4.2VSL REPORT SERIES

POST-TENSIONEDSLABS

Fundamentals of the design process

Ultimate limit state

Serviceability limit state

Detailed design aspects

Construction Procedures

Preliminary Design

Execution of the calculations

Completed structures

PUBLISHED BYVSL INTERNATIONAL LTD.

AuthorsDr. P. Ritz, Civil Engineer ETHP. Matt, Civil Engineer ETHCh. Tellenbach, Civil Engineer ETHP. Schlub, Civil Engineer ETHH. U. Aeberhard, Civil Engineer ETH

CopyrightVSL INTERNATIONAL LTD, Berne/Swizerland

All rights reserved

Printed in Switzerland

Foreword

With the publication of this technical report, VSLINTERNATIONAL LTD is pleased to make acontribution to the development of CivilEngineering.The research work carried out throughout theworld in the field of post-tensioned slabstructures and the associated practicalexperience have been reviewed and analysedin order to etablish the recommendations andguidelines set out in this report. The documentis intended primarily for design engineers,but we shall be very pleased if it is also of useto contractors and clients. Through our

representatives we offer to interested partiesthroughout the world our assistance endsupport in the planning, design and constructionof posttensioned buildings in general and post-tensioned slabs in particular.I would like to thank the authors and all thosewho in some way have made a contribution tothe realization of this report for their excellentwork. My special thanks are due to Professor DrB. Thürlimann of the Swiss Federal Institute ofTechnology (ETH) Zürich and his colleagues,who were good enough to reed through andcritically appraise the manuscript.

Hans Georg ElsaesserChairman of the Board and PresidentIf VSLINTERNATIONALLTDBerne, January 1985

Table of contents

Page1. lntroduction 21.1. General 21.2. Historical review 21.3. Post-tensioning with or

without bonding of tendons 31.4. Typical applications of

post-tensioned slabs 4

2. Fundamentals of the design process 62.1. General 62.2. Research 62.3. Standards 6

3. Ultimate limit state 63 1 Flexure 63.2 Punching shear 9

4. Serviceability limit state 1141 Crack limitation 1142. Deflections 1243 Post-tensioning force in

the tendon 1244 Vibrations 1345 Fire resistance 134Z Corrosion protection 13

Page5. Detail design aspects 135.1. Arrangement of tendons 135.2. Joints

6.Construction procedures 166.1.General 166.2. Fabrication of the tendons 166.3.Construction procedure for

bonded post-tensioning 166.4.Construction procedure for

unbonded post-tensioning 17

7. Preliminary design 19

8. Execution of the calculations 208.1. Flow diagram 208.2. Calculation example 20

9. Completed structures 269.1.Introduction 269.2.Orchard Towers, Singapore 269.3. Headquarters of the Ilford Group,

Basildon, Great Britain 289.4.Centro Empresarial, São Paulo,

Brazil 28

Page9.5. Doubletree Inn, Monterey,

California,USA 309.6. Shopping Centre, Burwood,

Australia 309.7. Municipal Construction Office

Building, Leiden,Netherlands 319.8.Underground garage for ÖVA

Brunswick, FR Germany 329.9. Shopping Centre, Oberes Muri-

feld/Wittigkooen, Berne,Switzerland 33

9.10. Underground garage Oed XII,Lure, Austria 35

9.11. Multi-storey car park,Seas-Fee, Switzerland 35

9.12. Summary 37

10. Bibliography 38

Appendix 1: Symbols/ Definitions/Dimensional units/Signs 39

Appendix 2: Summary of variousstandards for unbond-ed post-tensioning 41

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1. Introduction

1.1. GeneralPost-tensioned construction has for manyyears occupied a very important position,especially in the construction of bridges andstorage tanks. The reason for this lies in itsdecisive technical and economicaladvantages.The most important advantages offered bypost-tensioning may be briefly recalled here:- By comparison with reinforced concrete, a

considerable saving in concrete and steelsince, 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 againstcorrosion.

- Almost unchanged serviceability even after considerable overload, since temporary cracks close again after the overload has disappeared.

- High fatigue strength, since the amplitudeof the stress changes in the prestressingsteel under alternating loads are quite small.

For the above reasons post-tensionedconstruction has also come to be used inmany situations in buildings (see Fig 1).The objective of the present report is tosummarize the experience available todayin the field of post-tensioning in buildingconstruction and in particular to discussthe design and construction of post-tensioned slab structures, especially post-tensioned flat slabs*. A detailedexplanation will be given of the checkstobe carried out, the aspects to beconsidered in the design and theconstruction procedures and sequencesof a post-tensioned slab. The execution ofthe design will be explained with referenceto an example. In addition, already builtstructures will be described. In all thechapters, both bonded and unbundledpost-tensicmng will be dealt with.In addition to the already mentioned generalfeatures of post-tensioned construction, thefollowing advantages of post-tensioned slabsover reinforced concrete slabs may be listed:- More economical structures resulting

from the use of prestressing steels with avery high tensile strength instead of normal reinforcing steels.

- larger spans and greater slenderness (see Fig. 2). The latter results in reduceddead load, which also has a beneficialeffect upon the columns and foundationsand reduces the overall height of buildings or enables additional floors to be incorporated in buildings of a given height.

- Under permanent load, very good behavior in respect of deflectons and crackIng.

- Higher punching shear strength obtainable by appropriate layout of tendons

- Considerable reduction In construction time as a result of earlier striking of formwork real slabs.

* For definitions and symbols refer to appendix 1.

Figure 1. Consumption of prestressing steel in the USA (cumulative curves)

Figure 2: Slab thicknesses as a function of span lengths (recommended limis slendernesses)

1.2. Historical review

Although some post-tensioned slabstructures had been constructed in Europequite early on, the real development tookplace in the USA and Australia. The first post-tensioned slabs were erected in the USA In1955, already using unbonded post-tensioning. In the succeeding yearsnumerous post-tensioned slabs weredesigned and constructed in connection withthe lift slab method. Post-tensionmg enabledthe lifting weight to be reduced and thedeflection and cracking performance to beimproved. Attempts were made to improveknowledge In depth by theoretical studies and

experiments on post-tensioned plates (seeChapter 2.2). Joint efforts by researchers,design engineers and prestressing firmsresulted in corresponding standards andrecommendations and assisted in promotingthe widespread use of this form ofconstruction in the USA and Australia. Todate, in the USA alone, more than 50 millionm2 of slabs have been post tensioned.In Europe. renewed interest in this form ofconstruction was again exhibited in the earlyseventies Some constructions werecompleted at that time in Great Britain, theNetherlands and Switzerland.

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Intensive research work, especially inSwitzerland, the Netherlands and Denmarkand more recently also in the FederalRepublic of Germany have expanded theknowledge available on the behaviour ofsuch structures These studies form the basisfor standards, now in existence or inpreparation in some countries. From purelyempirical beginnings, a technically reliableand economical form of constructon hasarisen over the years as a result of the effortsof many participants. Thus the method is nowalso fully recognized in Europe and hasalready found considerable spreadingvarious countries (in the Netherlands, inGreat Britain and in Switzerland for example).

1.3. Post-tensioning with orwithout bonding of tendons

1.3.1. Bonded post-tensioningAs is well-known, in this method of post-tensioning the prestressing steel is placed Inducts, and after stressing is bonded to thesurrounding concrete by grouting withcement suspension. Round corrugated ductsare normally used. For the relatively thin floorslabs of buildings, the reduction in thepossible eccentricity of the prestressing steelwith this arrangement is, however, too large,in particular at cross-over points, and for thisreason flat ducts have become common (seealso Fig. 6). They normally contain tendonscomprising four strands of nominal diameter13 mm (0.5"), which have proved to belogical for constructional reasons.

1.32. Unbonded post-tensioningIn the early stages of development of post-tensioned concrete in Europe, post-tensioning without bond was also used tosome extent (for example in 1936/37 in abridge constructed in Aue/Saxony [D]according to the Dischinger patent or in 1948for the Meuse, Bridge at Sclayn [B] designedby Magnel). After a period without anysubstantial applications, some importantstructures have again been built withunbonded post-tensioning in recent years.In the first applications in building work in theUSA, the prestressing steel was grassed andwrapped in wrapping paper, to facilitate itslongitudinal movement during stressingDuring the last few years, howeverthemethod described below for producing thesheathing has generally become common.The strand is first given a continuous film ofpermanent corrosion preventing grease in acontinuous operation, either at themanufacturer’s works or at the prestressingfirm. A plastics tube of polyethylene orpolypropylene of at least 1 mm wall thicknessis then extruded over this (Fig. 3 and 4). Theplastics tube forms the primary and thegrease the secondary corrosion protection.

Strands sheathed in this manner are knownas monostrands (Fig. 5). The nominaldiameter of the strands used is 13 mm (0.5")and 15 mm (0.6"); the latter have come to beused more often in recent years.

1.3.3. Bonded or unbonded?This question was and still is frequently thesubject of serious discussions. The subjectwill not be discussed in detail here, butinstead only the most important argumentsfar and against will be listed:

Figure 5: Structure of a plastics-sheathed,greased strand (monostrantd)

Figure 4: Extrusion plant

Arguments in favour of post-tensioningwithout bonding:- Maximum possible tendon eccentricities,

since tendon diameters are minimal; of special importance in thin slabs (see Fig 6).

- Prestressing steel protected against corrosion ex works.

- Simple and rapid placing of tendons.- Very low losses of prestressing force due

to friction.- Grouting operation is eliminated.- In general more economical.Arguments for post-tensioning with bonding:- Larger ultimate moment.- Local failure of a tendon (due to fire,

explosion, earthquakes etc.) has only limited effects

Whereas in the USA post-tensioning withoutbonding is used almost exclusively, bondingis deliberately employed in Australia.

Figure 3: Diagrammatic illustration of the extrusion process

Figure 6 Comparison between the eccentricities that can be attained with various types oftendon

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Among the arguments for bonded post-tensioning, the better performance of theslabs in the failure condition is frequentlyemphasized. It has, however, beendemonstrated that equally good structurescan be achieved in unbonded post-tensioning by suitable design and detailing.It is not the intention of the present report toexpress a preference for one type of post-tensioning or the other. II is always possiblethat local circumstances or limitingengineering conditions (such as standards)may become the decisive factor in thechoice. Since, however, there are reasons forassuming that the reader will be less familiarwith undonded post-tensioning, this form ofconstruction is dealt with somewhat morethoroughly below.

1.4. Typical applications ofpost-tensioned slabs

As already mentioned, this report is con-cerned exclusively with post-tensioned slabstructures. Nevertheless, it may be pointedout here that post-tensioning can also be ofeconomic interest in the followingcomponents of a multi-storey building:- Foundation slabs (Fig 7).- Cantilevered structures, such as

overhanging buildings (Fig 8).- Facade elements of large area; here light

post-tensioning is a simple method of preventing cracks (Fig. 9).

- Main beams in the form of girders, latticegirders or north-light roofs (Fig. 10 and 11).

Typical applications for post-tensioned slabsmay be found in the frames or skeletons foroffice buildings, mule-storey car parks,schools, warehouses etc. and also in multi-storey flats where, for reasons of internalspace, frame construction has been selected(Fig. 12 to 15).What are the types of slab system used?- For spans of 7 to 12 m, and live loads up

to approx. 5 kN/m2

, flat slabs (Fig. 16) or slabs with shallow main beams running inone direction (Fig. 17) without column head drops or flares are usually selected.

- For larger spans and live loads, flat slabswith column head drops or flares (Fig 18),slabs with main beams in both directions(Fig 19) or waffle slabs (Fig 20) are used.

Figure 7: Post-tensioned foundation slab

Figure 9: Post-tensioned facade elements Figure 8: Post-tensioned cantilevered building

Figure 11: Post-tensioned north-light roofsFigure 10: Post-tensioned main beams

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Figure 12: Office and factory building

Figure 14: School

Figure 16: Flat Slab

Figure 17: Slab with main beams in one direction Figure 18: Flat slab with column head drops

Figure 20: Waffle slabFigure 19: Slab with main beams in both directions

Figure 13: Multi-storey car park

Figure 15: Multi-storey flats

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2. Fundamentals of thedesign process

2.1. GeneralThe objective of calculations and detaileddesign is to dimension a structure so that itwill satisfactorily undertake the function forwhich it is intended in the service state, willpossess the required safety against failure,and will be economical to construct andmaintain. Recent specifications thereforedemand a design for the «ultimate» and «serviceability» limit states.Ultimate limit state: This occurs when theultimate load is reached; this load may belimited by yielding of the steel, compressionfailure of the concrete, instability of thestructure or material fatigue The ultimateload should be determined by calculation asaccurately as possible, since the ultimatelimit state is usually the determining criterionServiceability limit state: Here rules mustbe complied with, which limit cracking,deflections and vibrations so that the normaluse of a structure Is assured. The rulesshould also result in satisfactory fatiguestrength.The calculation guidelines given in thefollowing chapters are based upon thisconcept They can be used for flat slabswith or without column head drops orflares. They can be convertedappropriately also for slabs with mainbeams, waffle slabs etc.

2.2. ResearchThe use of post-tensioned concrete and thusalso its theoretical and experimentaldevelopment goes back to the last century.From the start, both post-tensioned beamand slab structures were investigated. Noindependent research has therefore beencarried out for slabs with bonded pos-tensioning. Slabs with unbonded post-tensioning, on the other hand, have beenthoroughly researched, especially since theintroduction of monostrands.The first experiments on unhonded post-tensioned single-span and multi-span flatslabs were carried out in the fifties [1], [2].They were followed, after the introduction ofmonostrands, by systematic investigationsinto the load-bearing performance of slabswith unbonded post-tensioning [3], [4], [5],[6], [7], [8], [9], [10] The results of theseinvestigations were to some extent embodiedin the American, British, Swiss and German,standard [11], [12], [13], [14], [15] and in theFIP recommendations [16].Various investigations into beam structuresare also worthy of mention in regard to thedevelopment of unbonded post-tensioning[17], [18], [19], [20],[21], [22], [23].The majority of the publications listed areconcerned predominantly with bendingbehaviour. Shear behaviour and in particularpunching shear in flat slabs has also beenthoroughly researched A summary ofpunching shear investigations into normally

reinforced slabs will be found in [24]. Theinfluence of post-tensioning on punchingshear behaviour has in recent years been thesubject of various experimental andtheoretical investigations [7], [25], [26], [27].Other research work relates to the fireresistance of post-tensioned structures,including bonded and unbonded post-tensioned slabs Information on this field willbe found, for example, in [28] and [29].In slabs with unbonded post-tensioning, theprotection of the tendons against corrosion isof extreme importance. Extensive researchhas therefore also been carried out in thisfield [30].

2.3. Standards

Bonded post-tensioned slabs can bedesigned with regard to the specifications onpost-tensioned concrete structures that existin almost all countries.For unbonded post-tensioned slabs, on theother hand, only very few specifications andrecommendations at present exist [12], [13],[15]. Appropriate regulations are in course ofpreparation in various countries. Where nocorresponding national standards are inexistence yet, the FIP recommendations [16]may be applied. Appendix 2 gives asummary of some important specifications,either already in existence or in preparation,on slabs with unbonded post-tensioning.

