European design codes for FRC structures G. Plizzari

Transcription

1 European design codes for FRC structures University of Brescia, Italy

2 Eurocode 2 Annex to EN CEN TC 250/SC2/WG1/TG2 SFRC - Steel Fibre Reinforced Concrete This draft annex to EN is currently being prepared by CEN TC 250/SC2/WG1/TG2. It describes all additions and changes to EN , required for the application of SFRC within the scope of EN Unchanged parts of EN remain valid. European design codes for FRC structures Sharjah (UEA), April 23rd, /63

3 fib Model Code 2010 European design codes for FRC structures Sharjah (UEA), April 23rd, /63

4 fib Model Code: new contents New types of concrete (FRC) New types of reinforcement (fibres) New design criteria Design for service life Upgrading of structures Defined performance design Quality of execution European design codes for FRC structures Sharjah (UEA), April 23rd, /63

5 fib Model Code: Index 1. Scope 2. Terminology 3. Basic Principles 4. Design Principles 5. Materials 6. Interface characteristics 7. Design 8. Construction 9. Conservation 10. Dismantlement 5.1. Concrete 5.2. Reinforcing steel 5.3. Prestressing steel 5.4. Prestressing systems 5.5. Non-metallic reinforcement 5.6. Fibres / fibre reinforced concrete Joint chapters prepared by fib TG 8.3 Fiber reinforced concrete and fib TG 8.6 Ultra high performance fiber reinforced concrete European design codes for FRC structures Sharjah (UEA), April 23rd, /63

6 Model Code 2010: FRC structures FRC structures can be classified as: structures with linear elements (beams, and columns); walls; slabs; shells (e.g. thin walled members); three-dimensional members. A distinction should be made between structures with linear elements (statically determinate and indeterminate beams or frames), where the stress redistribution is limited to few sections, where strain localization may occur and structures with a higher degree of redundancy, where stress redistribution occurs in multiple cracks (as in slabs). European design codes for FRC structures Sharjah (UEA), April 23rd, /63

7 Main goal of the fib Model Code To provide guidance to engineers to properly (and safely) design FRC structural elements both at serviceability and ultimate limit states, based on the state-of-the-art knowledge CLASSIFICATION 22/04/2018 European design codes for FRC structures Sharjah (UEA), April 23rd, /63

8 FRC performance classes (New fib Model Code) Post-cracking residual strength can be classified by using two parameters, namely f R1k (representing the strength interval) and a letter a, b, c, d or e (representing the ratio f R3k /f R1k ). The strength interval is defined by two subsequent numbers in the series: 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 [MPa] while the letters a, b, c, d and e correspond to the ratios: a if 0.5 f R3k /f R1k 0.7 b if 0.7 f R3k /f R1k 0.9 c if 0.9 f R3k /f R1k 1.1 d if 1.1 f R3k /f R1k 1.3 e if 1.3 f R3k /f R1k SLS ULS The designer has to specify the class, the residual strength ratio and the material of the fibre European design codes for FRC structures Sharjah (UEA), April 23rd, /63

9 Constitutive law in uniaxial tension: s-w Experimental result: s N CMOD s w s f Ft =f ct f Fts s hardening f Fts f Ftu f Ftu Simplified constitutive law s - w softening f Ftu w u w f Fts 0.45 f R1 w s f Ftu f Ftu rigid-plastic f Ftu f Fts w u CMOD 3 ( f Fts 0.5 f R3 0.2 f R1) 0 w u w European design codes for FRC structures Sharjah (UEA), April 23rd, /63

10 Stress-strain relationship ε 1 = ε SLS = CMOD 1 /l cs ε 2 = ε ULS = w u /l cs (=2% or 1%) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

11 Partial safety factors ULS: FRC in compression FRC in tension Ordinary quality control As plain concrete SLS: g F = 1 FRC in tension (residual strength) g F = 1.5 European design codes for FRC structures Sharjah (UEA), April 23rd, /63

12 Optimized reinforcement: definition Place the best performing reinforcement (fibers and/or rebars) where required by tensile stresses in the structural elements European design codes for FRC structures Sharjah (UEA), April 23rd, /63

