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  • Prestressed concrete flat slabs

    Autor(en): Marti, P. / Ritz, P. / Thrlimann, B.

    Objekttyp: Article

    Zeitschrift: IABSE surveys = Revue AIPC = IVBH Berichte

    Band (Jahr): 1 (1977)

    Heft S-1: Prestressed concrete flat slabs

    Persistenter Link: http://dx.doi.org/10.5169/seals-43578

    PDF erstellt am: 12.11.2015

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  • IABSE SURVEYS S-1/77

    Prestressed Concrete Fiat SlabsDalles plates precontraintesVorgespannte Flachdecke

    MARTI P. RITZ P. THRLIMANN B.dipl. Ing. dipl. Ing. Prof. Dr.

    Institute of Structural Engineering,Swiss Federal Institute of Technology (ETH), Zrich

    SUMMARYA short review on the analysis and the design of prestressed flat slabs is given. Some newaspects concerning flexural behavior, punching, reinforcement arrangement and detailing arepresented. Different possible tendon layouts are compared. A new model for slabs with unbondedtendons and additional reinforcement is described.

    RfSUMEL'article rappelle les differentes methodes de calcul des dalles plates, precontraintes, sansChampignon. Les auteurs presentent certains aspects nouveaux concernant la flexion, lepoinconnement, les differentes possibilites de repartition des cbles, l'armature conventionnelleet les problemes constructifs. Ils presentent en outre un modele qui explique le comportement la flexion des dalles precontraintes avec des cbles non injectes et avec une armatureconventionnelle.

    ZUSAMMENFASSUNGNeben einem kurzen berblick ber die bliche Berechnungs- und Bemessungspraxis vonvorgespannten Flachdecken werden einige neue Gesichtspunkte hinsichtlich Biegeverhalten,Durchstanzen, Bewehrungsanordnung und besonderer Ausfhrungsprobleme dargelegt.Verschiedene Kabelanordnungen werden einander gegenbergestellt. Ein neues Modell frPlatten mit Kabeln ohne Verbund und zustzlicher schlaffer Bewehrung wird beschrieben.

  • IABSE SURVEYS S-1/77

    1. INTRODUCTION

    A brief survey of current practice in the analysis, the design and the construction of prestressed flat slabs is presented. Some new aspects are added. It isnot intended however, to give a complete review of the present knowledge in thisfield. For detailed information the reader is referred to the recommendations[1] and [2] and to the state-of-the-art reports [3] and [4].Fiat slabs are frequently used as structural Systems for buildings. The most important advantages are:- Flexibility for the use in industrial and office buildings, storehouses,

    schools, etc.- riinimum height from floor to floor.- Free headroom for garages and parking structures.- Reduction of construction time.

    Prestressing of flat slabs adds the following advantages:- Improvement of the deflection and cracking response under service loads.- Lower costs through the use of high-tensile steel in place of conventional

    reinforcement.- Greater span-depth ratio in comparison with conventionally reinforced slabs.

    The economical spans rnge from 6 to 15m.- Improvement of the punching resistance by placing tendons in the column lines.The majority of prestressed flat slabs is constructed using unbonded post-tensioned tendons in combination with additional nonprestressed reinforcement. Ifthe slab-thickness exceeds 30 cm bonded multiStrands are also used because theloss of effective height becomes acceptable.For the analysis and the design of prestressed flat slabs the following problemshave to be considered: Flexural behavior, shear strength, distribution of thetendons and special detailing problems.

    2. FLEXURAL BEHAVIOR

    2.1 GeneralsBonded and unbonded prestressed concrete slabs differ essentially in their flexural behavior. Usually applied analysis and design methods can be classified asfollows:A) Analysis of internal forces with methods based on the theory of elasticity.

    Design of cross-sections based on allowable stresses.

    B) Analysis of internal forces with methods based on the theory of elasticity.Design of cross-sections based on ultimate strength.

    C) Analysis and design with methods based on the theory of plasticity.

