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Presentatie prof. Kaufmann op de IDEA Concrete infomiddag

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Structural concrete design, dimensioning and detailing: from truss models to computer-aided stress fields.

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Presentatie prof. Kaufmann op de IDEA Concrete infomiddag

  1. 1. Structural concrete design, dimensioning and detailing: from truss models to computer-aided stress fields Prof. Dr. Walter Kaufmann ETH Zürich Institute of Structural Engineering 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 1
  2. 2. Historical background of limit analysis methods Truss models and stress fields FE-calculations and existing computer-aided tools DR-Design (ISD): Motivation and scope DR-Design (ISD): Model description DR-Design (ISD): Experimental validation Conclusions Structural concrete design, dimensioning and detailing: from truss models to computer-aided stress fields 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 2
  3. 3. “Ancestors” of limit analysis methods – Yield line method P. Marti et al., Aplication of yield line method (1999)A. Ingerslev «The Strength of Rectangular Slabs (1923) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 3
  4. 4. “Ancestors” of limit analysis methods – Hillerborg’s strip method H. Marcus «Die Theorie elastischer Gewebe …» (1924 / 1932) P. Marti et al., Application of Hillerborg’s Strip Method (1999) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 4
  5. 5. “Ancestors” of limit analysis methods – Truss models and stress fields E. Mörsch, «Der Eisenbetonbau» (1922) E. Mörsch, «Der Eisenbetonbau» (1908) K. W. Ritter, «Die Bauweise Hennebique» (1899) Modern truss models and stress fields 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 5
  6. 6. “Ancestors” of limit analysis methods – Truss models and stress fields K. W. Ritter, «Die Bauweise Hennebique» (1899) Emil Mörsch 1872-1950 Karl Wilhelm Ritter 1847-1906 E. Mörsch, «Der Eisenbetonbau» (1922) E. Mörsch, «Der Eisenbetonbau» (1908) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 6
  7. 7. “Ancestors” of limit analysis methods – Truss models and stress fields K. W. Ritter, «Die Bauweise Hennebique» (1899) M. Ritter, «Massivbau» (ca. 1940) P. Lardy, «Massivbau» (1951) E. Mörsch, «Der Eisenbetonbau» (1908) E. Mörsch, «Der Eisenbetonbau» (1922) E. Mörsch, «Der Eisenbetonbau» (1908) Truss models regarded as behavioural models State of art: Design based on semi-empirical models, e.g. «admissible tensile stresses» Situation until 1960s 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 7
  8. 8. “Ancestors” of limit analysis methods – Truss models and stress fields M. Ritter, «Massivbau» (ca. 1940) P. Lardy, «Massivbau» (1951) E. Mörsch, «Der Eisenbetonbau» (1908) Emil Mörsch 1872-1950 Pierre Lardy 1903-1958 Max Ritter 1884-1946 Truss models regarded as behavioural models State of art: Design based on semi-empirical models, e.g. «admissible tensile stresses» Situation until 1960s 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 8
  9. 9. Intrinsic problems of “admissible stress” design Ernst Melan 1890-1963 Drawbacks of «admissible stress design»: - Ultimate load cannot be reliably predicted (except for brittle materials) even if stresses are accurately known → no uniform safety level - Stresses cannot be «accurately» determined (restraint to imposed deformations e.g. hydration, shrinkage; construction stages; …) Ernst Melan (1938): Since (…) typically, the sequence of loading is arbitrary, asking for the state of stress under a certain load does not make sense. (Translated from German: «Da (…) die Reihenfolge der Belastungen willkürlich zu sein pflegt, hat die Frage nach einem Spannungszustand bei einer bestimmten Belastung keinen Sinn»). 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 9
  10. 10. Limit analysis methods – Application to Structural Concrete Intrinsic problems of admissible stress design: - initial stress state? - safety level? Truss models put on a consistent mechanical basis by the Theory of Plasticity [(Prager, Gvozdev). Lower-bound theorem: • Satisfy equilibrium and statical boundary coditions • Do not infringe yield condition (provide required strength) → Safe design → Independent of initial stresses ( ) 0Ζ = mΖ jσ (S) 0= iσ kσ εnΖ z Peter Marti *1949 Bruno Thürlimann 1923-2008 upper bound solutions («failure mechanisms») possible range of ultimate load lower bound solutions («equilibrium methods») P (Among other pioneers like e.g. D.C. Drucker, W.F. Chen, M.P. Nielsen, M. Braestrup, D.H. Clyde, C.T. Morley, P. Müller, J. Witteveen ,…) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 10
