Workshop on FIBER REINFORCED CONCRETE (FRC): MATERIALS, APPLICATIONS AND DESIGN ASPECTS

Transcription

1 Workshop on FIBER REINFORCED CONCRETE (FRC): MATERIALS, APPLICATIONS AND DESIGN ASPECTS UNIVERSITY OF SHARJAH, UNITED ARAB EMIRATES APRIL 2018 ORGANIZED BY Sustainable Construction Materials and Structural Systems Research Group, Department of Civil & Environmental Engineering, University of Sharjah SPONSORED BY University of Brescia, Italy Sharjah Research Academy, UAE JOINTLY WITH Structural Design Research Group, University of Brescia (Italy) KEY SPEAKERS Prof. Giovanni Plizzari, University of Brescia, Italy Prof. Salah Altoubat, University of Sharjah, UAE Prof. Mohamed Maalej, University of Sharjah, UAE Dr. Moussa Leblouba, University of Sharjah, UAE

2 Workshop on FIBER REINFORCED CONCRETE (FRC): MATERIALS, APPLICATIONS AND DESIGN ASPECTS UNIVERSITY OF SHARJAH, UNITED ARAB EMIRATES APRIL 2018 Fiber Reinforced Concrete Design concepts Prof. Salah Altoubat Department of Civil & Environmental Engineering SCMASS Research Group College of Engineering University of Sharjah

3 Outline 1. Introduction 2. Design concepts 3. Design for flexure 4. Design for flexure hybrid reinforcement 5. Design Examples 6. Slab on Ground Design 7. Design Example 8. Design for shear

4 1. Introduction Fibers influence the mechanical properties of concrete in all failure modes (compression, tension, shear, ); The most important variables governing the properties of FRC include: fiber bond efficiency (controlled by pullout test) and dosage rate; When a concrete matrix is subjected to tension, 12 stresses are transferred by interfacial shear. When the 13 matrix cracks, the stress gets transferred to the fibers, progressively; This process results in: increase in the load carrying capacity, the energy dissipation, and the ductility at serviceability and at ultimate limit design states for FRC. 5 The stages involved in FRC failure is schematically shown in Figure 1 and are summariz 6 as: 1) cracks form in cement matrix, 2) debonding and sliding between fiber and ma 7 8 bonded fiber bridging the cracks, 4) frictional sliding, deformation of anchorage, and e fiber pullout, and 5) potential fiber failure under tension. For specific types or geome 9 fibers, not all, or only some of the described stages may occur. The load level (or stres 10 carried by fibers in a cracked concrete section is referred to as residual load (or residual 11 cracking stress). The area under the load-deflection curves is the energy absorbed by t 14 system and is referred to as toughness and which is used for design purposes. Figure 2 different stages of crack control for an FRC beam under a flexural load test. There are, h certain types of fibers that do not pull out of the matrix, but elongate and provide the toug

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6 What do structural fibers add to concrete Material level 1) Toughness 2) Ductility FRC: Substantially enhance the postcracking response of the composite (toughness). Post-cracking response: is evaluated through toughness testing Toughness: area under the load deformation curve Structural level 1) Yield capacity, post-cracking capacity 2) Rotational capacity 3) Residual strength Toughness and ductility are key properties that Fibers impart to concrete structure 3) Yield strength

7 Where does FRC as structural material stand? Material characterization Structural Performance Structural design 1) Test Standards ASTM C 1609 JCI-SF 4 ASTM 1399 ASTM 1550 EN ) Specification 1) Demonstrated by experiment 2) Structural tests and models Progressing in North America Recognized in Europe Well established Recognized at research level Progressing

8 Requirements When fibers are intended to contribute to the structural performance of an element or structure, the FRC needs to be designed accordingly and the fibers contribution to the load-bearing capacity needs to be properly assessed and justified. Fibers intersect cracks when they initiate. This allows for a uniform distribution of the stresses that develop and slow down crack propagation

