PRESTRESSED HOLLOW CORE SLABS ON FLEXIBLE SUPPORT - DESIGN MODELS AND COMPUTATIONAL EXAMPLES

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1 JUNIORSTA 01.1 Conrete and Masonr Strutures PRESTRESSED HOLLOW CORE SLABS ON FLEXIBLE SUPPORT - DESIGN MODELS AND COMPUTATIONAL EXAMPLES Mateusz Surma 1 Astrat The aim o the paper is to ompare design models or prestressed Hollo Core as on leile support, alled Slim- Floor strutures. To models are disussed: the model o leile omposite eam Pajari-Leskelä and its development Roggendor, hih takes into aount the non-linear eets in onnetion o omposite eam. Both models have een developed on the asis o eperimental tests and FEM analsis. The paper shos the aults o the to models and the diretion o uture ork. Keords Design models, leile support, Hollo Core, preast, prestressed, Slim-Floor Strutures 1 SLIM-FLOOR STRUCTURES The prestressed Hollo Core (HC) as are urrentl the most popular solutions or long span loors (6 0 m). The main advantages o the preast elements i.e.: high stiness ith relativel lo height ( mm) and small seleight deide on their suess. Basi tehnologies o prodution (etrusion and ip-orming) elude the usage o an transverse reinorement in ross-setion o HC as. The onl reinorement are longitudinal prestressed strands hih ensure the ending apait and inrease the shear apait o non-reinored es Rd, hih is a deisive ondition ULS or HC as [1]. Originall HC as ere supported on non leile (rigid) supports, most oten on the alls. At the end o the 80s o the last entur, in Europe, the as supported on RC, PC, steel or omposite eams, alled Slim Floor Strutures, egan to e uilt. In this kind o strutures the at o the support s deormation is not irrelevant to the ork o the HC as. (see Fig.1) Fig. 1 Slim-Floor Struture [] INFLUENCE OF FLEXIBLE SUPPORT DFORMATIONS ON SHEAR CAPACITY OF HC SLABS When designing this tpe o strutures, the at that deormation o the as ours ith the inrease o deletion o supports should e taken into aount. As a onsequene, the omple stress state arises in the as transverse normal and shear stresses appear. HC as tend to move alongside the eams (gliding eet) (see Fig.). On the other hand, the ond ores, as ell as rition eteen the a ends and eam tend to prevent this displaement, hih generates inidental stress. The end o HC element is grouted together ith supporting eams, and this area is sujeted to negative ending moment hen the HC a is loaded. This leads to raking o the joint eteen illing onrete and the eam, eteen the illing onrete and the a end, or there ma e several raks in the same ross-setion o onnetion. Opening o these raks redues the stiness o the onnetion and eventuall shear lo eteen the a end and the eam is transmitted mainl the interae eteen the eam and the soit o the a []. 1 Mateusz Surma, MS., Crao Universit o Tehnolog, Civil Engineering Fault, Institute or Building Materials and Strutures, Warszaska, Krakó, POLAND, [email protected] 1

2 JUNIORSTA 01.1 Conrete and Masonr Strutures Fig. Transverse deormation o supporting eams These raks arise at the ottom side o the HC a, along strands under es (spalling and splitting) or in the longitudinal joints eteen the adjaent as and redue the ond eteen the tie reinorement and the a []. I the HC as are supported so lo on the eam that ending o the eam gives rise to transverse tensile stress at the ottom o the a, the soit o the a tends to rak longitudinall. Longitudinal raks redue the transverse ending stiness o the as. Sometimes the raks under the e tend to gro alongside the strands. This redues the ond eteen the strands and the onrete hih has a negative eet on shear apait o the a. As a result o the deletion o the eam, the dierene in ork shema o the HC elements, depending on its position along the eam, appears. The a in midspan o the eam is sujeted mainl to transverse ending moments. While the deletion o the eam the HC as are supported onl in the area o their outermost es []. The edge as are sujeted to shear deormation, hih is the main reason or reduing the shear apait. On the asis o series o eperimentall ull-sale tests [5] it has een shon that the ailure o the loor alas egins rom the outermost as. In addition, the lak o parallelism o opposite ends o the HC a ma e the reason or the additional stresses, as a result o the torsion (see Fig.). Fig. Stresses and strains o middle and outermost HC as on leile supports [] The result o transverse loads state in the Slim-Floor Strutures is raking and shear ailure o the HC as in their eakest area non-reinored edge es and redution o the shear apait Rd []. Despite the requent usage o the Slim-Floor Strutures, the onl reord that an e ound in the European standard [6] is that in ase o leile supports, the reduing eet o transversal shear stress on the shear apait shall e taken into aount. But there is no design proedure or model speiied. The i reommendations [6] and national standards applied in Finland, Seden and the Netherlands an e helpul. These douments are ased on a series o tests arried out in Finland in the ears [8] and ere reated on the asis o the design model Pajari [] and Leskelä [9]. The lak o heav ailures o Slim-Floor Strutures an e the reason or omitting a redution o shear apait o HC as (hih is the result o leile support) in the design alulations. In addition, the shear apait o HC as Rd is not ull used in man strutures. Hoever, the level o saet in the design ma prove to e unreliale, espeiall in short HC as, linearl loaded lose to the support. The omparison eteen the Pajari-Leskelä model and the Roggendor model [] is given in the urther part o the paper. DESIGN MODEL BY PAJARI - LESKELÄ This is a model o leile omposite eam, hih is a development o the onept o HC as on the non-leile (rigid) supports, as in [10] and [11]. The ailure riterion is ahieving the level o the tensile strength o onrete t the main stress σ 1. 1 t z ( 1 z ) z z t (1) The FEM analsis shos that the loalization o ritial ross-setion is in the range 0,5-0,5 h. The loation o the ross-setion depends on the eature geometr o the a (see Fig.).

