Time-dependent behaviour of concrete structures / Raymond Ian Gilbert and Gianluca Ranzi

Includes bibliographical references and index

Contents Preface Acknowledgements Notation and sign convention 1 Time-dependent deformation 1.1 Background 1.1.1 Concrete strain components 1.1.2 Typical concrete strain magnitudes 1.2 Creep of concrete 1.2.1 Creep mechanisms and influencing factors 1.2.2 Creep components 1.2.3 Effects of ageing 1.2.4 The creep coefficient, φ (t, τ), and the creep function, J (t, τ) 1.2.5 The principle of superposition 1.2.6 Tensile creep 1.2.7 The effects of creep on structural behaviour 1.3 Shrinkage of concrete 1.3.1 Types of shrinkage 1.3.2 Factors affecting shrinkage 1.3.3 The effects of shrinkage on structural behaviour 1.4 Time analysis - the basic problem 1.5 References 2 Material properties 2.1 Concrete 2.1.1 Introductory remarks 2.1.2 Compressive and tensile strength 2.1.3 Elastic modulus 2.1.4 Creep coefficient 2.1.5 Shrinkage strain 2.2 Steel reinforcement 2.2.1 General 2.2.2 Conventional, non-prestressed reinforcement 2.2.3 Prestressing steel 2.3 References 3 Design for serviceability - deflection and crack control 3.1 Introduction 3.2 Design objectives and criteria 3.3 Design actions 3.4 Design criteria for serviceability 3.4.1 Deflection limits 3.4.2 Crack width limits 3.5 Maximum span-to-depth ratio - minimum thickness Example 3.1 3.6 Deflection control by simplified calculation 3.6.1 Calculation of deformation 3.6.2 Load versus deflection response of a reinforced concrete member 3.6.3 Modular ratio theory 3.6.4 AS 3600-2009 and ACI 318-08 3.6.4.1 Instantaneous deflection 3.6.4.2 Time-dependent deflection Example 3.2 3.6.5 Eurocode 2 3.6.5.1 Instantaneous curvature 3.6.5.2 Time-dependent curvature Example 3.3 3.6.6 Recommended simplified approach 3.6.6.1 Instantaneous deflection 3.6.6.2 Time-dependent creep-induced curvature 3.6.6.3 Time-dependent shrinkage-induced curvature Example 3.4 3.7 Crack control 3.7.1 General 3.7.2 Simplified code-oriented approaches for flexural crack control 3.7.2.1 Gergely and Lutz 3.7.2.2 Frosch 3.7.2.3 Eurocode 2 - 1992 3.7.2.4 Eurocode 2 - 2004 3.7.2.5 ACI 318-08 Example 3.5 3.7.3 Tension chord model for flexural cracking in reinforced concrete Example 3.6 Example 3.7 3.7.4 Model for direct tension cracking in restrained reinforced concrete Example 3.8 3.8 References 4 Uncracked sections - axial loading 4.1 Preamble 4.2 The effective modulus method 4.2.1 Formulation 4.2.2 Example application (EMM) Example 4.1 4.3 The principle of superposition - step-by-step method (SSM) 4.3.1 Formulation 4.3.2 Example application (SSM) - Approach 1 4.3.2.1 At first loading (t = τO) 4.3.2.2 At the end of the j-th time step (id est t = τj) Example 4.2 4.3.3 Example application (SSM) - Approach 2 Example 4.3 4.4 The age-adjusted effective modulus method (AEMM) 4.4.1 Formulation 4.4.2 Example application (AEMM) - Approach 1 4.4.3 Determination of the ageing coefficient Example 4.4 4.4.4 Example application (AEMM) - Approach 2 Example 4.5 4.5 The rate of creep method (RCM) 4.5.1 Formulation 4.5.2 Discussion 4.5.3 Example application (RCM) Example 4.6 4.6 Comparison of methods of analysis 4.7 References 5 Uncracked sections - axial force and uniaxial bending 5.1 Introductory remarks 5.2 Overview of cross-sectional analysis 5.3 Short-term analysis of reinforced or prestressed concrete cross-sections Example 5.1 Example 5.2 5.4 Long-term analysis of reinforced or prestressed concrete cross-sections using the age-adjusted effective modulus