Flat slabs with spherical voids. Part I: Prescriptions for flexural and shear design

Transcription

1 Ata Tehnia Napoensis: Civil Engineering & Arhiteture Vol. 56, No. 1 (2013) Journal homepage: Flat slabs with spherial voids. Part I: Presriptions for fleural and shear design Mihai Bindea *1, Dumitru Moldovan 2, Zoltan Kiss 3 1,2,3 Tehnial University of Cluj-Napoa, Faulty of Civil Engineering. 15 C Daioviiu Str., , Cluj- Napoa, Romania Reeived 26 February 2013; Aepted 15 August 2013 Abstrat Muh of the volume of onrete plaed in any ivil struture is given by the floor system(s) used. The advent of new solutions that inorporate spherial hollow ores reate the premises for providing adequate guidelines to be used by pratiians, suitable to aommodations for a variety of onsite onditions. The here-in researh programme is aimed at answering the fundamental question of strutural behaviour for suh floor systems, subjeted to fleure and shear, as well as their limits of use. Rezumat Mare parte din volumul de beton pus în operă într-o strutură ivilă este reprezentat de sistemul de planşeu utilizat. Apariţia unor soluţii are înorporează goluri sferie reează premisele pentru a furniza pratiienilor de pretutindeni îndrumări lare, adaptabile situaţiilor onrete din pratiă. Studiul prezentat în ontinuare doreşte să răspundă unor întrebări fundamentale, preum omportarea struturală sau limitele utilizării aestora. Keywords: onrete slab, flat plate, spherial hollow ores, ommerial solutions, shear strength 1. Introdution Among the ast-in-plae floor systems in use for multistorey high strutures, flat plates are ommonly used based on the ability to fulfil tehnial and funtional requirements as well as the inreased speed of onstrution. Sine dead loads (own weight) of the floor system inreases as openings are inreasing, the middle height of the ross setion an be replaed (frequently) by (plasti spherial) hollow ores (Fig. 1), as it does not ontribute to the resistive apaity or the durability of the member. This solution allows the floor system to work two-ways while reduing own dead load. Some of the advantages of using a spherial hollow ore flat plate as ompared to the full flat plate are: - Redution in the volume of materials used in the struture (both onrete and steel) not just for the floor themselves; - Redution of labour osts and labour time for all trades involved in plaing reinforing bars; * Corresponding author: Tel./ Fa.: address: mihai.bindea@dst.utluj.ro

2 - Inrease openings while dereasing the no. of olumns, providing thus improved arhitetural floor layout and more lear volume; - Redution of the arbon dioide footprint reated by industrial ativities assoiated with its prodution; - Ahieve sustainability by use of reyled plasti materials for the hollow ores; Some disadvantages, inherent to any hollow ore system, that impair the use in atual pratie are: - Redution of setional rigidity; - Redution of punhing shear apaity; - Redution of shear apaity; Sine the advantages may be onsidered to out-weight the disadvantages, it may be appropriate to researh the appliability of this floor system as well as its limits, onsidering only the gravitational loads applied. Figure 1. Details for the spherial hollow ores flat slab system [2] [1]. 2. Generi details on loading levels In terms of maimum fores, flat plates develop maimum bending moments in edge strips at joints with supporting olumns as well as negative bending for the slab. Suh areas are subjeted also to punhing shear, therefore the hollow ores should be eliminated from the ross setion around the head of the olumn. In turn, the negative bending that develops around the resting areas on the olumns for a spherial hollow ore flat plate is idential in its harateristis with a full flat plate. Figure 2. Main parameters for fleural design Aording to EC2 [3] the ompressive stress blok for onrete may be assumed to be retangular. As long as the neutral ais lies above the upper limit of the hollow ores (top onrete area) there is no differene in terms of fleural design in-between the hollow and full flat plate (see Figure 2, illustrating the ase 0 with o the onrete over for the plasti ores). When the neutral ais lies lower so that it intersets the hollow ores, it is assumed that onrete surrounding the hollow ores an work spatially (the onrete strut varies from full height of the setion in-between two 68

3 onseutive hollow ores, to minimum for the vertial diameter passing through the spheres). It is therefore mandatory to study the parametri evolution of the neutral ais, for the inner middle span of an edge strip, for various load levels using approimate alulations methods, suh as the oeffiients method presented in [4] assuming a uniform layout for the supporting olumns (square bay). The parameters tested are: - openings: L= m; - load level: q k = kn/m 2. Tables 1 and 2 present the results of this analysis, while Figures 3 and 4 show the variation of the neutral ais as a funtion of the fore-mentioned parameters. Table 1: The neutral ais position for various load levels (inner panel) L h ne h eff o q k =5.0 kpa q k =10.0 kpa [m] [mm] [mm] [mm] p [%] [mm] o / p [%] [mm] o / Table 2: The neutral ais position for various load levels (end panel) L h ne h eff o q k =5.0 kpa q k =10.0 kpa [m] [mm] [mm] [mm] p [%] [mm] < o? p [%] [mm] < o? It may be onluded that for inner panels the perentage of reinforement is less than 0.50% for all load levels, while for end panels this threshold is not respeted only for load levels greater than 5.0 kn/m 2. In the ase of inreased load levels, the reinforement perentages inrease but are still below 0.8%. The neutral ais position is different for inner and end panels only for load levels bigger than 5.0 kn/m 2. Below this threshold, the neutral ais is always above the hollow ores for all load levels in all inner panels, while in end panels, the neutral ais lies somewhere at the hollow ore level only for load levels greater than 5.0 kn/m 2. 69

