STRUCTURAL APPLICATION OF STEEL FIBRE AS PRINCIPAL REINFORCING: CONDITIONS - DESIGN - EXAMPLES.

Transcription

1 STRUCTURAL APPLICATION OF STEEL FIBRE AS PRINCIPAL REINFORCING: CONDITIONS - DESIGN - EXAMPLES. Xavier Destrée, Consultant, Structural engineer TrefilARBED, Luxembourg Abstract During the last ten years, the structural use of steel fibres as only principal reinforcing has been developed. Such a new technique where steel fibres replace completely all traditional rebars and meshes, has been used repeatedly in some applications: - Free suspended industrial slabs resting on a grid of piles when the ground doesn t present any bearing capacity. - Groung bearing general rafts as general foundation under tanks, office towers or shopping malls. - Bridge slabs. Technical conditions regarding steel fibres and concrete specifications are reviewed hereafter as well as design methods, shrinkage and testing. Two practical examples are outlined, among the m 3 completed so far. 1. Introduction The present article should be considered by the reader as following a former one cited in the references (ref.2), included in the proceedings of the «3 ème Colloque International francophone sur les bétons renforcés de fibres métalliques» organised on June 11 th 1998 by the CRIB Sherbrooke Laval. The reader today should as well refer to reference 1, authored by P. ROSSI, where basics of steel fibre reinforced concrete slabs in free suspended situation, are considered. Full scale testing up to ultimate loading, of SFRC suspended slabs, concludes and confirms that 1. The observed ultimate loading intensity results of a completely ductile rupture process where the suspended slab deforms along yield lines where all rotations are concentrated. 291

2 2. The observed ultimate loading intensity depending on the case investigated, ranges from 3 to 4 times the first crack flexural loading. 3. Regardless of the Point Loading intensity, the slab never punches out. 4. Yield lines moment of Johanssen can be back calculated. Each ultimate loading case being back-calculated, using the observed experimental pattern of yield lines, leads to the same yield line moment intensity in case of same concrete and thickness of slab. 5. The yield-line moment intensity back-calculated from full scale suspended slab testing, is confirmed by laboratory testing results when circular slabs are subjected to center point loading up to rupture. 2. Typical structural steel fibre reinforced concrete specification In order to ensure capability of the material to develop yield lines according to the theory of Johanssen, it is essential to: - saturate the matrix with closely spaced steel fibres, taking into account the concrete aggregate grading as well as the maximal size of aggregate. - use fibres with the best possible anchoring to the matrix. Moreover the mix needs to remain completely workable and quite often pumpable. Two types of steel fibres have been used so far: - the Twincone type, a straight 1 mm diameter, 54 mm length, 1100 MPa wire fibre provided with conical ends anchoring as shown here below. - the Tabix Plus type, an undulated 1 mm diameter, 60 mm length, 1500 MPa wirefibre. Both Tabix Plus and Twincone are almost total anchorage fibres with a minimum fibrematrix relative displacement and showing a steel working stress of up to 900 MPa. In both cases, the dosage rates commonly used are 40, 45, and 50 kg/m³. The mix design should be as follows: - continuous aggregate grading from 0 to 20 mm. - cement type CEM I or III at kg/m³ content. - W/C ratio < 0.50 (W: free water) with a 30 to 60 mm slump of plain concrete. - required workability using a HRWRA (super Plasticizer), taking into account a loss of slump between 40 and 80 mm after introduction of steel fibres. The installation of the fibre concrete on site is with light surface vibration only. 292

