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An introduction to the development,benefits, design and construction ofin-situ prestressed suspended floors

A M Stevenson BSc(Hons), CEng, MICE, MIStructE

FOREWORDThis publication was commissioned by the ReinforcedConcrete Council, which was set up to promote betterknowledge and understanding of reinforced concretedesign and building technology.

Its members are Co-Steel Sheerness plc and Allied Steel& Wire, representing the major suppliers of reinforcingsteel in the UK, and the British Cement Association,representing the major manufacturers of Portland cementin the UK.

Theand

author, Mark Stevenson, is an Associate with GiffordPartners.

ACKNOWLEDGEMENTSThe Reinforced Concrete Council and the author aregrateful to Sami Khan, Peter Mathew, David Ramsey andall those who provided comments on the draft of thispublication, and for the photographic material suppliedb y P S C F r e y s s i n e t L i m i t e d . T h a n k s a r e a l s oextended to Alan Tovev of Tecnicom for his work inco-ordinating this publication.

ABOUT THIS PUBLICATIONThis publication aims to de-mystify the techniques of post-tensioned concrete floor construction in multi-storeybu i ld ings , w h i l s t l o o k i n g a t t h e e c o n o m i c s a n dpracticability of construction. It is intended for two broadcategories of reader.

Firs t ly, i t presents an introduction to the benefi ts ,constraints, principles and techniques for non-technicalprofessionals. These people will wish to understand thebroad issues of an essentially simple technique with whichthey may not be entirely familiar, without being swampedby equations. Sections 1 and 3 provide the briefestexecutive overview, whilst reading Sections 1 to 4 plus 7will give a broader picture.

Secondly, it can be used as a more technical review forthose who, in addition to the above issues, wish to explorefurther the principles of design and construction. In thiscase all sections should prove useful.

This publication is not intended to be a full technicalreference book for design, but it does address many of theissues often omitted from such works.

97.347 Published by the Brit ish Cement Association on behalf

First published 1994 industry sponsors of the Reinforced Concrete Council .

ISBN 0 7210 1481 XPrice Group D British Cement Association

Century House, Telford AvenueCrowthorne, Berkshire RGll 6YS

0 British Cement Association 1994 Tel (0344) 762676 Fax (0344) 761214

of the

All advice or information from the British Cement Association is intended for those who will evaluate the significance and limitations of its contents and takeresponsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information IS accepted. Readersshould note that all BCA publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version.

CONTENTSINTRODUCTION

DEVELOPMENT ANDAPPLICATIONS

Principles of prestressing

Development of post-tensioning

BENEFITS O F POST-TENSIONED CONSTRUCTION

RANGE AND SELECTION OFFLOORS

Forms of construction

Typical properties

Selection criteria

Comparison with other floor types

DESIGN CONSIDERATIONS

Theory and design 10

Restraint

Holes

CONSTRUCTION

Aspects of construction

DEMOLITION ANDSTRUCTURAL ALTERATIONS

Demolition

Structural alterations

REFERENCES

2

6

77

8

8

9

10

12

13

14

13

17

17

17

19

be properly evaluated while consideringfamiliar techniques.

other more

Over the last 20 years, many buildings with post-tensionedfloor slabs have been successfully constructed in the USA,South East Asia, Australia and the rest of Europe, yet ittook the construct ion boom of the la te 1980s, w i t hcorresponding increases in both steelwork prices anddelivery times, to generate significant interest in post-tensioned floor construction in the UK.

T h e p u r p o s e o f t h i s p u b l i c a t i o n i s t o w i d e n t h eunderstanding of post-tensioned floor construction andshow the considerable benefits and opportunities it offersto both the developer and designer. These include:

Rapid construction

Economy

Maximum design flexibility

Minimum storey heights

Minimum number of columns

Optimum clear spans

Joint-free, crack-free construction

Controlled deflections.

Post-tensioned floors may be totally of in-situ concrete ora hybrid of in-situ and precast concrete. Either may beprestressed or a combination of prestressed and reinforced.They can be designed as two-way spanning flat slabs,one-way spanning ribbed slabs, or as banded beam andslab construction. Flat slabs are supported, without theuse of beams, by columns with or without column heads.They may be solid or may have recesses formed in the soffitto create a series of ribs running in two directions (waffleor coffered slab). All these post-tensioned floors are furtherdescribed in Section 4, and shown in Figures 4.1 to 4.4.

This publication also aims to dispel the mytensioned concrete slabs by showing that:

ths about post-

They are not ‘unexploded bombs’

The floors can be demolished safely

Local failure does not lead to total collapse

Holes can be cut in slabs at a later date

The design is not necessarily complicated

They are compatible with fast-track construction

They do not require the use of high-strength concreteThe formwork does not carry any of the prestressingforces.

Post-tensioned concrete can satisfy all of the aboverequirements, and for this reason it is commonly usedthroughout most of the developed world.

There are a number of publications that highlight thesuitability of in-situ reinforced concrete frames for bothe c o n o m y a n d s p e e d o f c o n s t r u c t i o n i n h i g h - r i s ebuildings”, 2, 3). The use of post-tensioned concrete slabscomplements such a frame and helps maximise the benefitsfrom both economy and speed. An example of a prestigiouscity centre development using this form of construction isExchange Tower in Docklands(

Engineers have a responsibility to their clients to considerall available construction methods. Post-tensioned concretewill not always be the most suitable, but it should at least

DEVELOPMENT mANDAPPLICATIONSThe practice of prestressing can be traced back as far as 440BC, when the Greeks reduced bending stresses and tensionsin the hulls of their fighting galleys by prcstrcssing themwith tensioned ropes.

A further example, and one which demonstra tes thesimplicity of prestressing, is a traditional timber barrelwhere the tension in the steel hoops effectively compressesthe staves together to enhance both strength and stability.

One of the simplest examples of prestrcssing is that oftrying to lift a row of books as illustrated in Figure 2. 1. Tolift the books it is necessary to push them together, ie toapply a pre-compression to the row. This increases theresistance to slip between the books so that they can bclifted.

Figure 2.1 Lifting a row of books

This example also demonstrates one of the commonprinciples shared by most applications of prcstrcssing.There is generally a deficiency which can be offset by anefficiency which can be easily exploited. In the case of thebooks there is no grip between the books but the books canwithstand compression loads which can be easily applied.