  11. 11. Stoffel / Marti (1995) Sigrist / Marti (1992) Kaufmann / Marti (1995) Bachmann / Thürlimann (1965) Maier / Thürlimann (1985) Limit analysis methods – Validation by large scale experiments Large-scale testing indispensable for validaton and acceptance of limit analysis methods 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 11
  12. 12. “Ancestors” of limit analysis methods – Truss models and stress fields J. Schlaich et al., «Toward a Consistent Design of Structural Concrete» (1987) Jörg Schlaich * 1934 (Among many others like e.g. K. Schäfer, J.G. McGregor, …) Strut-and-tie models («Stabwerkmodelle»): Used for tracing the flow of forces and form finding (often based on elastic principal stress trajectories, and combined with graphic statics) Mechanical basis? Code compliant? Behavioural models / «Practitioner method»? 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 12
  13. 13. “Ancestors” of limit analysis methods – Truss models and stress fields J. Schlaich et al., «Toward a Consistent Design of Structural Concrete» (1987) Jörg Schlaich * 1934 (Among many others like e.g. K. Schäfer, J.G. McGregor, …) Strut-and-tie models («Stabwerkmodelle»): Used for tracing the flow of forces and form finding (often based on elastic principal stress trajectories, and combined with graphic statics) Mechanical background: Limit analysis metods! 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 13
  14. 14. Historical background of limit analysis methods Truss models and stress fields FE-calculations and existing computer-aided tools DR-Design (ISD): Motivation and scope DR-Design (ISD): Model description DR-Design (ISD): Experimental validation Conclusions Computer-aided stress field analysis of discontinuity concrete regions 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 14
  15. 15. Truss models and stress fields E. Mörsch, «Der Eisenbetonbau» (1922) E. Mörsch, «Der Eisenbetonbau» (1908) K. W. Ritter, «Die Bauweise Hennebique» (1899) Modern truss models and stress fields consistent mechanical basis: lower-bound theorem of limit analysis 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 15
  16. 16. Code provisions based on limit analysis in current EN 1992-1-1: Shear design Truss models and stress fields 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 16
  17. 17. Code provisions based on limit analysis in current EN 1992-1-1: Horizontal shear and torsion Truss models and stress fields 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 17
  18. 18. Truss models and stress fields [Tjhin & Kuchma, 2002] 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 18
  19. 19. Truss models and stress fields Code provisions based on limit analysis in current EN 1992-1-1: Strut and tie models 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 19
  20. 20. Truss models and stress fields x supF z infF− supF centred non-centred wfO x z infF− supF centred non-centred wfO supF q q 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 20
  21. 21. Truss models and stress fields 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 21
  22. 22. Anchor force NB: = stirrup forces + applied load Anchor force [Marti & Stoffel, 1999] Truss models and stress fields  Flow of forces (transparency)  Safe dimensioning  Consistent detailing  Tedious hand calculations (iterations, many load cases)  Even more so in assessment  Compressive strength fc? (depending on strain state)  Deformation capacity?  Serviceability checks (deformations, crack widths)? → FE-calculations used in engineering practice → Future of truss models? → Digitalisation required! (computer-aided tools) Design of Discontinuity: classic tools 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 22
  23. 23. Historical background of limit analysis methods Truss models and stress fields FE-calculations and existing computer-aided tools DR-Design (ISD): Motivation and scope DR-Design (ISD): Model description DR-Design (ISD): Experimental validation Conclusions Computer-aided stress field analysis of discontinuity concrete regions 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 23