3. Ultimate limit state

3.1. Flexure3.1.1. General principles of calculationBonded and unbonded post-tensionedslabs can be designed according to theknown methods of the theories of elasticityand plasticity in an analogous manner toordinarily reinforced slabs [31], [32], [33].A distinction Is made between the follow-ing methods:A. Calculation of moments and shear forces

according to the theory of elastimry; thesections are designed for ultimate load.

B. Calculation and design according to thetheory of plasticity.

Method AIn this method, still frequently chosen today,moments and shear forces resulting fromapplied loads are calculated according tothe elastic theory for thin plates by themethod of equivalent frames, by the beammethod or by numerical methods (finite differences,finite elements).

The prestress should not be considered asan applied load. It should intentionally betaken into account only in the determinationof the ultimate strength. No moments andshear forces due to prestress and thereforealso no secondary moments should becalculated.The moments and shear forces due toapplied loads multiplied by the load factormust be smaller at every section than theultimate strength divided by the cross-sectionfactor.The ultimate limit state condition to be metmay therefore be expressed as follows [34]:S ⋅ γ f ≤ R (3.1.)

γ mThis apparently simple and frequentlyencoutered procedure is not without itsproblems. Care should be taken to ensurethat both flexure and torsion are allowed forat all sections (and not only the section ofmaximum loading). It carefully applied thismethod, which is similar to the staticmethod of the theory of plasticity,

gives an ultimate load which lies on the sateside.In certain countries, the forces resulting fromthe curvature of prestressing tendons(transverse components) are also treated asapplied loads. This is not advisable for theultimate load calculation, since in slabs thedetermining of the secondary moment andtherefore a correct ultimate load calculationis difficult.The consideration of transverse componentsdoes however illustrate very well the effect ofprestressing in service state. It is thereforehighly suitable in the form of the loadbalancing method proposed by T.Y. Lin [35]for calculating the deflections (see Chapter4.2).

Method BIn practice, the theory of plasticity, is beingincreasingly used for calculation and designThe following explanations show how itsapplication to flat slabs leads to a stoleultimate load calculation which will be easilyunderstood by the reader.

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The condition to be fulfilled at failure here is:(g+q) u ≥ γ (3.2.)

g+qwhere γ=γf . γm

The ultimate design loading (g+q)u divided bythe service loading (g+q) must correspond to avalue at least equal to the safety factor y.The simplest way of determining the ultimatedesign loading (g+q)u is by the kinematicmethod, which provides an upper boundaryfor the ultimate load. The mechanism to bechosen is that which leads to the lowest load.Fig. 21 and 22 illustrate mechanisms for aninternal span. In flat slabs with usual columndimensions (ξ>0.06) the ultimate load can bedetermined to a high degree of accuracy bythe line mechanisms ! or" (yield lines 1-1 or2-2 respectively). Contrary to Fig. 21, thenegative yield line is assumed for purposes ofapproximation to coincide with the lineconnecting the column axes (Fig. 23),although this is kinematically incompatible. Inthe region of the column, a portion of theinternal work is thereby neglected, which leadsto the result that the load calculated in this waylies very close to the ultimate load or below it.On the assumption of uniformly distributed topand bottom reinforcement, the ultimate designloads of the various mechanisms arecompared in Fig. 24.In post-tensioned flat slabs, the prestressingand the ordinary reinforcement are notuniformly distributed. In the approximation,however, both are assumed as uniformlydistributed over the width I1/2 + 12 /2 (Fig. 25).The ultimate load calculation can then becarried out for a strip of unit width 1. The actualdistribution of the tendons will be inaccordance with chapter 5.1. The top layerordinary reinforcement should beconcentrated over the columns in accordancewith Fig. 35.The load corresponding to the individualmechanisms can be obtained by the principleof virtual work. This principle states that, for avirtual displacement, the sum of the work We

performed by the applied forces and of thedissipation work W, performed by the internalforces must be equal to zero.We+Wi,=0 (3.3.)If this principle is applied to mechanism !(yield lines 1-1; Fig. 23), then for a strip ofwidth I1/2 + 12/2 the ultimate design load (g+q)

u is obtained.internal span:

Figure 21: Line mecanisms

Figure 23: Line mecanisms (proposedapproximation)

Figure 22: Fan mecanisms

Figure 24: Ultimate design load of thevarious mecanisms as function of columndiemnsions

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Figure 25: Assumed distribution of thereinforcement in the approximationmethod

(g+q)u = 8 . mu . (1+ λ) (3.7.)

l2

2

Edge span with cantilever:

For complicated structural systems, thedetermining mechanisms have to be found.Descriptions of such mechanisms areavailable in the relevant literature, e.g. [31],[36].In special cases with irregular plan shape,recesses etc., simple equilibrium considera-tions (static method) very often prove to be asuitable procedure. This leads in the simplestcase to the carrying of the load by means ofbeams (beam method). The momentdistribution according to the theory of elasticitymay also be calculated with the help ofcomputer programmes and internal stressstates may be superimposed upon thesemoments. The design has then to be doneaccording to Method A.

3.12. Ultimate stength of across-section

For given dimensions and concrete qualities,the ultimate strength of a cross-section isdependent upon the following variables:- Ordinary reinforcement- Prestressing steel, bonded or unbonded - Membrane effectThe membrane effect is usually neglectedwhen determining the ultimate strength. Inmany cases this simplification constitutes aconsiderable safety reserve [8], [10].The ultimate strength due to ordinaryreinforcement and bonded post-tensioningcan be calculated on the assumption,which in slabs is almost always valid, thatthe steel yields, This is usually true also forcross-sections over intermediate columns,where the tendons are highly concentrated.In bonded post- tensioning, the prestressingforce in cracks is transferred to the concreteby bond stresses on either side of the crack .Around the column mainly radial cracks openand a tangentially acting concretecompressive zone is formed. Thus theso-called effective width is considerablyincreased [27]. In unbonded post-tensioning,the prestressing force is transferred to theconcrete by the end anchorages and, byapproximation, is therefore uniformlydistributed over the entire width at thecolumns.

Figure 27: Tendon extension without lateral restraint Figure 28: Tendon extension with rigid lateral restraint

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Figure 26: ultimate strenght of a cross-section (plastic moment)

For unbonded post-tensioning steel, thequestion of the steel stress that acts in theultimate limit state arises. If this steel stress isknown (see Chapter 3.1.3.), the ultimatestrength of a cross-section (plastic moment)can be determined in the usual way (Fig. 26):

mu=zs. (ds - xc ) + zp. (dp - xc) (3.9)2 2

wherezS= AS

.fsy (3.10.)zp= Ap.(σp∞ + ∆σp) (3.11.)

zs + zp (3.12.)b. fcd

xc =

3.1.3. Stress increase in unbonded post-tensioned steel

Hitherto, the stress increase in the unbondedpost-tensioned steel has either beenneglected [34] or introduced as a constantvalue [37] or as a function of thereinforcement content and the concretecompressive strength [38].A differentiated investigation [10] shows thatthis increase in stress is dependent both uponthe geometry and upon the deformation of theentire system. There is a substantialdifference depending upon whether a slab islaterally restrained or not. In a slab system,the internal spans may be regarded as slabswith lateral restraint, while the edge spans inthe direction perpendicular to the free edge orthe cantilever, and also the corner spans areregarded as slabs without lateral restraint. In recent publications [14], [15], [16], thestress increase in the unbonded post-

tensioned steel at a nominal failure state isestimated and is incorporated into thecalculation together with the effective stresspresent (after losses due to friction, shrinkage,creep and relaxation). The nominal failurestate is established from a limit deflection au.With this deflection, the extensions of theprestressed tendons in a span can bedetermined from geometrical considerations.Where no lateral restraint is present (edgespans in the direction perpendicular to the freeedge or the cantilever, and corner spans) therelationship between tendon extension andthe span I is given by:∆I

=4 . au . yp = 3 . au . dp (3.13.)I I I I I

whereby a triangular deflection diagram andan internal lever arm of yp = 0.75 • d, isassumed The tendon extension may easilybe determined from Fig. 27.For a rigid lateral restraint (internal spans) therelationship for the tendon extension can becalculated approximately as

∆I=2 . (au.)2 + 4 . au . hp (3.14.)

I I I I

Fig. 28 enables the graphic evaluation ofequation (3.14.), for the deviation of which werefer to [10]The stress increase is obtained from theactual stress-strain diagram for the steel andfrom the elongation of the tendon ∆Iuniformly distributed over the free length L ofthe tendon between the anchorages. In theelastic range and with a modulus of elasticityEp for the prestressing steel, the increase insteel stress is found to be

∆σp = ∆I . I . Ep = ∆I . Ep (3.15)I L L

The steel stress, plus the stress increase ∆σp

must, of course, not exceed the yeld strengthof the steel.In the ultimate load calculation, care must betaken to ensure that the stress increase isestablished from the determining mechanism.This is illustaced diagrammatically

in Fig 29 with reference to a two-span beam.It has been assumed here that the top layercolumn head reinforcement is protrudingbeyond the column by at least

Ia min ≥ I . (1 - 1 ) (3.16)

√1 + λ2

in an edge span and by at least

Ia min ≥ 1 . (1 − 1 ) (3.17)2 √1 + λ

in an internal span. It must be noted that Ia min

does not include the anchoring length of thereinforcement.In particular, it must be noted that, if I1 = I2,the plastic moment over the internal columnwill be different depending upon whetherspan 1 or span 2 is investigated.

Figure 29: Determining failure mechanisms for two-span beam

Figure 30: Portion of slab in column area; transverse components due to prestress in criticalshear contrary

Example of the calculation of a tendonextension:According to [14], which is substantially inline with the above considerations, thenominal failure state is reached when with adetermining mechanism a deflection au of1/40th of the relevant span I is present.Therefore equations (3.13) and (3.14) for thetendon extension can be simplified asfollows:Without lateral restraint, e.g. for edge spansof flat slabs:

∆I=0.075 . dp (3.18.)

With a rigid lateral restraint, e g. for internalspans of flat slabs:

∆I=0.05 . (0.025 . 1 + 2 . hp) (319.)

3.2. Punching shear

32.1. GeneralPunching shear has a position of specialimportance in the design of flat slabs. Slabs, whichare practically always under-reinforced againstflexure, exhibit pronounced ductile bending failure.In beams, due to the usually present shearreinforcement, a ductile failure is usually assured inshear also. Since slabs, by contrast, are providedwith punching shear reinforcement only in veryexceptional cases,because such reinforcement isavoided if at all possible for practical reasons,punching shear is associated with a brittle failure ofthe concrete.This report cannot attempt to provide generally validsolutions for the punching problem. Instead, onepossibile solution will be illustrated. In particular weshall discuss how the prestress can be taken intoaccount in the existing design specifications, whichhave usually been developed for ordinarilyreinforced flat slabs.In the last twenty years, numerous design formulaehave been developed, which were obtained fromempirical investigations and, in a few practicalcases, by model represtation. The calculationmethods and specifications in most common usetoday limit the nominal shear stress in a criticalsection around the column in relation to a designvalue as follows [9]:

(3.20.)

The design shear stress value Tud isestablished from shear tests carried out onportions of slabs. It is dependent upon theconcrete strength fc’ the bending reinforcementcontent pm’, the shear reinforcement contentpv’,the slab slenderness ratio h/l, the ratio ofcolumn dimension to slab thickness ζ, bondproperties and others. In the variousspecifications and standards, only some ofthese influences are taken into account.

3.2.2. Influence of post tensioningPost-tensioning can substantially alleviatethe punching shear problem in flat slabs ifthe tendon layout is correct.A portion of the load is transferred by the transversecomponents resulting from prestressing directly tothe column. The tendons located inside the criticalshear periphery (Fig. 30) can still carry loads in theform of a cable system even after the concretecompressive zone has failed and can thus preventthe collapse of the slab. The zone in which theprestress has a loadrelieving effect is hereintentionally assumed to be smaller than thepunching cone. Recent tests [27] havedemonstrated that, after the shear cracks haveappeared, the tendons located outside the crlncalshear periphery rupture the concrete verticallyunless heavy ordinary reinforcement is present,and they can therefore no longer provide a load-bearing function.If for constructional reasons it is not possible toarrange the tendons over the column within thecritical shear periphery or column strip bck definedin Fig. 30 then the transfer of the transversecomponents resulting

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from tendons passing near the columnshould be investigated with the help of aspace frame model. The distance betweenthe outermost tendons to be taken intoaccount for direct load transfer and the edgeof the column should not exceed ds on eitherside of the column.The favourable effect of the prestress can be taken account of as follows:1 The transverse component Vp∞ resulting

from the effectively present prestressing force and exerted directly in the region ofthe critical shear periphery can be subtracted from the column load resultingfrom the applied loads. In the tendons, theprestressing force after deduction of all losses and without the stress increase should be assumed. The transverse component Vp is calculated from Fig. 30 as

Vp=Σ Pi . ai = P. a (3.21.)

Here, all the tendons situated within the critical shear periphery should be considered, and the angle of deviation within this shear periphery should be used for the individual tendons.

2 The bending reinforcement is sometimestaken into account when establishing thepermissible 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 calculationA possible design procedure is shown in [14];this proof, which is to be demonstrated in theultimate limit state, is as follows:

Rd ≥ 1.4 . V g+q - Vp (3.22.)1.3 1.3

The design value for ultimate strength forconcentric punching of columns throughslabs of constant thickness withoutpunching shear reinforcement should beassumed as follows:

Rd = uc. ds

. 1.5 .Tud (3.23.)

Uc is limited to 16 . ds, at maximum and theratio of the sides of the rectangle surroundingthe column must not exceed 2:1.Tud can be taken from Table I.

If punching shear reinforcement must beincorporated, it should be designed bymeans of a space frame model with aconcrete compressive zone in the failurestate inclined at 45° to the plane of the slab,for the column force 1.8 Vg+q-Vp. Here, thefollowing condition must be complied with.

2. Rd ≥1.8 . Vg+q -Vp (3.24.)

For punching shear reinforcement, verticalstirrups are recommended; these must passaround the top and bottom slabreinforcement. The stirrups nearest to theedge of the column must be at a distancefrom this column not exceeding 0.5 • ds. Also,the spacing between stirrups in the radialdirection must not exceed 0.5 • ds (Fig.31).Slab connections to edge columns andcorner columns should be designedaccording to the considerations of the beamtheory. In particular, both ordinaryreinforcement and post-tensioned tendonsshould be continued over the column andproperly anchored at the free edge (Fig. 32).

Figure 31: Punching shear reinforcement

Figure 32: Arrangement of reinforcement at corner and edge columns

10

4. Serviceability limitstate

4.1. Crack limitation4.1.1. GeneralIn slabs with ordinary reinforcement orbonded post-tensioning, the development ofcracks is dependent essentially upon thebond characteristics between steel andconcrete. The tensile force at a crack isalmost completely concentrated in the steel.This force is gradually transferred from thesteel to the concrete by bond stresses. Assoon as the concrete tensile strength or thetensile resistance of the concrete tensilezone is exceeded at another section, a newcrack forms.The influence of unbonded post-tensioningupon the crack behaviour cannot beinvestigated by means of bond laws. Onlyvery small frictional forces develop betweenthe unbonded stressing steel and theconcrete. Thus the tensile force acting in thesteel is transferred to the concrete almostexclusively as a compressive force at theanchorages.Theoretical [10] and experimental [8]investigations have shown that normal forcesarising from post-tensioning or lateralmembrane forces influence the crackbehaviour in a similar manner to ordinaryreinforcement.In [10], the ordinary reinforcement content p*required for crack distribution is given as afunction of the normal force arising fromprestressing and from the lateral membraneforce 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 providedwith a negative sign.

