Idealized skeleton curve - envelope to hysteresis loops

Transcription

1 MODELLING THE BEHAVIOR OF CONCRETE MEMBERS: DEVELOPMENTS SINCE THE COMPLETION OF EN 998-3:5 Mihael N. Fardis Universit o Patras

2 Idealized skeleton rve - envelope to hsteresis loops Eetive elasti stiness: seant-to-ielding M Yield Ultimate moment, M u =M member deormation: hord-rotation rotation setion deormation: rvature δ Yield deormation moment M M <8M M res <.8M u δ u Ultimate deormation δ

3 Pratial a expressions ess s or the ield & ailure properties developed or EN 998-3:5 - their advanement anement sine 5

4 D. BISKINIS, G. ROUPAKIAS & M.N. FARDIS, Cli Deormation Capait o Shear-Critial RC Elements, Proeeding o ib Smposium, Athens, Ma 3. M.N.FARDIS & D.BISKINIS, Deormation Capait o RC Members, as Controlled b Flexure or Shear. Proeedings o International Smposium on Perormane-based Engineering or Earthquake Resistant Strutures honoring Pro. Shunsuke Otani Universit o Toko, Sept. 3, pp D.BISKINIS, G.K. ROUPAKIAS & M.N.FARDIS, Resistane and Design o RC Members or Cli Shear, 4th Greek National Conrete Conerene, Kos, Ot. 3, Vol. B, pp D.BISKINIS & M.N.FARDIS, Cli Strength and Deormation Capait o RC Members, inluding Members Retroitted or Earthquake Resistane, Pro. 5 th International Ph.D Smposium in Civil Engineering, Delt, June 4, Balkema, Rotterdam, p D.BISKINIS, G.K. ROUPAKIAS & M.N.FARDIS, Degradation o Shear Strength o RC Members with Inelasti Cli Displaements, ACI Strutural Journal, Vol., No. 6, Nov.-De. 4, pp M.N.FARDIS, D.BISKINIS, A. KOSMOPOULOS, S.N. BOUSIAS & A.-S. SPATHIS, Seismi Retroitting Tehniques or Conrete Buildings, Pro. SPEAR Workshop An event to honour the memor o Jean Donea, Ispra, April 5 (M.N.Fardis & P. Negro, eds.) S.N. BOUSIAS, M.N.FARDIS & D.BISKINIS, Retroitting o RC Columns with Deiient Lap-Splies, ib Smposium, Budapest, Ma 5. S.N. BOUSIAS, M.N.FARDIS, A.-S. SPATHIS & D.BISKINIS, Shotrete or FRP Jaketing o Conrete Columns or Seismi Retroitting, Pro. International Workshop: Advanes in Earthquake Engineering g or Urban Risk Redution, Istanbul, Ma June 5. D.BISKINIS & M.N.FARDIS, Assessment and Upgrading o Resistane and Deormation Capait o RC Piers, Paper no.35, st European Conerene on Earthquake Engineering & Seismolog (a joint event o the 3 th ECEE & the 3 th General Assembl o the ESC), Geneva, September 6. D.BISKINIS & M.N.FARDIS, Cli Resistane and Deormation Capait o RC Members, with or without Retroitting, 5th Greek National Conrete Conerene, Alexandroupolis, Ot. 6, Vol. B, pp D.BISKINIS, M.N.FARDIS, Eet o Lap Splies on Flexural Resistane and Cli Deormation Capait o RC Members, Beton & Stahlbetonbau,, 7 D.BISKINIS & M.N.FARDIS, Cli Deormation Capait o FRP-Wrapped RC Columns or Piers, with Continuous or Lap-Splied Bars, 8 th International Smposium on Fiber Reinored Polmer Reinorement or Conrete Strutures (FRPRCS-8), Patras, Jul 7. D.BISKINIS & M.N.FARDIS, Upgrading o Resistane and Cli Deormation Capait o Deiient Conrete Columns, in Seismi Risk Assessment and Retroitting with speial emphasis on existing low rise strutures (A.Ilki, ed.), Proeedings, Workshop, Istanbul, Nov. 7, Springer, Dordreht. D.BISKINIS & M.N.FARDIS, Cli Deormation Capait, Resistane and Eetive Stiness o RC Members with or without Retroitting, 4 th World Conerene on Earthquake Engineering, Beijing, paper , Ot. 8. D.BISKINIS & M.N.FARDIS, Chapter 5: Upgrading o Resistane and Cli Deormation Capait o Deiient Conrete Columns, in Seismi Risk Assessment and Retroitting with speial emphasis on existing low rise strutures (Ilki A et al, eds.), Springer, Dordreht, 9 D.BISKINIS & M.N.FARDIS, Ultimate Deormation o FRP-Wrapped RC Members, 6th Greek Nat. Conrete Conerene, Paphos, Ot. 9, paper 76 D.BISKINIS & M.N.FARDIS, Flexure-Controlled Ultimate Deormations o Members with Continuous or Lap-Splied Bars, Strutural Conrete, Vol., No., June, D.BISKINIS & M.N.FARDIS, Deormations at Flexural Yielding o Members with Continuous or Lap-Splied Bars, Strutural Conrete, Vol., No. 3, September, D.BISKINIS & M.N.FARDIS, Eetive stiness and li ultimate deormation o irlar RC olumns inluding eets o lap-spliing and FRP wrapping. Paper 8, 5th World Conerene on Earthquake Engineering, Lisbon, Sept.. D.BISKINIS & M.N.FARDIS, Stiness and Cli Deormation Capait o Cirlar RC Columns with or without Lap-Splies and FRP Wrapping, Bulletin o Earthquake Engineering, Vol., 3, DOI.7/s D.BISKINIS & M.N.FARDIS, Models or FRP-wrapped retangular RC olumns with ontinuous or lap-splied bars, Engineering Strutures, 3 (submitted).