3 JUNIORSTA 01.1 Conrete and Masonr Strutures Fig. Loalization o ritial ross-setion [] As or the non-leile supports the normal stress σ z is equal to zero, guaranteeing saet (see Fig. 5). Normal stress σ and transverse shear stress τ z (vertial) are deined similarl to the rigid earings and the are ased on the dependenies desried in () and (): P P e p M z () A I S z z, () I Fig. 5 Stress omponents in the HC e [] A more diiult issue is the identiiation o transverse shear τ z (horizontal) in the HC e, emerging rom the longitudinal ompressive transverse shear los ν in the omposite ross-setion, onsisting o the eam, the onrete grouting the joint and the upper lange o HC a orking at the length e [5]. The value o the ompressive transverse shear lo an e alulated the ormula: e. top ( EA). top () ( EI ) here: (EA).top om aial stiness o the hole upper lange, e.top entroidal distane o the top lange o the HC a rom the entroid ais o the omposite rosssetion, h.top thikness o the top lange o the HC a, ending stiness o the omposite ross-setion, EI om shear ore o the eam due to imposed load. On the asis o the ompressive transverse shear los (ν value), the value o the transverse shear stress τ z an e determined (see Fig. 6). The eat stress distriution τ z at the a length and the range o reliale ross-setion is still unknon. The model aknoledges τ z at the length = r, as the average value o the stress or the h distane. z here: r (5)

4 JUNIORSTA 01.1 Conrete and Masonr Strutures, sum o es idth in the HC a, idth o the HC a, l transverse shear ore rom the a supported on oth sides o the eam, ross-setion o HC es supported on oth sides o the eam. Fig. 6 Real and design distriution o τ z [] Based on the tests, it as ound that the stronger the omposite ation is, the greater is the redution o the shear apait Rd o the HC a. The value o eetive idth e is deined on the asis o tests using relationship eteen L (distane eteen zero ending moments) and L.0 (onstant eams span - 5m). Empiriall determined ator e.0, is dependent on the HC high and the material o the eam [5] (see Fig. 7). e L e.0.0 L (6) Fig. 7 Composite eam model [] The reduing ators o the transverse shear stress τ z aording to the eistene o topping (β t ) or illing ores (β ) and the tpe o support on the tensile or ompress eam lange (β ) ere determined on the asis o the tests [1]. In these tests the oserved shear apait o the HC as ahieved onl 0-70% o the shear apait otained in the reerene test, here the as ere supported on rigid earings. Based on these onlusions, German reommendations [1] limit the shear apait o the HC a to 50% and the permissile eam deletion to 1/00 L. This doument gives reommendations or the reinorement o the adjaent as joints, as ell as to their earing properties. DESIGN MODEL BY ROGGENDORF The model, similarl to the model Pajari-Leskelä, is ased on the assumptions or the rigid earings and on the same ailure riterion. Hoever, unlike the aove, it takes into aount the eets o raking in the interae eteen the eam and the HC a, as ell as eteen the HC a and illing onrete - oth o the eets appear ith inreasing the deletion o the eam. The inrease in the rak s idth in the joint results in appearing horizontal ompression ore in the upper elements o adjaent as in transverse diretion. It results in moving o the as along the longitudinal ais o the eam and emergene o the ond ore o rition. The horizontal ore is dependent on the value o the rition oeiient and the normal stress σ z. In the latter part o the alulations or the overmost a the value o transverse ore omp is put into pratie, hih arises at the time o the omposite ation appearane illing onrete in the onnetion (=µ omp ). Coeiient o rition µ is the main parameter o the model, depending on the harateristis o the interae surae, empiriall determined [8]. In order to determine the transverse shear stresses τ z and τ z the ross-setion o the HC as modeled as ierendeel truss (see Fig. 8). It is loaded the horizontal ompress ore and vertial line load v (the impat o ending eet), ausing internal ores in the outermost HC e.