A simple definition of prestressingthe example of the books, is:

, which relates well to

Principles of prestressingConcrete has a low tensile strength but is strong incompression: by pre-compressing a concrete element, sothat when flexing under applied loads it still remains incompression, a more efficient design of the structure canbe achieved. The basic principles of prestressed concreteare given in Figure 2.2, and further information on the

development of prestressing and prestressing materials isgiven in Reference 5.

Under an applied load, a prestressed beam will bend,reducing the built-in compression stresses; when the loadis removed, the prestressing force causes the beam toreturn to its original condition, illustrating the resilienceof prestressed concrete. Furthermore, tests have shownthat a virtually unlimited number of such reversals of theloading can be carried out without affecting the beam’sability to carry its working load or impairing its ultimateload capacity. In other words prestressing endows thebeam with a high degree of resistance to fatigue.

It is indicated in Figure 2.2 that if, at working load, thetensile stresses due to load do not exceed the prestress, theconcrete will not crack in the tension zone but, if theworking load is exceeded and the tensile stresses overcomethe prestress, cracks will appear. However, even after abeam has been loaded to beyond its working load, and welltowards its ultimate capacity, removal of the load resultsin complete closing of the cracks and they do not reappearunder working load.

There are two methods of applying prestress to a concretemember. These are:

1) By pretensioning - where the concrete is placed aroundpreviously stressed tendons. As the concrete hardens,it grips the stressed tendons and when it has obtainedsuff ic ient s t rength the tendons are re leased, thustransferring the forces to the concrete. Considerableforce is required to stress the tendons, so pretensioningis principally used for precast concrete where the forcescan be restrained by fixed abutments located at eachend of the stressing bed, or carried by specially stiffenedmoulds.

2) By post-tensioning - where the concrete is placed aroundsheaths or ducts containing unstressed tendons. Oncethe concrete has gained sufficient strength the tendonsare stressed against the concrete and locked off byspecial anchor grips. In this system, which is the oneemployed for the floors described in this publication,all tendon forces are transmitted directly to the concrete.Since no stresses are applied to the formwork, thisenables conventional formwork to be used.

Development of post-tensioningThe invention of prestressed concrete is often accredited toEugene Freyssinet who developed the f i rs t pract icalpost-tensioning system in 1939. The majdrity of the earlyapplications were in the design of bridge structures. Thesystems were developed around the use of multi-wiretendons located in large ducts cast into the concrete section,and fixed at each end by anchorages. They were stressed byjacking from either one or both ends, and then the tendonswere grouted within the duct. This is generally referred toas a bonded system as the grouting bonds the tendon alongthe length of the section.

The bonding is similar to the way in which bars are bondedin reinforced concrete. After grouting is complete there is

Prestressed concrete can most easily be defined as precompressedconcrete. This means that a compressive stress is put into aconcrete member before it begins its working life, and is positionedto be in areas where tensile stresses would otherwise develop underworking load. Why are we concerned with tensile stresses? For thesimple reason that, although concrete is strong in compression, itis weak in tension.

Consider a beam of plain concrete carrying a load.

As the load increases, the beam deflects slightly and then fallsabruptly. Under load, the stresses in the beam will be compressivein the top, but tensile in the bottom. We can expect the beam tocrack at the bottom and break, even with a relatively small load,because of concrete’s low tensile strength. There are two ways ofcountering this low tensile strength -by using reinforcement or byprestressing.

In reinforced concrete, reinforcement in the form of steel bars isplaced in areas where tensile stresses will develop under load. Thereinforcement absorbs all the tension and, by limiting the stress inthis reinforcement, the cracking of the concrete is kept withinacceptable limits.

IQ prestressed concrete, compressive stresses introduced into areaswhere tensile stresses develop under load will resist or annul thesetensile stresses. So the concrete now behaves as if it had a hightensile strength of its own and, provided the tensile stresses do notexceed the precompression stresses, cracking cannot occur in thebottom of the beam. The precompression stresses can also bedesigned to overcome the diagonal tension stresses. The normalprocedure is to design to eliminate cracking at working loads.

I 1I b 4 I

However, bending is only one of the conditions involved: there isalso shear. Vertical and horizontal shear forces are set up withina beam and these will cause diagonal tension and diagonalcompression stresses of equal intensity. As concrete is weak intension, cracks in a reinforced concrete beam will occur wherethese diagonal tension stresses are high, usually near the support.In prestressed concrete, the precompression stresses can also bedesigned to overcome these tension stresses.

Figure 2.2 Principles of prestressed concrete

no longer any reliance on the anchorage to transfer theprecompression into the sect ion. Another commonapplication is in segmental construction (Figure 2.3) whereprecast concrete bridge sections are prestressed togetherwith steel cables or bars, developing the simple idea ofcompressing the row of books.

Figure 2.3 Segmental construction in bridge decks

Applications in building have always existed in the designof large span beams supporting heavy loadings, but thesystems were not suitable for prestressing floor slabs,which cannot accommodate either the large ducts oranchorages.

T h e m o r e r e c e n t d e v e l o p m e n t o f p o s t - t e n s i o n i n gspecifically for in-situ floor slab construction has resultedin two systems: (1) bonded construction and (2) unbondedconstruction.

Figure 2.4 Bonded tendons in beam

With the bonded system (Figure 2.4) the prestressingtendons run through small continuous flattened ductswhich are grouted after the tendons are stressed. The

system has been used successfully in general floor slabconstruction and is often used for specialist applications.Cost-effective designs can be achieved by this system, theprincipal features of which are given below.

The most eff ic ient prestress design is when theprestressing tendon is positioned eccentrically in theconcrete section on a curved profile or deflected froma straight line. The size of the duct used in a bondedsystem and the minimum cover that must be providedmay control the maximum eccentricity that can beachieved.

The ducts are formed from spirally-wound or seam-folded galvanised metal strip. The limit on the curvature

or profile that can be achieved with the prestressingtendons is dependent on the flexibility of the ducts.

The ducts have to be grouted after stressing, whichintroduces a further trade into the construction process.

To offset these features in f loor s lab applicat ions,prestressing using unbonded systems Figure 2.5) wasdeveloped in the USA in the 1960s.

Figure 2.5 Unbonded tendons in a floor slab

From the early days of prestressed concrete bridge design,the benefits of not bonding the tendons to the concretestructure have been appreciated, and bridges have beenc o n s t r u c t e d w i t h u n b o n d e d t e n d o n s r u n n i n g b o t hinternally and externally to the structure. Systems foruse on br idge s t ructures were again based on largemulti-strand tendons. The main benefits to the bridgedesigner were that tendons were replaceable shouldcorrosion occur and, if external, could be inspected as partof routine maintenance.

