and Netherlands and Switzerland.
* For definitions and symbols refer to appendix 1.
2
Intensive research work, especially in
Switzerland, the Netherlands and Denmark
and more recently also in the Federal
Republic of Germany have expanded the
knowledge available on the behaviour of
such structures These studies form the basis
for standards, now in existence or in
preparation in some countries. From purely
empirical beginnings, a technically reliable
Figure 3: Diagrammatic illustration of the extrusion process
and economical form of constructon has
arisen over the years as a result of the efforts
of many participants. Thus the method is now
also fully recognized in Europe and has
already found considerable spreading
various countries (in the Netherlands, in
Great Britain and in Switzerland for example).
1.3. Post-tensioning with or
without bonding of tendons
1.3.1. Bonded post-tensioning
As is well-known, in this method of post-
tensioning the prestressing steel is placed In
ducts, and after stressing is bonded to the
surrounding concrete by grouting with
cement suspension. Round corrugated ducts
are normally used. For the relatively thin floor
slabs of buildings, the reduction in the Figure 4: Extrusion plant
possible eccentricity of the prestressing steel
with this arrangement is, however, too large, Arguments in favour of post-tensioning
in particular at cross-over points, and for this without bonding:
reason flat ducts have become common (see - Maximum possible tendon eccentricities,
also Fig. 6). They normally contain tendons
since tendon diameters are minimal; of
comprising four strands of nominal diameter
special importance in thin slabs (see Fig
13 mm (0.5"), which have proved to be
logical for constructional reasons. 6).
- Prestressing steel protected against
Figure 5: Structure of a plastics-sheathed,
greased strand (monostrantd) corrosion ex works.
1.32. Unbonded post-tensioning - Simple and rapid placing of tendons.
In the early stages of development of post- - Very low losses of prestressing force due
tensioned concrete in Europe, post- Strands sheathed in this manner are known to friction.
tensioning without bond was also used to as monostrands (Fig. 5). The nominal - Grouting operation is eliminated.
some extent (for example in 1936/37 in a diameter of the strands used is 13 mm (0.5") - In general more economical.
bridge constructed in Aue/Saxony [D] and 15 mm (0.6"); the latter have come to be Arguments for post-tensioning with bonding:
according to the Dischinger patent or in 1948 used more often in recent years. - Larger ultimate moment.
for the Meuse, Bridge at Sclayn [B] designed
- Local failure of a tendon (due to fire,
by Magnel). After a period without any
1.3.3. Bonded or unbonded? explosion, earthquakes etc.) has only
substantial applications, some important
This question was and still is frequently the limited effects
structures have again been built with
subject of serious discussions. The subject Whereas in the USA post-tensioning without
unbonded post-tensioning in recent years.
In the first applications in building work in the will not be discussed in detail here, but bonding is used almost exclusively, bonding
USA, the prestressing steel was grassed and instead only the most important arguments is deliberately employed in Australia.
wrapped in wrapping paper, to facilitate its far and against will be listed:
longitudinal movement during stressing
During the last few years, howeverthe Figure 6 Comparison between the eccentricities that can be attained with various types of
method described below for producing the tendon
sheathing has generally become common.
The strand is first given a continuous film of
permanent corrosion preventing grease in a
continuous operation, either at the
manufacturer’s works or at the prestressing
firm. A plastics tube of polyethylene or
polypropylene of at least 1 mm wall thickness
is then extruded over this (Fig. 3 and 4). The
plastics tube forms the primary and the
grease the secondary corrosion protection.
3
Among the arguments for bonded post- 1.4. Typical applications of Typical applications for post-tensioned slabs
tensioning, the better performance of the post-tensioned slabs may be found in the frames or skeletons for
slabs in the failure condition is frequently office buildings, mule-storey car parks,
emphasized. It has, however, been As already mentioned, this report is con- schools, warehouses etc. and also in multi-
demonstrated that equally good structures cerned exclusively with post-tensioned slab storey flats where, for reasons of internal
can be achieved in unbonded post- structures. Nevertheless, it may be pointed space, frame construction has been selected
tensioning by suitable design and detailing. out here that post-tensioning can also be of (Fig. 12 to 15).
It is not the intention of the present report to economic interest in the following What are the types of slab system used?
express a preference for one type of post- components of a multi-storey building: - For spans of 7 to 12 m, and live loads up
2
tensioning or the other. II is always possible - Foundation slabs (Fig 7). to approx. 5 kN/m , flat slabs (Fig. 16) or
that local circumstances or limiting - Cantilevered structures, such as slabs with shallow main beams running in
engineering conditions (such as standards) overhanging buildings (Fig 8). one direction (Fig. 17) without column
may become the decisive factor in the - Facade elements of large area; here light head drops or flares are usually selected.
choice. Since, however, there are reasons for post-tensioning is a simple method of - For larger spans and live loads, flat slabs
assuming that the reader will be less familiar preventing cracks (Fig. 9). with column head drops or flares (Fig 18),
with undonded post-tensioning, this form of - Main beams in the form of girders, lattice slabs with main beams in both directions
construction is dealt with somewhat more girders or north-light roofs (Fig. 10 and 11). (Fig 19) or waffle slabs (Fig 20) are used.
thoroughly below.
Figure 7: Post-tensioned foundation slab
Figure 9: Post-tensioned facade elements Figure 8: Post-tensioned cantilevered building
Figure 10: Post-tensioned main beams Figure 11: Post-tensioned north-light roofs
4
Figure 12: Office and factory building Figure 13: Multi-storey car park
Figure 14: School
Figure 16: Flat Slab Figure 15: Multi-storey flats
Figure 17: Slab with main beams in one direction Figure 18: Flat slab with column head drops
Figure 19: Slab with main beams in both directions Figure 20: Waffle slab
5
2. Fundamentals of the
design process
2.1. General 2.2. Research reinforced slabs will be found in [24]. The
The objective of calculations and detailed The use of post-tensioned concrete and thus influence of post-tensioning on punching
design is to dimension a structure so that it also its theoretical and experimental shear behaviour has in recent years been the
will satisfactorily undertake the function for development goes back to the last century. subject of various experimental and
which it is intended in the service state, will From the start, both post-tensioned beam theoretical investigations [7], [25], [26], [27].
possess the required safety against failure, and slab structures were investigated. No Other research work relates to the fire
and will be economical to construct and independent research has therefore been resistance of post-tensioned structures,
maintain. Recent specifications therefore carried out for slabs with bonded pos- including bonded and unbonded post-
demand a design for the «ultimate» and tensioning. Slabs with unbonded post- tensioned slabs Information on this field will
«serviceability» limit states. tensioning, on the other hand, have been be found, for example, in [28] and [29].
