Analytical Approaches for Reinforced Concrete

Chapter 1. Failure of Reinforced Concrete Members

1.1 Introduction

1.2 Typical structure of RC beam

1.3 Experimental observations - an RC practical

1.3.1 Beam 1

1.3.2 Beam 2

1.3.3 Beam 3

1.3.4 Beam 4

1.3.5 Beam 5

1.3.6 Beam 6

1.4 Failure modes

1.4.1 Evolution of failure modes

1.4.2 Safe failure mode and control of failure mode

1.4.3 The principle of weakest link

1.4.4 Other failure modes

1.5 Failure consequence, safety factor, and ductility

1.6 Limit state design approach

1.7 Structural design procedure

1.7.1 Design for serviceability limit states

1.7.2 Design for ultimate limit states

1.7.3 Design procedure

1.8 Design codes of practice

References

Chapter 2. Flexural Failure and Design Theory

2.1 Introduction

2.2 Failure process

2.2.1 Effect of loading type on failure point

2.3 Moment-curvature relationship

2.4 Typical response curves

2.5 Failure modes

2.6 Calculation of design moment

2.6.1 Moment taking

2.6.2 Moment redistribution

2.6.2.1 The mechanism of moment redistribution

2.6.2.2 Effect of redistribution to moment envelope

2.6.2.3 Determination of moment envelope

2.7 Conventional flexural theory

2.7.1 Solution of the equations

2.7.2 Stress block parameters

2.7.3 Discussions on stress block parameters

2.8 Miscellaneous relationships

2.8.1 Curvature of section

2.8.2 The theorem of plane section

References

Chapter 3. Deductive Approach to Flexural Theory

3.1 General Assumptions

3.2 RC Flexural Design Theorems

3.2.1 The first theorem

3.2.2 The second theorem

3.2.3 The third theorem

3.3 Numerical Illustrations

3.3.1 Flexural design parameters

3.3.2 Elastic compression reinforcement

3.3.3 Ultimate failure point

3.4 Ultimate Curvature and Curvature Ductility of RC Sections

3.4.1 Curvature ductility of plain concrete sections

3.4.2 Effect of longitudinal reinforcement on ductility of RC column sections

3.4.2.1 At critical axial load

3.4.2.2 For axial load levels lower than the critical load

3.4.2.3 For axial load levels higher than the critical axial load

3.4.3 Numerical studies

3.5 Derivation of the Theorems

3.5.1 Under-reinforce sections

3.5.2 Maximum reinforcement ratio for cm=cm,u

3.5.3 Elastic solutions

3.5.4 Transition stage

3.5.5 RC sections with elastic compression bars

3.5.6 Equivalent reinforcement ratio

3.5.7 Ultimate curvature

3.5.8 Derivation of cases with elastic bars

3.5.8.1 Flexural design with elastic tension reinforcement

3.5.8.2 Flexural design with elastic compression reinforcement

3.6 Alternative Flexural Design Procedure

3.6.1 Comparison with ACI 318

3.6.2 Design procedure

References

Chapter 4. Applications of the Flexural Theorems

4.1 Application to design of RC Members under Elevated Temperature

4.1.1 Stress-strain model of concrete under elevated temperature

4.1.2 Stress-strain relationship of steel bar under elevated temperature

4.1.3 Stress block parameters

4.1.4 Design example

4.1.5 Validation of results

4.1.6 Flexural analysis of RC members under elevated temperature

4.1.6.1 Flexural strength

4.1.6.2 Flexural design strain

4.1.6.3 Ultimate curvature

4.1.6.4 Parametric Studies

4.2 Stress Block Parameters for RC Members Reinforced with FRP Bar

4.2.1 Flexural failure of FRP-reinforced concrete beams

4.2.2 Stress strain relationships