  24. 24. FE-calculations [Cervenka Consulting / ATENA] 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 24
  25. 25. FE-calculations Linear elastic FE calculations • Equilibrium is satisfied (application of lower bound theorem of imit analysis) → ok, but … • Do not capture real behaviour (restraint stresses, cracking, redistribution, staged construction, …) • Non-symmetric strength of concrete only accounted for in last step (dimensioning based on yield conditions) • Often inefficient and / or unpractical reinforcement layouts; fc must be assumed (“safe value”) → Useful in design, but unable to predict realistic capacity in existing structures, nor cracking in new ones 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 25 1 sx sx x xz sz sz z xz a f n k n a f n k n− ≥ + ≥ + ( )c sx sx sz sz x zhf a f a f n n≥ + − + Direct reinforcement design (yield regime 1): Valid if concrete does not crush, i.e.:
  26. 26. FE-calculations Linear elastic FE calculations • Equilibrium is satisfied (application of lower bound theorem of imit analysis) → ok, but … • Do not capture real behaviour (restraint stresses, cracking, redistribution, staged construction, …) • Non-symmetric strength of concrete only accounted for in last step (dimensioning based on yield conditions) • Often inefficient and / or unpractical reinforcement layouts → Useful in design, but unable to predict realistic capacity in existing structures, nor cracking in new ones Nonlinear FE calculations • Capture real behaviour if correct mechanical models and material parameters are input • Require expert users, modelling and analysis time consuming • Input of (often many!) material parameters unknown at design stage required • Results non-transparent and sensitive to choice of mechanical model and material parameters (often ± arbitrary in design) • Often inefficient and / or unpractical reinforcement layouts → Limited use, mainly in assessment of existing structures and research 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 26
  27. 27. FE-calculations [Cervenka Consulting / ATENA] 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 27
  28. 28. FE-calculations 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 28  Powerful tools with lots of possibilities  Account for material and geometrical nonlinearities  Capture “real” behaviour if right parameters are used  ULS and SLS results provided  Expert users required  Many input parameters are unknown in design stage  Highly sensitive to seemingly unimportant input parameters  fct directly contributes to resistance in many cases (fct > 0 for numerical stability) → Code compliant, safe design? → Useful for design stage?[Cervenka Consulting / ATENA]
  29. 29. FE-calculations Linear elastic FE calculations • Equilibrium is satisfied (application of lower bound theorem of imit analysis) → ok, but … • Do not capture real behaviour (restraint stresses, cracking, redistribution, staged construction, …) • Non-symmetric strength of concrete only accounted for in last step (dimensioning based on yield conditions) • Often inefficient and / or unpractical reinforcement layouts → Useful in design, but unable to predict realistic capacity in existing structures, nor cracking in new ones Nonlinear FE calculations • Capture real behaviour if correct mechanical models and material parameters are input • Require expert users, modelling and analysis time consuming • Input of (often many!) material parameters unknown at design stage required • Results non-transparent and sensitive to choice of mechanical model and material parameters (often ± arbitrary in design) • Often inefficient and / or unpractical reinforcement layouts → Limited use, mainly in assessment of existing structures and research Alternative: Computer-aided truss models / stress fields (simplified nonlinear FE calculations) • Not a new idea: «It is time to bring these methods from the drawing board to the computer» [Marti 1985] • Surprising that no such tools were available until recently 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 29
