# Post-tensioned Concrete Floors Design Handbook LINK

The initial concept design by Project Engineer WSP was based on a proposal of post-tensioned slabs to many of the superstructure levels. The central cores form the overall stability system for the building. Wind loads acting on the building are transferred to the floor slabs from the curtain walling via the cladding brackets and the concrete floor slabs act as stiff diaphragms to transfer the wind loads to the cores.

## Post-tensioned Concrete Floors Design Handbook

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Following intensive development through the tender stages, Freyssinet was commissioned by the frame contractor Byrne Bros to provide the design, supply and installation of post-tensioned slabs and the additional design and detailing of the traditionally reinforced horizontal elements.

The typical floor plates to both towers are 200thk with an average of 4.8kg/m2 of PT and 13kg/m2 of traditional rebar, resulting in an overall of 196 tonnes of post-tensioning and 630 tonnes of associated traditional rebar. The total floor area of the post-tensioned slabs is approx. 44,600 m2 in 72 individual concrete pours.

CaIcuMon of tendon geometry Calculation of secondary effectsusing equivalent loads Calculation and detailing of anchoragebursting reinforcement Simplified Shear Check: Derivation ofFigures 17 and 18 V1"mlionof post-tensioned concrete floorsAdvenisemen!s

NOTATIONArea of concrete Area of prestressing tendons Area ofun-tensioned reinforcement Area of s h w reinforcement Drape oftendon Width of section Breadth of member; or for T-, I- andL-beams the breadth of the n i Effective depth of tensionreinforcement or tendons Depth t the cenaoid of the compressionzone o Shon-term modulus of elasticity of concrete Modulus ofelasticity of concrete at time of wnsfer Modulus of elasticity ofprestressing tendons Modulus of elasticity of un-tensionedreinforcement Eccentricity Compressive stress in concrete atextreme fibre used to calculate serviceability un-tensionedreinforcement requisemen Concrete suenglh at (initial) transfer(in N/mm? Stress in concrete at the level of the tendon due toinitial p r e s m s and dead load (in N/mm3 Tensile stress inconcrete at extreme fibre used lo calculate serviceabilityuntensioned reinforcement requirements Characteristic concrete cubestrength (in N/mmq Tensile stress in tendons at (benm) failure (inN/mml) Effective presuess (in tendon) after d l losses (in N/mrnz)Characteristic strength of prestressing steel (in N/mm2) Maximumdesign principal tensile stress (=0.24Jf,. in N/mm2) Characteristicstrength of bonded un-tensioned reinforcement (in N/mm3 Overalldepth of section Second moment of area Effective span length Lengthof tendon Length of tendon affected by wedge draw-in Moment due toapplied loads Moment necessary to pmduce zero stress in theconcrete at the extreme tension fibre Secondary moment due toprestress Ultimate resistance moment Resuess force Slope ofprestress force profile Characteristic strength of tendon (in 3 ) NPrestressing force in the tendon at the jacking end Prestressingforce at distance x from jack Distance between points ofcontra-flexure in tendon Length of a critical shear perimeter Shearforce due IO ultimate loads Ultimate shear resistance of concreteUltimate shear resistance of a section uncracked in flexureUltimate shear resistance of a section cracked in flexure Designeffective shear force Design shear suess at cross-section Designconcrete shear strength Uniformly dishiiuted load Neutral axisdepth Hl the side of the prestress end block af Half the side ofthe prestress anchor loaded area Top section modulus

INTRODUCTIONThe use ofpost-tensioned concrets flwrs in buildingshas been consistently growing in recent years. The greatest use ofhis type of consmcuon has b e n in the USA, and in California it isthe primary choice for concrete floors. Post-wsioned floors havealso k n used in Australia. Hong Kong, Singapore and Europe. Theiruse in the UK is now increasing rapidly. Typical applications havebeen: Offices Car parks Shopping cenms Hospitals ApamenE Indusmalbuildings These are illustraed in Figures 1, 2 and 3.

This report explains the overall concept of post-tensionedconcrete floor consmction as well as giving detailed designrecommendations. The intention is to simpliiy the tasks of thedesigner and contractor enabling them to produce effective andeconomic structures. Post-tensioned flwrs are not complex. Thelechniques, structural behaviour and design are simple and verysimilar to reinforced concrete smctures. The prestress tendonsprovide a suspension system within the slab and the simplearguments of the triangle of forces apply with the verticalcomponent df the tendon force carrying part of the dead and liveloading and the horizontal component reducing tensile stresses inthe concrete. Two design examples are given in Appendix A. Thereport is intended to be read in conjunction with BS8110"'. Thoseareas not covered in BS8110'" are descrited in detail in the reportwith reierences given as appropriate. Tne principles laid out inthe report may also be applied

to designs in accordance with E m o d e ECZ'fl, but some of thedetails will need to be modified. Two other Concrete Societypublications give useful background information to designers ofpost-tensioned floors. They are: Technical Report No. 21"'.Durability of Tendons in Prestressed Concrete and Technical ReportNo. Z3"I. P r i l Prestressing. ata It should be noted that sincethe integrity of the structm depends on a relatively small numberof prestressing tendons and anchorages the effect of workmanshipand quality of materials can be critical. This should be understcodby all parties involved in M design and construction.