5 Experimental Database. Range/mean o parameters in tests or alibration o expressions or the member hord rotation and seant stiness at ielding Parameter beams/olumns walls 653 retangular 4 retangular 9 members o non- 37 irlar retangular setion olumns min/max mean min/max mean min/max mean min/max mean setion depth or diameter, h (m). / / / / shear-span-to-depth ratio, L s /h / / / / 3.77 setion aspet ratio, h/b w. / / / (MPa) 9.6 / / / / axial-load-ratio, N/A -.5 /.9.6 /.86. / /.7.37 transverse steel ratio, w (%) / / /.44.7 / total longitudinal steel ratio tot (%) / / / / diagonal steel ratio, d (%) /.68.7 / transverse steel ield stress w, MPa 8 / / / / longitudinal steel ield stress, MPa 47 / / / /

6 Experimental Database. Range/mean o parameters in tests or alibration o expressions or ultimate rvature in monotoni or li loading Parameter 45 retangular beams/olumns 59 retangular walls 54 monotoni 6 li 3 monotoni 46 li min/max mean min/max mean min/max mean min/max mean setion depth or diameter, h (m). /.8.3. / / /..99 setion aspet ratio, h/b w 5/ /.5.. / / (MPa) 9.7 / / / / axial-load-ratio, N/A /.78.8 / / /..7 transverse steel ratio, w (%) / / / /.5.4 total longitudinal steel ratio tot (%) / / / / transverse steel ield stress w, MPa / / / / 56 5 longitudinal steel ield stress, MPa 77 / / / / 58 55

7 Parameter Experimental Database 3. Range/mean o parameters in tests or alibration o expressions or the member ultimate li hord rotation beams/olumns walls 59 retangular 95 retangular 53 members o non- 43 irlar retangular setion olumns min/max mean min/max mean min/max mean min/max mean setion depth or diameter, h (m). / / / / shear-span-to-depth ratio, L s /h / / / / 4. setion aspet ratio, h/b w. / / / (MPa). / / / / axial-load-ratio, N/A -. /.9.65 /.86.6 / /.7.5 transverse steel ratio, w (%).5 / / / / total longitudinal steel ratio tot (%) / / / / diagonal steel ratio, d (%) /.68.8 / transverse steel ield stress w, MPa 8 / / / / longitudinal steel ield stress, MPa 8 / / / /

8 Yield ed& ailure uepopeteso properties o RC setions

9 M-φ at ielding o setion w/ retangular ompression zone (width b, eetive depth d) p (, p ) setion analsis Yield moment (rom moment-equilibrium & elasti σ-ε laws): V s E E bd M Yield moment (rom moment-equilibrium & elasti σ-ε laws):, : tension & ompression reinorement ratios, v : web reinorement ratio, ~uniorml distributed between, : (all normalized to bd); = d /d. d E s / Curvature at ielding o tension steel: rom axial ore-equilibrium & elasti σ-ε laws ( = E s /E ): A B A / v v bd N B bd N A.5, d E d.8 Curvature at ~onset o nonlinearit o onrete:.5,.8 v v s v B bd N bd E N A

10 Moment at orner o bilinear envelope to experimental moment- deormation rve vs ield moment rom setion analsis Let: 85 beams/olumns, CoV:6.3%; Right: 4 ret. walls, CoV:6.9% median: M,exp =.99M,pred 3 median: M,exp =.5M,pred 75 M,exp (k knm) M,exp (kn Nm) M,pred (knm) Bias b +.5% or -%, beause orner o bilinear envelope o the experimental moment-deormation rve st ielding in setion. Same bias onsidered to appl to predited ield rvature M,pred (knm)

11 Empirial ormulas or ield rvature - setion w/ retangular ompression zone or beams or olumns: or walls: E d E h s.37 E d s s s.47 E h Empirial expressions don t have a bias w.r.to experimental ield moment; but satter is larger: In ~ test beams, olumns or walls: CoV: ~8%

12 Flexural ailures - olumns

13 Flexural ailures - beams

14 re (kn) Applied or Ap pplied ore (kn) Conventional deinition o ultimate deormation The value beond whih, an inrease in deormation annot inrease the resistane above 8% o the maximum previous (ultimate) resistane re (kn) Applied or Fore (kn N) 5 5 QRC Q-RC onventional -5ultimate -5 a a - - deormation oinides Deletion (mm) Deletion (mm) w/ real ailure onventional ultimate deormation beore real ailure b N) Applied ore (k Deletion (mm) Deletion (mm) b Displaement (mm)

15 Ultimate rvature o setion with retangular ompression zone, rom setion analsis Conrete σ-ε law: Paraboli up to, ε o, onstant stress (retangular) or ε o < ε < ε Steel σ-ε law: Elasti-peretl plasti, i steel strain rather low and onrete ails irst; Elasti-linearl strain-hardening, i steel strains are relativel high and steel breaks at stress and strain t, ε su.

16 Possibilities or ultimate rvature:. Setion ails b rupture o tension steel, ε s = ε su, beore extreme ompression ibers reah their ultimate strain (spalling), ε < ε Ultimate rvature ors in unspalled setion, due to steel rupture: su su. Compression ibres reah their ultimate strain (spalling): ε = ε the onined onrete ore beomes now the member setion. Two possibilities: i. The moment apait o the spalled setion, Μ Ro, never inreases above 8% o the moment at spalling, Μ R : Μ Ro <8Μ.8Μ R Ultimate rvature ors in unspalled setion, due to the onrete: ii. Moment apait o spalled setion inreases above 8% o the moment at spalling: Μ Ro >.8Μ R The onined onrete ore is now the member setion and Cases and (i) - applied or the onined ore -are the two possibilities or attainment t o the ultimate rvature φ su, φ allated as above but or the onined ore; the minimum o the two is the ultimate rvature. su d d M R bd ( )( ) ( )( ) 3 s o 3 o 4

17 Ultimate rvature o setion w/ retangular ompression zone or steel rupture: d su su t t o su t t o su 3 3 Steel ruptures beore onrete rushes, ater ompression steel ields, i ν: d su su su t v t su su su t v t su 3 3 ξ su allated rom axial ore equilibrium or: t v t su o t su 3 v t su o 3 ν=n/bd, ω, ω : tension & ompression meh. reinorement ratios, ωv: web meh. reinorement ratio ~uniorm distribution between ω, ω (ω= /); =d /d. su t t o su 3, ( ); Steel ruptures beore onrete rushes or ompression steel ields, i ν: su v su ξ su rom: ) ( 3 su su s t t v su o E ) ( 3 ) ( 3 ) ( su su s t t su t su o su su s t t su t su o su s su E E