  30. 30. Existing computer-aided tools Design of Discontinuity Regions: Existing computer-aided tools • AStruTie (HanGil) [HanGil, 2017] Idea StatiCa for specific details (corbels, piles caps…) AStrutTie (HanGil) (strut-and-tie → fc=? Realistic results?) [IDEA, 2017] CAST (Tjhin & Kutchma, 2002) (strut-and-tie → fc=? Realistic results?) [Mata-Falcón & Sánchez-Sevilla, 2006] 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 30
  31. 31. Spannungsfelder Design of Discontinuity Regions: Existing computer-aided tools 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 31 Stringer-Panel Models (Nielsen, 1971; Blaauwendraad & Hoogenboom, 1996; Marti & Heinzmann, 2012) [Blauwendraad, 2006]
  32. 32. Spannungsfelder Experimental crack pattern Hand-calculated stress fields Numerical results EPSF Design of Discontinuity Regions: Existing computer-aided tools [Mata-Falcón, 2015] [Mata-Falcón et al., 2014] [Muttoni & Fernandez Ruiz, 2007] EPSF elastic plastic stress fields (Fernández Ruiz & Muttoni, 2007)  Maintains advantages of hand calculations (transparent, safe design with fct = 0, consistent detailing)  Compressive strength fc determined automatically from strain state  Limited user-friendliness  Limited use for serviceability … no tension stiffening … no crack width calculation  No check of deformation capacity (perfectly plastic material) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 32
  33. 33. Historical background of limit analysis methods Truss models and stress fields FE-calculations and existing computer-aided tools DR-Design (ISD): Motivation and scope DR-Design (ISD): Model description DR-Design (ISD): Experimental validation Conclusions Computer-aided stress field analysis of discontinuity concrete regions 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 33
  34. 34. DR-Design (Discontinuity Region Design) Scope • Simple method for efficient, code-compliant design and assessment of discontinuity concrete regions • Including serviceability and deformation capacity verifications • Direct link to conventional RC design: concrete tensile strength ONLY for stiffness, standard material properties Inspirations • EPSF finite-element implementation (strain compatibility, automatic determination of kc from strain state) • Tension Chord Model TCM and Cracked Membrane Model CMM (tension stiffening, ductility and serviceability checks) Features of DR-Design • Maintains advantages of truss models and stress field design: Tensile strength of concrete does not contribute to strength! • Simple uniaxial constitutive laws for reinforcement and concrete in compression • Satisfies strain compatibility, accounting for tension stiffening • Covers all verifications typically required in design (ULS, SLS including crack widths) • Implemented in user-friendly FE-based software package IDEA StatiCa>Detail. • Checks deformation capacity (explicit strain limitations of concrete and reinforcement) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 34
  35. 35. DR-Design (Discontinuity Region Design) Scope • Simple method for efficient, code-compliant design and assessment of discontinuity concrete regions • Including serviceability and deformation capacity verifications • Direct link to conventional RC design: concrete tensile strength ONLY for stiffness, standard material properties Inspirations • EPSF finite-element implementation (strain compatibility, automatic determination of kc from strain state) • Tension Chord Model TCM and Cracked Membrane Model CMM (tension stiffening, ductility and serviceability checks) Development / Credits This project has received partial funding from Eurostars-2 joint programme, with co-funding from the European Union Horizon 2020 research and innovation programme 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 35
  36. 36. Historical background of limit analysis methods Truss models and stress fields FE-calculations and existing computer-aided tools DR-Design (ISD): Motivation and scope DR-Design (ISD): Model description DR-Design (ISD): Experimental validation Conclusions Computer-aided stress field analysis of discontinuity concrete regions 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 36
  37. 37. Model description DRD verification model: main assumptions • AStruTie (HanGil) based on [Kaufmann and Marti, 1998] Main assumptions: • Fictitious rotating, stress-free cracks (σc1,r=0) without slip • Average strains • Equilibrium at cracks: i. Maximum stresses: -σc3,r / σs,r ii. Concrete tensile strength neglected except for tension- stiffening: εm Suitable for elements with minimum transversal reinforcement. Slender elements without shear reinforcement would lead to conservative results. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 37