In an unbonded system the tendon is not grouted and remains free to move independently of the concrete. Thishas no effect on the serviceability design or performance ofa structure under normal working conditions. 1t does,

however, change both the design theory and structuralperformance at the ultimate limit state, which is precededby larger deflections with fewer, but larger, associatedcracks than with an equivalent bonded system. Thus, withan unbonded system there are obvious visual indicationsthat something is wrong well before failure occurs.

The economic advantages of an unbondcd system in floor

slab construct ion were identif ied, and systems weredeveloped in the 1960s specifically for this application.Tendons used today are typically either 12.9 mm or15.7 mm strands, coated in grease, within a protectivesheath. They are cast into the concrete slab with small(typically 130 mm x 70 mm) anchorages fixed to eachend. After concreting, and when the concrete has obtaineda specified compressive strength, the tendon is stressedvery simply using a small hand-held jack, completing thepost-tensioning operation.

The particular features of an unbonded system are:

Tendons can be located close to the surface of theconcrete to maximise the eccentricity (Figure 2.6).

Tendons are flexible and can be easily fixed to differentprofiles. They can be displaced locally around holes,(Figure 2.7), and to accommodate changes in slab shape(Figure 2.8).

The stressing operation is simple, and with no grouting,is suited to rapid construction methods.

The use of unbonded tendons permits an effective andcompetitive multi-storey construction to be carried out inpost-tensioned concrete.

-CL-- __ Q

---e-e

_ ---

I

C CBonded tendon

Cover - 50 m m minimumUnbonded tendon

Cover - Typically 30 - 40 mm

in the UK since the 1960s and some interest was generatedduring the early 1970s. However, it took the constructionboom of the 1980s to generate significant interest in post-tensioning of floors and the many schemes now completedhave demonstrated to clients, architects and engineers themany advantages of the system when used in multi-storeyconstruction. Figure 2.9(a) to (e) s h o w s e x a m p l e s o fbuildings using post-tensioned floors.

Figure 2.9(a) The Pavilion, London Docklands: post-tensioned flat slab

Figure 2.7 Flexibility of tendons allows displacementaround holes

Figure 2.9(b) Exchange Tower, London Docklands: post-tensioned ribbed slabs

Figure 2.8 Tendons displaced to accommodate changesin slab shape

The bonded and unbonded systems provide a range ofpost-tensioning methods available to the designer ofbuildings. In some instances the most economical designcan be achieved with a post-tensioned floor slab, usingunbonded tendons, supported on long-span post-tensionedb e a m s w i t h b o n d e d t e n d o n s . P o s t - t e n s i o n e d f l o o rconstruction can also be combined with conventionalreinforced concrete slabs to extend the range of concretefloor options.

The benefits of post-tensioned construction for floors werequickly appreciated in the USA and many other parts ofthe developed world, where i ts use in mult i -s toreyconstruction is widespread. Systems have been available

Figure 2.9(c) Office block, Hemel Hempstead: post-tensioned construction

Figure2.9(e) Windmill Hill, Swindon: post-tensionedwaffle slab

BENEFITS OFPOST-TENSIONEDCONSTRUCTION

The following are just a few of the many benefits to begained from using post-tensioned floor construction.

Long spans reduce the number of columns and foundations,providing increased flexibility for internal planning, andmaximising the available letting space of a floor.

Minimum floor thickness maximises the ceiling zoneavailable for horizontal services, minimises the selfweightand foundation loads, and keeps down the overall heightof the building.

Minimum storey height is achieved, as the need for deepdownstands is reduced, and slab thicknesses are kept to aminimum. As a result, the storey height of a concretebuilding can be less than that of a steel-framed building byas much as 300 mm per floor. This can give an extra storeyin a ten-storey building. Alternatively, it minimises theexterior surface area to be enclosed, as well as the verticalruns of mechanical and electrical systems. The reducedbuilding volume (Figure 3.1) will save on cladding costsand may reduce running costs of HVAC equipment.

Deflection of the slab can be controlled enabling longerspans to be constructed with a minimum depth ofconstruction.

Concrete building is up to 3.0 m lower than the steel alternative

_-_-_-_-_-_

I 1-I

7

Concrctc

IJ I/

10-storey building

Figure 3.2 Effect of post-tensioned construction onbuilding height and volume

Crack-free construction is provided by designing the wholeslab to be in compression under normal working loads.Appropriate details may also be incorporated to reducethe effects of restraint, which may otherwise lead tocracking (see Restraint in Section 5). This crack-free

construction is often exploited in car parks with concretesurfaces exposed to an aggresive environment.

Large area pours should be adopted on all concrete floorsin order to reduce the number of pours and increaseconstruction speed and efficiency (F igure 3.2). With

prestressed floors, when the concrete has reached a strengthof typically 12.5 N/mm2, part of the prestressing force canbe applied to control shrinkage cracking and thus furtheraid larger area pours.

1-1 by volume of concrete

Typical pour size limited

Figure 3.2 Large area pours for increased efficiency

Rapid construction is readily achieved in multi-storcybuildings as prestressing leads to less congested slabconstruction (Figure 3.3). Prefabrication of tendons reducesfixing time and early stressing enables forms to be strippedquickly and moved to the next floor.

Flexibility of layout can be achieved as the design methodscan cope with irregular grids, and tendons can easily bedeflected horizontally to suit the building’s geometry or toallow for openings in slabs.

Future flexibility is provided as knockout zones can beidentified for future service penetrations. Tried and testedmethods are available to enable large openings for stairs,escalators and other features to be formed subsequently(see Section 7).

Figure 3.3 Minimising the amount of site-fixedreinforcement speeds up construction

RANGE ANDSELECTION OF

FLOORSForms of constructionFor most multi-storey buildings there is a suitable concretef r a m i n g s y s t e m . F o r s p a n s g r e a t e r t h a n 6 . 0 m ,post- tensioned slabs s tar t to become cost-effect ive,and can be used alone or combined with reinforced concreteto provide a complementary range of in-situ concrete flooroptions. The three main forms of construction are givenbelow.