5 JUNIORSTA 01.1 Conrete and Masonr Strutures Fig. 8 Idealized rame model or the as ross-setion Transverse ores rom the ompress ore, speiied or the outermost e in truss model are alulated (see Fig. 9): z. 1 h. e 1 n(.. j j n h n h. e. e h. l ). (8) (7) Fig. 9 Internal ores in the outermost e On the asis o the values o (7) and (8) the transverse shear stresses τ z, and τ z, ere determined : z kz. m I omp S. (9) z k z. m l omp. (10) here the oeiients k z. and k. depend on the geometr o the a and the quantit o HC es m. Beause o the diiulties in determining the earing properties (the presene and the tpe o elastomers, the earing length, the stiness o the ring eams) it is diiult to deine the omponents o the transverse stresses τ z,v and τ z,v. The eet o ending is onsidered throughout the empirial oeiient []. On the asis o the FEM analsis and the eperimental tests it as ound that the ending eet depends on the stiness o eam and the HC a stiness. The stier the as in ontrast to the eam are, the greater the eam deletion and the stress onentration net to the support. The dimensionless ratio o eam stiness to transverse stiness o the HC as, hih an e ritten in the orm o α = (EI /L )/(EI.q / ), etter aptures the ratio o transverse stiness o the a impat than the sole stiness o the eam in the orm o EI /L. 5

6 JUNIORSTA 01.1 Conrete and Masonr Strutures The ator k ν an e derived rom []: k v L EI 1 (11) EI. q The shear apait o the HC as on leile support an e alulated etending the equation rom the standard [6] (point...1) the omponents o stresses, inluding raking in the joint and their onsequenes: Rd. t. S (1 I omp k z. ( m ) td 1 d td ( 1 1 d td k v z. ) 5 CONCLUSIONS The design models Pajari-Leskelä and Roggendor ill a gap in design standards and provide helpul proedures to design the HC as on the leile supports. The are not ontraditor, ut rather omplementar to eah other, sine the are ased on the same eperimental tests (1 loor elements onsidering the distintions o HC as, eams and earings). Hoever, the main shortoming o the model Pajari-Leskelä is the omission o the non-linear eets e.g.: raks in the joint, hih the model Roggendor tries to take into aount. The parameters rom the tests on oth o the models e.g.: value o rition oeiient µ appearing ater raking o the joint or reduing stress oeiient takes into aount eets o illing holes β. an raise ertain douts. The main issue or the uture researh is onsidering the role o the topping and its introdution to the model Roggendor. LITERATURE [1] CAPUANO G.: The HC Floor Design and Appliations, erona, ASSAP, 00. [] HEGGER J., ROGGENDORF T., KERKENI N.: Shear apait o prestressed hollo ore as in im loor onstrutions. Eng. Strut., vol. 1, 009, p [] PAJARI M.: Shear resistane o prestressed hollo ore as on leile supports. TT Puliations 8, Espoo, [] ROGGENDORF T.: Zum Tragverhalten von Spanneton-Fertigdeken ei iegeiher Lagerung. Dissertation, Aahen, 010. [5] PAJARI M., YANG L.: Shear apait o hollo ore as on leile supports. TT Researh Notes 1587, Espoo, 199 [6] EN 1168:005+A:011 Preast onrete produts Hollo ore as [7] FIB Bulletin 6: Speial design onsiderations or preast prestressed hollo ore loors. Lousanne, 000. [8] PAJARI M.: Prestressed hollo ore as supported on eams. TT Working Papers 18, Espoo, 010. [9] LESKELÄ M., PAJARI M.: Redution o the vertial shear resistane on hollo-ore as hen supported on eams. Proeedings o Conrete `9 Conerene, vol.1, Brisane, 1995, p [10] WALRAEN J.C., MERCX W.P.M.: The earing apait o prestressed hollo ore as. Heron, vol. 8, 198, p [11] GIRHAMMAR U.A.: Design priniples or simpl supported prestressed hollo ore as. Strutural Engineering Revie, vol., 199, p [1] Code Card 18: Design o hollo ore as supported on eams, 007. [1] Allgemeine auausihtlihe Zulassung Z DIBt, 009. REIEWER Andrzej Seruga, PhD, Crao Universit o Tehnolog, The Civil Engineering Fault, Institute or Building Materials and Strutures, proessor, Warszaska, Krakó, POLAND, [email protected] p pd ) (1) 6