4.2.3 Parametric studies

4.2.3.1 Effects of compressive strength of concrete

4.2.3.2 Effects of effective reinforcement ratio

4.2.4 Stress block parameters

4.2.5 Comparisons with existing design codes

4.2.5.1 ACI 440.1R-15

4.2.5.2 CSA-S806-12

4.2.6 Design examples

4.2.7 Comparison of models

References

Chapter 5. Bond Between Reinforcement and Concrete

5.1 Composite action

5.2 Bond of reinforcement

5.3 Bond mechanisms and bond-slip relationship

5.3.1 Adhesion

5.3.2 Mechanical interlock

5.3.3 Friction

5.4 Bond design of rebar

5.5 Anchorage design of rebar for flexural members

5.6 Beam action and arch action

5.7 Effect of crack on bond

5.8 Effect of bond on cracking

5.8.1 Crack formation in RC ties

5.8.2 Crack formation in RC beams

5.9 Evaluation of crack width and spacing

5.9.1 Design for cracking

5.9.2 Slip theory

5.9.3 No-slip theory

5.9.4 Mathematical modeling

5.9.5 Other models

5.10 Tension stiffening

5.11 Flexural strength calculation without considering slip

5.12 Frictional shear for RC joints

References

Chapter 6. Analytical Modeling of Composite Members

6.1 Structural rehabilitation

6.2 Mechanically bonded systems

6.2.1 Classic linear elastic theory

6.2.2 Equilibrium and compatibility

6.2.3 Governing differential equation

6.2.4 Solution for the case of cantilever column

6.2.5 Composite parameters

6.2.5.1 Parameters governing longitudinal slip

6.2.5.2 Parameters affecting flexural deformation

6.2.6 Slip distribution

6.2.7 Other studies on partial-interaction composite members

6.3 Adhesively bonded reinforcement

6.3.1 Failure modes

6.3.2 Flexural design approach

6.3.3 Measures to suppress interfacial debonding

6.4 Analytical solution of EBR pull off test

6.4.1 Governing equations

6.4.2 Analytical solutions

6.4.3 Snapback problem

6.4.4 Control of pull-off test

6.4.5 Peak strength

6.4.6 Parameter identification

6.5 Hybrid bonded reinforcement

6.5.1 Bond enhancement systems

6.5.2 Mechanisms of the HB system

6.5.3 Experimental tests

6.5.4 Bond Modeling

References

Chapter 7. Flexural Deflection

7.1 Introduction

7.2 Deflection under serviceability limit states

7.2.1 General

7.2.2 Short term flexural rigidity and tension stiffening

7.2.2.1 Transformed section

7.2.2.2 Effective moment of inertia

7.2.2.3 Smeared crack approach

7.2.2.4 Curvature modeling considering slip

7.2.3 Long-term deflection

7.2.3.1 Long-term effective modulus of concrete

7.2.3.2 Long-term curvature and deflection due to creep

7.2.3.3 Deflection due to shrinkage and temperature change

7.2.4 Superposition of flexural deflections

7.3 Deflection under ultimate limit states

7.3.1 Physical plastic hinge length and equivalent plastic hinge length

7.3.2 Factors affecting plastic hinge length

7.3.3 Existing plastic hinge length models

7.3.4 Numerical and analytical studies on plastic hinge length

7.3.4.1 Rebar yielding zone

7.3.4.2 Concrete softening zones

7.3.4.3 Curvature localization zone

7.3.4.4 Parametric studies

7.3.4.5 Effect of confinement and minimum jacket length

7.3.4.6 Equivalent plastic hinge length

7.3.4.7 Plastic hinge under cyclic loading

7.3.4.8 Effect of FRP-to-concrete interfacial bond on plastic hinge

7.3.5 The P- effect

7.3.5.1 Implications of the P- effect

7.3.5.2 Evaluation of the simplified method for the P- effect

References:

Chapter 8. Confined Concrete

8.1 Introduction

8.2 Confinement effects to compression failure of concrete

8.3 Strength modeling of confined concrete cylinders/circular columns

8.3.1 Active and passive confinement

8.3.2 Typical strength models

8.4 Strength modeling of non-circular columns

8.4.1 Confinement effectiveness of square jacket

8.4.2 Effective strain of FRP jacket

8.4.3 Development of models for FRP-confined square/rectangular columns

8.4.3.1 Empirical models

8.4.3.2 Unified models

8.4.3.3 Hoek-Brown’s model

8.4.4 Assessment of Models

8.5 Measures to increase confinement effectiveness for rectilinear columns

8.5.1 Increasing the rigidity of jacketing plate

8.5.2 Reducing longitudinal stress

8.5.3 Additional anchoring

8.5.4 Alteration of cross-section

8.5.5 Other means

8.6 Stress-strain relationship of concrete

8.6.1 Methods for stress-strain modelling

8.6.2 Existence and form of the one-dimensional stress-strain relationship

8.6.3 Stress-strain relationship of concrete confined by steel reinforcement

8.6.4 Stress-strain model of concrete for FRP confined columns

8.6.4.1 Models developed by Teng’s group (Lam and Teng 2003a&b; Teng et al. 2009)

8.6.4.2 The model proposed by Harajli et al. (2006)

8.6.4.3 The model proposed by Wu et al. (2007)

8.6.4.4 The model by Youssef et al. (2007)

8.6.4.5 The unified model by Wei and Wu (2012)

8.6.5 Stress-strain model of confined concrete under eccentric loading

8.6.5.1 Effect of load eccentricity on the stress-strain relationship of confined concrete

8.6.5.2 The stress-strain model by Wu and Jiang (2013a)

8.6.5.3 The stress-strain model by Cao et al (2018)

8.6.5.4 Effect of load path on stress-strain relationship

8.6.6 Analytical method for stress-strain modeling

8.6.6.1 The analytical method by Li et al. (2021)

8.6.7 Stress-strain model of confined concrete for repair works by Wu et al. (2014)

8.6.8 Stress-strain model of confined concrete under cyclic loading

8.6.9 Stress-strain model of concrete for axially loaded members with failure localization

References

Chapter 9. Ductility Modification Technologies

9.1 Introduction

9.2 Ductility deficient RC structures reinforced with non-ductile bars

9.3 Avenues for ductility

9.4 Compression yielding structural system

9.5 Compression yielding instruments

9.5.1 Compression yielding mechanisms

9.5.2 Compression yielding material

9.6 Test of CY beams

9.7 Ductility demand on CY zone

9.8 Design of CY members

9.9 CY columns

9.10 Fused structures

9.10.1 A new type of structural fuse

9.10.2 Cost analysis of the fused structures

9.10.3 Determination of safety margin for fused structures

9.11 Increasing concrete strength by reducing perforation

9.12 Failure localization and mitigation

9.12.1 Failure of RC column under concentric loading

9.12.2 Concrete cracking

9.12.3 Plastic hinge failure

9.12.4 Rebar necking

9.12.5 General rule for mitigation of failure localization

References

Chapter 10. Shear Failure of RC Members

10.1 Introduction

10.2 Shear failure process and failure modes

10.3 Shear resisting mechanisms

10.3.1 Shear transfer mechanisms of RC members without web reinforcement

10.3.2 Shear transfer of RC members with web reinforcement

10.4 Development of shear design approaches

10.5 Evaluation of existing shear strength models

10.5.1 Evaluation of total shear strength

10.5.2 Evaluation of shear strength components

10.5.3 Difference between Vc and Vcr

10.5.4 Other test observations

10.5.5 Summary of findings

10.6 Discussion on shear strength modeling

10.6.1 Classic mechanics for derivation of Vcr

10.6.2 Shear resisting system and individual shear mechanisms

10.6.3 Advanced models based on particular shear mechanisms

10.6.4 Criterion based design approach

10.6.5 Lower bound solution

10.7 Potential solutions

10.7.1 More sophisticated modeling of the load-deformation process for the major shear mechanisms

10.7.2 Design RC details of a potential shear failure zone to have a simple and desirable load path and failure mode

10.7.3 Using a structural fuse to convert the shear failure mode to another one

10.7.4 Developing shear strength model with AI technology

References

Chapter 11. Modeling

11.1 Introduction

11.2 Types of model

11.3 Principles of modeling

11.3.1 Accuracy versus complexity of model

11.3.2 Causality of model

11.3.3 Task driven modeling

11.4 Methods of modeling

11.4.1 Logic reasoning

11.4.2 Theoretical vs. empirical modeling

11.4.3 Linear vs. non-linear modeling

11.4.4 Forward vs. inverse modeling

11.4.5 Heuristic modeling

11.5 Evaluation of model

11.5.1 Fitting observations

11.5.2 Scope of model

11.5.3 Philosophical considerations

11.6 Selection of model

11.6.1 Quantitative models

11.6.2 Qualitative models

11.7 Modeling with theorems of plasticity

11.7.1 Theorems of plasticity

11.7.2 Application of the plasticity theorems

11.8 About safety factor

11.9 Detailing of structures

11.10 Size effect

11.11 Research approach

11.11.1 Scientific method

11.11.2 The four dimensions of research approach

11.11.3 Fostering creativity in research

References