Solid flat slabSpans: 6 m to 13 mAn efficient post-tensioned design can be achieved witha solid flat slab (Figure 4.1), which is ideally suited tomulti-storey construction where there is a regular columngrid. These are sometimes referred to as flat plate slabs.The benefits of a solid flat slab are the flush soffitand minimum construction depth, which are suited torapid construction methods. These provide the maximumflexibility for horizontal service distribution and keep slabweight low and building height down to a minimum.

The depth of a flat slab is usually controlled by deflectionrequirements or by the punching shear capacity aroundthe column. Pos t - t en s ion ing improves con t ro l o fdeflections and enhances shear capacity. The latter can beincreased further by introducing steel shearheads withinthe slab depth (Figure 4.1 (a)), column heads (Figure 4.1 (b)),or drop panels (Figure 4.1 (c)).

Beam and slabSpans: beams 8 m to 20 m, slabs 7 to 10 mIn modern construct ion, where there is general ly arequirement to minimise depth, the use of wide, sha

llow

band beams (Figure 4.2) is common. The beams, which areeither reinforced or post-tensioned, support the one-wayspanning slab and transfer loads to the columns.

Structural steel shearheadsor reinforcement assembliescan be used for increasedshear capacity

\Column

No drop or column head

(a) Solid flat slab

Column head - no drop

(b) Solid flat slab with column heads

Drop panel

(c) Solid flat slab with drop panel

Figure 4.1 Forms of solid flat slab

Figure 4.2 Band beam and slab

Ribbed slabSpans: 8 m to 18 mFor longer spans the weight of a solid slab adds to boththe frame and foundation costs. By using a ribbed slab,(Figure 4.3) which reduces the selfweight, large spanscan be economically constructed. The one-way spanningribbed slab provides a very adaptable structure able toaccommodate openings. As with beam and slab floors, theribs can either span between band beams formed withinthe depth of the s lab or between more t radi t ionaldownstand beams. For long two-way spans, waffle slabs(Figure 4.4) give a very material-efficient option capable ofsupporting high loads.

Figure 4.3 Ribbed slab

Figure 4.4 Waffle slab

Typical propertiesThe typical ranges of spans for the various forms ofc o n s t r u c t i o n a r e g i v e n i n Figure 4 . 5 a n d t h e i rcorresponding slab and beam depths in Table 4.1. Table4.2 gives the corresponding material quantities for themore common arrangements. The depths and quantitiesgiven are for an imposed loading of 5 kN/m2, but can bereduced when this is lowered. They will also depend onsuch things as number of panels in each direction, firerating, durability and vibration requirements. Althoughpost-tensioned floors are usually thinner and lighter thanreinforced floors, vibration is not normally a problem andis typically catered for by controlling the span/depthratio.

Reinforced concrete 1. 1Prestressed concrete

* For office loading of 5 kN/m2

Figure 4.5 Typical economical spans with different typesof slab

Table 4.1 Typical slab and beam depths*

SLAB TYPE

Solid flat slab

Solid flat slabwith droppedpanels

SLAB SLAB BEAM SPAN/SPAN D E P T H D E P T H D E P T H

m mm m m RATIO

6.0 200 --- 1 /308.0 250 --- 1/32

8.0 225 --- 1/3612.0 300 --- 1/40

One-way slab 6.0 150 300 l/40/20with band 8.0 200 375 l/40/21beams 12.0 300 550 l/40/22

One-way slab 6.0 175 375 l/34/16with narrow 8.0 225 500 l/36/16beams 12.0 325 750 l/37/16

Ribbed slab 8.0 300 --- 1 /2712.0 450 --- 1 /2715.0 575 --- 1/26

*Based on an imposed loading of 5 kN/m2.

Selection criteriaWhen faced with selecting the most economic frame forany particular building, it is not just the straight cost ofthe frame element which is compared. The effect of theframe on the cost of other building provisions is oftenthe governing criterion. The most important of these arethe external cladding, flexibility for future use and, inhighly serviced buildings, the services distribution bothhorizontally and vertically through the building.

Table 4.2 Material quantities*

SLABTYPE

SLABSPAN

mm

SLAB TENDON REBARDEPTH DENSITY DENSITY

m m tendons per kg/m2metre width

Flat slab

One-wayslab withband beam

6.0 200 1.4 t 8.58.0 250 2.3 t 12.0

6.0 150 3.2 6.58.0 200 3.0 7.5

Ribbed 8.0 300 2.5 10.0slab** 12.0 450 2.5 13.0

15.0 575 3.8 17.5

*Based on an imposed load of 5 kN/m2.

The tendon density is based on 15.7 mm diameter superstrand with a guaranteed ultimate tensile strength of 265 kN.

The rebar density is based on high yield bar, fY=460 N/mm2.

t Each way **Quantities per rib depend on rib spacing.

Distribution of servicesThe key to the successful design of most buildings is toco-ordinate the design across all disciplines in the team. Offundamental importance is the co-ordination of servicesand structure to ensure that clashes with beams, columns,etc do not happen, and that a practical discipline for bothprimary and secondary service holes is established andadhered to. It is desirable, therefore, to construct a framewhich provides the least hindrance to the distribution ofservices.

The other pressure on the design team is to keep toa minimum the depth of the cei l ing void used fordistribution, in order to keep down the overall height ofthe building and to minimise cladding costs.

It can be appreciated that the ideal floor slab to satisfy theabove criteria must be the thinnest possible and with aflush soffit, hence the reason that post-tensioned floorconstruction is so attractive in multi-storey construction.

Flexibility of useFor office construction, flexibility is mostly concernedwith likely future changes in the internal space planning.In many cases these do not substant ial ly affect thestructure. Core areas, primary services distribution andother major items usually remain fixed, although someadditional holes for minor services may be requiredsubsequently. On the other hand, applications such asretail or health care require a higher degree of flexibilityfor changes in services, and these should be considered atthe design stage.

Regardless of construction type, forming large holes inany existing structure is not straightforward. In post-tensioned design, careful considerat ion is necessarybefore breaking out any openings in an existing slab andthis is discussed later in Section 7. Smaller holes seldompresent problems as they may be readily formed betweenribs or grouped tendons. The positions of the tendons canbe marked on the slab’s soffit to aid identification forfuture openings (see Section 6).

CladdingThe depth of the overall floor construction has a directeffect on the cost of the external cladding, which oftencosts more than the frame. This is particularly relevant inmulti-storey construction where a few centimetres savedat each floor can show a significant overall cost saving.

