University of Stuttgart Institute of Construction Materials (IWB) 1/34 Discrete Bond Element for 3D Finite Element Analysis of RC Structures Steffen Lettow Institute of Construction Materials, University of Stuttgart, Germany fib Task Group 4.5 „Bond Models“ – 6 th Meeting, October , 2004, Edinburgh, UK –

University of Stuttgart Institute of Construction Materials (IWB) 2/34  BOND BEHAVIOUR ▫ Requirements & interaction  DISCRETE BOND ELEMENT ▫ Assumptions & implementation ▫ Bond element model (  -s relation) ▫ Influencing variables (  c,  s,  cyc )  NUMERICAL EXAMPLES ▫ Pull-out & splitting behaviour ▫ Influence of steel strain and cyclic loading ▫ Tension stiffening effect ▫ Behaviour of lapped splices ▫ Additional applications OUTLINE

University of Stuttgart Institute of Construction Materials (IWB) 3/34 BOND REQUIREMENTS Bond requirements for various situations: (1)SERVICEABILITY LIMIT STATE : high bond stiffness  small crack widths & small deflections (2)ULTIMATE LIMIT STATE: low bond stiffness  large rotation capacity & low contribution of concrete high bond stiffness  short anchorage lengths

University of Stuttgart Institute of Construction Materials (IWB) 4/34 BOND INTERACTION Bond behavior is mainly influenced by: (1)MATERIAL : -rib geometry and diameter of the reinforcement -characteristics of the concrete (2)GEOMETRY: -concrete cover and bar spacing -confining reinforcement (3)VARIABLE EFFECTS: -strain state in the reinforcement bar -stress state of the concrete around the bar -loading history

University of Stuttgart Institute of Construction Materials (IWB) 5/34 BOND BEHAVIOUR Idealisation of the transmission of forces in the bond zone and failure types: shearing of the concrete lugs  pull-out failure exceeding concrete tensile strength  splitting failure

University of Stuttgart Institute of Construction Materials (IWB) 6/34 ASSUMPTIONS & IMPLEMENTATION Simulation of the transmission of forces between reinforcement and concrete finite elements: longitudinal direction  non-linear springs lateral direction  infinitely stiff connection

University of Stuttgart Institute of Construction Materials (IWB) 7/34 BOND ELEMENT MODEL Use of modified MP equation allows for modelling of various materials. Menegotto-Pinto (MP) formulation:

University of Stuttgart Institute of Construction Materials (IWB) 8/34 BOND ELEMENT MODEL PARAMETERS Influencing factors for bond model: (1)INPUT BOND MODEL PARAMETERS: -rib geometry (shape of basic curve) -bond conditions (bond strength/stiffness) (2)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) (3)INTERACTION WITH FE MODEL: -bar spacing & confining reinforcement -concrete cover, concrete tensile strength (splitting failure - loss of bond)

University of Stuttgart Institute of Construction Materials (IWB) 9/34 TOTAL BOND RESISTANCE TOTAL BOND RESISTANCE: INFLUENCING PARAMETER: Influence of reinforcement strain Influence of concrete confinement Influence of cyclic loading history

University of Stuttgart Institute of Construction Materials (IWB) 10/34 INFLUENCE OF REINFORCEMENT STRAIN ss  s without influence of reinforcement strain with influence of reinforcement strain Influence of  s  s ≈ 10 %  s ≤  sy Reduction of bond stress with increasing strain in the reinforcing bar.

University of Stuttgart Institute of Construction Materials (IWB) 11/34 INFLUENCE OF CONCRETE CONFINEMENT cc  s without influence of concrete confinement with influence of concrete confinement Influence of  c  c ≤ 0 N/mm 2  c ≈ 15 N/mm 2 Increase of bond stress for higher transverse pressure in the confining concrete.

University of Stuttgart Institute of Construction Materials (IWB) 12/34 INFLUENCE OF CYCLIC LOADING (Eligehausen et al. (1983)) Deacrese of bond stress with increasing load cycles.