18 Ultimate rvature o setion w/ retangular ompression zone or onrete rushing: d Conrete rushes ater tension steel ields, w/o ompression steel ielding, i ν : o v 3 d ξ rom axial ore equilibrium, or: v 3 Conrete rushes w/ tension & ompression steel ielding i ν : ) ( 3 v v o Conrete rushes w/ tension & ompression steel ielding, i ν : o v o v 3 3 v o v 3 ξ rom: Conrete rushes ater ompression steel ields w/o tension steel ielding i ν : Conrete rushes ater ompression steel ields, w/o tension steel ielding, i ν : ξ rom: o v 3 ) ( 3 v v o

19 ν<ν s, - LHS Eq.(3.39)? no ν<ν s, - RHS Eq.(3.39)? no Unonined ull setion Steel rupture es es es δ satisies Eq.(3.38)? su rom Eq.(3.4) su rom Eq.(3.4) es Unonined ull setion Spalling o onrete over no ν<ν s, - RHS Eq.(3.39)? no φ su rom Eq.(3.36) Conined ore ater spalling o onrete over. Parameters are denoted b an asterisk and omputed with: b, d, d replaed b geometri parameters o the ore: b, d, d ; N,,, v normalized to b d, insteado bd; σ-ε parameters o onined onrete,,, used in lieu o, Rupture o tension steel ν*<ν* s, - LHS Eq.(3.39)? es * su rom Eq.(3.4) ν<ν, - LHS Eq.(3.44)? no ν<ν, - RHS Eq.(3.44)? es es no δ satisies Eq.(3.4a)? rom Eq.(3.47) rom Eq.(3.46) es no no ν<, - LHS Eq.(3.48)? no ν<, - RHS Eq.(3.48)? no ν*<ν* s, - RHS Eq.(3.39)? no es Failure o ompression zone (onrete) * su rom Eq.(3.4) φ su rom Eq.(3.36) es rom Eq.(3.45) es rom Eq.(3.49) ν*<ν*, - LHS Eq.(3.44)? es * rom Eq.(3.47) Compute moment resistanes: M R (o ull, unspalled setion) and M Ro (o onined ore, ater spalling o over). M Ro < 8M.8M R? no Ultimate rvature o onined ore ater spalling o onrete over es φ rom Eq.(3.37) no ν*<ν*, - RHS Eq.(3.44)? es * rom Eq.(3.45) no * rom Eq.(3.46) φ rom Eq.(3.37)

20 Test results vs ultimate rvature w/ ailure strains or li lexure per EN 998-3:5 : Steel: ε su :.5%, 5%, 6% or steel lass A, B, C per Euroode,8 ε.4.5 αρ /, s w,7 median: φ u,exp =.96φ u,pred exp (/m) φ u,e,6,5,4,3,, li, slip li, no-slip,,,3,4,5,6,7,8 φ u,pred (/m) li test results Cli all Conrete rushing Steel rupture Median C.o.V. 46.7% 55.% 38.% No

21 Test results vs ultimate rvature w/ ailure strains or li lexure per Biskinis & Fardis (adopted in ib MC): Monotoni lexure: max. available steel strain: (7/)ε su Cli lexure:. max. available steel strain: (3/8)ε su * w.35 h mm.85 ( ) K * w.35 h mm. ( ) K φ u,exp ( /m) median: φ u,exp =φ u,pred li, slip li, no-slip monotoni, slip monotoni, no-slip φ u,pred (/m) monotoni & li data, no. 474, median=., CoV=49.7% li test data: Cli Conrete Steel all rushing rapture Median C.o.V. 44.% 5.6% 34.% No

22 Yield ed& ailure uepopeteso properties o RC members

23 Flexural behavior at member level (Moment- hord rotation) Deinition o hord rotations, θ, at member ends Elasti moments at ends A, B rom hord rotations at A, B: Μ Α = (ΕΙ/L)(θ Α +θ Β ), Μ Β = (ΕΙ/L)(θ Β +θ Α )

24 Fixed-end rotation o member end due to bar slippage rom their anhorage zone beond member end Slippage o tension bars rom region beond end setion (e.g. rom join or ooting) rigid-bod rotation o entire shear span = ixed-end end rotation, θ slip (inluded in measured hord-rotations o test speimen w.r. to base or joint; doesn t aet measured relative rotations between an two member setions). I s = slippage o tension bars rom anhorage θ slip = s/(-ξ)d I bond stress uniorm over straight length l b o bar beond setion o maximum moment bar stress dereases along l b rom σ s (= L at ielding) at setion o maximum M to zero at end o l b s=σ s l b /(E s ) l b = bond ore demand d per unit length (=AA s σ s /(dd bl )=dd bl σ s /4), divided id d b ~bon strength (assume = ) ε s (=σ σ s /E s )/(-)d = φ At ielding o member end setion, slip 8 d bl ( L, in MPa )

25 Fixed-end rotation o member end due to rebar pull-out rom anhorage zone beond member end, at member ielding φ,measured /(φ,predited +,slip,/l gauge ) no.6 measurements w/ slip: median =., C.o.V = 34%.5 Ratio:.5 experimental-topredited ield.75 rvature (w/ orretion or.5.5 ixed-end- end rotation) in terms o gauge length.75 ) e to slip iniples +φ,due / (φ,st-pri φ,ex xp l gauge / h

26 Chord rotation o shear span at ielding o end setion per EN 998-3:5 Ret. beams or olumns: Ls av z h.4.5 Ret. or non-ret. walls: 3 Ls Ls av z.3 asl, slip 3 Shit rule : 3 Diagonal raking shits value o ore in tension reinorement to a setion at a distane rom member end equal to z (internal lever arm) z = d-dd in beams, olumns, or walls o barbelled or T-setion, z =.8h in retangular walls. a v =, i V R > M /L s ; a v =, i V R M /L s. V R = ore at diagonal raking per Euroode (in kn, dimensions in m, in MPa):.. R, max8 5 d d a sl =, i no slip rom anhorage zone beond end setion; a s l =, i there is slip rom anhorage zone beond end setion. V N A / 3 / 6 / 3, 35. b d w a sl, slip