Comparison with other floortypesFigure 4.6 (a-d) shows a comparison of various floordesigns carried out at the scheme stage for a multi-storeyhospital structure. The planning grid is 6.6 m square andthe floors have been designed for a total imposed load(dead and live) of 5.5 kN/m2.

Reinforcement estimateTendons - 2.1 kg/m each way

Rebnr - 12 kg/m’

(a) Post-tensioned flat slab

l-7I I

275

Reinforcement estimateRebar - 30 kg/m?

(b) Reinforced flat slab

1 Structural topping

\ Fire protectionrequired to beam

IPrecast unit

(c) Steel beam with precast units

Metal decking permanentformwork with concretetopping

Fire protection required to beam

(d) Steel beam with metal deck composite floor

DESIGNCONSIDERATIONS

Theory and designPrestressing methods are now widely available to allowthe eff icient and economical design of al l types ofstructures. Checks at both serviceability and ultimatelimit state are carried out to give the designer a goodunderstanding of the overall structural performance.Recommendations for the design of prestressed concreteare given in BS 8110 c6) Design methods for post-tensioned.flat slabs are relatively straightforward, and detailedguidance is available in Concrete Society TechnicalReports 17 c7), 25’“) and 43”).

At the serviceability condition the concrete section ischecked at all positions to ensure that both the compressiveand tensile stresses lie within acceptable limits. Stressesare checked in the concrete section at the initial conditionwhen the prestress is applied, and at serviceabil i tyconditions when calculations are made to determine thedeflections for various load combinations.

At the ultimate limit state the pre-compression in thesection is ignored and checks are made to ensure that thesection has sufficient moment capacity. Shear stresses arealso checked at the ultimate limit state in a similar mannerto that for reinforced concrete design, although the benefitof the prestress across the shear plane may be taken intoaccount.

In carrying out the above checks, extensive use can bemade of computers either to provide accurate models ofthe structure, taking into account the affect of otherelements and to enable different load combinations to beapplied, or to carry out both the structural analysis andprestress design.

The basic principles of prestressed concrete design can besimply understood by considering the stress distributionin a concrete section under the action of externally appliedforces or loads. It is not intended here to provide a detailedexplanation of the theory of prestressed concrete design,but Figure 5.1 outlines the principles.

The example shown on the right is included to illustratethe simplicity of the basic theory. In essence, the designprocess for serviceability entails the checking of the stressdis t r ibut ion under the combined act ion of both theprestress and applied loads, at all positions along thebeam, in order to ensure that both the compressive andtensile stress are kept within the limits stated in designstandards.

In addition the technique known as ‘load balancing’ offersthe designer a powerful tool. In this, forces exerted by theprestressing tendons are modelled as equivalent upwardforces on the slab. These forces are then proportioned tobalance the applied downwards forces (Figure 5.2). Bybalancing a chosen percentage of the applied loading it ispossible to control deflections and also make the mostefficient use of the slab depth.

L

Consider a beam withbeams’ centre line.

a force P applied at each end along the

This force applies a uniform compressive stress across the sectionequal to P/A, where A is the cross sectional area. The stressdistribution is shown below.

Consider next a vertical load W applied to the section and thecorresponding bending moment diagram applied to this alone.

W

The stress distribution from the flexure of the beam is calculatedfrom M/Z where M is the bending moment and Z the section

modulus . By considering the deflected shape of the beam it can beseen that the bottom surface will be in tension. The correspondingstress diagram can be drawn.

+ M/Z

Tension I- M/Z

Concrete i s strong in compression but not in tension. Only smalltensile stresses can be applied before cracks that limit theeffectiveness of the section will occur. By combining the stressdistributions from the applied precompression and the appliedloading it can be seen there is no longer any tension.

P/A + M/Z I’/ A + M/Z

rl+x=v-M/Z P/A M/Z = (0)

Figure 5.1 Principles of prestressed design

Applied load

Load balancing for uniform load

Applied load

LLoad balancing for point load

Figure 5.2 Load balancing of unbonded tendons in flatslab

In order to use the load balancing technique, theprestressing tendons must be set to follow profiles thatreflect the bending moment envelope from the appliedloadings. Generally parabolic profiles are used. In thecase of flat soffit slabs these are achieved by the use ofsupporting reinforcing bars placed on proprietary chairs(Figure 5.3 (a) and (b)).

Figure 5.3(a) Wire chairs

Figure 5.3(b) Plastic chairs for smaller cover

The supporting bars are fixed rigidly into position andthen the prestressing tendons laid and secured to them inorder to obtain the desired profile (Figure 5.4). Tendonsupport bars are required at a maximum of one metrecentres. With deeper ribbed slabs the required profile isobtained by tying the tendons to short lengths of bar wiredto the reinforcement links which are spaced off andsupported by the formwork.

Figure 5.4 Tendon profile obtained by varying height ofchairs

In the majority of prestressed slabs it will be necessaryto add reinforcement, either to control cracking or tosupplement the capacity of the tendons at the ultimateload condition. In one-way spanning slabs it is normalpractice to provide sufficient bonded reinforcement tocarry the selfweight plus a proportion of the imposedloading on the slab. This is to cater for the possibility ofthe loss of prestress in any one span resulting in theprogressive collapse in the other spans. Tests have shownthat in a two-way spanning slab there is a high degreeof inherent structural redundancy with the local loss ofprestress in one span having very little affect on otherspans (0).

At ‘the serviceability limit state, a prestressed slab isgenerally always in compression and therefore flexurec r a c k i n g i s u n c o m m o n . T h i s a l l o w s t h e a c c u r a t eprediction of deflections as the properties of the untrackedconcrete section are easily determined. Deflections cantherefore be estimated, and limited to specific values ratherthan purely controlling the span-to-depth ratio of the slab,as in reinforced concrete design.

In post-tensioned concrete floors, the load balancingtechnique can enable the optimum depth to be achievedfor any given span. The final thickness of the slab, as withthin solid slabs, may be determined by consideration ofthe punching shear around the column. Traditionally,dropped panels or column heads were used to cater forthis shear, but recent research and development has ledto the manufacture of prefabricated shear reinforcementand steel shear heads (11) (Figures 5.5 and 5.6). These thenallow the use of totally flat soffits (Figure 5.5) which givesobvious benefits both in terms of reduced overall depth,ease of service distribution and speed of construction.

In an effor t to reduce s t i l l fur ther the weights ofprestressed slabs, lightweight aggregate concretes can beused. These give obvious benefits in terms of reducedselfweight and foundation loads.

