Standardisation of UHPC in Germany Part II: Development of Design Rules, University of Siegen Prof. Dr.-Ing. Ekkehard Fehling, University of Kassel 1
Overvie Introduction: Work of the Task Group Design and Construction Material Models: UHPC in Compression and Tension Ultimate Limit State (ULS): Design for Bending ith or ithout Axial Force Conclusions and Outlook 2
Introduction Context State of research (e.g. DFG priority programme in Germany) Experience in practice (from pilot projects) Design rules for UHPC as supplement to Eurocode 2 for Germany Eurocode 2: Design of concrete structures International design recommendations for UHPC 3
Introduction Table of Contents (Status-quo of Work) [ ] 3. [ ] 5. [ ] 6. [ ] 7. Materials 3.1 Concrete 3.1.3 Elastic deformation 3.1.4 Creep and shrinkage 3.1.6 Design compressive and tensile strengths 3.1.7 Stress-strain relations for the design of sections 3.2 Reinforcing steel Structural analysis 5.8 Analysis of second order effects ith axial load Ultimate limit states (ULS) 6.1 Bending ith or ithout axial force 6.2 Shear 6.3 Torsion 6.5 Design ith strut and tie models Serviceability limit states (SLS) 7.3 Crack control 4
Materials: Concrete Stress-Strain Relation for the Design of Sections c f ck f cd f cd = cc. f ck / c ith cc = 0.85 c = 1.5 1.35 (high quality control) arctan (E cm /C) arctan E cm 0 c2 = c2u = -2,6 c adopted from strength classes C90/105 and C100/115 5
Materials: Concrete Additional Plastic or Softening Branch? Linear-plastic (acc. to draft of fib-bulletin UHPFRC ) Linear-softening characteristic curve in compression until reaching ultimate load E cd = E cm / 1.3 E cm non-brittleness criterion is satisfied non-brittleness criterion is not satisfied e.g.: c2 = -2.6 c2u = -3.15 (C150) e.g.: c2 = -2.6 c2u = -5.20 6
Materials: Concrete Impact of an Additional Plastic or Softening Branch 26 24 22 20 18 16 14 12 10 8 6 4 2 s1 10 = 10 (z/d) 10 = 10 (x/d) Example: C150 linear ( c2u = -2.60 ) linear-plastic ( c2u = -3.15 ) linear-softening ( c2u = -5.20 ) no significant change of internal lever arm 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45-2 c2 M -4 Eds Eds 2 b d fcd 7
Materials: Concrete Overvie: Stress-Strain Relations in Compression c (<0) 100 90 80 70 60 50 40 30 20 10 0 0 0.5 1 1.5 2 2.5 3 3.5 c (<0) C175 C150 C130 C100 C90 C80 C70 C60 C55 C50 C45 C40 C35 C30 C25 C20 C16 8
Materials: Concrete Tensile Behaviour of UHPFRC Uncracked state: Stress-strain relationship Cracked state: Stress-crack opening relationship cf cf f cft Fibre activation Fibre pull-out cf,cr f ct cf,cr f ct ct 0 u lf 2 Pure UHPC matrix Pure fibre contribution Superposition 9
Materials: Concrete Consistency ith RC Design Philosophy Neglecting contribution of UHPC matrix in tension Assuming cracked cross-section Fibre activation: cf fcft 2 0 0 cf cf Fibre pull-out: cf,cr f cft cf fcft 1 u f cft, 0 to be obtained experimentally! 2 [Li; Pfyl; Jungirth; Leutbecher and others] 0 u lf 2 10
ULS: Bending ith or ithout axial force Design for Bending and Axial Force Equilibrium at cracked cross-section: cf f cftd cftk fcftd cf CF f F cd M Ed N Ed F sd F fd k k 0 l 2 u f k = crack idth at the tensile edge 11
ULS: Bending ith or ithout axial force Design for Bending and Axial Force Equilibrium at cracked cross-section: cf f cftd cftk fcftd cf CF f F cd F sd F fd x k a. (h-x) M Ed N Ed k 0 k l 2 u f F fd = R. b. (h-x). f cftd k = crack idth at the tensile edge 12
ULS: Bending ith or ithout axial force Fibre activation Determining Fibre Contribution F fd For rectangular cross-sections: Begin of fibre pull-out at the tensile edge 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.83 0.56 0.46 R k a k a. R 0 1 2 3 4 5 6 7 8 9 10 k = crack idth at the tensile edge cf fcft 2 0 0 Range for 40 u / 0 100 Fibre pull-out: Conservative assumption Fibre activation: cf k / 0 fcft 1 u 2 13
ULS: Bending ith or ithout axial force Simplification by Stress Block From equations: Simplification: F cd F cd F fd 0.56 (h-x) 0.9 (h-x) F fd 0.55 (h-x) F sd F sd f cftd 0.9 f cftd fd F 0.83 h x b f cftd F 0.81 hx bf fd cftd 14
ULS: Bending ith or ithout axial force Observation in Bending Tests After onset of yielding: [Stürald] Bearing capacity is reached! Ultimate strains of concrete or reinforcing steel are not reached! Bending Moment moment M [knm] M [knm] 200 180 160 140 120 100 80 60 40 20 0 Yielding of rebars Rupture of rebars or crushing of concrete 0 5 10 15 20 Deflection f [mm] Durchbiegung f [mm] 15
ULS: Bending ith or ithout axial force Modifying Stress-Strain Relation of Reinforcing Steel s f tk,cal / S f yd = f yk / S ithout considering contribution of fibres hen considering contribution of fibres 0 f yd / E s f ud = 3,0? ud = 25 Assumption: f ud = f yd / E s + 1 s 16
ULS: Bending ith or ithout axial force Model vs. Test Results (Tests by Stürald) 200 180 Model: 185 (+3%) 160 Bending moment Moment M [knm] M [knm] 30 25 20 15 10 5 0 Model: 25.3 (-5%) = 5.4 % 0.5 vol.-% of fibres 0 10 20 30 40 50 60 70 80 90 100 Deflection Durchbiegung f [mm] f [mm] Bending Moment moment M [knm] M [knm] 140 120 100 80 60 40 20 High fibre contribution = 5.0 % 1.5 vol.-% of fibres Lo fibre contribution 0 0 5 10 15 20 Deflection f [mm] Durchbiegung f [mm] 17
Conclusions and Outlook Development of design rules as supplement to Eurocode 2 ULS: Linear stress-strain relation for UHPC in compression for design of sections, Design for bending should be consistent ith design philosophy of RC: Focus on fibre action but neglecting UHPC matrix in tension, Stress distribution in tension zone according to linear distribution of crack idth over height of tensile zone Simplification by use of stress block, Simultaneous action of rebars and fibres: localisation of strains in one crack Limitation of steel strains hen considering the contribution of fibres, Discussion of models for shear, punching, and torsion is ongoing. SLS: Proposals for crack idth limitation, minimum reinforcement, control of deflections etc. available and under discussion. 18
Thank you very much for your attention! c c Ac Fcd h - x (h - x) F fd F sd Legend: = 0.9 = 0.9 cf0d f cftd 19