University of Stuttgart Institute of Construction Materials (IWB) 13/34 PULLOUT BEHAVIOUR FE model of a pull-out test specimen (RILEM) with a short embedement length. Reinforcing bar with large concrete cover Realistic results by use of bond elements especially in descending branch (for large deformation). Dimensions: 200 x 200 x 200 mm Embedment length: l E = 5∙d s Material properties of steel & concrete same for both calculations.

University of Stuttgart Institute of Construction Materials (IWB) 14/34 pre-peak loadpeak load direction of pull-out STEEL AND BOND STRESS DISTRIBUTION WITHOUT BOND ELEMENT: No uniform decrease in steel stress & no constant bond stress distribution. WITH BOND ELEMENT: Uniform decrease in steel stress & constant bond stress distribution.

University of Stuttgart Institute of Construction Materials (IWB) 15/34 SPLITTING BEHAVIOUR Dimensions: Ø 60 x 60 mm Embedment length: l E = 5∙d s = 60 mm FE model of a pull-out test specimen encased by a steel ring (ringtest) with a short embedement length. (experimental investigations by Lettow et al. (2001)) 1D bar elements (reinforcement) with discrete bond elements 3D solid elements (concrete) 3D solid elements (steel ring)

University of Stuttgart Institute of Construction Materials (IWB) 16/34 BOND STRESS-SLIP DIAGRAM By use of adequate parameters in the basic bond model the calculated results agree very well with the measured curve. Comparison of experimental & numerical data

University of Stuttgart Institute of Construction Materials (IWB) 17/34 HOOP STRAINS AS FUNCTION OF SLIP Good agreement between measured & calculated hoop strains in the steel ring, which represent the splitting behaviour. Comparison of experimental & numerical data

University of Stuttgart Institute of Construction Materials (IWB) 18/34 BOND STRESS-SLIP DIAGRAM & CRACK PATTERN In the calculation with steel ring, failure takes place by pull-out. In the calculation without steel ring, splitting failure occurs due to lack of confinement. Formation of cracks in the concrete cover due to removal of the steel ring. principle tensile strains (  11 ) in the concrete elements

University of Stuttgart Institute of Construction Materials (IWB) 19/34 BOND BEHAVIOR AT INELASTIC STEEL STRAINS Dimensions: Ø 500 x 1000 mm Embedment length: l E = 40∙d s = 800 mm FE model of a pull-out test specimen with long embedment length. (experimental investigations by Shima et al. (1987)) 1D bar elements (reinforcement) with discrete bond elements 3D solid elements (concrete)

University of Stuttgart Institute of Construction Materials (IWB) 20/34 STEEL STRAIN DISTRIBUTION ALONG EMBEDMENT LENGTH With increase of the distance from the loaded end the inelastic steel strain decreases. Comparison of experimental & numerical data

University of Stuttgart Institute of Construction Materials (IWB) 21/34 STEEL STRAIN DISTRIBUTION OVER EMBEDMENT LENGTH The strain gradient is significantly influenced by the shape of the steel stress-strain diagram (f t /f y ; ε su ). Comparison of experimental & numerical data

University of Stuttgart Institute of Construction Materials (IWB) 22/34 INFLUENCE OF CYCLIC LOADING HISTORY Dimensions: Ø 520 x 200 mm Embedment length: l E = 5∙d s = 100 mm FE model of a pull-out test specimen with short embedment length under cyclic loading history. (experimental investigations by Simons (2003)) 1D bar elements (reinforcement) with discrete bond elements 3D solid elements (concrete) 3D solid elements (steel plate)

University of Stuttgart Institute of Construction Materials (IWB) 23/34 BOND STRESS-SLIP RELATION Good agreement between measured & calculated bond stress- slip curves. Comparison of experimental & numerical data

University of Stuttgart Institute of Construction Materials (IWB) 24/34 TENSION STIFFENING EFFECT Dimensions: 400 x 400 x 2000 mm FE model of a tension test specimen for determination of contribution of concrete between cracks. (experimental investigations by Mayer/Lettow et al. (2003)) 1D bar elements (reinforcement) with discrete bond elements 3D solid elements (concrete)