13 Reinforcement use in structural elements In structural elements both distributed and localized stresses are generally present Conventional rebars represent the best reinforcement for localized stresses Fibers represent the best reinforcement for diffused stresses Structural optimization generally requires the use of a combination of rebars and fibers Structural ductility is generally enhanced European design codes for FRC structures Sharjah (UEA), April 23rd, /63

14 From material to structural behavior Naaman, A.E. and Reinhardt, H. (eds), High Performance fiber reinforced cement composites HPFRCC4 RILEM Proceedings, PRO30, Rilem Publications S.A.R.L., Bagneux, France, European design codes for FRC structures Sharjah (UEA), April 23rd, /63

15 FRC and degree of redundancy of structures 1- Structural elements with low degree of redundancy Fibers can not generally replace the main flexural reinforcement but they can used to substitute the secondary reinforcement or the shear reinforcement Example: Box culverts Conventional reinforcement Optimized reinforcement European design codes for FRC structures Sharjah (UEA), April 23rd, /63

16 FRC and degree of redundancy of structures 1- Structural elements with low degree of redundancy Fibers can not generally replace the main flexural reinforcement but they can used to substitute the shear reinforcement Example: Linear elements (beams) Floor section Topping concrete layer Typical Concrete Floor used in Southern Europe RC spandrel wide-shallow beam Lightweight ribbed one-way reinforced concrete slab RC central wide-shallow beam Conventional Reinforcement for Wide Shallow Beams Wide Shallow Beams with Optimized Reinforcement FRC (V f =25kg/m 3 ) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

17 Verification Bending in of FRC safety Beams (ULS) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

18 Bending and/or axial force in linear members The bending failure is considered to occur when one of the following conditions arises: attainment of the maximum compressive strength, cu, in the FRC; attainment of the maximum tensile strength su, in the steel (if present); attainment of the maximum tensile strength, Fu, in the FRC. cu f cd f cd x x A sl su y f Fts /g F M N Sd Rd Fu hardening softening f Ftu /g F European design codes for FRC structures Sharjah (UEA), April 23rd, /63

19 Bending in FRC beams P/2 P/ /10 cm L=100cm European design codes for FRC structures Sharjah (UEA), April 23rd, /63

20 Flexural behavior of FRC beams Load-Displacement Curve (2 16) 80 Load [kn] PC Displacement P/2 [mm] P/ PC Failure Trave m d [KN] [KN] [KN] [mm] [mm] P/2 P/2 Failure 2 16-PC 81,48 89,82 84,84 20,54 110,50 5, ,20 96,24 75, ,01 8,97 P/2 P/ ,86 95,70 80,64 18,16 113,72 6, Failure European design codes for FRC structures Sharjah (UEA), April 23rd, /63

21 Fibers influence on flexural ductility r s = 0,67 % r s = 1,34 % 60 kg/m 3 30 kg/m 3 PC FRC: - Increase in concrete compressive toughness; - Optimization steel-toconcrete bond; - Tension Softening at crack; - More chance to stress concentration. For bonded beams r s = 0,67 %: concrete crushing steel rupture r s = 1,34 %: concrete crushing concrete crushing more ductile European design codes for FRC structures Sharjah (UEA), April 23rd, /63

22 Shear in beams without stirrups In FRC elements there is an additional contribution to shear resistance provided by fiber reinforcement: V = V c + V f V c represents the concrete contribution. V f represents the fiber contribution (post cracking strength). European design codes for FRC structures Sharjah (UEA), April 23rd, /63

23 Beams without shear reinforcement European design codes for FRC structures Sharjah (UEA), April 23rd, /63

24 Shear in beams with stirrups European design codes for FRC structures Sharjah (UEA), April 23rd, /63

25 Minimum shear reinforcement European design codes for FRC structures Sharjah (UEA), April 23rd, /63

26 FRC for Shear-Critical Beams I Several experimental results are available for beams with longitudinal rebars without stirrups. More results are needed for prestressed beams a V V d 2Ø24 Bars, L=4550 mm mm Steel Plate 200x90x30 mm 45 2Ø24 Deformed Bars a/d=2.5 Reinforcement Ratio of 1% 480 mm European design codes for FRC structures Sharjah (UEA), April 23rd, /63