Ultimate limit state: This occurs when the thoroughly researched, especially since the In slabs with unbonded post-tensioning, the
ultimate load is reached; this load may be introduction of monostrands. protection of the tendons against corrosion is
limited by yielding of the steel, compression The first experiments on unhonded post- of extreme importance. Extensive research
failure of the concrete, instability of the tensioned single-span and multi-span flat has therefore also been carried out in this
structure or material fatigue The ultimate slabs were carried out in the fifties [1], [2]. field [30].
load should be determined by calculation as They were followed, after the introduction of
accurately as possible, since the ultimate monostrands, by systematic investigations
limit state is usually the determining criterion into the load-bearing performance of slabs 2.3. Standards
Serviceability limit state: Here rules must with unbonded post-tensioning [3], [4], [5],
be complied with, which limit cracking, [6], [7], [8], [9], [10] The results of these Bonded post-tensioned slabs can be
deflections and vibrations so that the normal investigations were to some extent embodied designed with regard to the specifications on
use of a structure Is assured. The rules in the American, British, Swiss and German, post-tensioned concrete structures that exist
should also result in satisfactory fatigue standard [11], [12], [13], [14], [15] and in the in almost all countries.
strength. FIP recommendations [16]. For unbonded post-tensioned slabs, on the
The calculation guidelines given in the Various investigations into beam structures other hand, only very few specifications and
following chapters are based upon this are also worthy of mention in regard to the recommendations at present exist [12], [13],
concept They can be used for flat slabs development of unbonded post-tensioning [15]. Appropriate regulations are in course of
with or without column head drops or [17], [18], [19], [20],[21], [22], [23]. preparation in various countries. Where no
flares. They can be converted The majority of the publications listed are corresponding national standards are in
appropriately also for slabs with main concerned predominantly with bending existence yet, the FIP recommendations [16]
beams, waffle slabs etc. behaviour. Shear behaviour and in particular may be applied. Appendix 2 gives a
punching shear in flat slabs has also been summary of some important specifications,
thoroughly researched A summary of either already in existence or in preparation,
punching shear investigations into normally on slabs with unbonded post-tensioning.
3. Ultimate limit state
3.1. Flexure The prestress should not be considered as gives an ultimate load which lies on the sate
3.1.1. General principles of calculation an applied load. It should intentionally be side.
Bonded and unbonded post-tensioned taken into account only in the determination In certain countries, the forces resulting from
slabs can be designed according to the of the ultimate strength. No moments and the curvature of prestressing tendons
known methods of the theories of elasticity shear forces due to prestress and therefore (transverse components) are also treated as
and plasticity in an analogous manner to also no secondary moments should be applied loads. This is not advisable for the
ordinarily reinforced slabs [31], [32], [33]. calculated. ultimate load calculation, since in slabs the
A distinction Is made between the follow- determining of the secondary moment and
The moments and shear forces due to
ing methods: therefore a correct ultimate load calculation
applied loads multiplied by the load factor
A. Calculation of moments and shear forces is difficult.
must be smaller at every section than the
according to the theory of elastimry; the The consideration of transverse components
ultimate strength divided by the cross-section
sections are designed for ultimate load. does however illustrate very well the effect of
factor.
prestressing in service state. It is therefore
B. Calculation and design according to the The ultimate limit state condition to be met
highly suitable in the form of the load
theory of plasticity. may therefore be expressed as follows [34]:
balancing method proposed by T.Y. Lin [35]
S ⋅γ f ≤ R (3.1.) for calculating the deflections (see Chapter
Method A γm
4.2).
In this method, still frequently chosen today, This apparently simple and frequently
moments and shear forces resulting from encoutered procedure is not without its
Method B
applied loads are calculated according to problems. Care should be taken to ensure In practice, the theory of plasticity, is being
the elastic theory for thin plates by the that both flexure and torsion are allowed for increasingly used for calculation and design
method of equivalent frames, by the beam at all sections (and not only the section of The following explanations show how its
method or by numerical methods (finite maximum loading). It carefully applied this application to flat slabs leads to a stole
method, which is similar to the static ultimate load calculation which will be easily
differences,finite elements).
method of the theory of plasticity, understood by the reader.
6
The condition to be fulfilled at failure here is:
(g+q) u ≥ γ (3.2.)
g+q
where γ=γf . γm
The ultimate design loading (g+q)u divided by
the service loading (g+q) must correspond to a
value at least equal to the safety factor y.
The simplest way of determining the ultimate
design loading (g+q)u is by the kinematic
method, which provides an upper boundary
for the ultimate load. The mechanism to be
chosen is that which leads to the lowest load.
Fig. 21 and 22 illustrate mechanisms for an
internal span. In flat slabs with usual column
dimensions (ξ>0.06) the ultimate load can be
Figure 21: Line mecanisms Figure 22: Fan mecanisms
determined to a high degree of accuracy by
the line mechanisms ! or " (yield lines 1-1 or
2-2 respectively). Contrary to Fig. 21, the
negative yield line is assumed for purposes of
approximation to coincide with the line
connecting the column axes (Fig. 23),
although this is kinematically incompatible. In
the region of the column, a portion of the
internal work is thereby neglected, which leads
to the result that the load calculated in this way
lies very close to the ultimate load or below it.