  • IABSE SURVEYS S-1/77

    2.2 Bonded SystemsBending of bonded post-tensioned slabs may be analysed with the ordinary methodsof the elastic or plastic theory for thin plates with small deflection. When using elastic methods to calculate the internal forces the structural design iseither based on a comparison between stresses due to service loads and allowablestresses CA] or the ultimate strength of the cross-sections has to exceed theinternal forces due to service loads multiplied by a specified safety factor [B].When using plastic methods (C), deformations and cracks under service loads haveto be checked by using elastic methods.

    2.3 Unbonded SystemsUnbonded structures, however, show a different behavior not only at ultimate butalso at service loads. Since frictional forces between the tendons and the concrete are negligible, the strain in an unbonded tendon is nearly constant overits entire length. The assumption that the strain distribution over the depthof a cross-section is linear is no longer valid. Hence the application of theanalysis and design methods used for bonded Systems to unbonded prestressed Systems is unsatisfactory. After cracking the concrete forms a compressed shell orarch and the tendons a tension membrane as shown in Fig.1. Therefore, the analysis has to include these two Systems.

    z. 7-/ 7//--y

    A-r // 7+T- -//_/ Comp"V ess

    =

    nsion respectiveRing

    Tendons-

    Tension Membrane

    Concrete Compressed Shell

    Fig. 1. Static System of Simply Supported Unbonded Post-Tensioned Slab

    In present practice, however, unbonded and bonded Systems are analysed in a similar way as follows:Internal forces are analysed with the ordinary elastic theory of plates and corresponding approximate or numerical methods (beam method, equivalent frame method,finite differences and finite elements). The introduction of the transverse component of the prestressing force to balance a portion of the load on the structures leads to the load-balancing method described in [5]. When dealing withstatically indeterminate slab Systems, the load-balancing method offers considerable advantages. Since the elastic analysis needs to be made only for a fractionof the total load, simple approximate methods may be used without noticeable er-rors.

  • IABSE SURVEYS S-1/77

    The design starting with the elastically calculated internal forces may be donein two different ways. The first approach is based on allowable stresses CA]. Inthis case, the cross-section is stressed by a bending moment and a normal force,the latter being the prestressing force after all losses have been subtracted.In the second approach the ultimate strength of the different cross-sections hasto exceed the elastically calculated internal forces multiplied by a specifiedsafety factor (B). Both, the tendon force increase and the effective axial force,needed to calculate the ultimate strength, have to be estimated. The corresponding problem will be discussed later.A different approach is the use of plastic methods based on either the static(lower-bound) or the kinematic (upper-bound) theorem. To determine the ultimatestrength capacity the increase of the tendon force and possible axial forceshave again to be estimated.

    In addition, either using elastic analysis methods combined with allowable stresses or ultimate strength design or plastic methods, deformations and crackingbehavior have to be checked.

    Some of the above mentioned requirements are formulated in existing recommendations:ACI-ASCE Committee 423: "Tentative Recommendations for Prestressed Concrete Fiat

    Plates" [1]:Permissible stresses:Permissible tensile stresses in concrete f [kg/cm2] at service loadsT.p

    postive moments negative moments

    without additionalbonded reinforcement f. 0.53VFtp v c

    \

    f. 0tpwith additionalbonded reinforcement f_

    1 .S9-\/F"tp c f. 1.59-Jr^tp v c

    f'[kg/cm ]: concrete cylinder compressive strengthUiti!I|te_ strengt h_Tendon stress increase at design load (ACI 318-71)

    f'Af 700 kg/cm2 * JlnnC

    se & 100'pbut not more than 4200 kg/cm2, where f' is the specified compressive cylinder strength of concrete in [kg/cm2] and p the reinforcement ratio.

    The Concrete Society: "The Design of Post-tensioned Concrete Fiat Slabs inBuildings" [2] :

    Permissible_stresses2Permissible tensile stresses in concrete f. :At transfer: f_ 0.77* vfT unless bonded reinforcement is provided andtp et

    f_ 1.53' \Jf_

    with enough