Figure 33: Reinforcement content requiredto ensure distribution of cracks

Various methods are set out in differentspecifications for the assessment and controlof crack behaviour:- Limitation of the stresses in the ordinary

reinforcement calculated in the cracked state [40].

- Limitation of the concrete tensile stressescalculated for the homogeneous cross-section [12].

- Determination of the minimum quantity ofreinforcement that will ensure crack distribution [14].

- Checking for cracks by theoretically or empirically obtained crack formulae [15].

4.12. Required ordinary reinforcementThe design principles given below are inaccordance with [14]. For determining theordinary reinforcement required, a distinctionmust be made between edge spans, internalspans and column zones.

Edge spans: Required ordinary reinforcement (Fig. 34):ps ≥ 0.15 - 0.50 . pp (4.2)Lower limit: ps ≥ 0.05%

Figure 34: Minimum ordinary reinforcementrequired as a function of the post-tensionedreinforcement for edge spans

Internal spans:For internal spans, adequate crack distri-bution is in general assured by the post-

Figure 35: Diagrammatic arrangement of minimum reinforcement

tensioning and the lateral membranecompressive forces that develop with evenquite small deflections. In general, therefore,it is not necessary to check for minimumreinforcement. The quantity of normalreinforcement required for the ultimate limitstate must still be provided.

Column zone:In the column zone of flat slabs, considerableadditional ordinary reinforcement mustalways be provided. The proposal of DIN4227 may be taken as a guideline, accordingto which in the zone bcd = bc + 3 . ds (Fig. 30)at least 0.3% reinforcement must beprovided and, within the rest of the columnstrip (bg = 0.4 . I) at least 0.15% must beprovided (Fig. 35). The length of thisreinforcement including anchor length shouldbe 0.4 . I. Care should be taken to ensurethat the bar diameters are not too large.The arrangement of the necessary minimumreinforcement is shown diagrammatically inFig.35. Reinforcement in both directions isgenerally also provided everywhere in theedge spans. In internal spans it may benecessary for design reasons, such as pointloads, dynamic loads (spalling of concrete)etc. to provide limited ordinary reinforcement.

11

4.2. Deflections

Post-tensioning has a favourable influenceupon the deflections of slabs under serviceloads. Since, however, post-tensioning alsomakes possible thinner slabs, a portion of thisadvantage is lost.As already mentioned in Chapter 3.1.1., theload-balancing method is very suitable forcalculating deflections. Fig. 36 and 37illustrate the procedure diagrammatically.Under permanent loads, which may withadvantage be largely compensated by thetransverse components from post-tensioning,the deflections can be determined on theassumption of uncracked concrete.Under live loads, however, the stiffness isreduced by the formation of cracks. In slabswith bonded post-tensioning, the maximumloss of stiffness can be estimated from thenormal reinforced concrete theory. In slabswith unbonded post-tensioning, the reductionin stiffness, which is very large in a simplebeam reinforced by unbonded post-tensioning, is kept within limits in edge spansby the ordinary reinforcement necessary forcrack distribution,

Figure 38: Diagram showing components ofdeflection in structures sensitive to deflections

Figure 37: Principle of the load-balancing method

Figure 36: Transverse components and panel forces resulting from post-tensioning

and in internal spans by the effect of thelateral restraint.In the existing specifications, the deflectionsare frequently limited by specifying an upperlimit to the slenderness ratio (see Appendix 2).In structures that are sensitive to deflection,the deflections to be expected can beestimated as follows (Fig. 38):

a = ad-u + ag+qr - d + aq-qr (4.3.)

The deflection ad-u, should be calculated forthe homogeneous system making anallowance for creep. Up to the cracking loadg+qr’ which for reasons of prudence shouldbe calculated ignoring the tensile strength ofthe concrete, the deflection ag+qr--d should beestablished for the homogeneous systemunder short-term loading. Under theremaining live loading, the deflection aq-qr

should be determined by using the stiffnessof the cracked crosssection. For thispurpose, the reinforcement content fromordinary reinforcement and prestressing canbe assumed as approximately equivalent, i.e. p=ps+pp is used.In many cases, a sufficiently accurateestimate of deflections can be obtained ifthey are determined under the remainingload (g+q-u) for the homogeneous systemand the creep is allowed for by reduction ofthe elastic modulus of the concrete to

Ec =Ec (4.4.)

1+ ϕ

On the assumption of an average creepfactor ϕ = 2 [41] the elastic modulus of theconcrete should be reduced to

Ec =Ec (4 .5.)3

I

I

4.3. Post-tensioning force in thetendon

4.3.1. Losses due to frictionFor monostrands, the frictional losses arevery small. Various experiments havedemonstrated that the coefficients of frictionµ= 0.06 and k = 0.0005/m can be assumed.It is therefore adequate for the design toadopt a lump sum figure of 2.5%prestressing force loss per 10 m length ofstrand. A constant force over the entire lengthbecomes established in the course of time.For bonded cables, the frictional coefficientsare higher and the force does not becomeuniformly distributed over the entire length.The calculation of the frictional losses iscarried out by means of the well-knownformula PX = Po . e-(µa+kx). For the coeffi-cients of friction the average values of TableII can be assumed.The force loss resulting from wedge drawinwhen the strands are locked off in theanchorage, can usually be compensated byoverstressing. It is only in relatively shortcables that the loss must be directly allowedfor. The way in which this is done isexplained in the calculation example(Chapter 8.2.).

4.32. Long-term lossesThe long-term losses in slabs amount toabout 10 to 12% of the initial stress in theprestressing steel. They are made up of thefollowing components:

Creep losses:Since the slabs are normally post-tensionedfor dead load, there is a constantcompressive stress distribution over thecross-section. The compressive stressgenerally is between 1.0 and 2.5 N/mm2 andthus produces only small losses due tocreep. A simplified estimate of the loss ofstress can be obtained with the final value forthe creep deformation:

∆σpc=εcc. Ep=ϕn . σc . Ep (4.6.)

Ec

Although the final creep coefficient ϕn due to

early post-tensioning is high, creep lossesexceeding 2 to 4% of the initial stress in theprestressing steel do not in general occur.

Shrinkage losses:The stress losses due to shrinkage are givenby the final shrinkage factor scs as:

∆σps = εcs. Ep (4.7.)

The shrinkage loss is approximately 5% ofthe initial stress in the prestressing steel.

Table II - Average values of friction forbonded cables

12

Relaxation losses:The stress losses due to relaxation of thepost-tensioning steel depend upon the typeof steel and the initial stress. They can bedetermined from graphs (see [42] forexample). With the very low relaxationprestressing steels commonly used today, foran initial stress of 0.7 fpu and ambienttemperature of 20°C, the final stress loss dueto relaxation is approximately 3%.

Losses due to elastic shortening of theconcrete:For the low centric compression due toprestressing that exists, the average stressloss is only approximately 0.5% and cantherefore be neglected.

4.4. VibrationsFor dynamically loaded structures, specialvibration investigations should be carried out.For a coarse assessment of the dynamicbehaviour, the inherent frequency of the slabcan be calculated on the assumption ofhomogeneous action.

4.5. Fire resistanceIn a fire, post-tensioned slabs, like ordinarilyreinforced slabs, are at risk principally onaccount of two phenomena: spalling of theconcrete and rise of temperature in the steel.Therefore, above all, adequate concretecover is specified for the steel (see Chapter5.1.4.).

5. Detail design aspects

5.1. Arrangement of tendons

5.1.1. GeneralThe transference of loads from the interior ofa span of a flat slab to the columns bytransverse components resulting fromprestressing is illustrated diagrammatically inFig. 40.In Fig. 41, four different possible tendonarrangements are illustrated: tendons onlyover the colums in one direction (a) or in twodirections (b), the spans being ordinarilyreinforced (column strip prestressing);tendons distributed in the span andconcentrated along the column lines (c andd). The tendons over the colums (for columnzone see Fig. 30) act as concealed mainbeams.When selecting the tendon layout, attentionshould be paid to flexure and punching andalso to practical construction aspects(placing of tendons). If the transverse com-

The fire resistance of post-tensioned slabs isvirtually equivalent to that of ordinarilyreinforced slabs, as demonstrated bycorresponding tests. The strength of theprestressing steel does indeed decrease morerapidly than that of ordinary reinforcement asthe temperature rises, but on the other hand inpost-tensioned slabs better protection isprovided for the steel as a consequence of theuncracked cross-section.The behaviour of slabs with unbonded post-tensioning is hardly any different from that ofslabs with bonded post-tensioning, if theappropriate design specifications arefollowed. The failure of individual unbondedtendons can, however, jeopardize severalspans. This circumstance can be allowed forby the provision of intermediate anchorages.From the static design aspect, continuoussystems and spans of slabs with lateralconstraints exhibit better fire resistance.An analysis of the fire resistance ofposttensioned slabs can be carried out, forexample, according to [43].

4.6. Corrosion protection4.6.1. Bonded post-tensioningThe corrosion protection of grouted tendonsis assured by the cement suspensioninjected after stressing. If the groutingoperations are carefully carried out noproblems arise in regard to protection.The anchorage block-outs are filled with low-shrinkage mortar.

4.62. Unbonded post-tensioningThe corrosion protection of monostrandsdescribed in Chapter 1.3.2. must satisfy the

following conditions: - Freedom from cracking and no embrittle-

ment or liquefaction in the temperaturerange -20° to +70 °C

- Chemical stability for the life of the structure

- No reaction with the surrounding materials

- Not corrosive or corrosion-promoting- WatertightA combination of protective grease coatingand plastics sheathing will satisfy theserequirements.Experiments in Japan and Germany havedemonstrated that both polyethylene andpolypropylene ducts satisfy all the aboveconditions.As grease, products on a mineral oil base areused; with such greases the specifiedrequirements are also complied with.The corrosion protection in the anchoragezone can be satisfactorily provided byappropriate constructive detailing (Fig. 39), insuch a manner that the prestressing steel iscontinuously protected over its entire length.The anchorage block-out is filled withlowshrinkage mortar.

Figure 39: Corrosion protection in theanchorage zone

ponent is made equal to the dead load,thenunder dead load and prestress a completeload balance is achieved in respect of

flexure and shear if 50 % of the tendons areuniformly distributed in the span and 50 %are concentrated over the columns.

Figure 40: Diagrammatic illustration of load transference by post-tensioning

13

Figure 41: Possible tendon arrangements

Under this loading case, the slab is stressedonly by centric compressive stress. In regardto punching shear, it may be advantageousto position more than 50 % of the tendonsover the columns.In the most commonly encounteredcases, the tendon arrangement illustratedin Fig. 41 (d), with half the tendons in eachdirection uniformly distributed in the spanand half concentrated over the columns,provides the optimum solution in respectof both design and economy.

5.1.2. SpacingsThe spacing of the tendons in the spanshould not exceed 6h, to ensuretransmission of point loads. Over the column,the clear spacing between tendons or strandbundles should be large enough to ensureproper compaction of the concrete and allowsufficient room for the top ordinaryreinforcement. Directly above the column,the spacing of the tendons should beadapted to the distribution of thereinforcement.In the region of the anchorages, the spacingbetween tendons or strand bundles must bechosen in accordance with the dimensions ofthe anchorages. For this reason also, thestrand bundles themselves are splayed out,and the monostrands individually anchored.

5.1.3. Radii of curvatureFor the load-relieving effect of the verticalcomponent of the prestressing forces overthe column to be fully utilized, the point ofinflection of the tendons or bundles shouldbe at a distance ds/2 from the column edge(see Fig. 30). This may require that theminimum admissible radius of curvature beused in the column region. The extreme fibrestresses in the prestressing steel mustremain below the yield strength under theseconditions. By considering the naturalstiffness of the strands and the admissibleextreme fibre stresses, this gives a minimumradius of curvature for practical use ofr = 2.50 m. This value is valid for strands ofnominal diameter 13 mm (0.5") and 15 mm(0.6").

Table IV - Minimum concrete cover for the post-tensioning steel (in mm) in respect of the fireresistance period required

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.

Table III - Required cover of prestressingsteel by concrete (in mm) as a function ofconditions of exposure and concrete grade

5.1.4. Concrete coverTo ensure long-term performance, theprestressing steel must have adequateconcrete cover. Appropriate values areusually laid down by the relevant nationalstandards. For those cases where suchinformation does not exist, the requirementsof the CEB/FI P model code [39] are given inTable I I I.The minimum concrete cover can also beinfluenced by the requirements of fireresistance. Knowledge obtained frominvestigations of fire resistance has led torecommendations on minimum concretecover for the post-tensioning steel, as can beseen from Table IV. The values stated shouldbe regarded as guidelines, which can varyaccording to the standards of the variouscountries.For grouted tendons with round ducts thecover can be calculated to the lowest orhighest strand respectively.

5.2. JointsThe use of post-tensioned concrete and, inparticular, of concrete with unbondedtendons necessitates a rethinking of somelong accepted design principles. A questionthat very often arises in building design is thearrangement of joints in the slabs, in thewalls and between slabs and walls.Unfortunately, no general answer can begiven to this question since there are certainfactors in favour of and certain factorsagainst joints. Two aspects have to beconsidered here:

14

- Ultimate limit state (safety)- Horizontal displacements (serviceability

limit state)

5.2.1. Influence upon the ultimate limitstate behaviour

If the failure behaviour alone is considered, itis generally better not to provide any joints.Every joint is a cut through a load-bearingelement and reduces the ultimate loadstrength of the structure.For a slab with unbonded post-tensioning,the membrane action is favourablyinfluenced by a monolithic construction. Thisresults in a considerable increase in theultimate load (Fig. 42).

5.2.2. Influence upon the serviceabilitylimit state

In long buildings without joints, inadmissiblecracks in the load-bearing structure anddamage to non load-bearing constructionalelements can occur as a result of horizontaldisplacements. These displacements resultfrom the following influences:- Shrinkage- Temperature- Elastic shortening due to prestress - Creep due to prestressThe average material properties given inTable V enable one to see how such damageoccurs.In a concrete structure, the following averageshortenings and elongations can beexpected:Shrinkage ∆Ics = -0.25 mm/mTemperature ∆Ic t = -0.25 mm/m

to+0.15 mm/mElastic shortening(for an average centric prestress of 1.5N/mmz and Ec=30 kN/mm2) ∆Icel = -0.05 mm/mCreep ∆Icc = - 0.15 mm/m

These values should be adjusted for theparticular local conditions.When the possible joint free length of astructure is being assessed, the admissibletotal displacements of the slabs and wallsor columns and the admissible relativedisplacements between slabs and walls orcolumns should be taken into account.Attention should, of course, also be paid tothe foundation conditions.The horizontal displacements can be partlyreduced or prevented during the constructionstage by suitable constructional measures(such as temporary gaps etc.) without damageoccurring.

Shrinkage:Concrete always shrinks, the degree ofshrinkage being highly dependent upon thewater-cement ratio in the concrete, the cross-sectional dimensions, the type of curing andthe atmospheric humidity. Shortening due toshrinkage can be reduced by up to aboutone-half by means of temporary shrinkagejoints.

Temperature:In temperature effects, it is the temperaturedifference between the individual structuralcomponents and the differing coefficients ofthermal expansion of the materials that are ofgreatest importance.