27 Test-model omparison θ Beams/ret. olumns, no. tests: median=., CoV=3.%.5 θ,exp (% %).5 median: θ,exp =.θ,pred.5 ret. beams / olumns θ,pred (%)

28 , Test-model omparison θ Walls, no. tests: 386,,8,8 θ,exp (%),6,4 median: θ,exp =.97θ,pred θ,exp (%),6,4 median: θ,exp =.θ,pred, Retangular walls, Retangular walls Non-retangular Walls Non-retangular Walls,,4,6,8,,,4,6,8, θ,pred (%) θ,pred (%) Expression in EN 998-3:5 Modiied expression adopted in MC median=.97, CoV=3.% L az 5h s V.4545 asl, slip 3 3Ls median=., CoV=3.9%

29 Test-model omparisons - θ Cirlar olumns - not in EN 998-3:5: no. tests: 9 Ls avz Ls.7min ; asl, slip 3 5DD median=., CoV=3.7%,5 median: θ,exp =θ,pred p (%) θ,ex,5,5 irlar,5,5,5 θ,pred (%)

30 Eetive elasti stiness, EI e (or linear or nonlinear analsis) Part o EC8 (or design o new buildings): EI e : seant stiness at ielding =5% o unraked gross-setion stiness. - OK in ore-based design o new buildings (saesided or ores); - Unsae in displaement-based assessment or displaement demands). More realisti: M L EIe 3 seant stiness at ielding o end o shear span L s =M/V s

31 Test-model omparison EI e Beams/ret. olumns, no. tests: 66 6 median=., CoV=3.% EI e M 3 L s (M 3θ MNm L s /3 ) exp (M ) median: (M L s /3θ ) exp =M L s /3θ ) pred ret. beams / olumns (M L s /3θ ) pred (MNm )

32 Test-model omparison EI e Walls, no. tests: M L detail s median: 5 EI (M L s /3θ ) exp =.35(M L s /3θ ) e pred 3 (M L MNm s /3θ ) exp (M ) 4 3 With expression or θ in EN 998-3:5 median=.35 CoV=4.8% non-retangular walls retangular walls 3 4 ( / θ ) ( ) 4 median: (M L s /3θ ) exp =.98(M L s /3θ ) pred d (M L MNm s /3θ ) exp (M ) median: (M L s /3θ ) exp =.35(M L s /3θ ) pred non-retangular walls retangular walls (M θ L s /3θ ) pred (MNm ) (M L s /3θ ) pred (MNm ) 5 5 detail median: (M L s /3θ ) exp =.98(M L s /3θ ) pred 3 With new expression or θ o walls (adopted in MC) median=.98 CoV=4.% (M p (MNm L s /3θ ) exp ) (M (MNm L s /3θ ) exp ) 75 5 non-retangular walls 5 retangular walls 3 4 (M L s /3θ ) pred (MNm ) non-retangular walls retangular walls (M L s /3θ ) pred (MNm )

33 Test-model omparison EI e Cirlar olumns - not in EN 998-3:5, no. tests: 73 EI e M Ls 3 median=.99, CoV=3.% 4 75 median: median: 35 (M L s /3θ ) exp =.99(M L s /3θ ) pred (M L s /3θ ) exp =.99(M L s /3θ ) pred 5 (M exp (MNm m L s /3θ ) ) irlar (M L s /3θ ) pred (MNm ) (M exp (MNm L s /3θ ) ) detail irlar (M L s /3θ ) pred (MNm )

34 Empirial seant stiness to ielding, EI e, independent o amount o reinorement - not in EN 998-3:5 EIe L s N a.8 ln max ;.6.48 min[ 5; ( MPa)] E I h A (all variables known beore dimensioning the longitudinal reinorement) I there is slippage o longitudinal bars rom their anhorage zone beond the member end: a =.8 or olumns; a =. or beams or non-retangular walls (barbelled, T-, H-setion); a =.5 or retangular walls; a =. or members with irlar setion. I there is no slippage o longitudinal bars: eetive stiness x4/3

35 Test-model omparison Empirial EI e, independent o amount o reinorement - not in EN 998-3:5 6 Beams/olumns no. tests: 66 median=. CoV=36.% (M θ MNm L s /3θ ) exp (M ) median: (M L s/3θ ) exp =EI pred EI pred (MNm )

36 Test-model omparison Empirial EI e independent o reinorement, not in EN998-3: 5 Walls no. tests: 386 median=. CoV=44.6% (M xp (MNm L s /3θ ) ex ) median: (M L s /3θ ) exp =EI pred non-retangular walls retangular walls 3 4 (M xp (MNm L s /3θ ) ex ) 5 5 detail detail median: (M L s /3θ ) exp =EI pred EI pred (MNm ) EI pred (MNm ) 75 median: (M L s /3θ ) exp =EI pred 5 non-retangular walls retangular walls 5 5 detail median: (M L s /3θ ) exp =EI pred Cirlar olumns no. tests: 73 median=.995 CoV=3.4% (M xp (MNm L s /3θ ) ex ) EI pred (MNm ) irlar (M xp (MNm L s /3θ ) ex ) EI pred (MNm ) irlar

37 Flexure-ontrolled ultimate hord rotation rom rvature & plasti hinge length per EN 998-3:5 pl.5l pl θu θ θu θ ( φu φ ) Lpl Ls : ield rvature (setion analsis); Option : Coninement per Euroode αρ αρ sx sx w w.5.5 : :, o. sx s sx u min,, d su, ( su ) d Option : New, per EN 998-3:5 5αρsx w.5. 5αρ 3.7 / / w L.L.7h. 4 d pl b w sx w,.4.5 sx s / b w L L /3.h.d / : oninement eetiveness: index : onined; s h s b h retangular setion: α ρ s : stirrup ratio; b h 6bh s irlar setion & hoops: L s =M/V: shear span at member end; h α s h : enterline spaing o stirrups, D h: setion depth; D d b : bar diameter;, b, h : onined ore dimensions to enterline o hoop; b, : MPa i : enterline spaing along setion perimeter o longitudinal bars (index: i) engaged b a stirrup orner or ross-tie. pl.86 i