3 3. Testing All standard testings are used to check the conformity with the specifications outlined in 2. Standard beam specimen flexural testings (small 450 x 150 x 150 mm³ prismatic specimen) are of very little help here as it is impossible with them to observe any yield line. To observe yield lines and confirm rupture patterns observed with full scale testings, a simple method of testing has been developed. It consists in centre point loading of circular plates spanning at least 10 times their thickness. A typical 150 mm x 1500 mm testing set up as outlined in ref.1 (P. Rossi) p 161, enables to record a flexion diagram shown on fig.1. TABIX PLUS 1/60: 40 and 50 kg/m 3 TWINCONE 1/54: 45 kg/m 3 Fibres, C 40 concrete Fig. 1: Statical testing: center point loading Flexion diagram The final rupture pattern is the typical FAN pattern where the expression of the equilibrium of rotation of one circular sector gives: P ultimate = 2π M L where M L is the yield line moment of Johanssen. 293

4 The testing method seems to be very accurate with almost no dispersion of results, as different batches of the same mix design don t deliver different flexion diagrams. It is indeed a structural type of testing to demonstrate formation of yield-lines as opposed to small prismatic beam specimen testing being only a material testing. 4. Design Based on the analysis of results of full scale testings and circular plates laboratory testing, a plastic design according to the yield lines theory of Johanssen has been adopted. a. Plastic design This method is based on a pattern of yield-lines where almost all deformations are concentrated due to plastic rotation, and is such that: the moments of flexion acting on the yield lines are constant and equivalent to M L moment the elastic deformation is neglected the moments comply with the contour conditions at no section of the slab does the moment exceed M L b. Rupture mechanism The rupture mechanism to be considered is the least favourable for the proposed load and support, i.e. giving minimum ultimate loading intensity P ULT. c. Typical rupture patterns are considered in case of uniformly distributed loading: Central panel 1) Uniform thickness of slab (flat bottom slab) p ULT * L 2 N = 16 M L 45 LN L N is always calculated at the mid-depth of the slab 294

5 2) Pile heads LN h L LN H L N =span; h = thickness of the floor H =thickness of the floor and the pile heads; L =bearing from axis to axis; L N = L - p 2H + h p ULT * L 2 N = 16 M L d. Rupture pattern under leg loading Central panel Load on 4 rack feet p L P 4 P 4 P 4 P 4 L b b P ULT * L N = 8 M L * b b: distance between the axis of the aisles e. Simply supported edge panel edge panel H LN h beam p 295

6 L N = p h L H with restraint: p ULT * L 2 N = 16 * M L with single support: p ULT * L 2 N = 12 * M L f. Safety on rupture and design criteria Taking into account a safety on rupture s = 2.25, the following conditions should be fulfilled with: G MAX : own weight + permanent load Q I : variable load P (4 feet) = P rack ( 1.35 * G MAX * Q I ) * L 2 N 16 * M L 1.5 (central panel or restrained edge) ( 1.35 * G MAX * Q I ) * L 2 N 12 * M L 1.5 (single support edge panel) P (4pieds) *1.5*L 8b + G MAX *1.35+Q I * * L 2 M L 1.5 (central support with 4 rack feet) The flexural stress in service conditions is however limited to 5 N/mm Shrinkage As shown in 4.Design, flexural cracking under service loading is excluded, keeping in mind that the slab is completely cracked with a closely spaced pattern of minute cracks as there is an overall drying shrinkage movement restraint. The contraction movement restraint is generated by the contact with pileheads, the large bay size (2000 or 3000m² ) and then, the length of the bay up to 60m or even more in some cases. The random pattern of closely spaced cracks is quite helpful as it creates an overall shrinkage stresses relief. At this stage, the slab is no longer elastic. The bulk of the observed shrinkage cracks, according to the experience, are within 0.1mm to 0.5 mm range of opening and a maximum of 0.75 mm. We can compare with the theory derived from laboratory testing on free and on restrained shrinkage specimen of steel fibre reinforced concrete. According to Grzybowski and Shah (ref. 4), in restrained condition a 0.5% or 40 kg/m³ Steel fibre reinforcing, reduces the total crack opening by a factor 4 with reference to a plain mix. 296