Figure 42: Influence of membrane action upon load-bearing capacity

Table V -Average material properties of various construction materials

In closed buildings, slabs and walls in theinternal rooms are subject to low temperaturefluctuations. External walls and unprotectedroof slabs undergo large temperaturefluctuations. In open buildings, the relativetemperature difference is small. Particularconsiderations arise for the connection to thefoundation and where different types ofconstruction materials are used.

Elastic shortening and creep due toprestress:Elastic shortening is relatively small. Bysubdividing the slab into separate concretingstages, which are separately post-tensioned,

the shortening of the complete slab isreduced.Creep, on the other hand, acts upon theentire length of the slab. A certain reductionoccurs due to transfer of the prestress to thelongitudinal walls.Shortening due to prestress should be keptwithin limits particularly by the centricprestress not being made too high. It isrecommended that an average centricprestress of σcpm = 1.5 N/mm2 should beselected and the value of 2.5 N/mm2 shouldnot be exceeded. In concrete walls, therelative shortening between slabs and wallscan be reduced by approximately uniformprestress in the slabs and walls.

Figure 43: Examples of jointless structures of 60 to 80 m length

15

5.2.3. Practical conclusionsIn slabs of more than 30 m length, a uniform,«homogeneous» deformation behaviour ofthe slabs and walls in the longitudinaldirection should be aimed at. In openbuildings with concrete walls or columns, thisrequirement is satisfied in regard totemperature effects and, provided the agedifference between individual components isnot too great, is also satisfied for shrinkageand creep.In closed buildings with concrete walls orcolumns, a homogeneous behaviour forshrinkage and creep should be achieved. Inrespect of temperature, however, theconcreted external walls behave differentlyform the internal structure. If cooling downoccurs, tensile stresses develop in the wall.Distribution of the cracks can be ensured bylongitudinal reinforcement. The tensilestresses may also be compensated for bypost-tensioning the wall.If, in spite of detail design measures, theabsolute or relative longitudinal deformationsexceed the admissible values, the buildingmust be subdivided by joints.Fig. 43 and 44 show, respectively, someexamples in which joints can be dispensedwith and some in which joints are necessary.

Figure 44: Examples of structures that must be subdivided by joints into sections of 30 to 40 m length

6. Constructionprocedures

6.1. GeneralThe construction of a post-tensioned slab isbroadly similar to that for an ordinarilyreinforced slab. Differences arise in theplacing of the reinforcement, the stressing ofthe tendons and in respect of the rate ofconstruction.The placing work consists of three phases:first, the bottom ordinary reinforcement of theslab and the edge reinforcement are placed.The ducts or tendons must then bepositioned, fitted with supports and fixed inplace. This is followed by the placing of thetop ordinary reinforcement. The stressing ofthe tendons and, in the case of bondedtendons the grouting also, representadditional construction operations ascompared with a normally reinforced slab.Since, however, these operations are usuallycarried out by the prestressing firm, the maincontractor can continue his work withoutinterruption.A feature of great importance is the shortstripping times that can be achieved withpost-tensioned slabs. The minimum periodbetween concreting and stripping offormwork is 48 to 72 hours, depending uponconcrete quality and ambient temperature.When the required concrete strength isreached, the full prestressing force canusually be applied and the formwork strippedimmediately afterwards. Depending upon the

total size, the construction of the slabs iscarried out in a number of sections.The divisions are a question of the geometryof the structure, the dimensions, theplanning, the construction procedure, theutilization of formwork material etc. Theconstruction joints that do occur, aresubseqently subjected to permanentcompression by the prestressing, so that thebehaviour of the entire slab finally is thesame throughout.The weight of a newly concreted slab mustbe transmitted through the formwork to slabsbeneath it. Since this weight is usually lessthan that of a corresponding reinforcedconcrete slab, the cost of the supportingstructure is also less.

6.2. Fabrication of the tendons

6.2.1. Bonded post-tensioningThere are two possible methods of fabrica-ting cables:- Fabrication at the works of the prestressing

firm- Fabrication by the prestressing firm on the

siteThe method chosen will depend upon thelocal conditions. At works, the strands are cutto the desired length, placed in the duct and,if appropriate, equipped with dead-endanchorages. The finished cables are thencoiled up and transported to the site.

anchorages. The finished cables are thencoiled up and transported to the site.In fabrication on the site, the cables caneither be fabricated in exactly the samemanner as at works, or they can beassembled by pushing through. In the lattermethod, the ducts are initially placed emptyand the strands are pushed through themsubsequently. If the cables have stressinganchorages at both ends, this operation caneven be carried out after concreting (exceptfor the cables with flat ducts).

6.22. Unbonded post-tensioningThe fabrication of monostrand tendons isusually carried out at the works of theprestressing firm but can, if required, also becarried out on site. The monostrands are cutto length and, if necessary, fitted with thedead-end anchorages. They are then coiledup and transported to site. The stressinganchorages are fixed to the formwork. Duringplacing, the monostrands are then threadedthrough the anchorages.

6.3. Construction procedure forbonded post-tensioning

In slabs with bonded post-tensioning, theoperations are normally carried out asfollows:1. Erection of slab supporting formwork

16

Direction column Remainingstrip area

Vertical ± 5mm ± 5mm

Horizontal ± 20 mm ± 50 mm

2. Fitting of end formwork; placing ofstressing anchorages

3. Placing of bottom and edge reinforcement4. Placing of tendons or, if applicable, empty

ducts* according to placing drawing5. Supporting of tendons or empty ducts*

with supporting chairs according to support drawing

6. Placing of top reinforcement7. Concreting of the section of the slab8. Removal of end formwork and forms

for the stressing block-outs9. Stressing of cables according to stressing

programme10. Stripping of slab supporting formwork11.Grouting of cables and concreting of

block-outs

* In this case, the stressing steel is pushedthrough either before item 5 or beforeitem 9.

6.4. Construction procedure forunbonded post-tensioning

If unbonded tendons are used, theconstruction procedure set out in Chapter6.3. is modified only by the omission ofgrouting (item 11).The most important operations are illustratedin Figs. 45 to 52. The time sequence isillustrated by the construction programme(Fig. 53).All activities that follow one another directlycan partly overlap; at the commencement ofactivity (i+1), however, phase (i-1) must becompleted. Experience has shown that thoseactivities that are specific to prestressing(items 4, 5 and 9 in Chapter 6.3.) are withadvantage carried out by the prestressingfirm, bearing in mind the following aspects:

6.4.1. Placing and supporting of tendonsThe placing sequence and the supporting ofthe tendons is carried out in accordance withthe placing and support drawings (Figs. 54and 55). In contrast to a normally reinforcedslab, therefore, for a post-tensioned slab twodrawings for the prestressing must beprepared in addition to the reinforcementdrawings. The drawings for both, ordinaryreinforcement and posttensioning are,however, comparatively simple and thenumber of items for tendons and reinforcingbars is small.The sequence in which the tendons are to beplaced must be carefully considered, so thatthe operation can take place smoothly.Normally a sequence allowing the tendons

Table VI-Achievable accuracies in placing

Figure 53: Construction programme

17

to be placed without «threading» or«weaving» can be found without anydifficulty. The achievable accuracies aregiven in Table VI.To assure the stated tolerances, goodcoordination is required between all theinstallation contractors (electrical, heating,plumbing etc.) and the organization res-

ponsible for the tendon layout.Corresponding care is also necessary inconcreting.6.4.2. Stressing of tendonsFor stressing the tendons, a properlysecured scaffolding 0.50 m wide and of 2kN/m

2

load-bearing capacity is required atthe edge of the slab. For the jacks used

there is a space requirement behind theanchorage of 1 m along the axis and 120 mmradius about it. All stressing operations arerecorded for each tendon. The primaryobjective is to stress to the required load; theextension is measured for checkingpurposes and is compared with thecalculated value.

Figure 54: Placing drawing

Figure 55: Support drawing

18

7. Preliminary design

In the design of a structure, both thestructural design requirements and the typeof use should be taken into account. Thefollowing points need to be carefully clarifiedbefore a design is carried out:- Type of structure: car park, warehouse,

commercial building, residential building, industrial building, school, etc.

- Shape in plan, dimensions of spans, column dimensions; the possiblility of strengthening the column heads of a flat slab by drop panels

- Use: live load (type: permanent loads, moving loads, dynamic loads), sensitivityto deflection (e.g. slabs with rigid struc-tures supported on them), appearance(cracks), vibrations, fire resistance class, corrosive environment, installations (openings in slabs).

For the example of a square internal span ofa flat slab (Fig. 56) a rapid preliminary designwill be made possible for the design engineerwith the assistance of two diagrams, in whichguidance values for the slab thickness andthe size of the prestress are stated.

Figure 57: Recommended ratio of span to slab thickness as a function of service load to self-weight (internal span of a flat slab)

Figure 56: Internal span of a fla slab

Figure 58: Ratio of transverse component a from prestress to self-weight g as a function ofservice

The design charts (Figs. 57 and 58) arebased upon the following conditions:1. A factor of safety of y = 1.8 is to be

maintained under service load.2. Under self-weight and initial prestress the

tensile stress 6c;t for a concrete for whichf28 = 30 N/mm2 shall not exceed 1.0 N/mm2.

3. The ultimate moment shall be capable of being resisted by the specified minimum ordinary reinforcement or, in the case of large live loads, by increased ordinary reinforcement, together with the corresponding post-tensioning steel.

The post-tensioning steel (tendons in thespan and over the columns) and the ordinaryreinforcement are assumed as uniformlydistributed across the entire span. Thetendons are to be arranged according toChapter 5.1. and the ordinary reinforcementaccording to Fig. 35.From conditon 1, the necessary values areobtained for the prestress and ordinaryreinforcement as a function of the slabthickness and span. Conditon 2 limits the

c

maximum admissible prestress. In flat slabs,the lower face in the column region is usuallythe determining feature. In special cases,ordinary reinforcement can be placed there.The concrete tensile stress oct (condition 2)should then be limited to σct 2.0 N/mm2.With condition 3, a guidance value isobtained for economic slab thickness(Fig.57). It is recommended that the ratio I/hshall be chosen not greater than 40. Inbuildings the slab thickness should normallynot be less than 160 mm.Fig. 57 and 58 can be used correspondinglyfor edge and corner spans.

Procedure in the preliminary design of a flatslab:

Given: span I, column dimensions, live load q1. Estimation of the ratio I/h → self-weight g.2. With ratio of service load (g+q) to

selfweight g and span I, determine slab thickness h from Fig. 57; if necessary correct g.

3. With I, h and (g+q)/g; determine transverse component from Fig. 58 and from this prestress; estimate approximatequantity of ordinary reinforcement.

4. Check for punching; if necessary flare outcolumn head or choose higher concrete quality or increase h.

The practical execution of a preliminarydesign will be found in the calculationexample (Chapter 8.2.).

19

8. Execution of the calculations

8.1. Flow diagram

- Material properties:Concrete f28 = 35 N/mm2

fcd = 0.6 . f28= 21 N/mm2

Prestressing steel Monostrands ∅ 15 mm (0.6")Ap = 146 mm2

fpy = 1570 N/mm2

fpu = 1770 N/mm2

Ep = 1.95 ⋅ 105

N/mm2

very low relaxation (3%)Admissible stresses:- at stressing: 0.75 fpu

- after wedge draw-in: max. 0.70 fpu

Friction coefficients: µ=0.06k = 0.0005/m

Reinforcing steel fsy = 460 N/mm2

- Concrete cover:Prestressing steel cp = 30 mmReinforcing steel cs = 15 mm

- Long-term losses (incl. relaxation): assumed to be 10% (see Chapter 4.3.2.)

8.2.2. Preliminary design Determination of slab thickness:

Assumption: I/h = 35

→ h =8.40

= 0.24 m35

g = 0.24 ⋅ 25 = 6 kN/m2

q = 5 kN/m2

11 kN/m2

g+q=

11= 1.83; hence from Fig. 57g 6

→I/h = 36

h =8.40

= 0.233 m36

chosen: h=0.24 m

Determination of prestress:a) Longitudinal direction:

g+q= 1.83;κ = 0.24 ⋅ 1000

= 0.136;g 8.40

2

⋅ 25

hence from Fig. 58

→ u = 1.39; u = 1.39 . 6 = 8.34 kN/m2g

P =u . I2

8 . hp

hp = 0.144 .4.202

= 0.178 m (Fig. 60)3.78

2

P =8.34 ⋅ 8.402

= 413 kN/m8 . 0.178

on 7.80 m width: P = 7.80 - 413 = 3221 kN per strand: PL= 146 .1770 . 0.7 . 10-3 = 181 kN

Number of strands:np=3221

= 17.8181

→ 18 monostrands ∅ 15 mm on 7.80 m width

on 7.40 m width: np=7.40 . 17.8= 16.97.80

→ 17 monostrands ∅ 15 mm on 7.40 m width

c

c

20

8.2. Calculation example

8.2.1. Bases- Type of structure: commercial building

- Geometry: see Fig. 59

- Loadings:Live load p = 2.5 kN/m2

Floor finishes gB = 1.OkN/m2

Walls gw = 1.5 kN/m2

q = 5.0 kN/m2

Figure 59: Plan showing dimensions

Figure 60: Tendon profile in longitudinal direction (internal span) Figure 61: Tendon profile in transverse direction (internal span)

on 6.60 m width: np =6.60 . 17.8 = 15.17.80

→ 16 monostrands 0 15 mm on 6.60 m width

on 2.40 m width: np=2.40 . 17.8 = 5.57.80

→ 6 monostrands ∅ 15 mm on 2.40 m width

b) Transverse direction:

g+q =1.83;κ= 0.24 . 1000 = 0.158g 7.802 . 25

hence from Fig. 58

→ u = 1.41;u=1.41. 6 = 8.46kN/m2g

hp=0.135 . 7.802

= 0.167 m (Fig. 61)3.51

2

P=8.46 . 7.802= 385 kN/m

8 . 0.167

on 8.40 m width: P=8.40 . 385=3234 kN

Number of strands: np=3234

=17.9181

→18 monostrands 0 15 mm on 8.40 m width

on 7.20 m width: np=7.20 . 17.9 =15.38,40

→16 monostrands 0 15 mm on 7.20 m width

- Determination of ordinary reinforcement:a) Top reinforcement:In the region of the punching cone: ps=0.3% (Fig. 35) Average of effective depth of reinforcement in both directions:dsc = 240 - 15 - 15 = 210 mm (approx. value) Width bcd (Fig. 30):

bcd = bc+3dsc = 450 + 3 . 210 = 1080 mm

→ ASS = 0.003 . 210 . 1080 = 680 mm2

chosen: 7 ∅12 mm (Ass= 791 mm2)

In column strip:ps= 0.15% (Fig. 35)longitudinally:

bg = 0.4 . 7800 -1080 = 2040 mm

Asg =0.0015 .210 . 2040 = 643 mm2

chosen: 6 ∅12 mm (Asg=678 mm2)

21

Figure 62: Influence zone column 1 Figure 63: Tendon profile in critical shear periphery

transversely:bg = 0.4 ⋅ 8400 -1080 = 2280 mm Asg=0.0015 ⋅ 210 ⋅ 2280=718 mm2

chosen: 4+4 ∅ 12 mm (Asg= 904 mm2)

b) Bottom reinforcement:• Internal spans: none• Edge spans: ps ≥ 0.15 - 0.50 ⋅ pp (Formula 4.2.)