The main advantages of post-tensioned floors over conventionalreinforced concrete in-situ floors, may be summarised as follows:Increased clear spans Thinner slabs Lighter structures Reducedcracking and deflections Reduced storey height Rapid constructionBetter watertightness. ' .

Amount ofpnsbessThe amount of prestress provided is not usuallysufficient to prevent tensile stresses occurring in the slab underdesign load conditions. The structure should therefore beconsidered to be partially prestressed. The amount of prestressselected affects the un-tensioned reinforcement requirements. Thegreater the level of prestress, the less reinforcement is likely tobe required. Unlike reinforced concrete structures, a range ofaccepfable designs are possible for a given geomeuy and loading.The optimum solution depends on the relative costs of prestressingand un-tensioned reinforcementand on the ratio of live load to deadload.

Analytical techniquesThe design process is described in Section6. The analytical lechniques are the same as those used forreinforced concrete structures. The structure is normallysubdivided into a series of equivalent frames upon which theanalysis is based. These frames can be analysed using momentdistribution or other hand techniques, however it is now morecommon to make use of a plane frame computer analysis program. Inaddition to standard plane frame programs, there are available anumber of programs, specifically written for the design ofprestressed structures. These propams reduce the design time butare not essential for the design of post-tensioned floors. For morecomplicated flat slabs or for those which are be repeated manytimes, a grillage or finite element analysis of the flwr may bemore appropriate.

STRUCTURAL BEHAVIOUREffeects of prestressThe primary effects ofpresuess are a pre-compression of the flwr and an upward loadwithin the span which balances part of the downward dead and liveloads. In a reinforced concrete flwr, tensile cracking of theconcrete is a necessary accompaniment to k generation of economicstress levels in the reinforcement. In post-tensioned flwrs boththe presompression and the upward load in the span act to reducethe tensile stresses in the concrete. However, the level ofprestress is not usually enough to prevent all tensile crackingunder full design live loading at Serviceability Limit Slate. Underreduced live load much of the cracking will not be visible. The actof presUessing causes the flwr to bend, shorten, deflect androtate. If any of these effects are restrained, secondary effectsof prestress are set up. As slated above, if the level of prestressdoes not exceed approximately 2N/mm2 the secondary effects due tothe restraint to shonening are usually neglected. However, unlessthe floor can be considered to be statically determinate, thedisplacements of the flwr sets up secondary moments which cannot beneglected. Secondary effects are diszussed in more detail inSection 6.9 and the calculation of these effects is described inAppendix D.

There are several different types of post-tensioned floor. Someof the more common layouts are given in Figures 4.5.6.7 and 8. Animportant distinction between types of floors is whether they areone-way or two-way spanning structures.

Flexure in one-wayfloorsOne-way spanning floors are usuallydesigned Class 3 structures in accordance with BS8110"). Althoughcracking is allowed, it is assumed that the concrete section isuncradted and that hypothetical ensile stresses can be carried atServiceability Limit State. The allowable stresses are discussed inSecdon 6.10.1. The behaviour of one-way flwrs at loads less thanthat which would cause cracking can be assumed to be linear andelastic. BS811OW1 recommends that when the tensile stresses underdesign permanent loads are less than the allowable stresses forClass 2 suuctms, then the deflection may be predicted using grosssection properties, In other cases calculation of deflectionsshould be based on the moment-curvature relationship for crackedsections.

Tests and applications have demonsuated thata post-tensionedflat slabbehaves ns a flat plate almost regardless of tendonarrangement (see Figure 9). The effecrs-ofthe tendons-m;of course,critical tothe behaviour as they exert loads on the slab as well asprovide reinforcemenr The tendons exert equivalent vertical loadson the slab known as equivalent loads (see Section 6.7). and theseloads may be considered like any other dead or live load. Since thetendon effect is opposite to the effect of gravity loads, the netload causing bending is reduced. An additional effect of thetendons is the axial precompression which counteracts flexmaltensile skesses. Therefore, at service dead load, the net downwardload musing tending in the slab is normally very low and the flwris essentially under uniform axial compression. Examination of thedistribution.of moments for a flat plate in Egures 10 and 11reveals that hogging moments across a panel are sharply peaked inthe immediate vicinity of the column and that t moment at thecolumn face is b several times the moment midway behveen columns.It should k noted that the permissible snesses given in Table 2 ofSection 6.10.1 are average sbesses for the full panel. They arelower than those for one-way floors L allow for this o non-uniformdisnibution of moments across L e panel. h