7 According to Mangat and Azari (ref. 3), in free shrinkage condition a 0.5% steel fibre reinforcing reduces the free contraction by 10% with reference to a plain mix. We can now try to predict the structural fibre reinforced slab cracking in comparing to a simplistic prediction for plain concrete. The plain concrete cracking can be estimated as follows: E= N/mm² (at long term and in tension) Tensile strength = 3N/mm² and hence: Total drying shrinkage contraction: , quite a realistic value in case of W/C<0.5 of a carefully cured slab subjected to regular internal condition of temperature and humidity. This means one single crack of 3 mm opening every 10 m distance in case of a plain concrete. The fibre reinforced concrete should then crack as follows: 3mm x 90 %( reduction of free contraction ) x ¼ (total cracking reduction) = 0.67 mm and 2.5 m spacing. The experience shows that 0.67 mm opening is exceptional and that the observed cracking is of less opening at a closer spacing. 6. Examples of realisation a) Carlsberg Tetley Depot of m 2 (UK, completed in 1998) Example of application of structural free suspended steel fibre reinforced concrete. The data are summarised as follows: Pile grid = 3.60 m x 3.60 m - Pile head diameter = m UNIFORMLY DISTRIBUTED LOADING = 50 KN/m 2 RACKING LEG LOAD = 65 KN each placed back to back at 200 mm distance. The design of the slab as completed, was: Thickness: 250 mm, Concrete: C40 Fibre: TABIX PLUS 1/60 at 45 kg/cu.m dosage rate 297

8 As seen on the fig.2, the slab is designed with a flat bottom m spacing Slab thickness 250 mm 3.60 m spacing Fig. 2 Pile heads Dia : 600 mm b) Free suspended elevated slab only TWINCONE reinforced carrying the high speed train track (slab completed in 1995) (Fig.5 and Fig.6) TGV Line PARIS-BRUSSELS Bridge Slab over highway E42 at MAUBRAY (BELGIUM). The bridge slab of Length L = m x width W = m consists in a 400 mm thick TWINCONE CONCRETE SLAB, poured on PREFLEX COMPOSITE (Fig.3) TRANSVERSAL beams at m distance between each other. The clear span of the 400 mm thick TWINCONE SLAB is m. (Fig.4) 45 kg/m 3 of TWINCONE fibres is the only reinforcing of the slab. CONCRETE TYPE: C 40/50 298

9 HST TRACK PARIS BRUSSELS HIGHWAY HIGHWAY L=69.74 m x W=11.90 m 3,487 m between each composite PREFLEX beam Fig.3: Overall view on TGV/HST bridge slab TWINCONE concrete at 45 kg/ m 3 Fig.4: Cross sectional detail showing a preflex composite transversal beam and the TWINCONE concrete slab 299

10 Fig.5: Overall view of the TGV/HST bridge over Highway E42 Fig.6: Detailed view where PREFLEX COMPOSITES BEAMS are visible, together with TWINCONE SLAB spanning 3,487 m. 300

11 7. Conclusion Steel fibres are now used constantly as only reinforcement of concrete in free suspended slab applications. It results in tremendous cost savings and speed-up of slab installation omitting all traditional rebars as well as a better cracking control. On the other hand, more attention is needed regarding the concrete specification and supply. A disadvantage is the absence of any reference standard yield line testing method. 8. References 1. Les bétons de fibres métalliques, Pierre Rossi Presses de l Ecole Nationale des Ponts et Chaussées, 1998 pp and Troisième Colloque international francophone sur les bétons renforcés de fibres Métalliques LAVAL/CRIB, 1998 Planchers structurels en béton de fibres : justification du modèle de calcul. X. Destrée 3. Shrinkage of steel fibre reinforced cement composites. P.S. MANGAT, M. AZARI Materials and Structures, 1998 pp Shrinkage Cracking of Fiber Reinforced Concrete GRZYBOWSKI and SHAH ACI Materials Journal, March-April 90 pp