Formulation of application rules for lap splices in the new Model Code
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1 Splice Design Formulation of application rules for lap splices in the new Model Code fib TG 4.5 Bond models Stuttgart, Nov. 13 th, 2006 (by S. Lettow & R. Eligehausen) PAGE 1 OF?? Outline of presentation bond model in FE Program numerical results of splice tests equation for calculating splice strength comparison with experimental results procedure to obtain bond strength proposal 1 on basis of characteristic values proposal 2 on basis of probabilistic study formulation for design code (new MC) PAGE 2 OF??
2 Bond model in MASA3 Bond forces transfered by bond element: Pull-Out failure simulated by bond element model Splitting failure simulated by concrete material model PAGE 3 OF?? Bond model in MASA3 Influencing factors for bond model INPUT BOND MODEL PARAMETERS: rib geometry (shape of basic curve) bond conditions (bond strength/stiffness) VARIABLE BOND MODEL PARAMETERS: strain in the reinforcement (decrease of bond stress with increasing strain) stress in surrounding concrete (increase of bond stress with increasing compressive stress) cyclic loading history (decrease of bond stress with increasing load cycles) INTERACTION WITH FE MODEL: bar spacing & confining reinforcement concrete cover, concrete tensile strength PAGE 4 OF??
3 Bond model in MASA3 Actual bond stress transfer: τ =τ ( s) Ω Basic bond model: τ(s) (bond stress-slip relation) Influencing factors: Ω =Ωs Ωc Ωcyc Ω s Ω Ω c cyc I Influence of reinforcement strain Influence of concrete confinement Influence of cyclic loading history PAGE 5 OF?? Bond model in MASA3 Basic bond stress-slip relation PAGE 6 OF??
4 Bond model in MASA3 Influence of reinforcement strain Faktor Ωs [-] 1,25 Influence of Ωs Ωs(αs=0,85) without influence of reinforcement strain 1,00 with influence of reinforcement strain 0,75 0,50 εs εsy 0,25 0,00 0 εsy Stahldehnung εs [ ] 100 εs 10 % Reduction of bond stress with increasing strain in the reinforcing bar. PAGE 7 OF?? Bond model in MASA3 Influence of concrete confinement Influence of Ωc 2,25 without influence of concrete confinement Ωc(αc=0,20) Faktor Ωc [-] 2,00 with influence of concrete confinement 1,75 1,50 σc 0 N/mm2 1,25 1, Betonspannung σc [N/mm2] σc 15 N/mm2 Increase of bond stress for higher transverse pressure in the confining concrete. PAGE 8 OF??
5 Bond model in MASA3 Influence of cyclic loading Faktor Ωcyc [-] 1,25 1,00 0,75 0,50 0,25 Ω cyc 0, dissipierte Energie Λ/Λ 0 [%] Deacrese of bond stress with increasing load cycles. PAGE 9 OF?? Bond model in MASA3 Conclusions: the bond element has been implemented into a nonlinear 3D finite element code as a zero-thickness two-node finite element. the bond elemnt connects 1D truss/bar finite elements (reinforcement) with 3D solid/volume finite elements (concrete). the bond element is based on a bond stress-slip relationship which is controlled by basic model parameters. the bond element accounts for the influence of reinforcement strains, stress state of surrounding concrete and cyclic loading history. PAGE 10 OF??
6 Numerical Investigations Simalation of lap splices to investigate the main influencing parameters f cm and l s good bond conditions ( bottom cast bars ) no confinement by transverse pressure (p=0) no welded on transverse reinforcement minimum concrete strenght (f cm 15 N/mm 2 ) straight and ribbed bars in tension all bars lapped (100 % Splice) PAGE 11 OF?? Numerical Investigations Idealization & FE discretization s w Variation of the concrete strength and the lap length with and without transverse reinforcement. PAGE 12 OF??
7 Numerical Investigations Selection of FE models to simulate the three failure modes acc. to Eligehausen (1979) PAGE 13 OF?? Numerical Investigations Results without transverse reinforcement: Spannung am Stoßende σs [N/mm 2 ] concrete strength FE Modell A FE Modell B FE Modell C Betondruckfestigkeit f cm [N/mm 2 ] Spannung am Stoßende σs [N/mm 2 ] lap length FE Modell A FE Modell B FE Modell C Übergreifungslänge l s [mm] PAGE 14 OF??