On the assumption of uniformly distributed top
and bottom reinforcement, the ultimate design
loads of the various mechanisms are
compared in Fig. 24. Figure 24: Ultimate design load of the
In post-tensioned flat slabs, the prestressing various mecanisms as function of column
diemnsions
and the ordinary reinforcement are not
uniformly distributed. In the approximation, Figure 23: Line mecanisms (proposed
however, both are assumed as uniformly approximation) Figure 25: Assumed distribution of the
reinforcement in the approximation
distributed over the width I1 /2 + 12 /2 (Fig. 25). method
The ultimate load calculation can then be
carried out for a strip of unit width 1. The actual
distribution of the tendons will be in
accordance with chapter 5.1. The top layer
ordinary reinforcement should be
concentrated over the columns in accordance
with Fig. 35.
The load corresponding to the individual
mechanisms can be obtained by the principle
of virtual work. This principle states that, for a
virtual displacement, the sum of the work We
performed by the applied forces and of the
dissipation work W, performed by the internal
forces must be equal to zero.
(g+q)u = 8 . mu . (1+ λ) (3.7.)
We +Wi,=0 (3.3.) 2
If this principle is applied to mechanism ! l 2
(yield lines 1-1; Fig. 23), then for a strip of
Edge span with cantilever:
width I1/2 + 1 2/2 the ultimate design load (g+q)
u is obtained.
internal span:
7
For complicated structural systems, the tensioned steel at a nominal failure state is
determining mechanisms have to be found. estimated and is incorporated into the
Descriptions of such mechanisms are calculation together with the effective stress
available in the relevant literature, e.g. [31], present (after losses due to friction, shrinkage,
[36]. creep and relaxation). The nominal failure
In special cases with irregular plan shape, state is established from a limit deflection a .u
recesses etc., simple equilibrium considera- With this deflection, the extensions of the
tions (static method) very often prove to be a prestressed tendons in a span can be
suitable procedure. This leads in the simplest determined from geometrical considerations.
case to the carrying of the load by means of Where no lateral restraint is present (edge
beams (beam method). The moment Figure 26: ultimate strenght of a spans in the direction perpendicular to the free
distribution according to the theory of elasticity cross-section (plastic moment) edge or the cantilever, and corner spans) the
may also be calculated with the help of relationship between tendon extension and
computer programmes and internal stress For unbonded post-tensioning steel, the the span I is given by:
states may be superimposed upon these question of the steel stress that acts in the ∆I 4 . au . yp = 3 . au . dp (3.13.)
=
moments. The design has then to be done ultimate limit state arises. If this steel stress is I I I I I
according to Method A. known (see Chapter 3.1.3.), the ultimate
strength of a cross-section (plastic moment) whereby a triangular deflection diagram and
3.12. Ultimate stength of a can be determined in the usual way (Fig. 26): an internal lever arm of y = 0.75 • d, is
p
cross-section assumed The tendon extension may easily
For given dimensions and concrete qualities, mu =zs. (ds - xc ) + z p. (dp - x c) (3.9) be determined from Fig. 27.
the ultimate strength of a cross-section is 2 2 For a rigid lateral restraint (internal spans) the
dependent upon the following variables: where relationship for the tendon extension can be
- Ordinary reinforcement z S= AS.fsy (3.10.) calculated approximately as
- Prestressing steel, bonded or unbonded z p= A p.(σp∞ + ∆σp ) (3.11.)
- Membrane effect ∆I a .2 . a . hp (3.14.)
The membrane effect is usually neglected zs + zp (3.12.) =2 . ( u ) + 4 u
xc = I I I I
when determining the ultimate strength. In b . fcd
many cases this simplification constitutes a Fig. 28 enables the graphic evaluation of
considerable safety reserve [8], [10]. 3.1.3. Stress increase in unbonded equation (3.14.), for the deviation of which we
The ultimate strength due to ordinary post-tensioned steel refer to [10]
reinforcement and bonded post-tensioning Hitherto, the stress increase in the unbonded The stress increase is obtained from the
can be calculated on the assumption, post-tensioned steel has either been actual stress-strain diagram for the steel and
which in slabs is almost always valid, that neglected [34] or introduced as a constant from the elongation of the tendon ∆I
the steel yields, This is usually true also for value [37] or as a function of the uniformly distributed over the free length L of
cross-sections over intermediate columns, reinforcement content and the concrete the tendon between the anchorages. In the
where the tendons are highly concentrated. compressive strength [38]. elastic range and with a modulus of elasticity
In bonded post- tensioning, the prestressing A differentiated investigation [10] shows that Ep for the prestressing steel, the increase in
force in cracks is transferred to the concrete this increase in stress is dependent both upon steel stress is found to be
by bond stresses on either side of the crack . the geometry and upon the deformation of the
Around the column mainly radial cracks open entire system. There is a substantial ∆σp = ∆I . I . Ep = ∆I . E p (3.15)
and a tangentially acting concrete difference depending upon whether a slab is
I L L
compressive zone is formed. Thus the laterally restrained or not. In a slab system,
so-called effective width is considerably the internal spans may be regarded as slabs The steel stress, plus the stress increase ∆σp
increased [27]. In unbonded post-tensioning, with lateral restraint, while the edge spans in must, of course, not exceed the yeld strength
the prestressing force is transferred to the the direction perpendicular to the free edge or of the steel.
concrete by the end anchorages and, by the cantilever, and also the corner spans are In the ultimate load calculation, care must be
approximation, is therefore uniformly regarded as slabs without lateral restraint. taken to ensure that the stress increase is
distributed over the entire width at the In recent publications [14], [15], [16], the established from the determining mechanism.
columns. stress increase in the unbonded post- This is illustaced diagrammatically
Figure 27: Tendon extension without lateral restraint Figure 28: Tendon extension with rigid lateral restraint
8
3.2. Punching shear
32.1. General
Punching shear has a position of special
importance in the design of flat slabs. Slabs, which
are practically always under-reinforced against
flexure, exhibit pronounced ductile bending failure.
In beams, due to the usually present shear
reinforcement, a ductile failure is usually assured in
shear also. Since slabs, by contrast, are provided
with punching shear reinforcement only in very
exceptional cases,because such reinforcement is
avoided if at all possible for practical reasons,
punching shear is associated with a brittle failure of
the concrete.