  38. 38. Model description DRD verification model: concrete • AStruTie (HanGil)  Strain limitations of concrete specified by codes (explicitly considers the increasing brittleness of concrete with strength).  Imposed to the average strain over a characteristic crushing band length.  kc discrete values for hand calculations 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 38
  39. 39. Model description DRD verification model: concrete • AStruTie (HanGil)  kc (compression softening) automatically computed based on the transversal strain state.  Use of fib MC 2010 proposal for shear verifications (consistent with considered max. stresses) extended for general cases.  Strain limitations of concrete specified by codes (explicitly considers the increasing brittleness of concrete with strength).  Imposed to the average strain over a characteristic crushing band length. (standard user: only kc currently used, not εcu) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 39
  40. 40. Model description DRD verification model: concrete • AStruTie (HanGil) EN 1992-1-1, 6.5. Design with strut and tie models 6.5.2 (2): The design strength for concrete struts should be reduced in cracked compression zones and, unless a more rigorous approach is used, may be calculated from Expression (6.56).  Strain limitations of concrete specified by codes (explicitly considers the increasing brittleness of concrete with strength).  Imposed to the average strain over a characteristic crushing band length. (standard user: only kc currently used, not εcu) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 40
  41. 41. Model description DRD verification model: bond and reinforcement Bond model used exclusively for verifications of gradients of tension chord force Tension-stiffening:  Does not affect the strength of the reinforcement  Increases the stiffness  Reduces the ductility (can reduce the strength of the member) explicit failure criterion (rupture) *Bilinear naked steel input for design. More realistic laws for assessment & experimental validation. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 41
  42. 42. Model description DRD verification model: tension stiffening Stabilised crack pattern  Implementation of Tension Chord Model (TCM) [Alvarez, 1998; Marti et al., 1998]  Average crack spacing: assumed λ=0.67 for ρ>ρcr≈0.6%  Reinforcement is able to carry the cracking load without yielding 0 1 1sr y ctm cr f f n   σ = = + −  ρ  04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 42
  43. 43. Model description DRD verification model: tension stiffening Non-stabilised crack pattern for ρ<ρcr≈0.6%  Reinforcement is NOT able to carry the cracking load without yielding. Cracks are controlled by other reinforcement.  Independent cracks are assumed + bond model of Tension Chord Model.  Crack localization (size effect): stiffness of the whole rebar embedded in concrete > local stiffness near the crack → considered strain: average over lavg = length at which rebar is fully anchored (for ft ) Will be released for stirrups in ISD 9.1 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 43
  44. 44. Model description DRD verification model: tension stiffening Resulting tension chord behaviour  Fully cracked behaviour considered for design.  Uncracked initial stiffness can be considered for refined verification models. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 44
  45. 45. Model description DRD verification model: effective area of concrete in tension → suitable for numerical implementation and valid for automatic definition of ρc,eff in any region Maximum concrete area each rebar can activate (concrete at fct) (illustrated for rebars 3 and 4) Areas used in calculation 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 45
  46. 46. Model description DRD verification model: crack width – stabilised crack pattern WT4 [Walther, 1967] 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 46
  47. 47. Model description DRD verification model: crack width – non-stabilised crack pattern [Zhu et al., 2003] Assumed independent cracks at SLS Considered for: a) Regions with ρ < 0.6% (ρmin) b) Cracks triggered by geometric discontinuities at low loads T6Will be released in ISD 9.1 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 47