38 Test-model omparison ultimate hord rotation rom rvatures & plasti hinge length per EN 998-3:5, no. tests: Option : oninement per EC median=.88, CoV=5.3% 7,5 5 Cli loading median: θ u,exp =.88θ u,pred Option : new oninement per EC8-3 median=.9, CoV=5.% % Cli loading,5 median: θ u,exp =.9θ u,pred,5 θ u,e exp (%) 7,5 5 θ u,e exp (%) 7,5 5,5 beams & olumns ret. walls non-ret. setions,5 5 7,5,5 5 7,5 θ u,pred (%),5 beams & olumns ret. walls non-ret. setions,5 5 7,5,5 θ u,pred (%)

39 Flexure-ontrolled ultimate hord rotation o ret. beams, olumns, walls, non-ret. walls & irlar olumns rom rvatures & plasti hinge length b Biskinis i & Fardis, 3 -adopted d in ibmc Flexure-ontrolled ultimate hord rotation, aounting separatel or slippage in ield-penetration length, rom ielding till ultimate deormation: u a sl u, slip ( u ) L pl L pl LL s Coninement per ib MC: 3 4 w w 3. 5 Monotoni loading - Ret. beams, olumns, walls, non-retangular walls: αρw w 7 ε,.35.57, ho ( mm) su, mon su, nomin al Cli loading: αρ w w 3 ε 35,.35.4, ho ( mm) su, su, nomin al 8 Ret. beams/olumns/walls, non-ret. walls: Cirlar olumns: L L pl, mon h..44 min 9; L s h Ls L pl,.h min 9; 3 h L s.6d min 9 6 D pl,, ir ;

40 Post-ield ixed-end rotation o member end due to bar slippage rom ield penetration length beond member end, rom ielding till ultimate t lexural l deormation per Biskinis i & Fardis, 3 - adopted in ibmc (not in EN 998-3:5) Monotoni loading: 9.5 d 6 d / u, sli p bl u bl u Cli loading: 5.5 d or d / or u, slip 5 bl u bl u Complete pull-out o beam bars, due to short anhorage in orner joint

41 Test-model omparison Cli ultimate hord rotation rom rvatures & plasti hinge length per Biskinis & Fardis, Ret. beams/olumns/walls, non-ret. walls - no. tests: median=., CoV=43.% Cirlar olumns no. tests: 43, median=., CoV=3.3% 6,5 Cli loading median: θ u,exp =θ u,pred 4 median: θ u,exp =θ u,pred p (%) θ u,exp 7,5 5 (%) θ u,exp 8 6,5 beams & olumns ret. walls non-ret. setions s,5 5 7,5,5 θ u,pred (%) 4 irlar θ u,pred (%)

42 Empirial li lexure-ontrolled ultimate hord rotation o ret. beams/olumns/walls, non-ret. walls in EN998-3:5 & ibmc or: θ um w αρsx ν max(.; ω') Ls ρd.6(.3 ) 5 (.5 ) max(.; ω) h.5 αρsx pl ν max(.; ω'). Ls ρd θum θum θ.45 (.5 ) 5 (.75 ) max( (.; ; ω ) h, ': mehanial ratio o tension (inluding web) & ompression steel; : N/bh (b: width o ompression zone; N> or ompression); L s /h : M/Vh: shear span ratio; s α : oninement eetiveness ator : h s b h i α sx : A sh /b w s h : transverse steel ratio // diretion o loading; b h 6bh d : ratio o diagonal reinorement. Walls: st expression divided id d b.6; nd multiplied li b.6 Cold-worked brittle steel: st expression divided b.6; nd b. Non-seismiall detailed members with ontinuous bars Plasti part, pl um=θ um -, o ultimate hord rotation: divided b...35,3.35 w

43 Test-model omparison Empirial li ultimate hord rotation o members with seismi detailing per EN 998-3:5 no. tests Model or total um Model with um = + pl median=., CoV=37.8% median=., CoV=37.6%,5 Cli loading,, p,p Cli loading median: θ u,exp =θ u,pred,5 median: θ u,exp, p =θ u,pred exp (%) θ u, 7,5 5,exp (%) θ u, 7,5 5 5% ratile: θ u,exp =.5θ u,pred,5 beams & olumns ret. walls non-ret. setions,5 5 7,5,5 θ u,pred (%) 5% ratile: θ u,exp=.5θ u,pred,5 beams & olumns ret. walls non-ret. setions,5 5 7,5,5 θ u,pred (%)

44 Test-model omparison Empirial li ultimate hord rotation o members without seismi detailing per EN 998-3:5 no. tests 48 Model or total um median=., CoV=3.6% Model with um = + pl median=.99, CoV=3.8% median: θ u,exp =θ u,pred 8 median: θ u,exp =.99θ u,pred xp (%) θ u,ex 5 4 xp (%) θ u,ex θ u,pred (%) θ u,pred (%)

45 General empirial ultimate hord rotation o ret. beams/olumns/ walls & non-ret. walls per Biskinis & Fardis, adopted in ib MC (not in EN998-3:5) pl u hbw st (.55a w s. d.6a.5max.5;min;. min 9; 5. 5 ) sl α hbw st :. or hot-rolled or Tempore bars;.95 or brittle old-worked bars; α : = or li loading, 7,5 = or monotoni; α sl: = i slippage o long. bars rom 5 anhorage zone is possible, = otherwise;,5 b w : width o (one) web Non-seismiall detailed members: pl um=θ um - divided b.. h max(.; ) b w max(.; ; ) θ u,exp (%) L h li loading,5 median: θ u,exp =θ u,pred 3 w 5% ratile: θ u,exp =.5θ u,pred beams & olumns ret. walls non-ret. setions,5 5 7,5,5 θ u,pred (%) no. tests:, median=., CoV=37.6%