This report cannot attempt to provide generally valid
solutions for the punching problem. Instead, one
possibile solution will be illustrated. In particular we
Figure 29: Determining failure mechanisms for two-span beam shall discuss how the prestress can be taken into
account in the existing design specifications, which
have usually been developed for ordinarily
in Fig 29 with reference to a two-span beam. Example of the calculation of a tendon
reinforced flat slabs.
It has been assumed here that the top layer extension:
column head reinforcement is protruding According to [14], which is substantially in In the last twenty years, numerous design formulae
beyond the column by at least line with the above considerations, the have been developed, which were obtained from
nominal failure state is reached when with a empirical investigations and, in a few practical
Ia min ≥ I . (1 - 1 ) (3.16) determining mechanism a deflection au of cases, by model represtation. The calculation
λ 1/40th of the relevant span I is present. methods and specifications in most common use
√1 + 2 Therefore equations (3.13) and (3.14) for the today limit the nominal shear stress in a critical
tendon extension can be simplified as section around the column in relation to a design
in an edge span and by at least follows:
value as follows [9]:
Without lateral restraint, e.g. for edge spans
Ia min ≥ 1 . (1 − 1 ) (3.17) of flat slabs:
(3.20.)
2 √1 + λ
∆I=0.075 . dp (3.18.)
The design shear stress value Tud is
in an internal span. It must be noted that Ia min
established from shear tests carried out on
does not include the anchoring length of the With a rigid lateral restraint, e g. for internal
portions of slabs. It is dependent upon the
reinforcement. spans of flat slabs:
In particular, it must be noted that, if I1 = I2 , concrete strength f c’ the bending reinforcement
the plastic moment over the internal column content pm’, the shear reinforcement content
will be different depending upon whether ∆I=0.05 . (0.025 . 1 + 2 . hp ) (319.) pv’,the slab slenderness ratio h/l, the ratio of
span 1 or span 2 is investigated. column dimension to slab thickness ζ, bond
properties and others. In the various
specifications and standards, only some of
these influences are taken into account.
Figure 30: Portion of slab in column area; transverse components due to prestress in critical
shear contrary
3.2.2. Influence of post tensioning
Post-tensioning can substantially alleviate
the punching shear problem in flat slabs if
the tendon layout is correct.
A portion of the load is transferred by the transverse
components resulting from prestressing directly to
the column. The tendons located inside the critical
shear periphery (Fig. 30) can still carry loads in the
form of a cable system even after the concrete
compressive zone has failed and can thus prevent
the collapse of the slab. The zone in which the
prestress has a loadrelieving effect is here
intentionally assumed to be smaller than the
punching cone. Recent tests [27] have
demonstrated that, after the shear cracks have
appeared, the tendons located outside the crlncal
shear periphery rupture the concrete vertically
unless heavy ordinary reinforcement is present,
and they can therefore no longer provide a load-
bearing function.
If for constructional reasons it is not possible to
arrange the tendons over the column within the
critical shear periphery or column strip b defined
ck
in Fig. 30 then the transfer of the transverse
components resulting
9
from tendons passing near the column If punching shear reinforcement must be
should be investigated with the help of a incorporated, it should be designed by
space frame model. The distance between means of a space frame model with a
the outermost tendons to be taken into concrete compressive zone in the failure
account for direct load transfer and the edge state inclined at 45° to the plane of the slab,
of the column should not exceed ds on either for the column force 1.8 Vg+q -Vp . Here, the
side of the column. following condition must be complied with.
The favourable effect of the prestress can
be taken account of as follows:
2. Rd ≥1.8 . Vg+q -V p (3.24.)
1 The transverse component Vp ∞ resulting
from the effectively present prestressing
For punching shear reinforcement, vertical
force and exerted directly in the region of
stirrups are recommended; these must pass
the critical shear periphery can be
around the top and bottom slab
subtracted from the column load resulting
reinforcement. The stirrups nearest to the
from the applied loads. In the tendons, the
edge of the column must be at a distance
prestressing force after deduction of all
losses and without the stress increase from this column not exceeding 0.5 • ds. Also,
should be assumed. The transverse the spacing between stirrups in the radial
component Vp is calculated from Fig. 30 direction must not exceed 0.5 • ds (Fig.31).
as Slab connections to edge columns and
corner columns should be designed
Vp=Σ Pi . ai = P. a (3.21.) according to the considerations of the beam
theory. In particular, both ordinary
Here, all the tendons situated within the reinforcement and post-tensioned tendons
critical shear periphery should be should be continued over the column and
considered, and the angle of deviation properly anchored at the free edge (Fig. 32).
within this shear periphery should be
used for the individual tendons.
2 The bending reinforcement is sometimes
Figure 31: Punching shear reinforcement
taken into account when establishing the
permissible shear stress [37], [38], [39].
The prestress can be taken into account
by an equivalent portion [15], [16].
However, as the presence of concentric
compression due to prestress in the
column area is not always guaranteed
(rigid walls etc.) it is recommended that
this portion should be ignored.
3.2.3. Carrying out the calculation
A possible design procedure is shown in [14];
this proof, which is to be demonstrated in the
ultimate limit state, is as follows:
Rd ≥ 1.4 . V g+q - Vp (3.22.)
1.3 1.3
The design value for ultimate strength for
concentric punching of columns through
slabs of constant thickness without
punching shear reinforcement should be
assumed as follows:
Rd = uc . ds . 1.5 .Tud (3.23.)
Uc is limited to 16 . ds, at maximum and the
ratio of the sides of the rectangle surrounding
the column must not exceed 2:1.