Failure plane 1000

Figure 5.5 Typical shearhead detail

Figure 5.6 Steel shearhead in post-tensioned floor slab

Partial prestressing, which combines some prestressingwith the structural action of a traditional reinforcedsection, can also be economic. This form of constructioncan accommodate high tensile stresses at full designloading with the following benefits.

The non-prestressed steel helps crack control beforestressing is applied.Transfer stress problems are eliminated.If restraint or over-loading occurs, any cracks are betterdistributed.Deflect ion control and high span/depth rat ios aremaintained.Lower tendon density improves space for penetrations.

RestraintWhen planning a prestressed concrete structure, care mustbe taken to avoid the problems of restraint(“). This iswhere the free movement in the length of the slab underthe prestress forces is restrained, for example by theunfavourable positioning of shear walls (Figure 5.7(a)) orlift cores.

There are two components to the applied prestrcss: thed i r ec t ax i a l compres s ion i n t he conc re t e s ec t i ontransferred through the tendon anchorage, and theupward force from the tendon profile. If the slab isrestrained when the slab is stressed, force may be lost intothe restraining element instead of being fully transferredto the slab. This may result in a loss of axial compressionbut will not affect the upward force. A significant loss ofaxial compression force could cause the slab to crack.

Slab

(a) Plan of slab with four corner shear walls

Closure strip

(b) Alternatives for arrangement of closure strips

Restraint problems are not common, as the levels ofprestress are low, and well tested and simple methods areused, for example closure strips as shown in Figure 5.7(b)Wall infill strips (Figure 5.8) or temporary release details(Figure 5.9) are available for overcoming potential restraintproblems. Movement joints can also be incorporated w h e n

required.

ISlab to remainfully proppeduntil inflll stripc u r d

Infill later

/ Post-tensioned slab

Figure 5.9 Temporary release detail at top of supportingwall

HolesA particular design feature of post-tensioned slabs is thatthe distribution of tendons on plan within the slab doesnot significantly effect its ultimate strength. There is someeffect on strength and shear capacity, but this is generallysmall. This allows an even prestress in each direction of aflat slab to be achieved with a number of tendon layouts(Figure 5.10(a-c)).

Layout (a

Layout (b

This offers considerable design flexibility to allow forpenetrations and subsequent openings, and the adoptionof differing slab profiles, from solid slabs through to ribbedand waffle construction.

Figure 5.10(a) shows the layout of tendons banded over aline of columns in one direction and evenly distributed inthe other direction. This layout can be used for solid slabs,ribbed slabs, or band beam and slab floors. It offers theadvantages that holes through the slab can be easilyaccommodated and readily positioned at the constructionstage.

Figure 5.10(b) shows the tendons banded in one direction,and a combination of banding and even distribution in theother direction. This does not provide quite the sameflexibility in positioning of holes, but offers increasedshear capacity around column heads. Again, this layoutcan be used for both solid and ribbed slabs and bandedbeam construction.

Figure 5.10(c) shows banded and distributed tendons inboth directions and is logically suitable for waffle flatslabs, but may be employed for other slabs, depending ondesign requirements.

Holes through prestressed slabs can be accommodatedeasily if they are identified at the design stage. Small holes(less than 300 mm x 300 mm) can generally be positionedanywhere on the slab, between tendons, without anyspecial requirements. Larger holes are accommodated bylocally displacing the continuous tendons around the hole(Figure 2.7). It is good detailing practice to overlap anystopped off (or ‘dead-ended’) tendons towards the cornersof the holes in order to eliminate any cracking at thecorners (Figure 5.2 1). In ribbed slabs, holes can be readilyincorporated between r ibs or , for larger holes, byamending r ib spacings or by stopping-off r ibs andtransferring forces to the adjoining ribs.

Slab

Layout

Figure 5.10 Common layouts of unbonded tendons inflat slab

Holes are more difficult to accommodate once the slab hasbeen cast. They can, however, be carefully cut if thetendon positions have been accurately recorded or can beidentified (see Section 7). A better approach is to identifyat the design stage zones where further penetrations maybe placed. These zones can then be clearly marked on thesoffit of the slab.

Many of the major specialist concrete frame contractorshave experience with post-tensioned construction, andare aware of how it differs from using reinforced concreteand the benefits it offers. Those contractors less familiarmay be wary as there is definitely a learning curve tobe climbed in the early stages of a project. However,experience shows that once in their stride, all contractorscan achieve exceptional floor cycles with post-tensionedconstruction.

Aspects of constructionThe sequence of construction of post-tensioned slabs isstraightforward and typically includes the points givenbelow. A number of aspects such as prefabrication oftendons, the reduction in quantities of steel to be fixed andlarge pour sizes help to speed the construction.

Prefabrication of tendonsIn the case of an unbonded system, fabrication drawingsare produced from which each tendon is cut to lengthand assembled off-site with any dead-end anchorages.Tendons are individually colour-coded and delivered tosite in coils ready to be fixed (Figure 6.1). With a bondedsystem the ducting and tendons are cut and assembled onsite.

Figure 6.1 Colour-coded tendons ready for fixing

Sequence of installationIn any slab there will be both reinforcement and tendonsto be fixed (Figure 5.4). The fixing sequence is generally:(1) fix bottom mat reinforcement, (2) fix tendon supportbars to specified heights, (3) drape tendons across thesupport bars and secure, and (4) fix any top mat steel andcolumn head reinforcement.

Construction jointsThere are three types of construction joint that can be usedbetween areas of slab; these are shown in F i g u r e 6 . 2 ( a - c )

When used they are typically positioned in the vicinity of

a quarter or thirdr points of the span. The most commonlyused joint is the infill or closure strip, as this is an idealmethod of resolving problems of restraint, and it alsoprovides inboard access for stressing, removing the needfor perimeter access from formwork or scaffolding.

Pour 1 Pour 2

I I

(a) Construction joint with no intermediate stressing

(b) Construction joint with intermediate stressing

Pour 1 Pour 2

(c) Infill or closure strip

Figure 6.2 Details of slab construction joints

Construction joint with no stressing (6.2(a))The slab is cast in bays and stressed when all the bays arecomplete. For large slab areas, control of restraint stressesmay be necessary and ideally the next pour should becarried out on the following day.