longitudinally:

pp=np ⋅ Ap =

18 ⋅ 146= 0.17%

dp ⋅ b 200 ⋅ 7800

→ ps ≥ 0.15-0.50 ⋅ 0.17 = 0.065% → As ≥ 0.065 ⋅ 220 ⋅ 10 = 143 mm2/mchosen:∅ 6 mm, spacing 175 mm

transversely:

pp ≥ = 18 ⋅ 146= 0.16%

200 ⋅ 8400

→ps ≥ 0.07%→As ≥ 0.07⋅ 220 ⋅ 10 = 154 mm2/mchosen:∅ 6 mm, spacing 175 mm

Check for punching:Determining column 1 (Fig. 62): g+q = 11 kN/m2

Vg+q = 11. 7.60 . 8.60 = 719kN Prestress:50% within the critical shear periphery, i.e. 9 monostrands in eachdirection

Point of inflection:According to Fig. 30 the point of inflection ideally lies at a distance ds/2

from the column edge. In Figs. 60 and 61 it is assumed that thedimensions of the column are not yet known and the point of inflectionis adopted at a distance 0.051 from the column axis (value fromexperience). In Fig. 62 the dimensions of the column have beenestablished. Thus the real position of the point of inflection is known.The values given in Figs. 60 and 61 change accordingly (Fig. 63).

longitudinally :tga=

2 ⋅ 13= 0.078 = sina (Fig. 63a)

332

Vp=2.0.078.181.9.09=229kN(Factor 0.9=10% long-term losses)

transversely : tga=

2 ⋅ 12= 0.072 = sina (Fig. 63b)

332

Vp=2 . 0.072 . 181. 9 . 0.9 = 211 kNΣVp=440 kN

22

Figure 64: Tendon profile in longitudinal direction (edge span)

23

Figure 65: influence of wedge draw-in

Figure 66: Tendon profile in transverse direction (edge span andcantilever)

25

Figure 67: Tendon and reinforcement layout drawing

9. Completed structures

9.1. Introduction

In Chapters 9.2. to 9.11. ten projects aredescribed in which post-tensioned slabs wereused. They comprise structures covering awide range of applications and geographicalconditions. The post-tensioning in some ofthe slabs is bonded, in others unbonded.Thus a good overall view is obtained of thegreat variety of possible applications of post-tensioned slabs. In addition, the sequence ofthe descriptions is chronological, so that it ispossible to follow the course of developmentover the last eight years. In Chapter 9.12. themain technical data of the ten structures aresummarized in a table in order to enable aneasy comparison.

26

9.2. Orchard Towers, Singapore

Client Golden Bay Realty (Pte.)Ltd., Singapore

Architect Chng Heng Tat & Associates, Singapore

Engineer T.H. Chuah & Associates,Singapore

Contractor Lian Hup Construction Co.Pte. Ltd., Singapore

Post- VSL Systems Pte. Ltd.,tensioning SingaporeYears of construction 1972-74

IntroductionThis high-rise project consists of two similarbuilding complexes. Each comprises a moreor less flat, rectangular lower section and acentral, 24-storey block virtually square inplan. The front block contains spaces forshops and offices. The seven lower storeysof the rear block contain car parking areas,with flats in the multi-storey building above(Fig. 68).

Structural arrangementIn the front block the colums are generallyarranged in a grid of 6.85 x 6.40 m. The slabsare flat, 180 mm thick and post-tensioned inboth directions. In the storeys containing

27

Figure 68: The Orchard Towers shortly before completion

thanks to the use of post-tensioning. In theupper storeys the slabs are strengthenedwith post-tensioned edge beams, whichassist in supporting the heavy facadecladding.The column spacing in the rear building inthe central part of the low structure and in thestoreys of the high-rise section is 8.25 m inboth directions. In the low structure the mosteconomical arrangement proved to be acombined floor structure, namely low mainbeams in the transverse direction and thinflat slabs in the longitudinal direction. Thedepth of the slabs is 150 mm and that of thebeams 380 mm. By the use of this shallowstructural depth it was possible, withoutchanging the overall height of the building, toincorporate a complete additional storey forcar parking.The slabs of the rear high-rise building areflat. Their thickness ranges from 150 to 200mm. They are post-tensioned in bothdirections. Like the slabs of the low levelportion, some of them possess fairly largecantilevers.The post-tensioning ensures the necessarylimitation of deflections. As a result, problemssuch as those associated with service pipesetc. were largely eliminated. The advantages

of post-tensioning in respect ofwatertightness of the concrete becomeevident in the roof slabs.

ConstructionThe slabs of the low buildings were eachconstructed in two sections, a system whichfavoured the construction program and thecourse of the other work. In the high-riseslabs, the construction program provided forthe erection of one storey every fourteendays. After an initial phase, it was possible toreduce this cycle to 9 days. To permit earlyremoval of formwork and thus a rapidresumption of work on the next slab,stressing was carried out in two stages andthe formwork was transferred on the fourth orfifth day after concreting, i.e. at a concretestrength higher than 21 N/mm

2

(Fig. 69).

Post-tensioningFor all the slabs, bonded tendons were used.Each cable consists of four strands ∅ 13 mm(0.5"), lying in a flat duct and fitted with VSLanchorages. The service load per cable afterdeduction for all losses is 440 kN. The mainbeams in the rear low level building, whichare 1.83 m wide, each contain 6 cables. Inthe slab, the tendons are almost uniformly

shops the slabs cantilever out beyond theoutermost columns. In this region it waspossible to keep within the depth specified bythe architect for the load-bearing structure

Figure 69: View during construction

Figure 71: Plan and cable distribution in high-rise section of rear

Figure 70: Plan and cable distribution in low level portion of rear block

Figure 72: Plan and cable distribution in high-rise section of frontblock

distributed, the spacings ranging from 1.00 to1.45 m (Fig. 70).In the flat slabs of the high-rise building the

9.3. Headquarters of the Ilford Group, Basildon, Great Britain

Client Ilford Films, Basildon,Essex

Architect Farmer and Dark, LondonEngineer Farmer and Dark, LondonContractor Th. Bates & Son Ltd.,

RomfordPost- Losinger Systems Ltd.,tensioning ThameYears of construction 1974-75

IntroductionThe Ilford Group has had a new Head Officebuilding constructed at Basildon, tocentralize its administration. The buildingcomprises offices for 400 persons, acomputer centre, a department for technicalservices (laboratories), conference roomsand a lecture hall. Building commenced inthe middle of 1974. The work was completedonly one year later (Fig. 73).

Structural arrangementThe building comprises three post-tensionedslabs with a total area of 7,480 m2. Thebasement slab accounts for 1,340 m2 andthe two upper slabs for 3,070 m2 each. Thecolumn spacing was fixed at 12 m in bothdirections; only the end spans are shorter(6.10 to 7.30 m). The slab over the groundfloor cantilevers 0.40 m beyond the edgecolumns. All slabs are 300 mm thick. Theinternal columns are square. Their sidedimension is 600 mm.The lowest slab was designed for a live load(including partitions) of 8.5 kN/m2, and theother two slabs for 5 kN/m2. The detaileddesign was carried out on the basis of thetechnical report (then in draft) by theConcrete Society on «The design of post-tensioned flat slabs in buildings» (which, inthe meantime, has been issued in a revisedversion [13]). The higher loading of thebasement slab meant that it had to bestrengthened at the column heads by

Figure 73: The Headquarters of the Ilford Group

The total quantity of prestressing steelrequired for all the slabs was about 300metric tons.

9.4. Centro Empresarial,São Paulo, Brazil

Client LUBECA S.A. Administração eLeasing,São Paulo

Architect Escritório Técnico J.C.de Figueiredo Ferraz,São Paulo

Engineer Escritório Técnico J.C.de Figueiredo Ferraz,São Paulo

Contractor Construtora AlfredoMathias S.A., Sao Paulo

Post- Sistemas VSL Engenhariatensioning S.A., Rio de JaneiroYears of construction 1974-77

IntroductionThe «Centro Empresarial» (the name means«Administrative Centre» is a type of officesatellite town on the periphery of Sao Paulo.When completed it will comprise six multi-storey buildings, two underground car parksand a central building containing conferencerooms, post office, bank branches, dataprocessing plant and restaurants.A start was made on the foundation work inSeptember 1974. The first phase, i.e.approximately 2/3 of the centre, wascompleted at the beginning of 1977. There isat present no programme for the constructionof the second stage.

Structural arrangementThe «Centro Empresarial» is dividedstructurally into three different parts: themultistorey office buildings, the undergroundcar parks and the central block. Each of thehigh buildings comprises eleven storeys (twoof which are below ground), each of 53.50 x53.50 m area. To provide for maximumflexibility in use of the available buildingsurfaces a column spacing of 15 m waschosen. There are thus three spans of 15 mlength in each direction in each slab, with acantilever at each end of 4.25 m (Fig. 75).The slabs had to be light, simple to constructand of minimum possible depth. For a liveload of 5 kN/m

2

, the best method of meetingthese requirements was by using post-tensioning.In order to find the most economic solution, anumber of slab systems were compared: flatslab with hollow cores, one-way joistedbeams, drop panel slab and waffle slab. Thelast-named type proved to be the mostsuitable for the multi-storey buildings. Theslab depth was established at 400 mm,giving a slenderness ratio of 37.5. The slabitself is 60 mm thick, and the ribs which arespaced at 1.25 m between centres, are 170mm wide. The main beams over columns are2.50 m wide and give the structure greatstiffness (Fig. 76).

cables are also at more or less uniformspacings in both directions (Figs. 71 and 72).

flat drop panels of 2.60 m side dimensionand 50 mm additional depth.Post-tensioned flat slabs were chosen,because they proved to be cheaper than theoriginally intended, ordinarily reinforcedwaffle slabs of 525 mm depth. Thedifference in price for the slabs alone, i.e.without taking into account the effects onother parts of the structure, was more than20% and was evident both in the concreteand in the reinforcement and formwork [44].

ConstructionThe slabs were divided into a total of sevensections. It was initially intended that theseshould be constructed at intervals of tenweeks each. By the use of sufficientformwork materials, however, the contractorwas able to achieve an overlap of the cyclesand thus more rapid progress. This was alsonecessary, because the constructionprogramme was very tight, as Ilford had toleave their old offices by a specific date.The concrete used had to reach a strengthf28 of 41 N/mm2 for the lower slab and of30 N/mm

2

for the upper slabs.

Post-tensioningThe slabs were post-tensioned withmonostrands ∅ 15 mm (0.6"). The initialstressing force per strand was 173 kN, i.e.0.70 fpu. For the basement slab 70 strandswere required per 12 m span and for the twoupper slabs 60 strands. The strands wereindividually fitted with VSL anchorages; forpractical reasons, however, they werecombined into bundles of four.The load balancing method [35] was used fordetermining the prestressing force. Thisforce was selected so that the dead load and10% of the live load were fully balanced bythe transverse components fromprestressing. Where the remainder of the liveload led to tensile stresses, ordinaryreinforcement was used. In the columnregion, stirrups were required to withstandthe shear forces. This created someproblems in the placing of the tendons.

c

28

Figure 74: The Centro Empresarial (first phase)

Figure 76: Waffe slab during construction Figure 77: Flat slab during construction

Figure 75: Plan of the multi-storey buildings

The slabs of the two underground garages(four slabs each) are supported on a grid of7.50 x 10.00 m. They are 180 mm thick flatslabs (Fig. 77). The uppermost slab of eachgarage, which has to carry a soil loading of0.40 m, is 250 mm thick.The building complex for the central serviceswas designed as closely as possible alongthe same lines as the office towers. In thecentral block, ribbed slabs were adopted.The design of the slabs was generally inaccordance with the Brazilian prestressedconcrete standard P-NB-116, in so far as itcould be applied to post-tensioned slabs.The waffle slabs were designed on themethod of equivalent frames. The flat slabs

were designed by the load-balancingmethod.

Post-tensioningFor the waffle slabs, VSL cables of type 5-4in flat ducts (that is bonded post-tensioning) were used. One such cable wasnecessary in each rib; in each column-linebeam, 22 cables of this type had to beincorporated, equivalent to approximately70% of the total prestress. Due to this highconcentration, the cables had to be placed intwo layers. By the use of the flat ducts, it waspossible for the maximum eccentricity overthe columns to be achieved however.The cables were prefabricated in a hall on

the site. Two or three strands weresimultaneously unreeled from the coil bymeans of a VSL push-through machine andpushed directly into the duct. The tendonsthen had to be stored for a shorter or longerperiod since the demand for cables to be builtin often fluctuated appreciably. The «cablefactory» supplied up to 330 metric tons ofcables in the peak months. The cables werecoiled up for transport from the assembly hallto the place of installation. On the formworkthey were unrolled in a sequence that hadpreviously been tested with a model (Fig. 79).It had originally been intended to apply halfthe prestressing force three days afterconcreting and the full force after seven days.

Figure 78: The Centro Empresarial during construction Figure 78: The Centro Empresarial during construction

29

This procedure was later modified to fullstressing of most of the tendons after six orseven days. After the stressing operation hadbeen carried out at both ends of the cable,the protruding strands were cut off and theanchorage block-outs concreted in. Thecables were then grouted.The post-tensioning operations commencedin February 1975 and lasted 17 months.During this period, 1,670 metric tons ofprestressing steel and approximately 140metric tons of anchorages were built into the143,500 m2 of slabs.

9.5. Doubletree Inn, Monterey,California, USA

Client Doubletree Inc., Phoenix,Arizona

Architect Kivett Myers, AIA, KansasCity, Missouri

Engineer VSL Corporation, LosGatos, California

Contractor Baugh Construction,Seattle, Washington

Post- VSL Corporation, Lostensioning Gatos, CaliforniaYears of construction 1976-77

IntroductionThe Doubletree Inn at Fisherman's Wharf isa hotel comprising 374 guest rooms,conference rooms, restaurants, shops and aparking structure for 420 private cars (Fig.80).The project almost failed to get built. Thetender price for the original design, specifiedin reinforced concrete, was considerably

strand from the roll or by rolling them out.Tendons with intermediate stressinganchorages at the construction joints werehung rolled up from scaffolds until they couldbe extended further (Fig. 82).The service load per monostrand afterdeduction for all losses is 0.60 fpu, i.e. 110kN. To keep the frictional losses as low aspossible, cables exceeding 30 m in lengthwere stressed at both ends. The stressingoperation was carried out at a concretestrength of 17.5 to 21.0 N/mm2, that is atabout 0.625 to 0.75 f~8.

9.6. Shopping Centre, Burwood, Australia

Client Berbert Investment Co.Ltd., Sydney

Architect Hely, Horne, Stuart & Perry,Milsons Point, N.S.W.

Engineer Rankine -Hill Pty. Ltd.,Sydney

Contractor Concrete ConstructionsPty. Ltd., Potts Point,

N.S.W.Post- VSL Prestressing (Aust.)tensioning Pty. Ltd., Thornleigh, N.S.W.Years ofconstruction 1976-78

IntroductionBurwood is a suburb of Sydney. Theshopping centre, built there between May1976 and October 1978, predominantlyserves a large department store, but alsocomprises 68 specialist shops and threestoreys with car parking places (Fig. 83).

above that which the client was prepared topay. Other proposals also, including a variantinvolving prefabrication, were outside thestipulated limits.The VSL Corporation was consequentlycommissioned to look for possible savings. Itproposed that post-tensioned, in-situ flatslabs should be used and the earthquakeforces transmitted via the walls. This resultedin a cost reduction of more than half amillions US $ or of 20% in terms of the costof the concrete frame itself. The VSLCorporation was subsequently awarded thecontract for developing the design in detailand for supervising the entire civilengineering construction for the hotel and carparking.

