Structural Design of LoadBearing Fibre Concrete Structures Johan Silfwerbrand KTH Royal Institute of Technology, Stockholm Finnish Concrete Day, Helsinki, Oct. 23, 2014 Oct. 23, 2014 J Silfwerbrand, KTH 1 Fibre Concrete Outline Historical background Swedish committee work Presentation of the new Swedish standard for designing fibre concrete structures Concluding remarks Oct. 23, 2014 J Silfwerbrand, KTH 3 Historical Background Fibre concrete (FC) origins from the 19th century, there is an American patent from 1874. The modern development of FC started in USA in the mid 1950s. Swedish handbook on rock strengthening using shotcrete (Holmgren, 1992). Swedish report on steel fibre reinforced concrete (Svenska Betongföreningen, 1995). Swedish report on industrial concrete floors (including FC) (Svenska Betongföreningen, 2008). Swedish standard on design of FC structures (SIS, SS 812310:214, 2014). Oct. 23, 2014 J Silfwerbrand, KTH 4 Shotcrete for Rock Strengthening Oct. 23, 2014 J Silfwerbrand, KTH 5 Industrial Concrete Floors Fraktarna, Stockholm, 2001. Foto J Hedebratt. FC in Elevated Slabs J Hedebratt, 2012 Swedish Committee Work Aim: Guidelines for designing load-carrying fibre concrete structures. Start: 2007. Original aim: Addition to the Swedish strucutral concrete handbook BBK 04. But Eurocode 2 was introduced in Sweden in 2009. New aim: Addition to Eurocode 2. Draft version: Summer 2013. Release of printed version: Spring 2014. Oct. 23, 2014 J Silfwerbrand, KTH 8 Introduction 1 (2) The aim of the standard is to provide Swedish national guidelines for designing load-carrying FC structures according to Eurocode 2. The standard uses the same headings and numbering as Eurocode 2. Repetitions have been avoided, why the standard has to be read parallel to Eurocode 2. The language of the standard is English. Oct. 23, 2014 J Silfwerbrand, KTH 9 Introduction 2 (2) On purpose, the committee selected the word fibre concrete instead of steel fibre concrete or steel fibre reinforced concrete. The idea is that the standard should be materialindependent regarding fibre material. The standard authors are know that current synthetic fibres do provide rather modest performance if the fibre content is not enhanced substantially (which in turn may cause mixing & casting problems). Oct. 23, 2014 J Silfwerbrand, KTH 10 Aim The Standard applies to the design of buildings and other civil engineering works with steel or polymer fibres according to EN 14889-1 & EN 14889-2. The Standard does not cover glass, carbon, basalt or any other type of fibres. The Standard is intended to be used in conjunction with EN 1992-1-1 Eurocode 2 Design of concrete structures – Part 1-1 General rules & rules for buildings -1: Fibres for concrete - Part 1: Steel fibres – Definitions, specifications and conformity -2: Fibres for concrete - Part 2: Polymer fibres – Definitions, specifications and conformity Oct. 23, 2014 J Silfwerbrand, KTH 11 The Content is Connected to Eurocode 2 1 General 2 Bases of design 3 Materials 5 Structural analysis 6 Ultimate Limit State (ULS) 7 Serviceability Limit State (SLS) 8 Detailing of reinforcement and prestressing tendons – General 11 Lightweight aggregate concrete structures Oct. 23, 2014 J Silfwerbrand, KTH 12 Annexes O. P. Q. R. Calculations of strains & stresses in bending Production & conformity control of fibre concrete Execution control of fibre concrete Expected coefficient of variation for beam tests according to SS-EN 14651 S. Fibre concrete, statically indeterminate structures, and magnification factors Oct. 23, 2014 J Silfwerbrand, KTH 13 Definitions English Svenska Kommentar Fibre concrete Fiberbetong … the concrete matrix provides compressive strength & protection of the fibres whereas the fibres provide tensile strength … Steel fibre Stålfiber SS-EN 14889-1 Polymer fibre Polymerfiber SS-EN 14889-2 Designed concrete Betong med föreskrivna egenskaper SS-EN 206 Prescribed concrete Betong med föreskriven sammansättning SS-EN 206 1.5.2 Oct. 23, 2014 J Silfwerbrand, KTH 14 Basis of Design Structural components shall have structural system stability in ULS after a fully developed crack system though 1. Stress redistribution in statically indeterminate systems, 2. Combination of steel bar reinforcement or pretensioned steel reinforcement with fibre concrete. 