Construction joint with intermediate stressing (6.2(b))On completion of the first pour containing embededbearing plates, intermediate anchorages are fixed to allowthe tendons to be stressed. After casting of the adjacentpour, the remainder of the tendon is stressed. It issometimes necessary to leave a pocket around theintermediate anchorage to allow the wedges that anchorthe tendons during the first stage of stressing to moveduring the second stage of stressing.

Infill or closure strips (6.2(c))The slabs on either side of the strip are poured and stressed,and the strip is infilled after allowing time for temperaturestresses to dissipate and some shrinkage and creep to takeplace.

Pour size/jointsLarge pour areas are possible in post-tensioned slabs, andthe application of an early initial prestress, at a concretestrength of typically 12.5 N/mm2, can help to controlrestraint stresses. There are economical limits on thelength of tendons used in a slab, and these can be used asa guide to the maximum pour size. Typically these are35 m for tendons stressed from one end only and 70 m fortendons stressed from both ends.

The slab can be divided into appropriate areas by the useof stop ends (Figure 6.3) and, where necessary, bearingplates are positioned over the unbonded tendons as shownin Figure 6.4 to allow for intermediate stressing.

ConcretingCare must be taken when concreting (Figure 6.5) to preventoperatives displacing tendons, but apart from this, boththe placing and curing of the concrete is similar to that fora reinforced slab, although concreting is easier as there isno reinforcement congestion.

Figure 6.5 Placing concrete in post-tensioned slab

StressingConcrete cubes are taken and cured close to the slab toenable the strength gain of the concrete to be monitored.The cubes are taken during the pour and crushed at dailyintervals to monitor the strength gain of the concrete. Atabout one to three days, when the concrete has attaineda strength of typically 12.5 N/mm2, initial stressing oftendons to about 50% of their final jacking force is carriedout. (The actual concrete strength and tendon forcewill vary depending on loadings, slab type and otherrequirements.) These control restraint stresses and mayalso enable the slab to be self-supporting so that formworkcan be removed. Design checks on the frame are necessary,taking account of the reduced concrete‘strength, and it isrecommended that as soon as the formwork has beenremoved a secondary propping system is used until theslab is fully stressed.

With an unbonded system stressed from one end, theremote end is fixed by a dead-end anchorage (Figure 6.6).

Figure 6.4 Bearing plates positioned over tendons Figure 6.6 Dead-end anchorage

Figure 6.7 Stressing anchorage assembled with plasticrecess form

At the stressing end the tendon passes through a bearingplate and anchor which is attached to the perimeter formby a mandrel holding in place a reusable plastic recessform (Figure 6.7).

Figure 6.8 Stressing of tendons

Figure 6.9 Recessed anchorages showing wedges

The tendon is stressed with a hydraulic jack (Figure 6.8),and the resulting force is locked into the tendon by meansof a split wedge located in the barrel of the recessed anchor(Figure.6.9).

The anchors shown are for a single unbonded tendon.Anchorages for use with bonded tendons differ in detail,but perform the same general function. At about sevendays, when the concrete has attained its design strength(typically 25 N/mm2) the remaining stress is applied to thetendons.

T h e extension o f e a c h t e n d o n u n d e r l o a d i s t h e nrecorded and compared against the calculated value.Provided that it falls within an acceptable tolerance, thetendon is then trimmed. With an unbonded system, agreased cap is placed over the recessed anchor and theremaining void dry-packed. With a bonded system theanchorrecess is simply dry-packed and the tendon grouted.

Back proppingWhen designing the formwork systems for a multi-storeyconstruction, the use of to back-props (Figure 6. 10),through more than one floor to support the floor underconstruction, should be considered.

Figure 6.10 Back-propping of post-tensioned ribbed slab

Research into back-propping of slabs has been carried outby the Reinforced Concrete Council, and the results are tobe published shortly(17).

Slab soffit markingVarious methods exist for marking the slab soffit toidentify where groups of tendons are fixed. One way is toincrease the slab thickness over the width of the group oftendons - thus creating an identifying downstand - orpaint markings can be used as shown in Figure 6.11. Thisenables areas for small holes and fixings to be drilled aftercompletion, safe in the knowledge that tendons will not bedamaged.

Disciplines for soffit fixings can be agreed, indicating themaximum depth of fixing that can be used in any one area.

Figure 6.21 Marking of tendon positions in slab

DEMOLITIONAND STRUCTURAL

ALTERATIONSTwo of the most commonly considered aspects of the useof un-bonded tendons are the performance of the structureduring demolition and its ability to accept structuralalterations.

DemolitionIt is commonly thought that an unbonded post-tensionedslab is an ‘unexploded bomb’ that will detonate duringdemolition, and that the local failure of one part of astructure will lead to a total structural collapse. Researchtogether with case studies shows that, in structuresdesigned in accordance with current standards and goodpractice, the above concerns are unfounded.

Experience on actual buildings and in laboratory testsshows that when tendons are cut as a result of, forexample, partial collapse, the failure will not result inanchorages, lumps of concrete, or other material becomingmissiles. The scatter of debris will be no more severe thanin the collapse of an equivalent non-stressed structure.

During controlled demolitions, as with any structure, safetyprecautions are necessary, and de-tensioning must becarried out by an experienced demolition contractor.Several tried and tested techniques are available forde-tensioning. The most common are:

Heating the wedges until tendon slip occursBreaking out the concrete behind the anchorage untildetensioning occursDe-tensioning the strand, using jacks.

Because of the usual site problems of access and otherconstraints it is often necessary to use a combination oftechniques.

With regard to the concern that local failure could lead tototal collapse, again results from both tests and casestudies are available which demonstrate that total collapsedoes not happen(‘Q.

During demoli t ion, or if a partial collapse occurs, atwo-way spanning structure is likely to behave differentlyfrom a one-way spanning structure. A large, multi-bay,two-way, flat slab has a very high degree of inherentstructural redundancy. This redundancy, coupled withthe possibility of catenary action of the slab betweencolumns, gives very high ul t imate s t rength that issignificantly above that determined by calculation. It hasbeen proved that the loss of prestress in, for example, onepanel of the slab will not result in a failure of either thepanel concerned or the structure as a whole’“)).

However, in a continuous one-way spanning slab the lossof prestress in one span could result in a similar loss inother spans, and result in failure if the slab is prestressedonly. Design standards take account of this possibility,and the usual approach is to provide sufficient normalbonded reinforcement within the slab to support theself-weight of the slab and finishes and a proportion of theimposed load.