46 Eet o lap-spliing the olumn bars in the plasti hinge region

47 Members with ribbed bars lap-splied over length l o inside the plasti hinge region per EN 998-3:5 or other options EN 998-3:5:. Both bars in pair o lapped ompression bars ount as ompression steel.. For the ield properties (M,, θ ), the stress s o tension bars is: s = (l o /l o,min ), i l o < l o,min =(.3 / )d b 3. Ultimate hord rotation (, in MPa) θ u = + pl u(l o /l ou,min ), i l o < l ou,min = d b /[(.5+4.5α rs ω sx ) ],, in MPa, ω sx =ρ sx w / : meh. transverse steel ratio // loading, α rs =(-s h /b o )(-s h /b o )n restr /n tot (n restr /n tot : restrained-to-total lap-splied bars). Or, Eligehausen & Lettow 7 or ib MC: s / 3. l b d max 5. kk tr, d b max( db; mm) d b d kk tr n d b b k s nl A s h sh d = min[a/; ; ] ] d b, d 3d b max = max[α/; ; ] 5d b, in MPa

48 Test-model omparison: Yield moment & hord rotation, eetive stiness, ultimate li hord rotation - lapped ribbed bars per EN 998-3:5 75 median: M,exp =M,pred median: θ,exp =.5θ,pred 5,5 no.tests: 4 median=. CoV=.8% exp (KNm) M,e M no.tests: 9 median=.5 CoV=% θ,exp (%),5 θ M,pred (KNm),5,5 θ,pred (%) median: (M L s /3θ ) exp =.955(M L s /3θ ) pred median: θ u,exp =.35θ u,pred (M (MNm L s /3θ ) exp ) 5 5 no.tests: 9 median=.955 CoV=4.8% (M L s /3θ ) pred (MNm ) (%) θ u,exp EI e 4 no.tests: 8 median=.35 CoV=39.3% 8 6 θ u θ u,pred (%)

49 Test-model omparison: Yield moment & hord rotation, eetive stiness, - lapped bars, steel stress per Eligehausen & Letow 7 75 median: M,exp =.98M,pred no.tests: 9 median=.3 p (%) θ,ex CoV=.5%,5,5 median: θ,exp =.3θ,pred θ,5,5 θ,pred (%) no.tests: 4 Median=.98 CoV=% no.tests: 9 median=.97 CoV=4.6% (MNm ) M,exp (KNm m) (M L s /3θ ) exp M M,pred (KNm) 5 median: (M L s /3θ ) exp =.97(M L s /3θ ) pred 5 5 EI e (M L /3θ ) d (MNm )

50 Members with smooth hooked bars, with or without lap splie (o length l o ) in the plasti hinge per EN 998-3:5 Provided that lapping l o 5d b :. Yield properties M,, θ : As in members with ontinuous ribbed bars.. Ultimate li hord rotation: For ontinuous bars:.8θ um (: ~.95 or smooth bars /. or no seismi detailing) θ um = +.75 pl um (: ~.9 or smooth bars /. or no seismi detailing) For lapping l ti o 5d b : Test-model-ratio or θ um um x.9(+min(4, l o /d b )) or θ um = + pl um x.9 min(4, l o /d b ) L s or pl um not redued b l o no laps or laps Mdi Median C.o.V. 33.3% 33.4% no. tests 34 (ultimate ondition not neessaril ontrolled b region right above the lap)

51 Cli shear resistane sta o RC members

52 Cli shear resistane per EN 998-3:5 Shear resistane in pl. hinge ater lex. ielding, as ontrolled b stirrups (linear dea o V & V w with li plasti rotation dutilit ratio pl θ =(- )/ > V R h x min L s pl Ls N ;.55 A 5.5 min 5; μθ.6 max(.5; ρtot ).6 min5; A Vw h V w =ρ w b w z w, due to stirrups (b w : web width, z: internal lever arm; ρ w : shear rein. ratio) ρ tot : total t longitudinal l reinorement ratio h: setion depth x : depth o ompression zone at ielding A = b w d Shear resistane as ontrolled b web rushing (diagonal ompression) Walls, beore lexural ielding ( pl θ = ) or ater (li pl θ > ): V R V pl N Ls.6 min 5,.8 min.5,.5 max(.75, ). min, b z.85 A R Squat olumns (L s /h ) ater lexural ielding (li θ pl > ): 4 pl N. min 5,.35.45tot min, 4 bwz sin 7 A δ: angle between axis and diagonal o olumn (tanδ=.5h/l s ) tot h w

53 Test-model omparison: Cli shear resistane in plasti hinge (ater lexural ielding) as ontrolled b stirrups, per EN 998-3:5 no. tests: 36 median=.995 CoV=4.7% 8 6 V exp (kn N) 4 Retangular Cirlar walls & piers V pred (kn)

54 Test-model omparison: Cli shear resistane as ontrolled b web rushing (diagonal ompression), per EN 998-3:5 Walls Squat olumns N) V exp (k N) V exp (k V pred (kn) V pred (kn) no. tests: 6, median=., CoV=9.3% no. tests: 4, median=., CoV=9.6%

55 FRP Jakets per EN998-3:5

56 Experimental Database 4. Range and mean values o parameters in the tests o FRP-jaketed retangular olumns in the database Parameter 9 olumns with ontinuous bars (45 with CFRP, 4 with GFRP, 7 with AFRP and 3 with other omposite) 45 olumns with lapsplied bars (4 with CFRP, 3 with GFRP) min-max mean min-max mean eetive depth, d (mm) shear-span-to-depth span ratio, L s /h onrete strength, (MPa) vertial bar ield stress, (MPa) stirrup ield stress, w (MPa) axial-load-ratio, N/A transverse steel ratio, w (%) total vertial steel ratio, tot (%) geometri ratio o FRP, ρ (%) nominal FRP strength (MPa) elasti modulus o FRP, E (GPa) lapping-to-bar-diameter ratio, l o /d b