9 ACI 544: Fiber Reinforced Concrete ACI544-9R, and ACI 544.2R-17: Report on the Measurement of Fresh State Properties, Mechanical Properties, and Fiber Dispersion of Fiber-Reinforced Concrete ACI 544.8R-16 Report on Indirect Method to Obtain Stress-Strain Response of Fiber- Reinforced Concrete ACI544-4R: Design Guide for Fiber Reinforced Concrete 544.6R-15 Report on Design and Construction of Steel Fiber-Reinforced Concrete Elevated Slabs 544.7R-16 Report on Design and Construction of Fiber-Reinforced Precast Concrete Tunnel Segments ACI 544.5R-10 and New Document on Testing, Creep, Shrinkage, Service life, Crack Width Prediction

10 1. Introduction Since the fibers are randomly distributed with small spacing (compared to typical steel bars), the tensile stresses in FRC are borne by the fibers are early stages; In design, the type, size, geometry, and dosage rates for fibers is dependent on the application, loading level, and exposure conditions; Strain softening and strain hardening Fibers change the post-crack response of concrete from brittle to ductile under all types of loads.

11 2. Design concepts The material properties (such as the residual strength determined by standard tests ASTM C1609) are inserted into equations to determine the performance of an FRC element and its load-carrying capacity. Tensile strength of plain concrete is insignificant, hence, not taken into account in the design of conventional RC sections. Effective tensile strength of FRC sections is used in the design process. 2 Figure 9: Schematics of a typical stress-strain diagram for FRC in unia Direct tensile test on FRC is difficult, instead, the 3 compression, according to RILEM TC 162-TDF [Vandewalle etl residual tensile strength is derived from the measured flexural strength by means of conversion 4 factors. 1 tension compression Typical stress-strain diagram of FRC

12 KEY PROPERTY : Stress-strain diagram Stress Stress F c RILEM TC162 F c 10 % 1 % F ct,,3 0.37F eq ct, eq,1.5 Strain F ct, ax Strain F ct, ax Fiber Reinforced Concrete Plain Concrete Fct,eq,3 Fct,eq,1.5 Equivalent strength at deflection of 3 mm (L/150) Equivalent strength at deflection of 1.5mm (L/300)

13 Stress Post-cracking behavior The cracked section of fiber-reinforced concrete (FRC) does carry tensile load while plain concrete becomes ineffective after cracking as indicated in the stress-strain diagram Z Z Conventional RC FRC F c 10 % 1 % F ct, 0.37F eq,3 ct, eq,1.5 F ct, ax Strain Need to be characterized

14 2. Design concepts In the post-crack state, the residual flexural strength of FRC is typically between 2.5 and 3 times its residual tensile strength, hence, the tensile resistance is calculated from the flexural resistance using a factor between 0.4 and For design purposes, the tensile residual strength of FRC may be taken as 0.37 times the flexural strength obtained from a standard beam test. Two levels of design can be considered: design for serviceability limit state (SLS) at small deflections (cracks in the range of mm and design for ultimate limit state (ULS) with larger deflections (larger crack widths: mm).

15 2. Design concepts Standard test methods for FRC When ASTM C1609/1609M-12 is used to characterize FRC, parameters such as f D 600, f D T 150, R D,150 (or f e,3 ) may be used for design. D f 600 D f 150 : Residual strength at a deflection of L/600 (psi or MPa) : Residual strength at a deflection of L/150 (psi or MPa) Standard test m D T 150 : Toughness or area under the curve up to a deflection of L/150 T R D,150 : Equivalent flexural strength ratio at a deflection of L/150 (%) f e,3 R 150 T D D 150 T,150 2 fp b h : Equivalent flexural strength at a deflection of Schematics L/150 (psi or MPa) of a typical ASTM C1609/C1609M-12 test result (strain-softening FRC) and FRC beam under four-point flexural test. T f e,3 = f p R D,150 f p : Peak strength (psi or MPa) The Concrete Conven and Expos

16 ASTM C-1609 Standard Test Method for Flexural Performance of Fiber-Reinforced Concrete This test method provides for the determination of first-peak and peak loads and the corresponding stresses calculated by inserting them in the formula for modulus of rupture. It also requires determination of residual loads at specified deflections, and the corresponding residual strengths calculated by inserting them in the formula for modulus of rupture. At the option of the specifier of tests, it provides for determination of specimen toughness based on the area under the load-deflection curve up to a prescribed deflection To determine the first-peak, peak and residual strengths the respective load value is substituted in the modulus of rupture formula: Values of loads at specified deflection points are used for measuring residual strength of FRC f = PL bd 2 Where: f = the strength, MPa (psi), P = the load, N (lbf), L = the span length, mm (in.), b = the average width of the specimen, mm (in.), at the fracture, and d = the average depth of the specimen mm (in.), at the fracture.