  48. 48. Model description DRD verification model: crack width – crack kinematics s 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 48
  49. 49. Historical background of limit analysis methods Truss models and stress fields FE-calculations and existing computer-aided tools DR-Design (ISD): Motivation and scope DR-Design (ISD): Model description DR-Design (ISD): Experimental validation Conclusions Computer-aided stress field analysis of discontinuity concrete regions 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 49
  50. 50. Experimental validation DRD experimental validation • Direct tension experiments – Alvarez and Marti (1996)  Ultimate limit state  Load deformation behaviour  Crack width • Pure bending experiments – Frantz and Breen (1978)  Crack width distribution • Cantilever shear walls – Bimschas, Hannewald and Dazio (2010, 2013)  Load deformation behaviour under combined loading  Bearing capacity under combined loading • Beams with low amount of transversal reinforcement – Huber, Huber and Kolleger (2016)  Bearing capacity in shear (failures due to insufficient ductility of the transversal reinforcement) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 50
  51. 51. Experimental validation DRD experimental validation Alvarez and Marti (1996) - experimental setup/specimens [Avarez and Marti, 1996] Z1 Z1 Specimen Z1 Z2 Z4 Z8 Long. reinforcement 14xØ14 (ρ = 1%) 14xØ14 (ρ = 1%) 14xØ14 (ρ = 1%) 10xØ14 (ρ = 0.7%) Steel quality (ductility class) High High Normal High fck_cube (MPa) 50 90 50 50 Loading: pure tension 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 51
  52. 52. Experimental validation DRD experimental validation Alvarez and Marti (1996) - ultimate state [Avarez and Marti, 1996] Specimen Z1 Z2 Z4 Z8 Experiment Vexp (kN) εm,exp (%) 1294 6.7 1295 6.8 1275 0.6 924 6.4 DR-Design Vcalc (kN) εm,calc (%) 1275 7.0 1282 4.6 1242 0.4 918 6.5 Safety factor Strength: Vexp/Vcalc Deform. capacity: εm,exp/εm,calc 1.01 0.96 1.01 1.48 1.03 1.50 1.01 0.98 V: Peak load εm: Average tensile strain 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 52
  53. 53. Experimental validation DRD experimental validation Alvarez and Marti (1996) Load deformation behaviour Neglecting tension-stiffening overestimates the deformation capacity up to 5 times (depending on ρ, the ductility of the reinforcement…) 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 53
  54. 54. Experimental validation DRD experimental validation Alvarez and Marti (1996) - crack width 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 54
  55. 55. Experimental validation DRD experimental validation Frantz and Breen (1980) - experimental setup/specimen • AStruTie (HanGil) Specimen RS-3 Main reinforcement 2xØ15.88 6xØ12.7 Web reinforcement 6xØ6 Loading: pure bending [Frantz and Breen, 1980] d (mm) 885 mm 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 55
  56. 56. Experimental validation DRD experimental validation Frantz and Breen (1980) – crack width 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 56
  57. 57. Experimental validation DRD experimental validation Bimschas et al. (2010, 2013) – experimental setup/specimens VK1: first yielding of reinforcement [Bimschas, 2010] 1370 kN ±V Specimen VK1 VK3 VK6 Effective height (m) 3.30 3.30 4.50 Section depth (m) 1.50 1.50 1.50 Section width (m) 0.35 0.35 0.35 ρsl (%) 0.82 1.23 1.23 ρst (%) 0.08 0.08 0.08 Loading: constant normal force N = -1370kN; quasi-static cyclic loading with increasing amplitudes in horizontal direction. Note: DR-Design aims to describe the backbone of the cyclic response using a monotonic model. Strain penetration into the foundation is not considered. εu=8.4% 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 57
  58. 58. Experimental validation DRD experimental validation Bimschas et al. (2010, 2013) – peak load [Bimschas, 2010] VK1: peak strength VK1: failure Concrete crushing in compression Specimen VK1 VK3 VK6 Experiment* Vexp (kN) 728 876 647 DR-Design Vcalc(kN) 730 860 650 Vexp/Vcalc 1.00 1.02 1.00 Note: DR-D aims to describe the behaviour of the backbone until concrete peak horizontal strength is reached, (≠ to loss of vertical bearing capacity). *mean peak horizontal load of North and South directions. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 58