27 Typical experimental results from NSC beams 400 Normal Strength Concrete, f' c = 24.8 MPa Load [kn] kg/m 3, 30/0.6 V d 30 kg/m 3, 30/ kg/m 3, 12/0.18 V NSC1-PC NSC1-FRC1 NSC1-FRC Displacement [mm] 30 Ø 0.38 Ø Crack Width [mm] Normal Strength Concrete, f' c = 24.8 MPa Average First Cracking CPT TPT V V V 30 kg/m 3, 30/0.6 NSC1-PC NSC1-FRC1 NSC1-FRC d Load [kn] V 30 kg/m 3, 30/ kg/m 3, 12/0.18 f c = 24.8 MPa. 30 Fibers: 0,38% of macro-fibers, 30 mm long with aspect ratio = 50 0,19% of micro-fibers, Ø 0.18 Ø 0.6 Ø mm long with aspect ratio = Ø 1.0 European design codes for FRC structures Sharjah (UEA), April 23rd, /63

28 Typical experimental results from HSC beams High Strength Concrete 50 kg/m 3, 80/30 f c = 60 MPa. Ø 0.38 Load [kn] kg/m 3, 45/30 V d HSC-PC HSC-FRC1 HSC-FRC Displacement [mm] V Fibers: 0,6% of macro-fibers, Low carbon (45/30) or High carbon (80/30) Ø 0.62 Ø Ø 0.62 V Crack Width [mm] High Strength Concrete Average First Cracking HSC-PC HSC-FRC1 HSC-FRC2 CPT TPT V V d 50 kg/m 3, 45/30 V 50 kg/m 3, 80/30 Reinforcement optimization requires that fiber tensile 50 strength must be related to concrete compressive strength 12 Ø 0.18 Ø 0.18 Ø Load [kn] European design codes for FRC structures Sharjah (UEA), April 23rd, /63

29 Wide Shallow Beams with b=750 mm W750 PC W750 FRC25 European design codes for FRC structures Sharjah (UEA), April 23rd, /63

30 Wide Shallow Beams with b=1000 mm W1000 MSR W1000 FRC35 European design codes for FRC structures Sharjah (UEA), April 23rd, /63

31 Example of Application for Shear p = 35 kn/m 200 d 2Ø24 Bars 6 m 500 mm 500 2Ø24 Deformed Bars p u 35 kn / m ( ULS) h 500 mm; d 460mm f 30 MPa; f 500 MPa ck c s yk g 1.5; g fcd 20 MPa; f yk 435 MPa f 2 MPa ( EC2) ctk M max p l kn m Vmax p l kn As 904 mm rl 0.98% b d 200 mm 460 mm M u w 161 kn m European design codes for FRC structures Sharjah (UEA), April 23rd, /63

32 Example of Application for Shear VRd, ct k (100 r1 fck ) 0.15 scp b d 49 kn W g c Minimum Shear Reinforcement meters requiring design shear reinforcement; 2.8 meters requiring minimum shear reinforcement. Minimum Shear Reinforcement: Design Shear Reinforcement: s 0.75 d 345 mm Asw VR, ds z fyd VRd VRd, ct 56 kn f s ck rw,min f s 321 mm yk 2 mm 2 8@ 300 mm European design codes for FRC structures Sharjah (UEA), April 23rd, /63

33 Example of Application for Shear Assume 30 kg/m 3 of steel fibers having l/ =67 and fftk,u=0.90 MPa (tested at the University of Brescia) V V Rd, F Rd, F 0.18 Ftk, u 1 3 k (100 r1 (1 7.5 ) f ck ) g c f ctk f 0.15 s Minimum shear reinforcement f ck f Ftuk MPa Design Shear Reinforcement 1 1 ( (1 7.5 ) 20) OK Asw VR, ds z fyd VRd VRd, ct 24 kn s 2 6@ 300 mm s 420 mm European design codes for FRC structures Sharjah (UEA), April 23rd, / CP b W d kn Minimum Shear Reinforcement 2.3

34 Example of optimized shear reinforcement Plain concrete FRC European design codes for FRC structures Sharjah (UEA), April 23rd, /63