17 Flexural Stress 17 Equivalent flexural strength, f e,3 f p f e,3 Deflection (mm) 3, (L/150) Equivalent Flexural Strength: Have the same toughness, T 150,3.0, obtained from experiment to a deflection of L/150 (same area under load-deflection curve) ASTM C JSCE, JCI-SF4 NBN B f e,3 (MPa) = For Span, L= 450 mm f e,3 L( mm) T150,3.0 ( Nmm) L( mm) W(mm) D(mm) T = 3 WD 150, T WD 150,3.0 2 fe,3 R e,3 (%) = 100 f p 2

18 Stress 11 conjunction with the similar method of RILEM TC 162-TDF (Vanverwalle et al, 2003). 3. Design for flexure (Fiber Reinforced Section) D M n FRC = f bh2 6 FRC section Schematics of stress block for a cracked RC and FRC flexural member Figure 11: Schematics of stress block for FRC in a flexural member (ASTM C1609 parameters) 0.37F e,3 F c 14 (Eq. 5) 10 % 1 % F e,3 0.37F ct, eq,1.5 F ct, ax Strain 15

19 135 account the compressive in these stresses calculations. are carried Eq. by 4 shows concrete the while classical the tensile equation stresses for the are moment carried by capacity fiber- of a 3. Design for flexure 146 cracked reinforced RC concrete. section. The tensile strength of fiber-reinforced concrete, f t-frc, can be much higher RC section than that of plain concrete and is in fact taken into account in these calculations. For ULS design the tensile strength of fiber-reinforced concrete, f t-frc, is equal to 0.37 times the flexural residual strength of fiber-reinforced concrete, f e3, measured from ASTM C1609/1609M-12 test. Eq. 5 shows the calculations for the moment capacity of a cracked FRC section, developed in M n RC = 11 A s f y conjunction d a with the similar method of RILEM TC 162-TDF (Vanverwalle et al, 2003) Figure 10: Schematics of stress block for RC in a flexural member FRC section 17 D M n FRC = f bh Figure Schematics 11: Schematics of stress of block stress block for a cracked for FRC in RC a and flexural FRC member flexural (ASTM member C1609 parameters)

20 11 conjunction with the similar method of RILEM TC 162-TDF (Vanverwalle et al, 2003). Hybrid reinforcement could be a viable option where either the fiber dosage rate or the 4. Design 6 for flexure hybrid reinforcement 7 reinforcement ratio is too high and impractical. The nominal bending moment for a hybrid fiber- 8 FRC section 9 reinforced concrete (FRC*) section, M n-frc* is calculated according to the following equations from the force equilibrium in the cross section shown in Figure 13. The calculation for the 10 moment bh 2 capacity of a cracked FRC section is shown in Eq. 7.The design of flexural members M n FRC = f e, with 6 hybrid reinforcement is further discussed by Mobasher et al. (2015). 13 FRC section with hybrid reinforcement 14 Figure 11: Schematics of stress block for FRC in a flexural member (ASTM C1609 parameters) b f c f c 0.1h h d 0.9h T=A s.f y (Eq. 5) T=A s.f y f t f t M n FRC = f e,3 bh A s f y (d 0.03h) Normal Stresses/Forces (Actual) Normal Stresses/Forces (Simplified) Schematics Figure of stress 13: Schematics block for a of cracked stress block FRC in (with a concrete and without beam with hybrid hybrid reinforcement

21 Ultimate resistance Assumptions Plane section remains plane Stress in tension and compression are derived from stress-strain diagram For FRC with additional rebars, the strain in tension is limited to 10% at the level of rebars The maximum crack width is limited to 1.5 mm (RILEM TC162)

22 Post-cracking behavior The cracked section of fiber-reinforced concrete (FRC) does carry tensile load while plain concrete becomes ineffective after cracking as indicated in the stress-strain diagram Z Z Conventional RC FRC

23 Stresses in fiber reinforced concrete at ultimate loading (%) Fiber Reinforced Concrete + bar reinforcement Fiber Reinforced Concrete RILEM TC162