Tud can be taken from Table I. Figure 32: Arrangement of reinforcement at corner and edge columns
10
4. Serviceability limit
state
4.12. Required ordinary reinforcement tensioning and the lateral membrane
4.1. Crack limitation
The design principles given below are in compressive forces that develop with even
4.1.1. General quite small deflections. In general, therefore,
accordance with [14]. For determining the
In slabs with ordinary reinforcement or it is not necessary to check for minimum
ordinary reinforcement required, a distinction
bonded post-tensioning, the development of must be made between edge spans, internal reinforcement. The quantity of normal
cracks is dependent essentially upon the spans and column zones. reinforcement required for the ultimate limit
bond characteristics between steel and state must still be provided.
concrete. The tensile force at a crack is Edge spans:
almost completely concentrated in the steel. Required ordinary reinforcement (Fig. 34): Column zone:
This force is gradually transferred from the ps ≥ 0.15 - 0.50 . pp (4.2) In the column zone of flat slabs, considerable
steel to the concrete by bond stresses. As Lower limit: ps ≥ 0.05% additional ordinary reinforcement must
soon as the concrete tensile strength or the always be provided. The proposal of DIN
tensile resistance of the concrete tensile 4227 may be taken as a guideline, according
zone is exceeded at another section, a new to which in the zone bcd = bc + 3 . ds (Fig. 30)
crack forms. at least 0.3% reinforcement must be
The influence of unbonded post-tensioning provided and, within the rest of the column
upon the crack behaviour cannot be strip (b g = 0.4 . I) at least 0.15% must be
investigated by means of bond laws. Only provided (Fig. 35). The length of this
very small frictional forces develop between reinforcement including anchor length should
the unbonded stressing steel and the be 0.4 . I. Care should be taken to ensure
concrete. Thus the tensile force acting in the Figure 34: Minimum ordinary reinforcement that the bar diameters are not too large.
steel is transferred to the concrete almost required as a function of the post-tensioned The arrangement of the necessary minimum
exclusively as a compressive force at the reinforcement for edge spans reinforcement is shown diagrammatically in
anchorages. Fig.35. Reinforcement in both directions is
Theoretical [10] and experimental [8] generally also provided everywhere in the
investigations have shown that normal forces edge spans. In internal spans it may be
arising from post-tensioning or lateral Internal spans: necessary for design reasons, such as point
membrane forces influence the crack For internal spans, adequate crack distri- loads, dynamic loads (spalling of concrete)
behaviour in a similar manner to ordinary bution is in general assured by the post- etc. to provide limited ordinary reinforcement.
reinforcement.
In [10], the ordinary reinforcement content p*
required for crack distribution is given as a
function of the normal force arising from Figure 35: Diagrammatic arrangement of minimum reinforcement
prestressing and from the lateral membrane
force n.
Fig. 33 gives p* as a function of p*, where
p* = pp - n (4.1.)
dp . σpo
If n is a compressive force, it is to be provided
with a negative sign.
Figure 33: Reinforcement content required
to ensure distribution of cracks
Various methods are set out in different
specifications for the assessment and control
of crack behaviour:
- Limitation of the stresses in the ordinary
reinforcement calculated in the cracked
state [40].
- Limitation of the concrete tensile stresses
calculated for the homogeneous cross-
section [12].
- Determination of the minimum quantity of
reinforcement that will ensure crack
distribution [14].
- Checking for cracks by theoretically or
empirically obtained crack formulae [15].
11
4.3. Post-tensioning force in the
tendon
4.3.1. Losses due to friction
For monostrands, the frictional losses are
Figure 36: Transverse components and panel forces resulting from post-tensioning very small. Various experiments have
demonstrated that the coefficients of friction
µ= 0.06 and k = 0.0005/m can be assumed.
It is therefore adequate for the design to
adopt a lump sum figure of 2.5%
prestressing force loss per 10 m length of
strand. A constant force over the entire length
becomes established in the course of time.
For bonded cables, the frictional coefficients
are higher and the force does not become
uniformly distributed over the entire length.
The calculation of the frictional losses is
carried out by means of the well-known
formula PX = Po . e-( µa +kx). For the coeffi-
cients of friction the average values of Table
II can be assumed.
Figure 37: Principle of the load-balancing method The force loss resulting from wedge drawin
when the strands are locked off in the
anchorage, can usually be compensated by
and in internal spans by the effect of the overstressing. It is only in relatively short
4.2. Deflections
cables that the loss must be directly allowed
lateral restraint.
for. The way in which this is done is
Post-tensioning has a favourable influence In the existing specifications, the deflections
explained in the calculation example
upon the deflections of slabs under service are frequently limited by specifying an upper (Chapter 8.2.).
loads. Since, however, post-tensioning also limit to the slenderness ratio (see Appendix 2).
makes possible thinner slabs, a portion of this In structures that are sensitive to deflection,
advantage is lost. the deflections to be expected can be 4.32. Long-term losses
estimated as follows (Fig. 38): The long-term losses in slabs amount to
As already mentioned in Chapter 3.1.1., the
about 10 to 12% of the initial stress in the
load-balancing method is very suitable for prestressing steel. They are made up of the
calculating deflections. Fig. 36 and 37 a = ad-u + ag+qr - d + a q-qr (4.3.) following components:
illustrate the procedure diagrammatically.
Under permanent loads, which may with The deflection ad-u, should be calculated for Creep losses:
advantage be largely compensated by the the homogeneous system making an Since the slabs are normally post-tensioned
transverse components from post-tensioning, allowance for creep. Up to the cracking load for dead load, there is a constant
g+qr ’ which for reasons of prudence should compressive stress distribution over the
the deflections can be determined on the
cross-section. The compressive stress
assumption of uncracked concrete. be calculated ignoring the tensile strength of
generally is between 1.0 and 2.5 N/mm 2 and
Under live loads, however, the stiffness is the concrete, the deflection ag+qr --d should be thus produces only small losses due to
reduced by the formation of cracks. In slabs established for the homogeneous system creep. A simplified estimate of the loss of
with bonded post-tensioning, the maximum under short-term loading. Under the stress can be obtained with the final value for
loss of stiffness can be estimated from the remaining live loading, the deflection aq-qr the creep deformation:
normal reinforced concrete theory. In slabs should be determined by using the stiffness
with unbonded post-tensioning, the reduction of the cracked crosssection. For this ∆σpc=εcc . Ep =ϕn . σ c . Ep (4.6.)