University of Stuttgart Institute of Construction Materials (IWB) 25/34 STEEL STRESS-STRAIN DIAGRAM Measured & calculated steel stress-strain curves show a smaller deformation capacity compared to the plain steel. Comparison of experimental & numerical data

University of Stuttgart Institute of Construction Materials (IWB) 26/34 BOND COEFFICIENT (ε sm /ε sr ) DIAGRAM Good agreement between experimental & numerical results over the entire steel strain range. Comparison of experimental & numerical data

University of Stuttgart Institute of Construction Materials (IWB) 27/34 CRACK PATTERN & STRAIN DISTRIBUTION principle tensile strains in 1D bar elements (reinforcement) principle tensile strains in 3D solid elements (concrete) test specimen Comparison of experimental & numerical data Localisation of steel strains at the cracks and reduction of the steel strains between two cracks (contribution of concrete) is clearly visible.

University of Stuttgart Institute of Construction Materials (IWB) 28/34 LAPPED SPLICE BEHAVIOUR Numerical modell, primary structure and moment diagram (dead load ignored) FE model of a slab with overlapping reinforcement (welded mesh). (experimental investigations by Bigaj/Lettow (2000)) Dimensions: 700 x 200 x 4300 mm

University of Stuttgart Institute of Construction Materials (IWB) 29/34 By varying the bond input parameters different failure types can be simulated. FE analysis using no bond elements low bond strength high bond strength LOAD DEFLECTION DIAGRAM Comparison of experimental & numerical data deflection [mm] load [kN] test no. 1 (steel failure) test no. 2 (concrete failure) calc. no. 1 (steel failure) calc. no. 2 (concrete failure) calc. no. 3 (cocnrete failure)

University of Stuttgart Institute of Construction Materials (IWB) 30/34 principle tensile strains (  11 ) in the concrete elements at peak load STRAIN DISTRIBUTION IN SPLICE REGION principle tensile strains (  11 ) in the concrete elements WITHOUT BOND ELEMENTS: Brittle failure – spalling of top concrete cover. WITH BOND ELEMENTS (low bond strength): Ductile failure – rupture of reinforcing steel. WITH BOND ELEMENTS (high bond strength): Brittle failure – spalling of top concrete cover.

University of Stuttgart Institute of Construction Materials (IWB) 31/34 ADDITIONAL APPLICATIONS ... studying the influence of bond on the structural performance of thin textile reinforced and prestressed concrete plates. (by Krüger (2004) at Stuttgart) ... modelling the effects of corrosion on bond between plain reinforcement bars and concrete. (by Cairns/Pregartner (2004) at Edinburgh) ... investigating the influence of bond on the behaviour of headed bars spliced with headed bars and headed bars spliced with reinforcement bars. (by Appl (2004) at Stuttgart) The new discrete bond element has also been used for:

University of Stuttgart Institute of Construction Materials (IWB) 32/34 SUMMARY ... has been implemented into a nonlinear 3D finite element code as a zero-thickness two-node finite element. ... connects 1D truss/bar finite elements (reinforcement) with 3D solid/volume finite elements (concrete). ... is based on a bond stress-slip relationship which is controlled by basic model parameters. ... accounts for the influence of reinforcement strains, stress state of surrounding concrete and cyclic loading history. The discrete bond element:

University of Stuttgart Institute of Construction Materials (IWB) 33/34 ... of pull-out tests with short and long embedment length, of tension and bending tests on RC members show a good agreement between experimental and numerical results. ... demonstrate that the discrete bond element is able to distinguish between pull-out and splitting failure modes. ... indicate that the discrete bond element is able to predict transfer of bond stresses from the reinforcement into the concrete realistically under monotonic and cyclic loading. The numerical investigations: CONCLUSION

University of Stuttgart Institute of Construction Materials (IWB) 34/34  … is needed to verfiy the basic bond element model parameters and the variable influencing factors.  … is needed to check the potential and the accuracy of the discrete bond element model.  … can be very helpful to understand & clarify bond behaviour between reinforcement and concrete in detail.  … can be supportive of developing a harmonised european bond test or improving appraisal factors for bond properties of ribbed reinforcing steel. (proposal for research has been submitted to ) Further research work: OUTLOOK