Structural arrangementThe hotel comprises 24,150 m2 ofposttensioned slabs, and the car parking9,750 m2. In the hotel the spans and the slabdepths vary considerably. In general the ratiospan/slab depth is 44 to 45. The car parkingis a three-storey building of dimensions 39 x86 m. The spans here are usually 8.28 m,and the slab depths 190 mm (Fig. 81).The slabs were designed in accordance withthe American standards UBC 1970 and ACI318-71, in conjunction with [12]. The live loadassumed in the hotel area was from 1.9 to4.8 kN/m2. For the car parking, a live load of1.4 kN/m2 was adopted.

Post-tensioningAs is general in the USA, monostrands ∅13 mm (0.5") were used for this project also.The tendons were cut to length at works anddelivered to the site rolled up. They wereplaced either by pulling the

Figure 81: car parking of the Doubletree Inn

Figure 83: Main hall of the Burwood Shopping CentreFigure 82: Scaffolds at construction joints with rolls of tendon

Figure 80: The Doubletree Inn

30

Structural arrangementThe building comprises five storeys in total. Itis 103 m long and 74 m wide. All the slabs(total area 28,500 m2) are posttensioned(bonded post-tensioning). The longitudinalcolumn spacing is 4.04 - 12 ⋅ 7.90 - 4.04 m,the transverse spacing 4.65 - 8 ⋅ 8.40 m (Fig.84). The slabs are 170 mm thick flat slabs,with main beams along the transversecolumn lines. The live load is generally 6kN/m2).

Figure 85: Formwork system Figure 86: Pushing-through the strands

Figure 87: Positioned cables Figure 88: Anchorage with stressed strands

Figure 84: Cross-section

ConstructionRapid speed of construction was of theutmost importance in this project. VSLPrestressing Ltd. had already been broughtin at an early stage, co-operating not only indeveloping the design for the project but alsoin planning the construction sequence andprogramming. It was therefore possible toadapt the design to suit the posttensioningand the formwork system. For the type ofslab referred to, VSL Prestressing Ltd. haddeveloped a special formwork system, whichis especially applicable to regular, flatstructures. The formwork panels are soconstructed that they can be easily adaptedto a column grid of 8 to 12 m (Fig. 85).The slabs for the shopping centre wereconstructed in a total of 28 stages. The twolargest slabs, that over the basement andthat over the ground floor, which both coverthe entire building area, were each sub-divided into eight sections.

Post-tensioningAll the cables consist of four strands Ø13mm (0.5") and have an ultimate strength of736 kN. The strands were pushed into the flatducts (Fig. 86). In each of the main beamsthere are four cables; in each of the spansbetween them there are three tendons. Thepost-tensioning of the slab transversely tothe main beams consists of uniformlydistributed cables at 1.20 m spacing (Fig.87). The total requirement for post-tensioningsteel was almost 160 metric tons.24 hours after each concreting operation, apartial prestress was applied, i.e. one strandof each 4-strand cable was fully stressed.After 36 hours, a second strand was fullystressed in the longitudinal direction, topermit the formwork to be transferred. After 7days all the remaining strands were stressed(Fig. 88). Grouting of the cables was carriedout from one day to eight weeks afterstressing.

9.7. Municipal ConstructionOffice Building, Leiden,Netherlands

Client Municipal Public Works of Leiden

Architect FA. Temme, City Architect,Leiden

Engineer Engineering Office van derHave, Rotterdam

Contractor IBB-KondorB.V.,LeidenPost-tensioning Civielco B.V, LeidenYears of construction 1977-78

IntroductionIn order to centralize different services andthereby improve co-operation, the town ofLeiden decided to erect a new administrativebuilding. On May 17, 1977 the first pile wasofficially driven. Towards the end of 1978 thestructure was completed and on February12, 1979, i.e. exactly 50 years after the

31

Figure 89: The finished Municipal Construction Office Building Figure 91: The building during construction

Figure 90: Section of the building

destruction of the historic town hall by fire,the official opening took place (Fig. 89).

Structural arrangementThe building forms a group around threesides of an inner courtyard. It comprises abasement for bicycles and four abovegroundstoreys (Fig. 90). Its shape in plan is quitecomplicated and is an expression ofindividualistic architecture.The ground floor slab (area 2,000 m2)consists of prefabricated elements supportedon beams. The other slabs (flat slabs) wereconstructed of post-tensioned, in-situconcrete, unbonded post-tensioning beingused. The column spacing in both directionsis alternately 7.20 and 3.60 m. All slabs are240 mm thick. They are strengthened in thecolumn head regions. The live load varies,but on average is about 4 kN/m2.The design was based upon earlier projectsinvolving post-tensioned slabs, since the firstDutch guidelines did not appear until early1978. In addition, use was made of thespecifications of the VB 1974 [45]. Thecalculations were carried out with the use ofcomputer programmes, the finite elementmethod being used.Particular attention was given to theconnection between slab and columns, espe-

9.8. Underground garage forÖVA Brunswick,FR Germany

Client Öffentliche Versicherungs-Anstalt, Brunswick

Architect Laskowski and Schneidewind, Brunswick

Engineer Office of Meinecke & Dr.Odewald, Brunswick

Contractor Telge & Eppers, BrunswickPost-tensioning SUSPA Spannbeton

GmbH, LangenfeldYear ofconstruction 1979

IntroductionIn the course of extending its buildings, ÖVABrunswick had a single-storey, undergroundcar park for 99 private cars constructedinside already existing buildings. The roof ofthe structure, of area approximately 2,290m

2, consists of a post-tensioned flat slab,

cially at the corner columns where largestress concentrations occur. As mentioned,the slabs were therefore locally reinforced byusing appropriate reinforcement.

ConstructionEach slab consists of three independentparts, separated by expansion joints. Inconstruction (Fig. 91), the larger parts weresub-divided into sections of about 350 m

2

topermit rational use of the formwork. Theinfluence of horizontal movements(stressing, creep and shrinkage) on the slabswas limited by forming the connection withthe stiff cores subsequently.The slabs were not designed for carrying theconcrete weight of the slab above. This wastherefore transferred in every case to two

tlower slabs. To achieve rapid construction, itwas necessary to apply the prestress asquickly as possible. Partial stressing wascarried out three days and full stressingabout 14 days after concreting.

Post-tensioningThe prestressing consists of monostrands ∅ 13 mm (0.5") of 184 kN ultimate load.These were cut to length on site, fitted withanchorages and transferred in bundles bythe crane onto the formwork. Placing of themonostrands and ordinary reinforcement of a350 m2 section required approximately threedays. In total, some 6,000 m2 of slab areawas post-tensioned, requiring approximately37 metric tons of prestressing steel.

for which unbonded post-tensioning wasused. This was the frist time a partially post-tensioned flat slab with unbonded tendonswas carried out in the FR Germany [46].

Construction of the slab took place duringduring the Summer of 1979. On account ofthe high groundwater level, the floor of thecar park was to be kept as

Figure 92: Plan of the underground parking

32

Figure 93: Section II during construction Figure 94: Section I II during concreting

high as possible, to avoid expensivewatertight tanking and drainage duringconstruction. Therefore, after an ordinarilyreinforeced slab 500 mm thick had initiallybeen designed, an alternative solution inpost-tensioned concrete was developed,which provided a reduction in slab depth of150 mm and the saving of two column axesaccompanied by an increase in spans from5.0 to 7.5 m. The post-tensioned slab wasalso satisfactory from the economic aspect.

Structural arrangementThe slab, of total length 86.50 m and width18.20 and 33.50 m respectively, is divided bypermanent joints into three sections. Thespans of the internal bays vary longitudinallybetween 5.00 and 7.50 m, and transverselybetween 7.10 and 8.75 m. The edge spansrange from 4.40 to 5.00 m. The slab depth is350 mm (Fig. 92).The slab was designed for a soil overburdenof 0.40 m (7.5 kN/m2) and a heavy goodsvehicle of class SLW 30 (equivalent loading11.8 kN/m2), since the slab was locatedpartly beneath a road. Account had to betaken of additional loads in individual spans.The design method adopted was not inaccordance with DIN 4227, Part 1, thestandard that was then in general use forpost-tensioned structures, and it was also notyet possible to base the design upon Part 6«Components with unbonded post-tensioning» [15], which was in preparation. Auniform balancing loading of 16.3 kN/m2 wasassumed, i.e. self-weight plus soiloverburden including road pavement.At that time there was also no generalapproval issued for the VSL monostrandtendon*. An agreement was thereforerequired for the particular case, and this wasgranted by the Responsible Authority forConstruction of Lower Saxony, on therecommendation of the Institut fürBautechnik, Berlin.

ConstructionFormwork erection, reinforcement placingand concreting were carried out for the threeparts of the slab in succession (Figs. 93 and94). The tendons were cut to length at works,fitted with the dead-end anchorage and rolledup. During placing they were unrolled,

* In the meantime this approval has been granted.

starting from the deadend anchorage, andwere pushed through the stressinganchorages fixed to the formwork. Two, threeor four strands were combined together intobundles.Four or five days after concreting the strandswere stressed in one stage to 0.75 fpu andanchored at 0.70 fpu. This steel stressexceeds the value of 0.55 fpu until nowgenerally the maximum allowed in post-tensioned concrete in the FR Germany. Thisvalue, however, is to be increased in the nearfuture. In [15] the increased value wasalready adopted for unbonded post-tensioning as this method would have beenat an economical disadvantage againstbonded. post-tensioning [47]. After stressingthe protruding ends of the strands were cutoff, the stressing anchorages closed with agrease-filled plastics cover, and the block-outs filled with mortar.

Post-tensioningThe tendons used consist of monostrands ∅ 15 mm (0.6"), each of 140 mm2 cross-sectional area and 247.8 kN ultimate load.Placing of the strands was carried out bythree to four operatives. This work and theplacing of the top reinforcement was carriedout for an equivalent of 1,000 m2 slab areain approximately 7 working days. 7.3 kg ofprestressing steel and 18.3 kg of ordinaryreinforcement were required per m2 slab.

9.9. Shopping Centre, Oberes Murifeld / Wittigkofen, Berne, Switzerland

Client Kleinert GeschaftshäuserAG, Berne

Architect Joint Venture Thormann &Nussli AG, Berne /0. Senn, Basle

Engineer Engineering officeWalder AG, Berne

Contractor General contractorLOSAG AG, BerneBuilding contractorLosinger AG, Berne

Post- VSL INTERNATIONAL LTD.tensioning (formerly Spannbeton AG)Year ofconstruction 1979

IntroductionThe building complex serves as a shoppingcentre for the new development of OberesMurifeld/Wittigkofen at the periphery of thecity of Berne. It comprises various shops, arestaurant, several storage areas, a carparking hall and an office floor.

Structural arrangementThe building comprises three storeys, thetwo lower ones of reinforced/post-tensionedconcrete and the upper in structural steelframing. The slabs over the basement andground floor are flat slabs with unbondedpost-tensioning. The column spacinglongitudinally is 13 x 5.00 m and transversely4.25 - 5 x 8.50 - 4.25 m. In axis 7, the slabsare divided in the transverse direction byexpansion joints. In total, 4,657 m2 of slabwere post-tensioned. Both concrete slabsare 240 mm thick. The slab over thebasement can carry a live load of 5 kN/m2

and that over the ground floor a live load of 3kN/m2. The connection between the slabsand the load-bearing walls and columns ismonolithic (Figs. 95 and 96).

ConstructionEach slab was constructed in three sections.Sections I and II were separated by aconstruction joint, sections I I and III by theexpansion joint (Fig. 95). The sub-dividingmade possible a rational use of formworkand rapid construction progress. This wasof great importance, since the construction ofthe entire shopping centre was subject to avery tight construction schedule. 51/2 monthsafter commencement of excavation thegreater part of the building was to be handedover to the client. It was possible to achievethis date, thanks not least to the choice ofpost-tensioned flat slabs. Only 14 weekswere required for the construction of theslabs.The average working times per slab section,after erection of formwork, were:- 1 day for placing the bottom reinforcement,which was of mesh throughout and onlyrequired local additional reinforcement,

- 2 days for placing the tendons,- 1 day for placing the top reinforcement.

33

These operations were carried out with someoverlap. Only 4 days after concreting fullstressing could be applied. For this, aconcrete strength of 22.6 N/mmz wasrequired.The tendons were cut to length at works,fitted with the dead-end anchorages andtransported to site rolled up. Strands andbundles of the same length were identified bythe same colour. At the intermediateanchorage locations, the tendons weretemporarily stored resting on a 3.5 m wideformwork overhang (Fig. 97).

Post-tensioningThe choice of post-tensioning by areas gavenot only the most economic solution but alsothat with the minimum slab thickness andminimum deflections. Monostrands Ø15 mm(0.6") of 146 mm

2cross-section and 257.8

kN ultimate strength were used for thetendons. In total, 21 metric tons ofprestressing steel, 596 stressinganchorages, 596 dead-end anchorages and138 intermediate stressing anchorages wererequired. Along the colum lines, two and Figure 95: Plan of the slab above ground floor

Figure 96: Cross-section (axis 10)

Figure 98: Monostrands with intermediate an chorages atconstruction joint

Figure 99: Anchorage block-outs before being filled whit mortar

Figure 97: Storage of tendons at construction joint

Figure 100: Installed cables of the third section Figure 102: Cables in column region

34

three strands were combined into bundles.Between them, single strands are uniformlydistributed (spacing approx. 0.60 and 1.00 mrespectively). The requirement forprestressing steel in the lower slab was 4.7kg/m2, in the upper 4.6 kg/m2. Thecorresponding figures for the ordinaryreinforcement are 9.5 and 7.9 kg/m2 (Figs.98 and 99).

composed of 0.60 m backfill (10 kN/m2) and

a live load of 5 kN/m2. The slab and side

walls are connected together monolithically.

ConstructionThe slab, which is post-tensioned withbonded tendons, was constructed in threesections. After placing of the bottomreinforcement, consisting of mesh, the ductswere made up from 10 m lengths, placed atthe specified sequence and fixed to theanchorages. Pushing-through of the strandwas then carried out. After they had beenassembled, the tendons were equipped withthe necessary supports beneath (concreteblocks and stirrups). The tendons were fixedlaterally by attaching the supports to thebottom mesh reinforcement (Fig. 100).Finally, the top reinforcement above the

columns was placed. Ten days afterconcreting the cables were stressed.

Post-tensioningSince there was not sufficient time to gothrough an approval procedure for unbondedtendons, grouted VSL cables, type 5-4, of699 kN ultimate strength each were used.The four strands of each tendon are laid in aflat duct. The transverse cables havestressing anchorages at both ends. Thecontinuous cables in the longitudinaldirection also have stressing anchorages atboth ends, with couplers between them ateach construction joint. In the two end spans,additional cables were necessary; thesehave buried dead-end anchorages type H(Figs. 101 and 102).