57 FRP-wrapping o plasti hinges in retangular members with ontinuous bars per EN 998-3:5 M R, M : Enhaned b FRP jaket (b 9% w.r.to allated w/o oninement) EN 998-3:5: inrease negleted. Eetive (elasti) stiness EI e : unaeted b FRP; pre-damage: 35% drop EN998-3:5: Flexure-ontrolled ultimate hord rotation, θ u : Coninement b FRP inreases that due to the stirrups b α ρ e,e /, where: ρ =t /b w : FRP ratio // diretion o loading;,e : FRP eetive strength:,e min u,, ε u, E min min.5;.7 u,, E : FRP tensile strength & Modulus; ε u, : FRP limit strain. CFRP/AFRP: ε u, =.5%; GFRP: ε u, =% FRP-oninement eetiveness: h R b R 3bh b, h: sides o setion; R: radius at setion orner u,, ε u, E ρ

58 Test-model omparison - ield properties or FRP-wrapping o retangular olumns with ontinuous bars per EN 998-3:5 no.tests: 3 (pre-damaged or not) median=.9, CoV=9.4% no.tests: 59 (no pre-damage) median=.3, CoV=37.3% 5 3 non-predamaged median (non-predamaged) predamaged median (predamaged) median: M,exp =.9M,pred,5 (KNm) M,exp M,pred (KNm) M θ,exp (%),5,5 θ,5,5,5 3 θ,pred (%) EI e (no pre-damage), no.tests: 59, median=., CoV=3%

59 Yield properties or FRP-wrapping o the plasti hinge and ontinuous bars Biskinis & Fardis 7, 3 Yield moment, M : Strength o FRP-onined onrete, instead o, in setion-analsis or φ, M, inluding the allation o the onrete Elasti Modulus, E ; E ma be estimated per ibmc, using instead o : E =( (MPa)) /3 b a x u, rom (widel used) Lam & Teng 3: 3.3 b u, : eetive strength o FRP: u, =E (k e ε u, ) E : Elasti Modulus o FRP, ε u, : FRP ailure strain, k e : FRP eetiveness ator, equal to.6 per Lam & Teng (~same results using other FRP-oninement models: Teng et al 9, Samaan et al 998, Bisb et al 5, Ilki et al 8, Wang et al ) Chord rotation at ielding, θ, eetive stiness, EI e : Yield rvature φ allated with (as above) & multiplied times orretion ator.6 EI e = M L s /3

60 Test-model omparison - ield properties or FRP-wrapping o ret. olumns with ontinuous bars per Biskinis & Fardis 7, 3 no.tests: 3 (pre-damaged or not) median=.6, CoV=9.3% no.tests: 59 (no pre-damage) median=., CoV=37.3% 5 3 non-predamaged median (non-predamaged) predamaged median (predamaged) median: M,exp =.6M,pred.5 xp (KNm m) M,ex 5 5 M θ,exp (% %) M,pred (KNm) θ,pred (%).5.5 θ EI e (no pre-damage): no.tests: 59, median=.99, CoV=3.4%

61 Extension o empirial ultimate plasti hord rotation o ret. olumns with ontinuous bars & FRP-wrapping - Biskinis & Fardis 7, 3 Pre-damaged or not: θ pl u.85 with: aρ asl.5a.5 u, e a.6 min.4; ρ ν max., ω' max., ω u,.3..5min.4; =.8 or CFRP or polaetal iber (PAF) sheets, =.8 or GFRP or AFRP. u, =E (k e ε u, ): eetive FRP strength ρ Ls h u,.35 5 αρ w w αρu, e.75 ρd

62 Test-model omparison ultimate li hord rotation or FRP-wrapping o ret. olumns with ontinuous bars: no. tests 8 (pre-damaged or not) EN 998-3:5 v Biskinis & Fardis 7, 3 EN 998-3:5 Biskinis & Fardis 3 median=.9, CoV=3.6% median=.5, CoV=3.4% 5 5 median (all): θ u,exp =.9θ u,pred median (all): θ u,exp =.5θ u,pred θ u,e exp (%) 5 θ u,e exp (%) 5 CFRP jaket 5 AFRP jaket GFRP jaket PAF jaket θ u,pred (%) CFRP jaket 5 AFRP jaket GFRP jaket PAF jaket θ u,pred (%)

63 Alternative ultimate li hord rotation or ontinuous bars & FRP-wrapping per GCSI (KANEPE).5.5 wd Test-to-predited ultimate li hord rotation, θ u no.tests: 8, FRP l t i ti median=.75, CoV=54.5% 5% ω wd : FRP volumetri ratio α: FRP-oninement eetiveness ator CFRP (adopted here also or AFRP and PAF):.35 GFRP: FRP eetive strength:.7, e u, ψ: redution ator or number o laers (k); ψ= ork<4 k μ θ 4 θ θ u or k 4 μ δ μ 3 φ θ u,e exp (%) median (all): θ u,exp =.75θ u,pred CFRP jaket AFRP jaket GFRP jaket PAF jaket θ upred (%)

64 FRP-wrapped retangular members with ribbed bars lap-splied over length l o in the plasti hinge: EN 998-3:5 & other options EN 998-3:5:. Both bars in pair o lapped ompression bars ount as ompression steel.. For the ield properties (M,, θ ), the stress s o tension bars is: s = (l o /l o,min ), i l o < l o,min =(. / )d b (, in MPa), l o,min : one-third shorter than without t FRP. 3. Ultimate hord rotation θ u = + pl u(l o /l ou,min ), i l o < l ou,min = d b /[( α l ρ,e ) ], : MPa, ρ =t /b w : FRP ratio // loading,,e : eet. FRP strength (MPa), α l = α (4/n tot ) (n tot : total lap-splied bars; onl the 4 orner bars restrained). Or, Eligehausen & Lettow 7 or ibmc: s / 3 l b d max 5. d b d b d max( db; mm) d = min[a/; ; ] ] d b, d 3d b max = max[α/; ; ] 5d b, in MPa. kk tr, kk tr n d b b k s n s l A h sh k n E t s E

65 Test-model omparison - Yield properties or FRP-wrapping o ret. olumns with bars lap-splied over length l o per EN998-3:5, no.tests 45 M : median=.75, CoV=.5% θ : median=.75, CoV=7.7% 75 5 median: M,exp =.75,pred.75.5 median: θ,exp =.75θ,pred (KNm) M,exp exp (%) θ, M.5 θ M,pred (KNm) θ,pred (%)