3. External normal forces maintain equilibrium. 2.3.2.1 Oct. 23, 2014 J Silfwerbrand, KTH 15 Shrinkage & Creep 1 (2) Shrinkage & creep shall be considered in ULS through 1. Stresses caused by restrained shrinkage & creep are superposed to mechanical stresses (theory of elasticity) or 2. Effects of shrinkage & creep are considered by increased ductility demand – in practice: design for fR,3 instead of fR,1 or for fR,4 instead of fR,2. (theory of plasticity). 2.3.2.2 Oct. 23, 2014 J Silfwerbrand, KTH 16 Shrinkage & Creep 2 (2) In case of bending, distinguish between compressive creep & flexural creep. In case of polymer fibre concrete, long-term tests should be conducted (at elevated temperature if such temperature occurs in reality). 2.3.2.2 Oct. 23, 2014 J Silfwerbrand, KTH 17 Partial Factors for Materials Design situations c for concrete s for s for pre- reinforcing stressing steel steel f for fibre concrete Persistent & transient 1,5 1,15 1,15 1,5 Exceptional 1,2 1,0 1,0 1,2 SLS 1,0 1,0 1,0 1,0 2.4.2.4 Oct. 23, 2014 J Silfwerbrand, KTH 18 Testing Fibre Concrete 3 point bending tests on notched FC beams according to SS-EN 14651 fR,i = (3/2)(FR,il)/(bwhsp); i = 1, 2, 3, 4 Oct. 23, 2014 J Silfwerbrand, KTH 19 Testing FC According to Svenska Betongföreningen F/2 F/2 h l/3 l/3 l/3 b l = 450 mm, b = 125 mm, h = 75 mm Flexural Tensile Strength According to Svenska Betongföreningen (1) Cracking strength (3) Residual strength (2) Ultimate strength Max flexural stress fflu fflcr fflres 2 3 1 cr 5.5cr 10.5cr 15.5cr Midspan deflection Residual Flexural Tensile Strength Characteristic residual flexural tensile strength of fibre concrete = characteristic value of the flexural tensile strength after cracking ffl,res = R10,Xffl,cr/100; X = 20, 30, 40, … Comparison between the international EN 14651 & the Swedish SBF test method: fR,1 ≈ R10,20ffl,cr/100 fR,2 ≈ R10,30ffl,cr/100 Oct. 23, 2014 J Silfwerbrand, KTH 22 Classifying Residual Flexural Tensile Strength 1 (3) Classes defined for all four levels of the residual flexural tensile strength fR,1, fR,2, fR,3 & fR,4 For everyone, six steps with the interval = 1,0 MPa. In total: 4×6 = 24 classes. Residual flexural tensile strength are determined thrugh beam testing according to SS-EN 14651 after 28 days. The classes are based on the characteristic value (lower 5 % fractile). 3.5.1 Oct. 23, 2014 J Silfwerbrand, KTH 23 Classifying Residual Flexural Tensile Strength 2 (3) Class R1 fR,1 Class R2 MPa fR,2 Class R3 MPa fR,3 Class R4 MPa fR,4 MPa R11 1.0 R21 1.0 R31 1.0 R41 1.0 R12 2.0 R22 2.0 R32 2.0 R42 2.0 R13 3.0 R23 3.0 R33 3.0 R43 3.0 R14 4.0 R24 4.0 R34 4.0 R44 4.0 R15 5.0 R25 5.0 R35 5.0 R45 5.0 R16 6.0 R26 6.0 R36 6.0 R46 6.0 3.5.1 Oct. 23, 2014 J Silfwerbrand, KTH 24 Classifying Residual Flexural Tensile Strength 3 (3) Example of classifying: C30/37 – R13/R32 Compressive strength = 30 MPa (cylinder) 37 MPa (cube) Residual flexural tensile strength = 3 MPa in class R1 Residual flexural tensile strength = 2 MPa in class R3 All values = characteristic values 3.5.1 Oct. 23, 2014 J Silfwerbrand, KTH 25 Prerequisite on Fibre Concrete C1 = 100×fR,1/fctk,0,05 ≥ 50 % 100×fR,3/fR,1 ≥ 50 % The intention is to ensure a certain ductility of the fibre concrete. 3.5.1 Oct. 23, 2014 J Silfwerbrand, KTH 26 Bending Hardening or Bending Softening? 3.5.1 Oct. 23, 2014 J Silfwerbrand, KTH 27 Characteristic Residual Tensile Strength f ft,R1 0,45 f R,1 f ft,R3 0,37 f R,3 3.5.1 Oct. 23, 2014 J Silfwerbrand, KTH 28 Design Residual Tensile Strength Ultimate Limit State (ULS): f ftd,R1 f det f ft,R1 f f ftd,R3 f det f ft,R3 f Serviceability Limit State (SLS): f ftd,R1 f Oct. 23, 2014 f ft,R1 f 3.5.2 J Silfwerbrand, KTH Fibre Orientation Factor f Factor considering the fibre orientation in the concrete. f ≥ 0,5 For horizontally cast concrete members, set f = 1,0 (width > 5×thickness). For other members, select 0,5 < f ≤ 1,0 dependent on member dimensions, fibre length, & casting procedure. For SLS, f = 1,0. 3.5.2 Oct. 23, 2014 J Silfwerbrand, KTH 30 Factor Considering Degree of Statically Determination det Statically indeterminate structures provides possible stress redistribution. There are several cross sections to consider. The probability that several cross section have low strength is less than the probability for just one single low strength cross section (= the case for statically determinate structures). Slabs have considerably larger possibilities to stress redistribution than beams. Annex S is a background document for the tabled values. 