Ec
in stiffness, which is very large in a simple purpose, the reinforcement content from
beam reinforced by unbonded post- ordinary reinforcement and prestressing can
tensioning, is kept within limits in edge spans be assumed as approximately equivalent, Although the final creep coefficient ϕn due to
by the ordinary reinforcement necessary for i.e. p=ps+pp is used. early post-tensioning is high, creep losses
crack distribution, In many cases, a sufficiently accurate exceeding 2 to 4% of the initial stress in the
estimate of deflections can be obtained if prestressing steel do not in general occur.
they are determined under the remaining
Shrinkage losses:
Figure 38: Diagram showing components of load (g+q-u) for the homogeneous system
The stress losses due to shrinkage are given
deflection in structures sensitive to deflections and the creep is allowed for by reduction of by the final shrinkage factor scs as:
the elastic modulus of the concrete to
∆σps = εcs . E p (4.7.)
Ec = Ec
I
(4.4.)
1+ ϕ
The shrinkage loss is approximately 5% of
the initial stress in the prestressing steel.
On the assumption of an average creep
factor ϕ = 2 [41] the elastic modulus of the
Table II - Average values of friction for
concrete should be reduced to bonded cables
Ec =Ec
I
(4 .5.)
3
12
Relaxation losses: The fire resistance of post-tensioned slabs is following conditions:
The stress losses due to relaxation of the virtually equivalent to that of ordinarily - Freedom from cracking and no embrittle-
post-tensioning steel depend upon the type reinforced slabs, as demonstrated by ment or liquefaction in the temperature
of steel and the initial stress. They can be corresponding tests. The strength of the range -20° to +70 °C
determined from graphs (see [42] for prestressing steel does indeed decrease more - Chemical stability for the life of the
example). With the very low relaxation rapidly than that of ordinary reinforcement as structure
prestressing steels commonly used today, for the temperature rises, but on the other hand in - No reaction with the surrounding
an initial stress of 0.7 pu and ambient
f post-tensioned slabs better protection is materials
temperature of 20°C, the final stress loss due provided for the steel as a consequence of the - Not corrosive or corrosion-promoting
to relaxation is approximately 3%. uncracked cross-section. - Watertight
The behaviour of slabs with unbonded post- A combination of protective grease coating
Losses due to elastic shortening of the tensioning is hardly any different from that of and plastics sheathing will satisfy these
concrete: slabs with bonded post-tensioning, if the requirements.
For the low centric compression due to appropriate design specifications are Experiments in Japan and Germany have
prestressing that exists, the average stress followed. The failure of individual unbonded demonstrated that both polyethylene and
loss is only approximately 0.5% and can tendons can, however, jeopardize several polypropylene ducts satisfy all the above
therefore be neglected. spans. This circumstance can be allowed for conditions.
by the provision of intermediate anchorages. As grease, products on a mineral oil base are
From the static design aspect, continuous used; with such greases the specified
systems and spans of slabs with lateral requirements are also complied with.
constraints exhibit better fire resistance. The corrosion protection in the anchorage
An analysis of the fire resistance of zone can be satisfactorily provided by
4.4. Vibrations posttensioned slabs can be carried out, for appropriate constructive detailing (Fig. 39), in
For dynamically loaded structures, special example, according to [43]. such a manner that the prestressing steel is
vibration investigations should be carried out. continuously protected over its entire length.
For a coarse assessment of the dynamic The anchorage block-out is filled with
behaviour, the inherent frequency of the slab lowshrinkage mortar.
can be calculated on the assumption of 4.6. Corrosion protection
homogeneous action. 4.6.1. Bonded post-tensioning
The corrosion protection of grouted tendons
is assured by the cement suspension
injected after stressing. If the grouting
4.5. Fire resistance operations are carefully carried out no
In a fire, post-tensioned slabs, like ordinarily problems arise in regard to protection.
reinforced slabs, are at risk principally on The anchorage block-outs are filled with low-
account of two phenomena: spalling of the shrinkage mortar.
concrete and rise of temperature in the steel.
Therefore, above all, adequate concrete 4.62. Unbonded post-tensioning
cover is specified for the steel (see Chapter The corrosion protection of monostrands Figure 39: Corrosion protection in the
5.1.4.). described in Chapter 1.3.2. must satisfy the anchorage zone
5. Detail design aspects
5.1. Arrangement of tendons ponent is made equal to the dead load,then flexure and shear if 50 % of the tendons are
under dead load and prestress a complete uniformly distributed in the span and 50 %
5.1.1. General load balance is achieved in respect of are concentrated over the columns.
The transference of loads from the interior of
a span of a flat slab to the columns by
transverse components resulting from Figure 40: Diagrammatic illustration of load transference by post-tensioning
prestressing is illustrated diagrammatically in
Fig. 40.
In Fig. 41, four different possible tendon
arrangements are illustrated: tendons only
over the colums in one direction (a) or in two
directions (b), the spans being ordinarily
reinforced (column strip prestressing);
tendons distributed in the span and
concentrated along the column lines (c and
d). The tendons over the colums (for column
zone see Fig. 30) act as concealed main
beams.
When selecting the tendon layout, attention
should be paid to flexure and punching and
also to practical construction aspects
(placing of tendons). If the transverse com-
13
Table III - Required cover of prestressing
steel by concrete (in mm) as a function of
conditions of exposure and concrete grade
1) for example, completely protected against
weather, or aggressive conditions, except for
brief period of exposure to normal weather
conditions during construction.
2) for example, sheltered from severe rain or
against freezing while saturated with water,
buried concrete and concrete continuously under water.
3) for example, exposed to driving rain, alternate
wetting and drying and to freezing while wet,
subject to heavy condensation or corrosive fumes.
5.1.4. Concrete cover
To ensure long-term performance, the
prestressing steel must have adequate
concrete cover. Appropriate values are
usually laid down by the relevant national
standards. For those cases where such
information does not exist, the requirements
of the CEB/FI P model code [39] are given in
Table I I I.
The minimum concrete cover can also be
influenced by the requirements of fire
resistance. Knowledge obtained from
investigations of fire resistance has led to
recommendations on minimum concrete
cover for the post-tensioning steel, as can be
seen from Table IV. The values stated should
be regarded as guidelines, which can vary
Figure 41: Possible tendon arrangements
according to the standards of the various
countries.