method (AEMM) Example 5.3 Example 5.4 5.5 Long-term analysis of reinforced and prestressed cross-sections using the step-by-step procedure Example 5.5 Example 5.6 5.6 Composite steel-concrete cross-sections Example 5.7 Example 5.8 5.7 Composite concrete-concrete cross-sections 5.7.1 Short-term analysis 5.7.2 Time analysis - AEMM Example 5.9 5.7.3 Time analysis - SSM Example 5.10 5.8 References 6 Uncracked sections - axial force and biaxial bending 6.1 Introduction 6.2 Short-term analysis Example 6.1 Example 6.2 Example 6.3 6.3 Long-term analysis using the age-adjusted effective modulus method (AEMM) Example 6.4 Example 6.5 6.4 Long-term analysis using the step-by-step method 7 Cracked sections 7.1 Introductory remarks 7.2 Short-term analysis 7.2.1 Axial force and uniaxial bending Example 7.1 Example 7.2 7.2.2 Axial force and biaxial bending 7.3 Time-dependent analysis (AEMM) 7.3.1 Axial force and uniaxial bending Example 7.3 Example 7.4 7.3.2 Axial force and biaxial bending 7.4 Short- and long-term analysis using the step-by-step method 7.4.1 Axial force and uniaxial bending 7.4.1.1 Instantaneous analysis 7.4.1.2 Time analysis 7.4.2 Axial force and biaxial bending 7.5 References 8 Members and structures 8.1 Introductory remarks 8.2 Deflection of statically determinate beams 8.2.1 Deflection and axial shortening of uncracked beams Example 8.1 8.2.2 Control of deflection using non-prestressed reinforcement 8.2.3 Deflection and axial shortening of cracked beams Example 8.2 8.3 Statically indeterminate beams and slabs 8.3.1 Discussion 8.3.2 Determination of redundants Example 8.3 Example 8.4 8.3.3 Effects of deformation or settlement at the supports Example 8.5 8.3.4 Further effects of creep in prestressed construction Example 8.6 8.4 Two-way slab systems 8.4.1 Discussion 8.4.2 Slab deflection models 8.4.3 Two-way edge-supported slabs Example 8.7 8.4.4 Flat slabs Example 8.8 8.5 Slender reinforced concrete columns 8.5.1 Discussion 8.5.2 An iterative method of analysis Example 8.9 8.6 Temperature effects 8.6.1 Introduction 8.6.2 Temperature distributions 8.6.3 Temperature analysis of cross-sections Example 8.10 8.6.4 Temperature effects in members and structures Example 8.11 8.7 Concluding remarks 8.8 References 9 Stiffness method and finite-element modelling 9.1 Introduction 9.2 Overview of the stiffness method 9.3 Member loads Example 9.1 9.4 Time analysis using AEMM Example 9.2 9.5 Time analysis using SSM Example 9.3 9.6 Time analysis using the finite-element method 9.6.1 Load vector to account for time effects using the AEMM 9.6.2 Load vector to account for time effects using the SSM 9.6.3 Remarks on the consistency requirements for finite elements Example 9.4 9.7 Analysis of cracked members 9.7.1 Approach 1 9.7.2 Approach 2 9.8 References Appendix A Analytical formulations - Euler-Bernoulli beam model A.1 Introduction A.2 Kinematic model A.3 Weak formulation (global balance condition) A.4 Finite element formulation A.4.1 Age-adjusted effective modulus method A.4.2 Step-by-step method A.5 Strong formulation (local balance condition) A.5.1 Instantaneous analysis A.5.1.1 Stiffness matrix A.5.1.2 Equivalent nodal actions for member loads A.5.1.3 Post-processing of the instantaneous solution A.5.2 Age-adjusted effective modulus method (AEMM) A.5.2.1 Equivalent nodal actions at time τk A.5.2.2 Post-processing of the solution at time τk A.5.3 Step-by-step method (SSM) A.5.3.1 Equivalent nodal actions at time τk A.5.3.2 Post-processing of the solution at time τi A.6 References Index