8 Numerical Investigations Results with transverse reinforcement: Spannung am Stoßende σs [N/mm 2 ] concrete strength FE Modell A FE Modell B FE Modell C Betondruckfestigkeit f cm [N/mm 2 ] Spannung am Stoßende σs [N/mm 2 ] lap length FE Modell A FE Modell B FE Modell C Übergreifungslänge l s [mm] PAGE 15 OF?? Proposed equation PAGE 16 OF??
9 Proposed equation PAGE 17 OF?? Comparison with test results Results from statistical analysis: Database all test data no transverse reinforcement with transverse reinforcement Number of tests Average Value Maximum Value Minimum Value Standard Deviation CoV (15%) (16%) (13%) 5th Percentile th Percentile PAGE 18 OF??
10 Comparison with test results 1000 bond database Measured Steel Stress f sm [N/mm 2 ] trendline (linear) Predicted Steel Stress f sm [N/mm 2 ] Measured versus predicted steel stress PAGE 19 OF?? Comparison with test results 2,0 Ratio f sm measured /fsm predicted [-] 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 bond database trendline (linear) 0,2 0, Related bond (anchorage/splice) lenght l b /d b [-] Influence of related bond length PAGE 20 OF??
11 Comparison with test results Ratio f sm measured /fsm predicted [-] 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 bond database trendline (linear) 0,2 0, Concrete strength f cm or f ck resp. [N/mm 2 ] Influence of concrete strength PAGE 21 OF?? Comparison with test results 2,0 Ratio f sm measured /fsm predicted [-] 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 bond database trendline (linear) 0,2 0,0 1,0 1,5 2,0 2,5 3,0 Concrete confinement c d /d b [-] Influence of concrete confinement c d PAGE 22 OF??
12 Comparison with test results Ratio f sm measured /fsm predicted [-] 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 bond database trendline (linear) 0,2 0, Concrete confinement c max /c d [-] Influence of concrete confinement c max PAGE 23 OF?? Comparison with test results 2,0 Ratio f sm measured /fsm predicted [-] 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 bond database trendline (linear) 0,2 0, Bar diameter d b [mm] Influence of bar diameter PAGE 24 OF??
13 Basic equation Basic assumption in design: Bond stress is constant along the bond length Characteristic bond resistance is given as: f bk = f 0 bk η 1 η 2 η 3... With f 0 bk = bond resistance for worst condition η i = factor to take into account bond conditions, confinement by cover or reinforcement etc. 1 PAGE 25 OF?? Determination of bond strength Principle procedure to obtain the minimum bond strength for worst case conditions: minimum concrete cover minimum spacing of splices minimum transverse reinforcement PAGE 26 OF??
14 Determination of bond strength Proposal 1 Study on basis of equation for characteristic splice strength c c d max 10 mm for φ 10mm = φ for φ> 10 mm 15 mm for φ 14 mm = φ for φ> 14 mm 0 for φ 14 mm Ast nst nl,st = 2 As =π db 4 for φ> 14 mm l 0.25 b 15 l 0.25 b 15 fsk = ( fck ) = 18.2 ( fck ) db db db db equation is valid for diameter smaller than 16mm and the assumption that f c,test =f ck PAGE 27 OF?? Determination of bond strength Proposal 1 Steel stress in the bar f sm [N/mm 2 ] bar diameter φ=12 mm σ s =500 N/mm 2 C25/30 bond length l b /d b 92 f bk = f yk 4 l b d b Bond length l b /d b [-] PAGE 28 OF??