For grouted tendons with round ducts the
Under this loading case, the slab is stressed 5.1.3. Radii of curvature cover can be calculated to the lowest or
only by centric compressive stress. In regard For the load-relieving effect of the vertical highest strand respectively.
to punching shear, it may be advantageous component of the prestressing forces over
to position more than 50 % of the tendons the column to be fully utilized, the point of
over the columns. inflection of the tendons or bundles should 5.2. Joints
In the most commonly encountered be at a distance ds/2 from the column edge The use of post-tensioned concrete and, in
cases, the tendon arrangement illustrated (see Fig. 30). This may require that the particular, of concrete with unbonded
in Fig. 41 (d), with half the tendons in each minimum admissible radius of curvature be tendons necessitates a rethinking of some
direction uniformly distributed in the span used in the column region. The extreme fibre long accepted design principles. A question
and half concentrated over the columns, stresses in the prestressing steel must that very often arises in building design is the
provides the optimum solution in respect remain below the yield strength under these arrangement of joints in the slabs, in the
of both design and economy. conditions. By considering the natural walls and between slabs and walls.
stiffness of the strands and the admissible Unfortunately, no general answer can be
extreme fibre stresses, this gives a minimum given to this question since there are certain
5.1.2. Spacings radius of curvature for practical use of factors in favour of and certain factors
The spacing of the tendons in the span r = 2.50 m. This value is valid for strands of against joints. Two aspects have to be
should not exceed 6h, to ensure nominal diameter 13 mm (0.5") and 15 mm considered here:
transmission of point loads. Over the column, (0.6").
the clear spacing between tendons or strand
bundles should be large enough to ensure Table IV - Minimum concrete cover for the post-tensioning steel (in mm) in respect of the fire
proper compaction of the concrete and allow resistance period required
sufficient room for the top ordinary
reinforcement. Directly above the column,
the spacing of the tendons should be
adapted to the distribution of the
reinforcement.
In the region of the anchorages, the spacing
between tendons or strand bundles must be
chosen in accordance with the dimensions of
the anchorages. For this reason also, the
strand bundles themselves are splayed out,
and the monostrands individually anchored.
14
- Ultimate limit state (safety)
- Horizontal displacements (serviceability
limit state)
5.2.1. Influence upon the ultimate limit
state behaviour
If the failure behaviour alone is considered, it
is generally better not to provide any joints.
Every joint is a cut through a load-bearing
element and reduces the ultimate load
strength of the structure.
For a slab with unbonded post-tensioning,
the membrane action is favourably
influenced by a monolithic construction. This
results in a considerable increase in the
ultimate load (Fig. 42).
5.2.2. Influence upon the serviceability Figure 42: Influence of membrane action upon load-bearing capacity
limit state
In long buildings without joints, inadmissible
cracks in the load-bearing structure and Table V -Average material properties of various construction materials
damage to non load-bearing constructional
elements can occur as a result of horizontal
displacements. These displacements result
from the following influences:
- Shrinkage
- Temperature
- Elastic shortening due to prestress
- Creep due to prestress
The average material properties given in
Table V enable one to see how such damage
occurs.
In a concrete structure, the following average
shortenings and elongations can be In closed buildings, slabs and walls in the the shortening of the complete slab is
expected: internal rooms are subject to low temperature reduced.
Shrinkage ∆Ics = -0.25 mm/m fluctuations. External walls and unprotected Creep, on the other hand, acts upon the
Temperature ∆Ic t = -0.25 mm/m roof slabs undergo large temperature entire length of the slab. A certain reduction
to+0.15 mm/m fluctuations. In open buildings, the relative occurs due to transfer of the prestress to the
Elastic shortening temperature difference is small. Particular longitudinal walls.
(for an average centric prestress of 1.5 considerations arise for the connection to the Shortening due to prestress should be kept
N/mmz and Ec= foundation and where different types of within limits particularly by the centric
30 kN/mm2 ) ∆Icel = -0.05 mm/m construction materials are used. prestress not being made too high. It is
Creep ∆Icc = - 0.15 mm/m recommended that an average centric
prestress of σcpm = 1.5 N/mm2 should be
These values should be adjusted for the Elastic shortening and creep due to selected and the value of 2.5 N/mm2 should
particular local conditions. prestress: not be exceeded. In concrete walls, the
When the possible joint free length of a Elastic shortening is relatively small. By relative shortening between slabs and walls
structure is being assessed, the admissible subdividing the slab into separate concreting can be reduced by approximately uniform
total displacements of the slabs and walls stages, which are separately post-tensioned, prestress in the slabs and walls.
or columns and the admissible relative
displacements between slabs and walls or
columns should be taken into account. Figure 43: Examples of jointless structures of 60 to 80 m length
Attention should, of course, also be paid to
the foundation conditions.
The horizontal displacements can be partly
reduced or prevented during the construction
stage by suitable constructional measures
(such as temporary gaps etc.) without damage
occurring.
Shrinkage:
Concrete always shrinks, the degree of
shrinkage being highly dependent upon the
water-cement ratio in the concrete, the cross-
sectional dimensions, the type of curing and
the atmospheric humidity. Shortening due to
shrinkage can be reduced by up to about
one-half by means of temporary shrinkage
joints.
Temperature:
In temperature effects, it is the temperature
difference between the individual structural
components and the differing coefficients of
thermal expansion of the materials that are of
greatest importance.
15
5.2.3. Practical conclusions
In slabs of more than 30 m length, a uniform,
«homogeneous» deformation behaviour of
the slabs and walls in the longitudinal
direction should be aimed at. In open
buildings with concrete walls or columns, this
requirement is satisfied in regard to
temperature effects and, provided the age
difference between individual components is
not too great, is also satisfied for shrinkage
and creep.
In closed buildings with concrete walls or
columns, a homogeneous behaviour for
shrinkage and creep should be achieved. In
respect of temperature, however, the
concreted external walls behave differently
form the internal structure. If cooling down
occurs, tensile stresses develop in the wall.