24 Stress 8. Example Solved Examples Assume an 8 (200 mm) precast panel reinforced with #4@16 placed in mid-section to provide postcrack moment capacity. Find the value of f 150 D for FRC to provide the same level of post-crack flexural Example: strength Assume as rebar. an Assume 8 (200 mm) 5,000precast psi concrete panel and reinforced grade 60 with steel #4@16 and a moment placed in capacity factor of 0.9 for mid-section steel. to provide post-crack moment capacity. Find the value of f D 150 for FRC to provide the same level of.43 post-crack h flexural strength as Zrebar. Assume 5,000 psi 200 concrete and grade 60 steel and a moment capacity factor of 0.9 for steel. a a M n RC. As. Fy.( d ) ,000 31, M A. F s y 0.85 f ' n FRC c. b. M , , n RC.57 h 31,120 lb F ct 0.17in in. f D 150 b. h 6 D 6M n FRC 6 31,120 f psi (1.86 MPa) 2 2. b. h lb in 1000 Specify Fiber Dosage Accordingly 10 % 1 % F ct, 0.37F eq,3 ct, eq,1.5 F ct, ax F c Strain

25 Stress Example 2: Determine the moment capacity of the concrete slab that is reinforced with fibers (0.5% of Fiber below) F c STRUX % 1 % F ct, 0.37F,3 ct,,1.5 F ct, ax Strain ASTM 1609 Results for the fibers used is shown in the next slide

26 Stress Example: Determine the moment capacity Fibers % 1 % F ct, 0.37F,3 ct,,1.5 F ct, ax F c Strain T D 45900N mm 45. 9J 150 D 150T T fe 04MPa f 150 e MPa 2 bd bd 2 M f bh 7. 62kN m n e3 D

27 Stress Example: Determine the Tension capacity Fibers % 1 % F ct, 0.37F,3 ct,,1.5 F ct, ax F c Strain T D 45900N mm 45. 9J 150 D 150T T fe 04MPa f 150 e MPa 2 bd bd T 0.37 f 3bh 113. kn n e 2 D

28 Example: ACI 318 cracking control w Z 0.076Z f 3 s d c A Gergely-Lutz ACI requires that the term Z does not exceed 175 for interior exposure and 145 for exterior exposure (based on 0.4 mm and 0.3 mm crack width) f s Stress in the steel f f s s M A jd s M A jd s 0.37F ct, eq,3 A s Steel fibers A ct (For RC) (For RC with fibers) Wider cracks a way from rebar Uniform crack width Z Z Conventional RC FRC

29 Example: ACI 318 cracking control 50 KN w Z (1.1x10 f 3 s d c A 5 ) Z Gergely-Lutz (mm) ' F c 30MPa mm 2 A s 760mm 4000 mm 200 M f 244MPa s A jd s w = 3 mm. (For RC) M 0.37Fct, eq, 3Act 0.37*1.28*0.9*350*200 fs MPa A jd A 760 s s w 0. 2mm with 3.5 kg of synthetic fibers

30 Example: 6 Slabs with 4 x 4 - W4 The steel ratio is 1000 A s, sh, temp bh 150 ~ 4x4 ' F c 25MPa F y 400MPa Z 20000N / m Z f 3 s dc A d c 75mm 1000x120 A 10 f s 207MPa 12000mm 2 h w Crack Width 2 / h 1 (1.1x ) Z w 0. 57mm

31 Stress Required STRUX 90/40 to Obtain Same Z-Value Fibers 150 F c % 1 % h.57 h F ct Z 0.37F ct, 0.37F eq,3 ct, eq,1.5 F ct, ax Strain F 0.3F ct Fct 0.3Fct, eq, 3hb fs, eq As A s, 207MPa F ct, eq, MPa f eq ct, eq,3 s hb Specify Dosage of fibers accordingly

32 Failure and moment capacity of SOG Horst Falkner, Braunschweig,1995 Plain Concrete Fiber

33 FRC versus PC slabs Bending moment distribution after cracking is different Plain concrete exhibit a regular hinge Fiber concrete exhibit plastic hinge (yield capacity Final design of PC slab is governed by slab stiffness and interaction with sub-base Final design of FRC slab is governed by the interaction between positive and negative moment as a function of slab stiffness and subbase