3.5.2 Oct. 23, 2014 J Silfwerbrand, KTH 31 Values of the Factor det 1 (3) Case Type of structural member No det 1 2 1 1,4 3 4a Statically determinate beams Statically indeterminate beams Rectangular slabs with 2 opposite edges simply supported (others free) Simply supported circular slabs 1 1,4 3.5.2 Oct. 23, 2014 J Silfwerbrand, KTH 32 Values of the Factor det Case Type of structural member No 4b Rectangular slabs with ≥ 3 edges simply supported 5a Circular slabs with clamped edges 5b 5c Rectangular slabs with ≥ 1 edge clamped (others simply supported) Slabs-on-grade 2 (3) det 1,4 2 2 2 3.5.1 Oct. 23, 2014 J Silfwerbrand, KTH 33 Values of the Factor det Case Type of structural member No 5d Interior spans of pile-supported slabs 5e Interior spans of columnsupported slabs 5f Interior spans of simply supported continuous slabs 3 (3) det 2 2 2 3.5.1 Oct. 23, 2014 J Silfwerbrand, KTH 34 ULS – Bending Moment c fcd c = fcd c = fcd c x fctd fftd,R1 st ft ftu x x fftd,R1 fftd,R3 Fst = st Ast Fst = st Ast ft fftd,R3 ft fftd,R3 a) a) General stress distribution b) 1st simplified distribution c) 2nd simplified distribution Fst = st Ast fftd,R3 b) ft f ftd,R 1 c) ft f ftd,R 1 f ftd,R 3 ftud 6.1 Oct. 23, 2014 J Silfwerbrand, KTH 35 ULS – Shear In cases without shear reinforcement: VRd,cf 1/ 3 0.18 f ct,R3 f ck 0.15 cp bw d k 100 1 7.5 f ctk C Fibre contribution Conventional reinforcement is needed. Consciously choice of the committee (safe side). The equation is based on an Italian proposal that has been found to represent test data from the literature best (Mondo, 2011). 6.2.2 Oct. 23, 2014 J Silfwerbrand, KTH 36 ULS – Punching In cases without shear reinforcement: 1/ 3 f ct,R3 0,18 f ck 0,15 cp k 100 1 7,5 vRd,cf C f ctk Fibre contribution For FC ground-supported slabs & column bases without conventional reinforcement: vRd,cf = vRd,f = (k/2)CfR,3/f k = thickness dependent factor in EC 2, 6.2.2 C = constant = 0,45 6.4.4 Oct. 23, 2014 J Silfwerbrand, KTH 37 Recommended Values of Max Crack Width wmax (mm) Exposure class L50 L100 Note X0, XC1 - - Crack width does not influence durability. XC2, XC3 0,5 0,4 XC4 0,4 0,3 XS1, XS2, XD1, XD2 0,3 0,2 XS3, XD3 0,2 0,1 Combination with reinf. necessary. The values deal with the case ”fibres only” considering durability. 7.3.1 Oct. 23, 2014 J Silfwerbrand, KTH 38 Minimum Reinforcement As, min s k c k 1 k f f ct,eff Act f ftd,R1 kf 1 .0 f ct m 7.3.2 Oct. 23, 2014 J Silfwerbrand, KTH 39 Control of Cracking without Direct Calculation s,f s s As b 4 h d f ct,0 1 1 k f 2 s f ct,eff f ct,0 1 1 k f 2 s,f = modified bar reinforcement size for FC s = steel stress according to EC 2, Table 7.2N As = tensile reinforcement area h = section height d = internal level arm for the bar reinforcement b = width of the tensile zone fct,0 = 2,9 MPa 7.3.3 Oct. 23, 2014 J Silfwerbrand, KTH 40 Computation of Crack Widths The calculation is based on the same principle as used for RC in EC 2. Calculate characteristic crack width wk. Calculate strain difference (sm-cm) using one of two alternatives. Calculate max crack spacing sr,max. Calculate max crack width at bending wmax. Calculate max crack width for restraint stresses wmax. 7.3.4 Oct. 23, 2014 J Silfwerbrand, KTH 41 Minimum Reinforcement in Beams Minimum reinforcement: As,min = Ac(kcfctm – fdetfct,R3)/fyk Condition for ”fibre only” cases: fdetfct,R3 > kcfctm Ac = tensile concrete area (in bending), hct = h/2 kc = stress distribution coefficient (in bending) 9.2.1.1 10 sept 2014 J Silfwerbrand, KTH 42 Concluding Remarks Finally, there is a standard for designing loadbearing FC structures! The expectation is that this standard shall provide the structural engineers with an additional alternative. It is essential that the guidelines are solid and solidly supported by the society. New fibres are welcome but new fibre concretes have still to fulfil the requirement and the spirit of the guidelines. Do not put fibres against conventional reinforcement – combination is in many cases the optimal solution. Oct. 23, 2014 J Silfwerbrand, KTH 43

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