Distribution of the cracks can be ensured by
longitudinal reinforcement. The tensile
stresses may also be compensated for by
post-tensioning the wall.
If, in spite of detail design measures, the
absolute or relative longitudinal deformations
exceed the admissible values, the building
must be subdivided by joints.
Fig. 43 and 44 show, respectively, some
examples in which joints can be dispensed Figure 44: Examples of structures that must be subdivided by joints into sections of 30 to
with and some in which joints are necessary. 40 m length
6. Construction total size, the construction of the slabs is anchorages. The finished cables are then
procedures carried out in a number of sections. coiled up and transported to the site.
The divisions are a question of the geometry In fabrication on the site, the cables can
6.1. General of the structure, the dimensions, the either be fabricated in exactly the same
The construction of a post-tensioned slab is planning, the construction procedure, the manner as at works, or they can be
broadly similar to that for an ordinarily utilization of formwork material etc. The assembled by pushing through. In the latter
reinforced slab. Differences arise in the construction joints that do occur, are method, the ducts are initially placed empty
placing of the reinforcement, the stressing of subseqently subjected to permanent and the strands are pushed through them
the tendons and in respect of the rate of compression by the prestressing, so that the subsequently. If the cables have stressing
construction. behaviour of the entire slab finally is the anchorages at both ends, this operation can
The placing work consists of three phases: same throughout. even be carried out after concreting (except
first, the bottom ordinary reinforcement of the The weight of a newly concreted slab must for the cables with flat ducts).
slab and the edge reinforcement are placed. be transmitted through the formwork to slabs
The ducts or tendons must then be beneath it. Since this weight is usually less
positioned, fitted with supports and fixed in than that of a corresponding reinforced 6.22. Unbonded post-tensioning
place. This is followed by the placing of the concrete slab, the cost of the supporting The fabrication of monostrand tendons is
top ordinary reinforcement. The stressing of structure is also less. usually carried out at the works of the
the tendons and, in the case of bonded prestressing firm but can, if required, also be
tendons the grouting also, represent carried out on site. The monostrands are cut
additional construction operations as to length and, if necessary, fitted with the
compared with a normally reinforced slab. 6.2. Fabrication of the tendons dead-end anchorages. They are then coiled
Since, however, these operations are usually up and transported to site. The stressing
carried out by the prestressing firm, the main 6.2.1. Bonded post-tensioning anchorages are fixed to the formwork. During
contractor can continue his work without There are two possible methods of fabrica- placing, the monostrands are then threaded
interruption. ting cables: through the anchorages.
A feature of great importance is the short - Fabrication at the works of the prestressing
stripping times that can be achieved with firm
post-tensioned slabs. The minimum period - Fabrication by the prestressing firm on the
between concreting and stripping of site
formwork is 48 to 72 hours, depending upon The method chosen will depend upon the 6.3. Construction procedure for
concrete quality and ambient temperature. local conditions. At works, the strands are cut bonded post-tensioning
When the required concrete strength is to the desired length, placed in the duct and, In slabs with bonded post-tensioning, the
reached, the full prestressing force can if appropriate, equipped with dead-end operations are normally carried out as
usually be applied and the formwork stripped anchorages. The finished cables are then follows:
immediately afterwards. Depending upon the coiled up and transported to the site. 1. Erection of slab supporting formwork
16
2. Fitting of end formwork; placing of
stressing anchorages
3. Placing of bottom and edge reinforcement
4. Placing of tendons or, if applicable, empty
ducts* according to placing drawing
5. Supporting of tendons or empty ducts*
with supporting chairs according to
support drawing
6. Placing of top reinforcement
7. Concreting of the section of the slab
8. Removal of end formwork and forms
for the stressing block-outs
9. Stressing of cables according to stressing
programme
10. Stripping of slab supporting formwork
11.Grouting of cables and concreting of
block-outs
* In this case, the stressing steel is pushed
through either before item 5 or before
item 9.
6.4. Construction procedure for
unbonded post-tensioning
If unbonded tendons are used, the
construction procedure set out in Chapter
6.3. is modified only by the omission of
grouting (item 11).
The most important operations are illustrated
in Figs. 45 to 52. The time sequence is
illustrated by the construction programme
(Fig. 53).
All activities that follow one another directly
can partly overlap; at the commencement of
activity (i+1), however, phase (i-1) must be
completed. Experience has shown that those
activities that are specific to prestressing
(items 4, 5 and 9 in Chapter 6.3.) are with
advantage carried out by the prestressing
firm, bearing in mind the following aspects:
6.4.1. Placing and supporting of tendons
The placing sequence and the supporting of
the tendons is carried out in accordance with
the placing and support drawings (Figs. 54
and 55). In contrast to a normally reinforced
slab, therefore, for a post-tensioned slab two
drawings for the prestressing must be Figure 53: Construction programme
prepared in addition to the reinforcement
drawings. The drawings for both, ordinary
reinforcement and posttensioning are,
however, comparatively simple and the
number of items for tendons and reinforcing
bars is small.
The sequence in which the tendons are to be
placed must be carefully considered, so that
the operation can take place smoothly.
Normally a sequence allowing the tendons
Table VI-Achievable accuracies in placing
Direction column Remaining
strip area
Vertical ± 5mm ± 5mm
Horizontal ± 20 mm ± 50 mm
17
to be placed without «threading» or ponsible for the tendon layout. there is a space requirement behind the
«weaving» can be found without any Corresponding care is also necessary in anchorage of 1 m along the axis and 120 mm
difficulty. The achievable accuracies are concreting. radius about it. All stressing operations are
given in Table VI. 6.4.2. Stressing of tendons recorded for each tendon. The primary
To assure the stated tolerances, good For stressing the tendons, a properly objective is to stress to the required load; the
coordination is required between all the secured scaffolding 0.50 m wide and of 2 extension is measured for checking
2
installation contractors (electrical, heating, kN/m load-bearing capacity is required at purposes and is compared with the
plumbing etc.) and the organization res- the edge of the slab. For the jacks used calculated value.
Figure 54: Placing drawing
Figure 55: Support drawing
18