4 Figure 3. Inner panel neutral ais variations. Figure 4. End panel neutral ais variations. 3. Shear design for spherial hollow ores flat plates In terms of fleural design, as long as live loads fulfil the 5.0 kn/m 2 threshold, there are no differenes as ompared to the full flat plate. The situation is very muh different in terms of shear design, sine the presene of hollow ores hanges the behaviour of the member. Several models are presented net, with speial emphases on EC2 [3] and ModelCode2010 [5]. 3.1 Aording to EC2 [2], for no shear reinforement For a strip of 1 m in width: 1 VRd CEd k l f k 3,, k1 p bw d (1) But not less than VRd, min k1 p bw d (2) 70

5 Figure 5. Minimum width b w aording to EC2 [3]. 3.2 Aording to Model Code 2010 [4], for no shear reinforement Several models may be used depending on the ompleity and therefore the results intended MC 2010 [5]. The resistive apaity of onrete is: f k VRd, k z bw (3) with a maimum value of 8 MPa for f k. The k oeffiient may be determined for three degrees of approimation as: 200 k 0.15 first degree (4) z k 0 seond degree (5) k 0.15 third degree (6) k z dg with is the longitudinal strain in onrete measured at half the depth of the ross setion M Ed z VEd 0.5N Ed Ap f p0, (7) 2 E A E A dg s s p p k is a oeffiient taking into aount the maimum aggregate size 48 k dg 1.15 (8) 16 d g f p0 is the stress for tendons when the orresponding level onrete has nil strains d g is the maimum aggregate size It may be onluded that previously ited referenes have in ommon the use of the minimum width in tension b w. Considering the situation of a setion plan plaed perpendiular to a transverse row of ores and summing the onrete areas in-between those, it may be onluded that b w is 10% of the orresponding dimension for a full flat plate leading to a resistive apaity in shear that is about 90% less. 3.3 Aording to BubbleDek [8] and Cobia [7] BD DP V Rd 0.6 VRd, with, (9) V, is the shear apaity of the full flat plate having the same height and transverse DP Rd reinforement as Eq. (3). 71

6 The above inde of 0.6 was established empirially after analysing a series of researh programmes from Denmark, Germany or Netherlands [6]. M. Aldejohann [7] proposed the net equation in 2009: ADG V Rd, DG k DG VRd,, (10) ADP with o k DG , if (11) o k DG , if (12) 0 is the onrete over for the hollow ores, is the position of the neutral ais, A DG is the area of onrete given by a 45 o degrees tilted plan interseting the entre of a transverse row of hollow ores. Figure 6. Establish area A DG aording to [7] It may be onluded that taking into aount the frequeny of load levels on flat slabs, sine the ratio of 0 over is bigger than 1.2 Eq. (10) may be applied only for inreased openings and loads. 4. Conlusions Sine hollow ore flat plates for retangular strutural layouts are supporting medium load levels that plae the neutral ais somewhere on top of the hollow ores, giving reinforement perentages lower that 0.5% with the eeption of middle spans for higher load levels, it may be onluded that urrent EC2 [3] fleural design model may be suessfully used in design, similar to a full flat plate. Similar onlusions annot be etrapolated for shear design, sine both the EC2 [3] and MC 2010 [5] provide diminished values for the hollow ores flat plate as ompared to the full flat plate. Eq. (10) may be used suessfully instead for medium and high load levels. For low load levels additional researh is mandatory to fully establish the shear behaviour. 5. Referenes [1] [2] [3] SR EN , Euroode 2: Proietarea struturilor de beton, Partea 1-1: Reguli generale şi 72

7 reguli pentru lădiri. [4] GP , Ghid pentru proietarea planşeelor dală în zone seismie, Buureşti, februarie [5] Fib Speial Ativity Group 5, Model Code 2010 First Complete Draft, marh [6] Călin, S., Gînţu, R., Dasălu, G., Summary of tests and studies done abroad on the BubbleDek system, Buletinul Institutului Politehni Iaşi, Seţia Construţii. Arhitetură, Tomul LV (LIX), Fas. 3, 2009, pp [7] Aldejohann, M., Zum Querkrafttragverhalten von Hohlkorperdeken mit zweiahsiger Lastabtragung, Dissertation Der Fakultat fur Ingenieurwissenshaften, Abteilung Bauwissenshaften der Universitat Duisburg-Essen, Essen 2008, [8] BubbleDek UK Head Offie, BubbleDek Voided Flat Slab Solution Tehnial Manual and Douments, June