  59. 59. Experimental validation DRD experimental validation Bimschas et al. (2010, 2013) – load deformation behaviour Failure mode: concrete crushing in compression. Failure is considered when the strain limit criteria specified in codes for sectional analysis is reached on average over the crushing band length. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 59
  60. 60. Experimental validation DRD experimental validation Bimschas et al. (2010, 2013) – stress fields specimen VK1 Note: Refined analysis considers the initial uncracked stiffness, as well as the actual stress-strain relationship of the reinforcement. Moreover, no concrete strain limitation is considered. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 60
  61. 61. Experimental validation DRD experimental validation: Bimschas et al. (2010, 2013) – load deformation behaviour [%] σsr/ft σc3r/(fc·kc) σsr>fy 1370 kN 250 kN 84º 1370 kN 500 kN 80º 1370 kN 750 kN 79º σsr<0 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 61
  62. 62. Experimental validation DRD experimental validation Huber et al. (2016) – experimental setup/specimens Øw (mm) fy (MPa) ft (MPa) εu (%) 4 653 710 4.9 6 569 658 3.1 12 552 654 3.4 Specimen R1000m35 R1000m60 R500m352 R500m351 Section depth 1.00 m 1.00 m 0.50 m 0.50 m Section width 0.30 m 0.30 m 0.15 m 0.15 m ρw 0.094 % 0.094 % 0.084 % 0.094 % Øw Ø6 Ø12 Ø4 Ø6 fc 29.6 MPa 60.9 MPa 35.9 MPa 37.9 MPa 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 62
  63. 63. Experimental validation DRD experimental validation Huber et al. (2016) – ultimate load • Neglecting tension stiffening leads to unsafe load predictions and does not capture the real failure mode (stirrup rupture). • Higher impact of strain localization in real size elements  use of existing experimental databases could underestimate the impact of these failures. Cold-formed steel with same ft & fy  less ductile & less predicted load (≈10%) than standard bilinear steel law. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 63
  64. 64. Experimental validation DRD experimental validation Huber et al. (2016) – stress fields specimen R1000m35 776 kN θ=40.5º 937 kNStirrups yielding θ=36.5º εz=20‰ σsrz=600 MPa<ft ε1=23‰  kc=0.41 σc3r=12 MPa σc3r/(fc·kc)=1.00 εz=5.4‰ σsrz=638 MPa=ft ε1=6.4‰  kc=0.64 σc3r=7.7 MPa σc3r/(fc·kc)=0.42 *Results at the most restrictive concrete and steel finite elements (minimum kc & maximum σsrz) DRD (No tens.-stiff.) DRD [%] σsr/ft σc3r/(fc·kc) σsr>fy 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 64
  65. 65. Experimental validation DRD experimental validation Huber et al. (2016) – shear concrete crushing verifications  Is there a clear link to kc prescribed for hand calculations? Impact of strain localization? [SIA 262:213; fib MC 2010] Concrete crushing  Tension-stiffening required to capture the failure mode. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 65
  66. 66. Historical background of limit analysis methods Truss models and stress fields FE-calculations and existing computer-aided tools DR-Design (ISD): Motivation and scope DR-Design (ISD): Model description DR-Design (ISD): Experimental validation Conclusions Computer-aided stress field analysis of discontinuity concrete regions 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 66
  67. 67. Conclusions Why use truss models and stress fields (and limit analysis methods in general) • Powerful tools for the design of concrete structures. • They are transparent, allow to trace the of flow of forces and give the engineer full control over the design. Future of truss models and stress fields • Due to their drawbacks (time-consuming, not useful for SLS) these methods will not survive as hand calculations. • They need to be implemented in user-friendly computer programs, but maintaining their advantages. • The DRD-method, implemented in the program Idea Statica Detail, developed jointly by ETH Zürich and Idea-RS, will hopefully contribute to the survival of these methods in structural concrete design. 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 67
  68. 68. Acknowledgements DR-DESIGN Project Team Funding: 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 68
  69. 69. Thank you for the attention 04.06.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 69

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