66 Test-model omparison - ield properties o FRP-wrapped irlar olumns with lap-splied li bars per EN998-3:5 (Biskinis & Fardis 7, 3) no.tests: 4 median=. no.tests: 4 CoV=5.% median=.98 CoV=% M,exp (KNm) median: M,exp =M,pred M M pred,pred (KNm) 8 xp (%) θ,ex,5,5 median: θ,exp =.98θ,pred,5,5 θ,pred (%) no.tests: 4 θ median=.96 CoV=.% (M xp (MNm L s /3θ ) ex ) 6 4 EI e median: (M L s /3θ ) exp =.96(M L s /3θ ) pred (M L s /3θ ) pred (MNm )

67 Extension o empirial ultimate plasti hord rotation or retangular members with lap-splied bars & FRP-wrapping Biskinis & Fardis 7, 3 Required lapping or no adverse eet o lap-splie on ultimate deormation db lou,min aρ u n tension, e with: aρ u, e u, =E (k e ε u, ) a min.4; ρ u,.5min.4; n tension : number o lapped bars on tension side o setion pl l I l o o <l ou,min, θ pl u is redued as: ulap, min, u l ou,min i (αρ u / ),e negleted in θ pl u i /n tension.5 ρ u, pl

68 Test-model omparison ultimate li hord rotation o FRP-wrapped o retangular olumns w/ lap-splied bars, no.tests 44 (pre-damaged or not) EN998-3:5 v Biskinis & Fardis 7, 3 EN 998-3:5 median=.89, CoV=36.3% 3% Biskinis & Fardis 3 median=.5, CoV=3.% % median: θ u,exp, p =.885θ u,pred median: θ u,exp =.5θ u,pred 8 8 xp (%) θ u,ex 6 4 xp (%) θ u,ex θ u,pred (%) θ u,pred (%)

69 Extension o ultimate plasti hord rotation model with rvatures and plasti hinge length to irlar olumns with lap-splied li bars & FRP-wrapping Biskinis i & Fardis 3. L pl s a sl u slip ( ) L 5L u u pl, 5 u, slip 5. d bl u L pl,, ε as in members (FRP-wrapped or not) with ontinuous bars Steel strain at ultimate deormation o member depends on lap length, i l o < l ou,min : l su o su, l.. lou,min l l l o o,min with: ou,min 5 6 6a / sh h d bl E s θ u,exp (% %) median: θ u,exp =.97θ u,pred Test-to-predition ratio, no.tests: 37 median=.97, CoV=38.6% θ upred (%)

70 V Cli shear resistane o FRP-wrapped retangular members as ontrolled b diagonal tension, per EN998-3:5 R h x min L s pl Ls N,.55A.5min 5,.6max(.5, tot).6min 5, A Vw V V =min(ε u u, E u u,, u u,)ρ b w z/ : FRP-ontribution to li shear resistane: ρ :FRP ratio, ρ = t /b w ; u, :FRP tensile strength. V w =ρ w b w z w : ontribution tib ti o web steel l(b w : web width, z: int. lever arm; ρ w : steel ratio) ρ tot : total longitudinal steel ratio,4 h: setion depth, x : depth o ompression zone A = b w d Test-to-predition ratio vs μ, no. tests median=.99, CoV=4.8%: V u,pred V u,exp /V,8,6,4, h,5,5,5 3 3,5 4 4,5 5 dutilit In a FRP-retroitted member the shear resistane as ontrolled b diagonal tension annot exeed the shear resistane o old member as ontrolled b web rushing

71 RC jakets per EN998-3:5

72 Conrete Jakets (ontinued/anhored in joint; w/ or w/o lap splies in old member) Callation assumptions: Full omposite ation o jaket t& old onrete assumed (jaketed member: monolithi ), even or minimal shear onnetion at interae (roughened interae, steel dowels epoxied into old onrete: useul but not essential); o monolithi member = that o the jaket (avoid large dierenes in old & new ) Axial load onsidered to at on ull, omposite setion; Longitudinal reinorement o jaketed olumn: mainl that o the jaket. Vertial bars o old olumn onsidered at atual loation between tension & ompression bars o omposite member (~ web longitudinal reinorement), with its own ; Onl the transverse reinorement o the jaket is onsidered or oninement; For shear resistane, the old transverse reinorement taken into aount onl in walls, i anhored in the (new) boundar elements The detailing & an lap-spliing o jaket reinorement are taken into aount. Then: M R & M o jaketed member: ~% o θ o jaketed member or pre-ield (elasti) stiness: ~5% o Shear resistane o jaketed member: ~% o Flexure-ontrolled ultimate deormation θ u : ~% o those o monolithi member allated w/ assumptions above. I jaket bars are not ontinued/anhored in the joint: The jaket is onsidered onl to onine ull the old olumn setion.

73 54 jaketed members w/ or w/o lap splies: test-to-allated as monolithi M,al M,exp/ M EI exp / EI* e M. ontinuous bars plain 5db laps deormed 5db laps 4.4 plain 5db laps deormed 3db laps deormed 45db laps non-anhored jaket bars group average st. dev. o group mean EI.5 e..5,eq.()&() θ,exp/ θ (3)) / ( θ* + θ u pl Eq.( θ u,exp θ θ u a b d e g h i j k a: no treatment, b: no treatment, predamage, : welded U-bars, d: dowels, e: roughened, : roughened / predamage, g: U-bars+ roughened, h: U-bars+roughened / predamage, i: roughened+dowels, j: roughened+dowels / predamage a b d e g h i j

74 Steel jakets per EN998-3:5

75 Steel Jakets (not ontinued/anhored in joint) Jaket stops beore the joint (several mm gap to joint ae) Flexural resistane, pre-ield (elasti) stiness & lexureontrolled ultimate deormation o RC member is not enhaned b jaket (lexural deormation apait ~same as in old member inside id jaket, no beneit rom oninement); 5% o shear resistane o steel jaket, V j=a j jh, an be relied upon or shear resistane o retroitted member (suppression o shear ailure beore or ater lexural ielding); Lap-splie lamping via rition mehanism at jaketmember interae, i jaket extends to ~.5 times splie length and is bolt-anhored to member at end o splie region & ~/3 its height rom the joint ae (anhor bolts at third-point o side)