ๅพฎไฟกๅพ็_20200924164600
CompatibleStressFieldDesign_1stEd.July2020
Contents
1 Introduction
1.1 Current structural concrete practice
1.2 Computer-aided truss models and stress fields
1.3 The Compatible Stress Field Method
2 Structural concrete design with strut-and-tie models and stress fields
2.1 Introduction
2.2 Historical background
2.3 Limit analysis methods
2.3.1 Theorems
2.3.2 Application to structural concrete
2.4 Strut-and-tie models and stress fields
2.5 Code provisions
Ties
Struts
Nodal zones
Further provisions
3 The Compatible Stress Field Method
3.1 Scope of the method
3.2 Main assumptions and limitations
3.3 Constitutive models
3.3.1 Concrete
3.3.2 Reinforcement
3.3.3 Verification of anchorage length
3.3.4 Tension stiffening
Stabilized cracking
Non-stabilized cracking
3.4 Reinforcement design
3.4.1 Workflow and goals
3.4.2 Reinforcement locations
Linear analysis
Topology optimization
3.4.3 Amount of reinforcement
Overview
Definition of the optimization problem
Optimization algorithm
Constitutive model
Interpretation of results
3.5 Verification of the structural element
3.5.1 Safety format factor
3.5.2 Ultimate limit state analysis
3.5.3 Serviceability limit state analysis
Long term effects
Crack width calculation
3.6 Finite element implementation
3.6.1 Introduction
3.6.2 Supports and load transmitting components
3.6.3 Geometric modification of cross-sections
3.6.4 Load transfer at trimmed ends of beams
3.6.5 Finite element types
Concrete
Reinforcement
Anchorage length verification: bond elements
Anchorage length verification: spring elements
3.6.6 Meshing
Concrete
Reinforcement
Bearing plates
Loads and supports
3.6.7 Solution method and load-control algorithm
3.6.8 Results and verifications
Ultimate limit state verifications
Serviceability limit state verifications
4 Basic validations
4.1 Introduction
4.2 Uniaxial tension including crack widths
4.2.1 Case description
4.2.2 Modeling with the CFSM
4.2.3 Comparison with theoretical constitutive models
4.2.4 Mesh size sensitivity
4.2.5 Conclusions
4.3 Uniaxial compression
4.3.1 Case description
4.3.2 Modeling with the CSFM
4.3.3 Results and comparison to codes
4.3.4 Mesh size sensitivity
4.3.5 Conclusions
4.4 Pull-out of reinforcing bars
4.4.1 Case description
4.4.2 Modeling with the CSFM
4.4.3 Comparison with analytical results
4.4.4 Mesh size sensitivity
4.4.5 Conclusions
5 Comparison with codes
5.1 Introduction
5.2 Comparison between the CSFM and the strut-and-tie model
5.2.1 Case description
5.2.2 Modeling with the CSFM
5.2.3 Ultimate limit state design
Base model results
Impact of reinforcement anchorage
5.2.4 Serviceability limit state analysis
Stress limitation
Crack width
Deflection
5.2.5 Optimization of the locations and directions of reinforcing bars
5.2.6 Conclusions
5.3 A Eurocode-based beam analysis
5.3.1 Case description
5.3.2 Modeling with the CSFM
5.3.3 Ultimate limit state
Ultimate moment resistance according to Prochรกzka (2006)
Ultimate moment resistance according to IDEA StatiCa RCS
Ultimate moment resistance according to the CSFM
5.3.4 Serviceability limit state
Stress limitation
Crack widths
Deflections
5.3.5 Conclusions
5.4 Beam analysis according to ACI 318-14
5.4.1 Case description
5.4.2 Modeling with the CSFM
5.4.3 Ultimate limit state
Ultimate moment resistance according to IDEA StatiCa RCS
Ultimate moment resistance according to the CSFM
5.4.4 Serviceability limit state
Deflection according to analytical calculations
5.4.5 Conclusions
5.5 Analysis of a T-beam in a four-point bending configuration
5.5.1 Case description
5.5.2 Modeling with the CSFM
5.5.3 Ultimate limit state
Ultimate moment resistance according to IDEA StatiCa RCS/Beam
Ultimate moment resistance in IDEA StatiCa Detail
5.5.4 Serviceability limit state
Stress limitation
Crack widths
Deflections
5.5.5 Conclusions
6 Experimental validation
6.1 Introduction
6.1.1 Definition of failure modes
6.2 Four-point bending tests on T-beams
6.2.1 Experimental setup
6.2.2 Material properties
Failure modes and ultimate loads
Load-deformation response
Crack widths at service loads
6.2.5 Conclusions
6.3 Cantilever wall-type bridge piers
6.3.1 Experimental setup
6.3.2 Material properties
Failure modes and ultimate loads
Load-deformation response
6.3.5 Conclusions
6.4 Shear tests in beams with low amounts of stirrups
6.4.1 Material properties
Failure modes and ultimate loads
Load-deformation response
6.4.4 Conclusions
6.5 Concrete pier caps
6.5.1 Experimental setup
6.5.2 Material properties
Failure modes and ultimate loads
6.5.5 Conclusions
7 Conclusions
Appendix A: Hypotheses of IDEA StatiCa RCS/Beam software
A.1 Main hypotheses
A.2 Calculation assumptions for ULS checks
A.2.1 Interaction diagram
A.2.2 Response of the cross-section (method of limited deformation)
A.3 Calculation assumptions for SLS checks
A.3.1 Stiffness for calculating short-term effects
A.3.2 Stiffness for calculating long-term effects, including creep effects
References
Notation
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