2 Scheiben und Träger 2.6 Kontinuierliche Spannungsfelder 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 1
Kontinuierliche Spannungsfelder Overview and nomenclature 2. Scheiben und Träger Application to real-life structures 2.1 Spannungsfelder = Stress fields (discontinuous) Tedious hand calculations (iterations, Equilibrium considerations: Lower bound solutions many load cases) 2.2 Bruchmechanismen = Failure mechanisms Digitalisation required! Kinematic considerations: Upper bound solutions 2.3 Träger – Verformungsvermögen = Beams – Deformation capacity Concepts only developed for particular elements Deformation capacity? 2.4 Scheibenelemente – Fliessbedingungen Serviceability checks = Membrane elements – Yield conditions (deformations, crack widths)? 2.5 Scheibenelemente – Last-Verformungsverhalten = Membrane elements – Load deformation behaviour Computer-aided tool for a general plane stress element 2.6 Kontinuierliche Spannungsfelder = Continuous stress fields Implements same mechanical concepts Equilibrium & kinematic considerations: Overcomes the stated limitations Exact solutions (simultaneously lower + upper bound) 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 2
Kontinuierliche Spannungsfelder Real-life structures B Continuity/Bernouilli regions D Discontinuity regions: static and geometric discontinuities are always present [Tjhin & Kuchma, 2002] 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 3
Kontinuierliche Spannungsfelder Dimensioning/assesment of real-life structures B Continuity/Bernouilli regions • Classic tools: hand calculations feasible; cover all verifications • Computer-aided tools: − Many available applications for member design: direct implementation of code verifications/mechanical models D Discontinuity regions • Classic tools (discontinuous stress fields…): deformation capacity?; serviceability aspects?; hand calculations non- feasible/productive • Computer aided-tools: a) Linear elastic FE-calculations: Non-symmetric strength of concrete only accounted for in the last step (dimensioning based on yield conditions); unable to predict realistic capacity in existing structures, nor cracking in new ones b) Non-linear FE-calculations: complex, typically consider tensile strength for equilibrium (differ from classic mechanical models), code compliant? c) Gap between a & b for simple but realistic, code-compliant tool, consistent with classic mechanical models Continuous stress fields = Computer-aided stress fields = Simplified non-linear FE-calculation 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 4
Kontinuierliche Spannungsfelder Dimensioning/assesment of Discontinuity Regions: Existing computer-aided tools AStrutTie (HanGil) CAST (Tjhin & Kutchma, 2002) Idea StatiCa for specific details (strut-and-tie → fc=? Realistic results?) (strut-and-tie → fc=? Realistic results?) (corbels, piles caps…) [Mata-Falcón & Sánchez-Sevilla, 2006] [HanGil, 2017] [IDEA, 2017] 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 5
Kontinuierliche Spannungsfelder Dimensioning/assesment of Discontinuity Regions: Existing computer-aided tools Stringer-Panel Models (Nielsen, 1971; Blaauwendraad & Hoogenboom, 1996; Marti & Heinzmann, 2012) [Blauwendraad, 2006] 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 6
Kontinuierliche Spannungsfelder Dimensioning/assesment of Discontinuity Regions: Existing computer-aided tools EPSF elastic plastic stress fields (Fernández Ruiz & Muttoni, 2007) Experimental Numerical Hand-calculated Maintains advantages of hand crack pattern stress fields results EPSF calculations (transparent, safe design with f ct = 0, consistent detailing) Compressive strength f c determined automatically from strain state [Mata-Falcón et al., 2014] Limited user-friendliness Limited use for serviceability … no tension stiffening … no crack width calculation No check of deformation capacity (perfectly plastic material) [Muttoni & Fernandez Ruiz, 2007] [Mata-Falcón, 2015] 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 7
Kontinuierliche Spannungsfelder DRD (discontinuity region design) method - Implemented in commercial software IdeaStatiCa Detail Continuous stress fields = Computer-aided stress fields 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: standard material properties, concrete tensile strength totally neglected for equilibrium (only its influence to the stiffness is accounted) Inspirations • EPSF FE-implementation (strain compatibility, automatic determination of concrete reduction factor 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 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 8
Kontinuierliche Spannungsfelder DRD: design process 1) Definition of geometry, loads and load combinations a) BIM connections: export data from a global model for the analysis of a detail b) Standalone application: Full definition in standalone user-friendly application 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 9
Kontinuierliche Spannungsfelder DRD: design process 2) Reinforcement design a) Location of reinforcement: definition by user. Several design tools are provided to identify where the reinforcement is required (for complex regions): Linear elastic Topological stress flow optimization b) Amount of reinforcement: can be automatically designed for all or part of the reinforcement. Not yet released in current version (Idea Statica Detail 9.1) 3) Verification models to check all code requirements a) Load-bearing capacity b) Serviceability verifications (deformations, crack width…) 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 10
Kontinuierliche Spannungsfelder DRD verification model: main assumptions • AStruTie (HanGil) Main assumptions: • Fictitious rotating- stress-free cracks ( σ c1,r =0) without slip • Average strains • Equilibrium at cracks: i. Maximum stresses: - σ c3,r / σ s,r ii. Concrete tensile strength neglected except for tension- stiffening: ε m based on [Kaufmann and Marti, 1998] Suitable for elements with minimum transversal reinforcement. Slender elements without shear reinforcement would lead to conservative results. 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 11
Kontinuierliche Spannungsfelder DRD verification model: concrete • AStruTie (HanGil) k c discrete values for hand calculations 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. 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 12
Kontinuierliche Spannungsfelder DRD verification model: concrete • AStruTie (HanGil) Strain limitations of concrete specified by codes k c (compression softening) automatically computed based (explicitly considers the increasing brittleness of on the transversal strain state. concrete with strength). Use of fib MC 2010 / SIA 262:213 proposal for shear Imposed to the average strain over a characteristic verifications (consistent with considered max. stresses) crushing band length. extended for general cases. 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 13
Kontinuierliche Spannungsfelder DRD verification model: bond and reinforcement Tension-stiffening: Does not affect the strength of the reinforcement Increases the stiffness Reduces the ductility (can reduce the strength of the member) Bond model used exclusively for explicit failure bond verifications *Bilinear naked steel input for design. More criteria realistic laws for assessment & experimental validation. 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 14
Kontinuierliche Spannungsfelder DRD verification model: tension stiffening Stabilized crack pattern for ρ > ρ cr ≈ 0.6% Reinforcement is able to 1 σ = = + − carry the cracking load without yielding f f n 1 sr y ctm 0 ρ cr Implementation of Tension Chord Model (TCM) [Alvarez, 1998; Marti et al., 1998] Average crack spacing: assumed λ =0.67 18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 15
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