34 FRC versus PC slabs Collapse load of FRC slab is a function of the sum of the negative and positive moment M ult ( M + + M ) P u Resisted Moment by fiber (Plastic Hinge) Collapse load of PC slab is a function of the cracking moment M M ult M cracking

35 Flexural capacity F d M ult F ct F ct bh 6 2 Plain concrete R F d M e, 3 Re,3 Fct *(1 + ) 100 R 1 + e,3 F * 100 ult F F e,3 ct ct bh 6 2 Fiber reinforced concrete Ductility factor, toughness dependent

36 Collapse Load for Point Load on Slab on Grade Using Yield Line Theory For a/l 0.2: (where a is the equivalent radius of the load patch, and l is the relative stiffness), the ultimate load carrying capacity of the slab will be obtained from the following equations: For Center Load P u For Edge Load For Corner Load L is the radius of relative stiffness

37 Example: 125 mm Slab with Center Point Load of 100 kn over m 2 Given Parameters Ground Supported Slab Thickness of Slab = 125 mm Concrete class S40 Elastic modulus of Concrete = MPa Modulus of Subgrade Reaction 68 MPa/m Joint spacing variable (6 m) P = 100 kn Area = m2 a = equivalent radius = 89.2 mm radius of relative stiffness = = 538 mm For Center Load For Edge Load Residual moment by fibers Cracking moment by plain concrete 5.16 MPa Use Factored Load = P u = 1.5*100 = 150 kn For center point load Re,3 will be equal to 25.6 % Fe,3 = 0.256*5.16 = 1.32 MPa fiber content

38 7. Slabs on ground Slabs on ground are designed according to ACI 360R specifications. Steel fibers are typically used at a dosage rate between 10 and 36 kg/m 3 as the sole reinforcement. Synthetic fibers are used at a dosage rate between 1.8 and 4.5 kg/m 3 as the sole reinforcement. The residual strength of FRC is used for design and specifying FRC slabs.

39 5. Design for shear As per ACI 318, if used in lieu of stirrups in flexural members, steel fibers must have an aspect ratio T between 50 and 100 and provide a minimum of R D,150 of 75% when tested according to ASTM C1609 (ACI 318 sec 5.6.6). Altoubat et al. (2015) have shown that synthetic macrofibers can also provide the required shear resistance in flexural members when used at a proper dosage rate. For members with conventional longitudinal reinforcement but without shear reinforcement, the shear capacity for FRC is given by (Model Code 2010 sec ): V Rd,F = 0.18 γ c k 100 ρ l f Ftuk f ctk f ck σcp b w d For members with conventional longitudinal reinforcement and shear reinforcement, the contribution of fibers can be added to the equation: V Rd = V Rd,F + V Rd,s

40 Macro Synthetic Fiber Improve Shear Strength of RC Beams Shear Behavior of Macro-Synthetic Fiber Reinforced Concrete Beams without Stirrups, ACI Materials Journal, Vol. 106, No. 4, July August, 2009, pp Effect of Synthetic Macro-Fibers on Shear Behavior of Concrete Beams, ACI- Special Publications, SP248, Deflection and Stiffness Issues in FRC and Thin Structural Elements, 2007, pp Shear Strength of Beams reinforced with synthetic macro fibers, Eighth RILEM Conference on fiber reinforced Concrete BEFIB2012, Portugal, 2012

41 fib-mc2010 Formulations V V + V Rd Rd, F Rd, s Fibers contributions embedded in concrete Fiber contribution depends on residual tensile strength Formulas based on characteristic properties V Rd, F f Ftu k. 100 l c f f Ftuk ctk. f ck cp b wu ( wu ) ffts.( ffts 0.5. fr fr 1) f Fts 0.45 fr,1 Based on linear post-cracking behavior constitutive model w d f 0. 51f Ftuk Ftu f R, j 3F L 2bh j 2 sp

42 Residual Flexural Tensile Strength Parameters (EN 14651) j CMOD j F R,j (MPa) for V f =0.5% F R,j (MPa) for V f =0.75% F R,j (MPa) for V f =1.0%

43 Analysis: Prediction versus Experimental fib-mc2010 and RILEM can be both safely used to predict shear strength of SNFRC The fib-mc2010 predict shear strength of long beams with reasonable accuracy but is more conservative for short beams

44 Prof. Salah Altoubat Coordinator