Structural alterationsSome views on the ability of post-tensioned slabs toaccommodate minor alterations, such as core drillingservice holes, or more major alterations like forming largeopenings for escalators, suggest that such alterations toother forms of construction are straightforward. The truthis that in all cases any alteration that affects the existingstructure needs to be carefully considered and designedby an engineer. For example, coring a hole through areinforced concrete slab, which cuts through a reinforcingbar, will reduce the strength of that slab. Similarly,forming a large opening in any structure will require theeffects on adjacent areas of the structure to be assessed,and may require the introduction of additional supportmembers to ensure that the overall structural integrity ismaintained.

Forming smaller openings through post-tensioned slabscan be more straightforward than in other structures. Insolid slabs the tendons are usually regularly spaced acrossthe slab with quite large gaps between, and holes mayreadily be formed between ribs of ribbed slabs (Figure 7.1).

‘)Tendons in ribs I

Possible zone

for holes

I0 0 0 0

Tendons spaced across slab

Figure 7.2 Zones where holes can be readily formed inpost-tensioned slabs

Methods exist for marking the slab soffit to identifytendon locations (Figure 6.11). Once this has been done,small holes can be formed in the ‘clear’ zones without anydetrimental effect on the structural performance.

Even when a soffit marking and other zoning systems areused it is recommended that the position of each proposedhole is referred back to the designer for comment andapproval.

When forming large openings in structures after initialconstruction, regard must be given to the original designconcept. Post-tensioned slabs are no different from otherforms of construction in this respect.

Providing a large hole in a slab with bonded tendons is nota problem, since the operation is. similar to that for areinforced section. Therefore attention is given here onlyto forming a large hole through a slab with unbondedtendons. Figure 7.2 illustrates the typical stages involved.

In forming larger openings it is likely that more than onegroup of tendons will be affected and will need to beremoved. As mentioned above, techniques already existfor de-tensioning; similarly, there are techniques availablefor re-anchoring tendons and re-tensioning. It is thereforepossible to remove tendons which cross an openingwithout affecting the remaining areas of the slab whichthose same tendons pass through and support.

At a practical level, the main effect with unbondedtendons is that areas of slab remote from the area underconsideration, but affected by de-tensioning, will need tobe fully propped for the duration of the work.

When considering a flat slab design, it will generally benecessary to locate openings away from areas of bandedtendons, typically beam strips, in order to minimise anyreinstatement that may be required. This does not undulyrestrict internal planning, since it is normal for around twothirds of the floor to contain tendons that are widelyspaced, thus reducing the number which will intersect anyintended hole (Figure 7.2(a)). Even in two-way spanningslabs there is considerable space for holes betweentendons.

The eventual cutting of the tendons will temporarilyreduce the load capacity of the slab for the entire lengthof the unbonded tendons. Effects are minimal at somedistance from the anchor points since the slab remainseffectively prestressed by the other tendons. In mostcircumstances it is sufficient simply to restrict loadings onthe slab during the operation thus avoiding the need foranything other than local propping.

Prior to starting any breaking out, it is necessary to locatethe tendon positions. The tendons are usually locatedsingly or in pairs at approximately 1 m centres, and may befound using an appropriate cover meter. A small hole isusually broken to expose the tendon about 400 mmfrom the final face of the opening. Alternatively, thesurrounding concrete can be broken away exposing thetendons along the entire length of the opening (Figure7.2(b)). It is usual to have an engineer present during thisstage of the operation to ensure that no premature damageoccurs to the tendons.

(a) Locating hole in slab

Figure 7.2 Forming large openings post-construction

The uncovered tendons can then be detensioned one bvone (Figure 7.2(b)). The strands are usually flame-cutwithin this hole, as this causes the strand to yield ratherthan break suddenly. Alternatively the tendon can be cutusing a disc. In this case the procedure is to slip a bearingplate over the tendon and against the concrete face. Specialjacks are then positioned against the bearing plates andused to take up the load in the tendon. This relieves theload in the length of the tendon between the jacks. Thetendon is then cut and the pressure gradually releasedfrom the jacks until the tendon is completely detensioned.

In both cases, the strand will draw back slightly into thesheath when cut, depending on the stressed length. Withall the strands cut in the area required, all the remainingconcrete can be broken out back to the final face. This isachieved more easily than with a reinforced concrete slabsince the reinforcement quantities are minimal.

Having stripped back the sheathing, a standard anchoragecan then be fitted to the tendon. This is set into the parentconcrete using a fast-setting epoxy or cementitious mortar(Figure 7.2(c)). Once the mortar has set the tendon may berestressed. When restressing is completed satisfactorily,the excess tendon is cut off and capped.

Once the anchors are reinstated, further work is mainlycosmetic. Any desired edge profile can be formed, eg nibo r upstand, using a small cage of l inks around theperimeter. (Figure 7.2(d)). Pouring concrete into the edgestrip completes the operation. An example of a hole formedafter construction to accommodate a spiral staircase isshown in Figure 7.3.

The above technique is a method of forming a large hole ina post- tensioned f lat s lab. The slab may be whollyprestressed or combined with reinforced concrete. Forexample, McAlpine’s offices at Hemel Hempstead (shownin Figure 7.4) were constructed with post-tensioned bandbeams, with a reinforced coffer slab between, that alloweda 4 m x 4 m hole to be broken out for an atrium withoutstructural modification.

It cannot be over-emphasised that a slab may be designedto accommodate a wide range of future alterations, whetherthese are predetermined or not.

As has been shown, introducing large holes into a post-tensioned slab is straightforward, and can be carried out ina similar time to that taken for a reinforced slab.

Llmlt of concrete breakout

I Tendon cut here after

Ipressurising jacks

I

II

I J

Horseshoe plates

Local hole or section removed to give access to tendons

(b) Exposing tendons

Cementitiousor epoxy mortar

----=

-_=

-----

(c) Reinstating anchorages

Perimeter reinforcement cage(as required)

(d) Constructing hole to final profile

Figure 7.2 Continued

Figure 7.3 Example of hole formed post-construction

Figure 7.4 Atrium formed post-construction

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with particular regard to the use of unbonded tendons.Design recommendations. Technical Report No. 17.Wexham, The Concrete Society, 1979. 16 pp.

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POST-TENSIONED CONCRETE FLOORS IN MULTI-STOREY BUILDINGS

A M Stevenson

BRITISH CEMENT ASSOCIATION PUBLICATION 97.34769.025.2:24.102.46