9.10. Underground garageOed XI I, Linz, Austria

Client Wohnungsaktiengesell-schaft,Linz

Architect Franz Reitzenstein,Salzburg

Engineer Hellmut Preisinger, LinzContractor Josef Pirkl & Georg Eysert,

LinzPost-tensioning Sonderbau GesmbH,

ViennaYears of construction 1979-80

IntroductionThe single-storey, soil covered undergroundcar park forms part of a development in asuburb of Linz. It provides places forapproximately 110 private cars. A costcomparison prepared during optimization ofthe slab gave a price advantage for the post-tensioned solution over reinforced concrete.Construction was carried out betweenNovember 1979 and May 1980.

Structural arrangementThe slab is 75.30 m long and 33.90 m wide.It contains no permanent joints.Longitudinally, the spans are 7.65 - 8 x 7.50- 7.65 m, and transversely 4.85 - 8.05 - 8.10- 8.05 - 4.85 m. The slab is flat, 300 mm thickand is strengthend at each column with asquare drop panel of 2.20 m side dimensionand an additional 300 mm depth, since dueto the high loading punching shear was thedetermining factor. The column dimensionsare 0.25 x 0.60 m. The applied load is

9.11. Multi-storey car park,Saas-Fee, Switzerland

Client Community of Saas-FeeEngineer Schneller+Schmidhalter+

Ritz, BrigContractor

Anthamatten&Kaibermatten AG, Saas-Fee

Post-tensioningVSL INTERNATIONAL LTD.(formerly Spannbeton AG)

Years of construction1979-80

IntroductionSaas-Fee, a well-known Summer and Win-

ter resort in the Alps of the Valais, is about1800 m above sealevel and can only bereached by road. The ever-increasingnumber of holiday-makers who bring theirown cars and the shortage of parking placesespecially in winter led the local communityauthorities to construct an 8-storey car parkcontaining approximately 950 parking spaces(Fig. 103). Construction commenced inOctober 1979. The construction period wasabout one year.Two different supporting systems werespecified in the invitation for tenders. Onevariant consisted of a completelyprefabricated solution with in-situ concreteover the slab elements. The other proposalwas based upon a monolithic in-situ concrete

design with post-tensioned flat slabs. Thisproved to be economically and technicallysuperior.

Structural arrangementThe car park is an open, unheated buildingwith ventilation. It is 83.3 m long, 34.8 m wideand 25.5 m high. The column spacing is auniform 7.50 m in the longitudinal direction.Transversely, the spacings are 4.50 − 7.60 −2x4.765 − 7.60 − 4.50 m. The core containingthe staircase and the lift shafts is locatedvirtually at the centre. This core, togetherwith cross-beams connecting the slabs to theend supporting walls, assures the horizontalstability of the structure (Figs. 104 to 106).

Figure 101: Cable layout drawing

35

In the end spans and in the central span, theslabs are horizontal; in between, they have a4.5% gradient in the longitudinal direction,thus serving also as ramps. This form ofstructure results in a separation over 2 x 4spans along the longitudinal axis of eachfloor.The seven lower slabs are 200 mm thick.They are designed for a live load of 2 kN/m

2

The loading of the roof slab is composed at amaximum of the snow load of 11.5 kN/mzand a roof garden of 4 kN/m2. The thicknessof the roof slab is therefore 250 to 400 mm.The high loading also necessitatedstrengthening at the column heads. It waspossible to dispense with expansion joints inall the slabs.

ConstructionDue to its high elevation, Saas-Fee has along winter season in which no constructionwork is possible. In addition, sudden coldspells and falls of snow must be expected inspring and autumn. Only the period from theend of May to the middle of October 1980was therefore available for building the mainstructure. This meant that on average onehalf slab (area 1,450 m2) together with theassociated columns and walls had to beerected each week. Furthermore, due toreasons associated with formwork and post-tensioning, the half slabs at the uphill sidealways had to be two storeys in advance(Fig. 107). Fig. 108 shows the constructionprogramme of two half slabs situated onadjacent levels.The required minimum concrete strength forstressing was reached normally three daysafter concreting. One half slab couldtherefore be fully stressed each Tuesday andthe formwork then stripped from it.

Post-tensioningThe slabs were designed on the principlesfor unbonded post-tensioning set out inthis document. The monostrands used are ofnominal diameter 15 mm (0.6"), have across-section of 146 mm

2

and an ultimatestrength of 257.8 kN. 50% of the tendons arelocated in the column lines, 50% in the span.Some of the tendons over the columns areformed into bundles of two.In the longitudinal direction, the strands weredivided by a non-stressed inter-media

Figure 106: Cross-section Figure 107: View during construction

Figure 103: The car park during construction

Figure 104: Plan

Figure 105: Longitudinal section

36

anchorage into sections of 46.3 and 37 mlength. This enabled a reduction in the freestrand length to be achieved with acorresponding increase in the ultimatestrength. The ends of all the monostrands inthe longitudinal direction are fitted with VSLstressing anchorages. The strands in thetransverse direction also utilize intermediateanchorages in the horizontal areas of theslabs. These anchorages are, however,located at the construction joints andtherefore served as stressing anchorages(Fig. 109). The remaining transverse strandshave a deadend anchorage at one end andstressing anchorages at the other.In the seven lower slabs, the quantity of post-tensioning steel is 3.7 kg/m

2, and in the roof

slab it is 6.0 kg/m2. The quantities of ordinary

reinforcement required were 6.4 kg/m2

and12 kg/m

2respectively (including 1 kg/m

2

fixing steel for the tendons in each case).This low reinforcement content is explainedby the fact that no bottom reinforcement wasnecessary in the internal spans.

9.12. Summary

Some important data for the slabs describedin Chapters 9.2. to 9.11. are summarized inTable VIl. When a comparison is being madebetween the values, it must be rememberedhowever that different standards were usedfor different projects and the design methodshave progressively developed in the courseof time.

Figure 108: Extract from the construction programme

Figure 109: Construction joint with stressed intermediate anchorages

Table VI I - Main data of the structures described in Chapters 9.2. to 9.1 1.

37F=Flab slab B=Slab with main beams w=Waffle slab

10. Bibliography

[1] Scordelis A.C., Pister KS., Lin TY: Strength of a Concrete Slab Prestressed in Two Directions. Journal of the American ConcreteInstitute, Proceedings Vol. 53, No. 3, September 1956.

[2] Scordelis A.C, Lin T.Y., Itaya R.: Behavior of a Continuous Slab Prestressed in Two Directions. Journal of the American ConcreteInsititute, Proceedings Vol. 56, No. 6, December 1959.

[3] Gamble WL.: An Experimental Investigation of the Strength and Behavior of a Prestressed Concrete Flat Plate. Report T 8.0-9, Division of Building Research, C.S.I.R.O., Melbourne, Australia,

1964.[4] Lu F.: Strength and Behavior of a Nine-Bay Continuous

Concrete Slab Prestressed in Two Directions. University of Canterbury, Christchurch, New Zealand, March 1966.

[5] Brotchie J.F., Beresford F.D.: Experimental Study of a Prestressed Concrete Flat Structure. Civil Engineering Trans-actions, Institution of Engineers, Sydney, October 1967.

[6] Burns N.H., Hemakom R.: Strength and Behavior of Post-Tensioned Flat Plates with Unbonded Tendons. Preliminary Report, University of Texas, Austin, May 1974.

[7] Hemakom R.: Strength and Behavior of Post- Tensioned FlatPlates with Unbonded Tendons. Ph. D. Dissertation, Univer-sity of Texas, Austin, December 1975.

[8] Ritz P., Marti P.. Thürlimann B.: Versuche über das Biegetrag-verhalten von vorgespannten Platten ohne Verbund. Institut fur Baustatik and Konstruktion ETH Zürich, Bericht Nr. 7305-1, Birkhäuser Verlag Basel and Stuttgart, Juni 1975.

[9] Marti P., Ritz P., 7hürlimann B.: Prestressed Concrete Flat Slabs. Surveys S-1/77, International Association of Bridge and Structural Engineers (IABSE), Zurich, February 1977.

[10] Ritz P.: Biegeverhalten von Flatten mit Vorspannung ohne Verbund. Institut für Baustatik and Konstruktion ETH Zürich, Bericht Nr. 80, Birkhauser Verlag Basel and Stuttgart, Mai 1978.

[11] ACI-ASCE Committee 423: Tentative Recommendations for Concrete Members Prestressed with Unbonded Tendons. Journal of the American Concrete Institute, Proceedings Vol. 66, No. 2, February 1969.

[12] ACIASCE Committee 423: Tentative Recommendations for Prestressed Concrete Flat Plates. Journal of the American Concrete Institute, Proceedings Vol. 71, No. 2, February 1974.

[13] The Concrete Society: Flat slabs in post-tensioned concretewith particular regard to the use of unbonded tendons design recommendations. Technical Report No. 17, The Concrete Society, London, 1979.

[14] Swiss Society of Engineers andArchitects (SIA): Ultimate load behaviour of slabs. Draft by the Working Party No. 5 of the Commission for the Revision of the Standard 162, 1979. (unpublished)

[15] DIN 4227, Ted 6: Spannbeton, Bauteile mit Vorspannung ohne Verbund. Entwurf Marz 1980, Beuth-Verlag, Berlin and Köln.

[16] Fédération Internationale de la Précontrainte (FPI) : Recommendations for the design of flat slabs in post-tensioned concrete (using unbonded and bonded tendons). Cement and Concrete Association, Wexham Springs, Slough SL3 6PL, May 1980.

[17] Baker A.L.L.: Recent Research in Reinforced Concrete and itsApplication to Design. Journal of the Institution of Civil Engineers, Vol. 35, No. 4, February 1951.

[18] MattockA.H: A study of the Ultimate Moment of Resistance of Prestressed and Reinforced Concrete Beams, with Particular Reference to Bond Conditions. Ph. D. Dissertation, University ofLondon, 1955.

[19] Rüsch H., Kordina K., Zelger C.: Bruchsicherheit bei Vorspannung ohne Verbund. Deutscher Ausschuss für Stahlbeton (DAfStb), Heft 130, Verlag W. Ernst and Sohn, Berlin, 1959.

[20]Warwaruk J., Sozen M.A., Siess C.P:: Strength and Behavior in Flexure of Prestressed Concrete Beams. University of Illinois, Engineering Experiment Station Bulletin No. 464, 1962.

[21] Mattock A.H., YamazakiJ., Kattula B.T.: Comparative Study of Prestressed Concrete Beams, With and Without Bond. Journal of the American Concrete Institute, Proceedings Vol. 68, No. 2, February 1971.

[22] Tam A., Pannell FN: The Ultimate Moment of Resistance of Unbonded Partially Prestressed Reinforced Concrete Beams. Magazine of Concrete Research, Vol. 28, No. 97, December 1976.

[23] Copier WJ.: Spannbeton ohne Verbund. Heron, Vol. 21, 1976,No. 2, Delft, Netherlands.

[24] Joint ASCE-ACI Task Committee 426: The Shear Strength of Reinforced Concrete Members - Slabs. Journal of the StructuralDivision, ASCE., Vol. 100, No. STB, August 1974.

[25] Marti P., Pralong J., Thürlimann B.: Schubversuche an Stahlbeton-Platten. Institut für Baustatik and Konstruktion ETH Zürich. Bericht Nr: 7305-2, Birkhäuser Verlag Basel and Stuttgart, September 1977.

[26] Nielsen M.P., Braestrup MW., Jensen B.C., Bach F: ConcretePlasticity. Specialpublication udgivet of Dansk Selskab for Bygningsstatik, Lingby, October 1978.

[27] Pralong J., Brändli W., Thürlimann B.: Durchstanzversuche an Stahlbeton- and Spannbetonplatten. Institut für Baustatik and Konstruktion ETH Zurich, Bericht Nr. 7305-3, Birkhäuser VerlagBasel, Boston, Stuttgart, Dezember 1979.

[28] Fédération Internationale de la Precontrainte (FIP): Fireresistance of prestressed concrete structures. Report of the Commission; Sixth Congress of FIP Prague 1970.

[29] Gustaferro A.H: Fire Resistance of Post-Tensioned Structures. Journal of the Prestressed Concrete Institute, March/April 1973.

[30] Tanaka Y., Kurauchi M., Nagi H., Masuda Y.: Evaluation of Corrosion Protection of Unbonded Tendons. Post-Tensioning Institute (PT), October 1978.

[31] Wood R.H: Plastic and Elastic Design of Slabs and Plates.Thames and Hudson, London, 1961.

[32] Tlhürlimann B.: Flachentragwerke. Vorlesungsautographie,Abt. fur Bauingenieurwesen, ETH Zurich, 1977.

[33] Thurlimann B.: Plastische Berechnung von Flatten. Vor-lesungsautographie, ETH Zurich, 1974.

[34] Swiss Society of Engineers and Architects (SIA): Ultimatestrength and Plastic Design of Reinforced and Prestressed Concrete Structures. Directive 34 concerning the Structural Design Standard SIA 162, Zurich, 1976.

[35] Lin T.Y.: Load Balancing Method for Design and Analysis of Prestressed Concrete Structures. Journal of the American Concrete Institute, Proceedings Vol. 60, No. 6, June 1963.

[36] Sawczuk A., Jaeger T.: Grenztragfahigkeits-Theorie der Flatten.Springer-Verlag Berlin/Gottingen/Heidelberg,1963.

[37] DIN 4227: Spannbeton, Richtlinien für Bemessung and Ausführung. Arbeitsgruppe Beton- and Stahlbetonbau,1953/60.

[38] American Concrete Institute (ACI): Building Code Requirementsfor Reinforced Concrete (ACI 318-77). ACI, Michigan, 1977.

[39] Comité Euro-International du Béton / Fédération Internationale de la Précontrainte (CEB/FFIP): Model Code for Concrete Structures. November 1976.

[40] Swiss Society of Engineers and Architects (SIA): Structures in Concrete, Reinforced Concrete and Prestressed ConcreteCalculation, Detailing and Execution. Standard 162, Zurich, 1968.

[41] Dischinger F.: Elastische and plastische Verformung derEisenbetontragwerke. Bauingenieur 20 (1939).

[42] VSL INTERNATIONAL LTD.: VSL Post-tensioning. Berne, 3.80.[43] Gustaferro A.H.: Rational Design for Fire Endurance of Post-

Tensioned Structures. Post-Tensioning Institute Seminar October5,1979, Chicago, Illinois.

[44] Held L: Flat slabs - the answer to steel shortage? New Civil Engineer, 16 January 1975.

[45] VB 1974 (Voorschriften Beton), consisting of NEN 3861 to NEN3867 (Parts A to G). Nederlands Norma lisatie-Instituut, Rijswijk(ZH).

[46] Gerber C., Özgen E: Flachdecke mit Vorspannung ohneVerbund. Beton- and Stahlbetonbau 75 (1980).

[47] Wolfef E.: Flachdecken mit Vorspannung ohne Verbund.Bauingenieur 55 (1980).

[48] DAfStb Heft 240: Hilfsmittel zur Berechnung der Schnittgrossenand Formanderungen von Stahlbetontragwerken. Verlag W. Ernst and Sohn, Berlin, 1979.