15 Determination of bond strength for Proposal 1 Steel stress in the bar f sk [N/mm 2 ] σ s =600 N/mm 2 σ s =500 N/mm 2 σ s =400 N/mm 2 bond length l b /d b 61 bond length l b /d b 92 bond length l b /d b characteristic bond length l b /d b [-] bar diameter φ=12 mm C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/50 C50/60 C55/67 C60/75 C70/85 C80/95 C90/105 C100/115 PAGE 29 OF?? Determination of bond strength for Proposal 1 For C 25/30 (Ø = 12 mm): f bk =(92) = 1.36 N/mm 2 For C 50/60 (Ø = 12 mm): f bk =(68) = 1.84 N/mm 2 For C 90/105 (Ø = 12 mm): f bk =(52) = 2.40 N/mm 2 Grade C 20/25 C 25/30 C 40/50 C 50/60 C 90/ f cm [N/mm 2 ] f bk [N/mm 2 ] f bd [N/mm 2 ] PAGE 30 OF??
![Determination of bond strength for Proposal 1 Bond Strength f bk [N/mm 2 ] 4,0 3,5 3,0 2,5 2,0 1,5 1,0 600 500 400 fbk=0,25*[fck^0,5] 0,5 0,0 0 20 40 60 80 100 120 Concrete Strength f ck [N/mm 2 ]](/docs-images/87/97332173/images/16-1.jpg "Bond strength as a function of concrete strength PAGE 31 OF?? Determination of bond strength for Proposal 2 Determination of required bond length based on a probabilistic study.")
16 Determination of bond strength for Proposal 1 Bond Strength f bk [N/mm 2 ] 4,0 3,5 3,0 2,5 2,0 1,5 1, fbk=0,25*[fck^0,5] 0,5 0, Concrete Strength f ck [N/mm 2 ] Bond strength as a function of concrete strength PAGE 31 OF?? Determination of bond strength for Proposal 2 Determination of required bond length based on a probabilistic study. Assumption: Probability of brittle concrete failure is p f =10-6 Proposal 2: Probabilistic study on basis of mean eq. PAGE 32 OF??
17 Determination of bond strength for Proposal 2 PAGE 33 OF?? Determination of bond strength for Proposal 2 For C 25/30 (Ø = 12 mm): f bk =(98) = 1.28 N/mm 2 For C 50/60 (Ø = 12 mm): f bk =(72) = 1.74 N/mm 2 For C 90/105 (Ø = 12 mm): f bk =(55) = 2.27 N/mm 2 Grade C 20/25 C 25/30 C 40/50 C 50/60 C 90/ f cm [N/mm 2 ] f bk [N/mm 2 ] f bd [N/mm 2 ] PAGE 34 OF??
18 Determination of bond strength for Proposal 2 4,0 Bond Strength f bk [N/mm 2 ] 3,5 3,0 2,5 2,0 1,5 1,0 fbk=0,23*[fck^0,5] Daten aus Studie 1 0,5 0, Concrete Strength f ck [N/mm 2 ] Bond strength as a function of concrete strength PAGE 35 OF?? Proposal for new model code Basic Bond strength:? PAGE 36 OF??
19 Proposal for new model code Table of characteristic and design Bond strength for different concrete strengths: PAGE 37 OF?? Proposal for new model code The influencing factors are: PAGE 38 OF??
20 Proposal for new model code cont.: PAGE 39 OF?? Proposal for new model code Basic Bond Length: PAGE 40 OF??
21 Proposal for new model code Design Bond Length: PAGE 41 OF?? Proposal for new model code PAGE 42 OF??
22 Proposal for new model code PAGE 43 OF?? Comparison with test results 1000 Measured Steel Stress σs [N/mm 2 ] bond database Predicted Steel Stress σ s [N/mm 2 ] PAGE 44 OF??
23 Comparison with test results 5,0 4,5 bond database Ratio σsmeasured /σ spredicted [-] 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0, Related Bond (anchorage/splice) Lenght l b /d b [-] PAGE 45 OF?? Comparison with test results 5,0 4,5 bond database Ratio σsmeasured /σ spredicted [-] 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0, Concrete Strength f cm [N/mm 2 ] PAGE 46 OF??
24 Comparison with test results 5,0 4,5 bond database Ratio σsmeasured /σ spredicted [-] 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 1,0 1,5 2,0 2,5 3,0 Concrete Confining c min /d s [-] PAGE 47 OF?? Comparison with test results 5,0 4,5 bond database Ratio σsmeasured /σ spredicted [-] 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0, Bar diameter d s [mm] PAGE 48 OF??
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