35 Torsion in beams European design codes for FRC structures Sharjah (UEA), April 23rd, /63

36 Verification of safety (ULS) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

37 Slabs European design codes for FRC structures Sharjah (UEA), April 23rd, /63

38 FRC and degree of redundancy of structures 2- Structural elements with a high degree of redundancy Fibers can partially replace the main flexural reinforcement. Conventional rebars are placed only in the areas of the structures with subjected to localized stresses. Example: Elevated slabs Slab with Optimized Reinforcement Loading set-up FRC (V f =30kg/m 3 ) Localized reinforcement Aim of the optimization: to find a best combination between rebar contend and FRC toughness (volume fraction of FRC) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

39 Bending Ductility in requirements FRC Beams European design codes for FRC structures Sharjah (UEA), April 23rd, /63

40 Design principles Favorable effects of stress redistribution European design codes for FRC structures Sharjah (UEA), April 23rd, /63

41 Verification Bending of in serviceability FRC Beams(SLS) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

42 Stress limitation European design codes for FRC structures Sharjah (UEA), April 23rd, /63

43 Crack width control European design codes for FRC structures Sharjah (UEA), April 23rd, /63

44 Crack development Durability of in FRC elements European design codes for FRC structures Sharjah (UEA), April 23rd, /63

45 Experimental Program II b Two fiber typologies: b b LVDT Base of measurement 4 LVDTs, one for each side of the specimen Macro (M): Hook ended, 30 mm long, 0.62 mm diameter Reinforcement Micro (m): Straight, 13 mm long, 0.2 mm diameter mm European design codes for FRC structures Sharjah (UEA), April 23rd, /63

46 Variation of the rebar diameter Experimental Program III vil 950 b Reinforcement Variation of the longitudinal steel ratio, ρ=3,24% to 1,24% Variation of the specimen size, b Variation of the rebar diameter Vf b [mm] As [mm 2 ] Ac,eff [mm 2 ] Reinf. Ratio (%) Clean cover [mm] Denomination # of specimens 0* N 50/ ,5%* N 50/10-0,5/M ,0 %* ,24 20 N 50/10-1/M 3 Bar diameter f=10 mm 0,5%+0,5%* N 50/10-1/M+m 3 1%+1% N 50/10-2/M+m 3 0* N 80/ ,5%* N 80/10-0,5/M ,0 %* ,24 35 N 80/10-1/M 3 Bar diameter 0,5%+0,5%* f=20 mm N 80/10-1/M+m 3 1%+1% N 80/10-2/M+m 3 0* N 100/ ,5%* N 100/20-0,5/M ,0 %* ,24 40 N 100/20-1/M 3 0,5%+0,5%* N 100/20-1/M+m 3 1%+1% N 100/20-2/M+m 3 Bar diameter f=30 mm 0* N 150/ ,5%* N 150/20-0,5/M ,0 %* ,41 65 N 150/20-1/M 3 0,5%+0,5%* N 150/20-1/M+m 3 1%+1% N 150/20-2/M+m 3 0* N 150/ ,5% N 150/30-0,5/M ,0 % ,24 60 N 150/30-1/M 3 0,5%+0,5% N 150/30-1/M+m 3 1%+1% N 150/30-2/M+m 3 0* N 200/ ,5% N 200/30-0,5/M ,0 % ,80 85 N 200/30-1/M 3 0,5%+0,5% N 200/30-1/M+m 3 1%+1% N 200/30-2/M+m 3 European design codes for FRC structures Sharjah (UEA), April 23rd, /63

47 Experimental Results Comparison specimens N 50/ r = 3,24% Comparison specimens N 80/ r = 1,24% Axial load, N [kn] Bare bar Ф 10 Average response plain Average response Vf=0,5% Average response Vf=0,5%+0,5% Average response Vf=1% ΔN Plain ΔN SFRC Vf=0,5% ΔN SFRC Vf=0,5%+0,5% ΔN SFRC Vf=1% Axial load, N [kn] Bare bar Ф 10 Average response plain Average response Vf=0,5% Average response Vf=0,5%+0,5% Average response Vf=1% ΔN Plain ΔN SFRC Vf=0,5% ΔN SFRC Vf=0,5%+0,5% ΔN SFRC Vf=1% Average strain [ ] Average strain [ ] DN: combined effect of tension stiffening and residual tensile stresses European design codes for FRC structures Sharjah (UEA), April 23rd, /63

48 Results Plain Concrete FRC w European design codes for FRC structures Sharjah (UEA), April 23rd, /63

49 Comparison against code provisions Average crack spacing [mm] Average crack spacing: comparison with standard formulations Plain SFRC Vf=0,5% SFRC Vf=0,5%+0,5% SFRC Vf=1% CEB - FIP Model Code, 1978 Eurocodice 2, 1991 CEB - FIP Model Code, 1993 Eurocodice 2, 2003 CEB, FIP Model Code 1978: s m sb 2 c k 10 1 k CEB, FIP Model Code 1993: s m ρ eff 2 ρ eff f/r eff [mm] European design codes for FRC structures Sharjah (UEA), April 23rd, /63

50 Fibers for Durability durability of of FRC beams European design codes for FRC structures Sharjah (UEA), April 23rd, /63

51 Cracking and durability European design codes for FRC structures Sharjah (UEA), April 23rd, /63

52 Exposure in aggressive (marine) environment 10 beams has been exposed for more than 2 years in a coastal zone, under a load equal to 50% of the ultimate load Aim of the research: evaluate the influence of fibers on mechanical behaviour of FRC in short and long term bending test European design codes for FRC structures Sharjah (UEA), April 23rd, /63

53 Materials (UNI 11039) Ø Ø Longitudinal bars Diameter Yield strength (MPa) Ultimate strength (MPa) 14mm Stirrups 8mm European design codes for FRC structures Sharjah (UEA), April 23rd, /63

54 Tests for determining material properties (UNI 11039) LOAD (kn) % steel V f =0,6% V f =0,9% 06S 09P TQ % polyester CTOD (microns) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

55 Crack monitoring Crack width, crack length and crack position have been measured during the exposure period. The crack width has been measured with a digital microscope (200x magnification) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

56 Cracking monitoring pp1 pp2 st1 st2 tq In FRC beams the crack widths were in the range of 0.1 to 0.2 mm, without overcome the threshold of 0.2 mm. In plain beam the 93.3% of cracks had a crack width over 0.1 mm, while the 60% over 0.2 mm. European design codes for FRC structures Sharjah (UEA), April 23rd, /63

57 Crack width (mm) Cracking monitoring Average of crack widths between the loading points PC steel polyester TQ1_E ST1_E ST2_E POL1_E POL2_E Crack width reduction of the FRC beams respect to the plain beam (Dw /%). Beams Dw /% ST1-2_E 54% POL1-2_E 53% European design codes for FRC structures Sharjah (UEA), April 23rd, /63

58 Cracking behavior at SLS ST1-2_E 43% POL1_E 37% POL2_E 43% Crack width reduction of the FRC beams respect to the plain beam. SLE (50kN) LONG TERM BEAMS SLE (50kN) ST1-2 35% POL1-2 28% SHORT TERM BEAMS European design codes for FRC structures Sharjah (UEA), April 23rd, /63

59 Cracking behavior at ULS Crack width reduction of the FRC beams respect to the plain beam. SLU (100kN) ST1-2_E 56% POL1_E 25% POL2_E 54% LONG TERM BEAMS SLU (100kN) ST1-2 41% POL1-2 39% SHORT TERM BEAMS European design codes for FRC structures Sharjah (UEA), April 23rd, /63

60 Carbonation depth CARBONATION DEPTH CHLORIDE CONTENT European design codes for FRC structures Sharjah (UEA), April 23rd, /63

61 Carbonation depth between the cracks European design codes for FRC structures Sharjah (UEA), April 23rd, /63

62 Carbonation depth at cracks K (mm/anni ^0.5) TQ_E ST1_E ST2_E POL1_E POL2_E t armature (anni) European design codes for FRC structures Sharjah (UEA), April 23rd, /63

63 Thank you for your kind attention! University of Brescia, Italy European design codes for FRC structures Sharjah (UEA), April 23rd, /63