38

Appendix 1: Symbols/ Definitions/Dimensional units/ Signs

SymbolsAp Cross-sectional area of post-tensioning steelApc Cross-sectional area of post-tensioning steel at

columnApf Cross-sectional area of post-tensioning steel

in spanAs Cross-sectional area of ordinary reinforcementAsc Cross-sectional area of ordinary reinforcement at

columnAsf Cross-sectional area of ordinary reinforcement in

spanAsg Cross-sectional area of ordinary reinforcement in

column stripAss Cross-sectional area of ordinary reinforcement in

column lineC (C 20) Concrete grade (20=fcd)D Compressive forceE Modulus of elasticityEc Modulus of elasticity of concreteEc Reduced modulus of elasticity of concreteEp Modulus of elasticity of prestressing steelF (F 60) Fire resistance class (60 = fire resistance time in

minutes)I Second moment of a plane areaL Free length of tendon between two anchoragesMg Bending moment due to distributed permanent loadMq Bending moment due to distributed variable loadMu Ultimate resistance momentP Post-tensioning forcePl Post-tensioning force per strandPo Post-tensioning force at stressing anchorage prior to

wedge draw-inPx Post-tensioning force at point xR Ultimate strength of the cross-sectionRd Design value for ultimate strength of cross-sectionS Moments and shear forces due to applied loadsVg Column load due to dead loadVg+q Column load due to dead load plus live loadVp Transverse component from prestressing inside the

critical shear peripheryVp∞ Transverse component from prestressing inside the

critical shear periphery at time t = ∞ (after deductionof all losses)

Vq Column load due to live loadVu Punching resistance force (failure)We Virtual work of applied forcesWi Virtual work of internal forcesZa Tension force at supportZp Tension force due to post-tensioned reinforcementZs Tension force due to ordinary reinforcementa Deflectionad-u Deflection due to permanent load minus transverse

component from prestressingag+qr-d Deflection due to cracking load minus permanent

loadaq-qr Deflection due to live load minus portion of live load

in cracking loadau Limit deflectionb Widthbc Column dimension (width, diameter)bcd Width of punching conebck Width of column linebg Width of column stripcp Concrete cover to post-tensioned reinforcementcs Concrete cover to ordinary reinforcement

I

d Permanent loaddp Effective depth of post-tensioned reinforcementdpc Effective depth of post-tensioned reinforcement at

columndpf Effective depth of post-tensioned reinforcement in

spands Effective depth of ordinary reinforcementdsc Effective depth of ordinary reinforcement at columndsf Effective depth of ordinary reinforcement in spane Base of Napierian logarithmsec Eccentricity of the parabola of post-tensioned rein-

forcement at columnef Eccentricity of the parabola of post-tensioned rein-

forcement at centre of spanek Eccentricity of the parabola of post-tensioned rein-

forcement in cantileverep Average eccentricity of post-tensioned reinforcement

(average of both directions)fc Compressive strength of concrete (cube, prism or

cylinder strength, depending upon country)fc Compressive strength of concrete at 28 daysfcd Design value for compressive strength of concretefct Tensile strength of concretefpu Characteristic strength of post-tensioning steelfpy Yield strength of post-tensioning steelfs Characteristic strength of reinforcing steelfsy Yield strength of reinforcing steelg Self-weight of slab (yc · h)(g+q)u Ultimate design loadgB Distributed weight of slab surfacinggw Distributed load due to weight of wallsh Slab thicknesshp Sag of tendon parabolak Wobble factorI Length of spanl1 Length of span 1I2 Length of span 2la min Minimum length of reinforcement (anchoring length

not included)Ik Length of cantileverlI Length of span in longitudinal directionIq Length of span in transverse directionmmin Smallest negative moment over column with ad-

joining cantilevermu Plastic moment (in span)muc Plastic moment at columnn Lateral membrane force per unit widthnp Number of tendonsq Distributed variable loadqr Proportion of distributed variable load in cracking loadro Radius of curvaturer Radiust Timeu Transverse component from prestressing per length

unituc Smallest convex envelope which is completely sur-

rounding the column at a distance of d s/2w Influence length of wedge draw-inx Distancexc Depth of compressed concrete zoneyp Internal lever arm (post-tensioning steel)α Angle of deviation of the tendonsβ Ratio, coefficientγ Safety factor

28

k

39

Yc Volumetric weight of concreteYf Load factor (partial safety factor)Ym Cross-sectional factor (partial safety factor)δ Coefficientεcc Creep strain of concreteεcs Final shrinkage factor of concreteεs Final shrinkage factorεt Coefficient of thermal expansionη Coefficientχ Coefficientλ Ratio, coefficientµ Coefficient of frictionξ Ratio of column dimension to span lengthζ Ratio of column dimension to slab depthp Reinforcement contentp* Reinforcement content (fictive figure)Pm Bending reinforcement contentpp Content of prestressing steelPs Content of ordinary reinforcementPv Content of shear reinforcementσc Concrete stressσcpm Average centric concrete stress due to prestressσct Concrete tensile stress

σpo Stress in post-tensioning steelσp∞ Stress in post-tensioning steel at time t = ∞ in

undeformed system after deduction of all lossesσpu Stress in post-tensioning steel at failure (of load-bearing

structure)TSd Nominal shear stressTud Design shear stressϕ Creep coefficientϕn Final creep coefficient∆P Difference in post-tensioning force∆I Tendon elongation∆Ic Wedge draw-in∆Icel Elastic strain of concrete∆Icc Creep strain of concrete∆Ics Shrinkage strain of concrete∆Ict Concrete strain due to temperature∆p Loss of force in tendon due to friction∆σp Increase of stress in prestressing steel∆σpc Loss of stress in prestressing steel due to creep∆σps Loss of stress in prestressing steel due to shrinkageΣ Sum∅ Diameter

DefinitionsSlab Plate in the form used in building construction as load-bearing element in every storey or as roofFlab slab Slab with parallel top and bottom facesOne-way foisted slab Flat slab reinforced on its lower face at uniform intervals by ribs running in one direction onlyWaffle slab Flat slab reinforced on its lower face by ribs in orthogonal patternMain beams Relatively broad beams of shallow depth which reinforce a slab along the column axes. They may be arranged

in only one direction or orthogonally.Plate Flat, more or less horizontal panel which is supported at at least three points or two opposite linesTendon, cable Prestressing cable consisting of one or more strands, which may be grouted or ungroutedMonostrand Prestressing cable consisting of one strand which is not groutedBundle Several monostrands bundled togetherExtruding The process of applying the grease layer and plastics sheath onto a bare strand for producing monostrandsDesign calculation Determination by calculation of the stresses and loads of a structureDetailed design Determination of the dimensions of the load-bearing structure and its components on the basis of the design

calculationUltimate load The load at which failure of the structural element just takes placeUnder-reinforced Said of a cross-section, in which the proportion of reinforcement is sufficiently low for failure always to be

initiated by yield of the steelPrecompressed tensilezone Zone subjected to tensile stresses in service state but under compression immediately after stressing of

tendonsColumn head strengthening Strengthening of a column directly below the slab to increase the resistance to punching. The strengthening

consists either of a uniform thickening of the slab in the region of the column or of a mushroom-shaped flaringof the column at the top.

Column strip Strip-shaped portion of a slab, the longitudinal axis of which coincides with the column axisColumn line Strip-shaped portion of a slab, the longitudinal axis of which coincides with the column axis and the width of

which is given by the critical shear peripheryWedge draw-in The movement of the wedges during the anchoring operation, in which the wedges press into the strands and

consequently draw in through a small distance in the bore of the anchorage until they jam. The movementresults in a corresponding loss of prestressing force.

Dimensional unitsIn this report units of the SI system are exclusively used (mm, m, N, kN, N/mm2, kN/m2). Weights are given in kilogram (kg) or metric tons (t).Formulae which were originally obtained in another system have been converted to the SI system.

Signs

The following sign rules are used:- Compressive force, compressive stress: -- Tension force, tensile stress: +

- Moments:

• when the upper fibre of the cross-section is tensioned: -

• when the lower fibre of the cross-section is tensioned: +

- Shortening: -- Lengthening: +

40

41

Appendix 2: Summary of various standars for unbonded post-tensioning

South East Asia/Australia(Operating Unit 1)

REGIONAL OFFICEVSL Prestressing (Aust.) Pty. Ltd. 6 Pioneer AvenueTHORNLEIGH, NSW 2120 AustraliaPhone: 61 - 2 - 9484 59 44 Fax: 61- 2 - 9875 38 94

AU STRALLA - QueenslandVSL Prestressing (Aust.) Ply. Ltd. VIRGINIAPhone: 61 - 7 - 326 564 00 Fax: 61 - 7 - 326 575 34

AUSTRALIA - New SouthWalesVSL Prestressing (Aust.) Pty. Ltd.THORNLEIGHPhone: 61 - 2 - 9484 59 44 Fax: 61 - 2 - 9875 38 94

AUSTRALIA - SouthernDivisionVSL Prestressing (Aust.) Pty. Ltd.NOBLE PARKPhone: 61 - 3 - 9795 03 66 Fax: 61 - 3 - 9795 05 47

BRUNEI DARUSSALAMVSL Systems (B) Sdn. Bhd. BANDAR SERI BEGAWAN Phone: 673 - 2 - 380 153/2-38182Fax: 673 - 2 - 381 954

GUAMVSL Prestressing (Guam) Inc.TUMONPhone: 67 - 646 80 61Fax: 67 - 649 08 50

INDONESIAPT VSL Indonesia JAKARTAPhone: 62 - 21 - 570 07 86 Fax: 62 - 21 - 573 68 49

MALAYSIAVSL Engineers (M) Sdn. Bhd.KUALA LUMPURPhone: 60 - 3 - 242 47 11Fax: 60 - 3 - 242 93 97

NEW ZEALANDPrecision Precasting (Wgtn.)Ltd..OTAKIPhone: 64 - 6 - 364 81 26Fax: 64 - 6 - 364 83 44

SINGAPOREVSL Singapore Pte. Ltd.SINGAPOREPhone: 65 - 336 29 23Fax: 65 - 337 64 61

THAILANDVSL (Thailand) Co. Ltd.BANGKOKPhone: 66 - 2 -237 32 88/89/90

North East Asia(Operating Unit 2)

REGIONAL OFFICEVSL North East Asia1508 Devon House979 King's Road - Ouarrv BavHONG KONGPhone: 852 - 2590 22 22Fax: 852 - 2590 95 93

HONG KONGVSL Hong Kong Ltd.Quarry BayPhone: 852 - 2590 22 88Fax: 852 - 2590 02 90

JAPANVSL Japan CorporationTOKYOPhone: 81 - 33 - 346 89 13Fax: 81 - 33 - 345 9153

KOREAVSL Korea Co. Ltd.SEOULPhone: 82 - 2 - 574 82 00Fax: 82 - 2 - 577 00 98

PHILIPPINESVSL Philippines Inc.QUEZON CITYPhone: 63 - 2 - 633 1739Fax: 63 - 2 - 633 1740

TAIWAN R.O.C.VSL Taiwan Ltd.TAIPEIPhone: 886 - 2 - 2759 6819Fax: 886 - 2 - 2759 6821

VIETNAMVSL HanoiRepresentative OfficeHANOIPhone: 84 - 4 - 8245 488Fax: 84 - 4 - 8245 717

USA - North America(Operating Unit 3)

REGIONAL OFFICEVSL CorporationCrosspointc 11 Plaza2840 Plaza Place - Suite 200RALEIGH. NC 27612USAPhone: 1 - 919 - 781 6272Fax: l - 919 - 7816892

WESTVSL CorporationSAN JOSE, CAPhone: 1 - 408 - 866 - 5000Fax: 1- 408 - 374 - 4113

NORTHEASTVSL CorporationWASHINGTON, D.C.Phone: 1 - 703 - 451 - 4300Fax: 1 - 703 - 451 - 0862

SOUTHEASTVSL CorporationMIAMI, FLPhone: 1 - 305 - 592 - 5075Fax: 1 - 305 - 592 - 5629

MIDWESTVSL CorporationDALLAS. TXPhone: 1 - 972 - 647 - 0200Fax: 1 - 972 - 641 - 1192

Europe, Middle East, SouthAmerica and Africa(Operating Unit 4.5)

REGIONAL OFFICERepresentative OfficeLOdyssee - Bat. A2-12 Chemin des Femmes97886 MASSY CedexFrancePhone: 33 - 1 - 6919 43 16Fax: 33 - I - 69 19 43 17

AUSTRIAGrund and Sonderbau GesmbHVIENNAPhone: 43 - 1 - 878 17 0Fax: 43 -1 - 87817 762 od 782

BOLIVIAPrestress VSL of Bolivia JaureguiLtdLA PAZPhone: 591 - 2 - 321 874Fax: 591 - 2 - 371 493

CHILEVSL SistemasSANTIAGOPhone: 56 - 2 - 233 10 81Fax: 56 - 2 - 233 67 39CZECH REPUBLICVSL Systcmy (CZ) s. r. o.PRAGUEPhone: 42 - 2 - 67 07 24 20Fax: 42-2-67072406

FRANCEVSL France S.A.EGLYPhone: 33 - 1 - 69 2614 00Fax: 33 - 1 - 60 83 89 95

GREAT BRITAINBalvac Whitley Moran Ltd.DERBYSHIREPhone: 44 - 773 54 26 00Fax: 44 - 773 54 27 00

GREECEVSL Systems A/EATHENSPhone: 30 -1 - 363 84 53Fax: 30 - 1 - 360 95 43

INDIAKillick Prestressing Ltd.BOMBAYPhone: 91 - 22 - 578 44 81Fax: 91 - 22 - 578 47 19

NETHERLANDSCivielco B.VAT LEIDENPhone: 31- 71 - 576 89 00Fax: 31 - 71 - 572 08 86Stronghold Benelux B.V.Phone: 31 - 70 - 511 5145Fax: 31 - 70 - 517 66 24

NORWAYVSL Norge ASSTAVANGERPhone: 47 - 51 - 56 37 01Fax: 47 - 51 - 56 27 21

PERUPretensado VSL del Peru SALIMA

Phone: 51 - 476 - 04 23/26 Fax: 51 - 476 - 04 77

PORTUGALVSL Preyuipc SA. LISBONPhone: 351 - I - 793 85 30 Fax: 351 - 1 - 793 09 01

Stronghold Portugal PORTOPhone: 351 - 2 - 370 00 21 Fax: 351 - 2 - 379 39 73

SOUTH AFRICASteeledale Systems (Pty) Ltd.JOHANNESBURGPhone: 27 - 11 - 613 77 41/9 Fax: 27 - 11- 613 74 04

SPAINCTT StrongholdBARCELONAPhone: 34 - 3 - 200 87 11Fax: 34 - 3 - 209 85 90

SWEDENInternordisk SpannanmcringAS.DANDERYDPhone: 46 - 8 - 753 02 50 Fax: 46 - 8 - 753 49 73

SWITZERLANDVSL (Switzerland) Ltd. LYSSACHPhone: 41 - 34 - 44799 11Fax: 41 - 34 - 445 43 22

UNITED ARAB EMIRATESRepresentative OfficeDubaiPhone: 971 - 4 - 555 220Fax: 971 - 4 - 518 244

THE COMBINATION OF A WORLD-CLASS SPECIALIST CONTRACTOR

WITH THE RESPONSIVENESS OF A LOCALLY BASES PARTNER

HEADQUARTERS

VSL International Ltd.Bernstrasse 9

LYSSACH - CH 3421Switzerland

Phone: 41 - 34 - 447 99 11Fax: 41 - 34 - 445 43 22http:\\www.vsl-intl.com

Your post-tensioning specialist contractor: