Reinforced Concrete Beams, Columns and Frames: Section and Slender Member Analysis

This book is focused on the theoretical and practical design of reinforced concrete beams, columns and frame structures. It is based on an analytical approach of designing normal reinforced concrete structural elements that are compatible with most international design rules, including for instance the European design rules – Eurocode 2 – for reinforced concrete structures. The book tries to distinguish between what belongs to the structural design philosophy of such structural elements (related to strength of materials arguments) and what belongs to the design rule aspects associated with specific characteristic data (for the material or loading parameters). A previous book, entitled Reinforced Concrete Beams, Columns and Frames – Mechanics and Design, deals with the fundamental aspects of the mechanics and design of reinforced concrete in general, both related to the Serviceability Limit State (SLS) and the Ultimate Limit State (ULS), whereas the current book deals with more advanced ULS aspects, along with instability and second-order analysis aspects. Some recent research results including the use of non-local mechanics are also presented. This book is aimed at Masters-level students, engineers, researchers and teachers in the field of reinforced concrete design. Most of the books in this area are very practical or code-oriented, whereas this book is more theoretically based, using rigorous mathematics and mechanics tools. Contents 1. Advanced Design at Ultimate Limit State (ULS). 2. Slender Compression Members – Mechanics and Design. 3. Approximate Analysis Methods. Appendix 1. Cardano’s Method. Appendix 2. Steel Reinforcement Table. About the Authors Jostein Hellesland has been Professor of Structural Mechanics at the University of Oslo, Norway since January 1988. His contribution to the field of stability has been recognized and magnified by many high-quality papers in famous international journals such as Engineering Structures, Thin-Walled Structures, Journal of Constructional Steel Research and Journal of Structural Engineering. Noël Challamel is Professor in Civil Engineering at UBS, University of South Brittany in France and chairman of the EMI-ASCE Stability committee. His contributions mainly concern the dynamics, stability and inelastic behavior of structural components, with special emphasis on Continuum Damage Mechanics (more than 70 publications in International peer-reviewed journals). Charles Casandjian was formerly Associate Professor at INSA (French National Institute of Applied Sciences), Rennes, France and the chairman of the course on reinforced concrete design. He has published work on the mechanics of concrete and is also involved in creating a web experience for teaching reinforced concrete design – BA-CORTEX. Christophe Lanos is Professor in Civil Engineering at the University of Rennes 1 in France. He has mainly published work on the mechanics of concrete, as well as other related subjects. He is also involved in creating a web experience for teaching reinforced concrete design – BA-CORTEX.

Table of Contents:
Preface  ix Chapter 1. Advanced Design at Ultimate Limit State (ULS)  1 1.1. Design at ULS – simplified analysis 1 1.1.1. Simplified rectangular behavior – rectangular cross-section 1 1.1.2. Simplified rectangular behavior – T-cross-section 16 1.1.3. Comparison of design between serviceability limit state and ultimate limit state 22 1.1.4. Biaxial bending of a rectangular cross-section 28 1.2. ULS – extended analysis 37 1.2.1. Bilinear constitutive law for concrete – rectangular cross-section 37 1.2.2. Parabola–rectangle constitutive law for concrete – rectangular cross-section 44 1.2.3. T-cross-section – general resolution for bilinear or parabola–rectangle laws for concrete 53 1.2.4. T-cross-section – general equations for composed bending with normal forces 66 1.3. ULS – interaction diagram 82 1.3.1. Theoretical formulation of the interaction diagram 82 1.3.2. Approximation formulations 94 1.3.3. Graphical results for general cross-sections 98 Chapter 2. Slender Compression Members – Mechanics and Design 103 2.1. Introduction 103 2.2. Analysis methods 103 2.2.1. General 103 2.2.2. Requirements to second-order analysis 105 2.3. Member and system instability 105 2.3.1. Elastic critical load and effective (buckling) length 105 2.3.2. System instability principles 110 2.3.3. Concrete column instability – limit load 110 2.4. First- and second-order load effects 112 2.4.1. Global and local second-order effects 112 2.4.2. Single members 113 2.4.3. Frame mechanics – braced and bracing columns 115 2.4.4. Moment equilibrium at joints 119 2.5. Maximum moment formation 120 2.5.1. Maximum first- and second-order moment at the same section 120 2.5.2. Maximum first- and second-order moment at different sections 124 2.5.3. Curvature-based maximum moment expression 136 2.5.4. Unbraced frame application example 141 2.6. Local and global slenderness limits 144 2.6.1. Local, lower slenderness limits – general 144 2.6.2. EC2 – local lower slenderness limits 148 2.6.3. NS-EC2 – Local lower slenderness limits 150 2.6.4. Comparison of the EC2 and NS-EC2 limits 155 2.6.5. Local upper slenderness limit 156 2.6.6. Global lower slenderness limit 159 2.7. Effect of creep deformations 163 2.7.1. General 163 2.7.2. Effects on load and deformation capacity 165 2.7.3. Approximate calculation of creep effects 169 2.8. Geometric imperfections 176 2.8.1. Imperfection inclination 176 2.8.2. Stiffening structural elements 176 2.8.3. Stiffened and isolated structural elements 180 2.9. Elastic analysis methods 181 2.9.1. Principles, equilibrium and compatibility 181 2.9.2. Equilibrium and compatibility at multiple sections 183 2.9.3. Optimization 185 2.10. Practical linear elastic analysis 187 2.10.1. Stiffness assumptions 187 2.10.2. EC2 approach 189 2.10.3. ACI 318 approach 190 2.11. Simplified analysis and design methods 191 2.11.1. General 191 2.11.2. Simplified second-order analysis 192 2.11.3. Method based on nominal stiffness 194 2.11.4. Method based on nominal curvature 200 2.12. ULS design 204 2.12.1. Simplified design methods 204 2.12.2. Alternative design methods 205 2.12.3. Design example – framed column 207 Chapter 3. Approximate Analysis Methods 213 3.1. Effective lengths 213 3.1.1. Definition and exact member analysis 213 3.1.2. EC2 effective length of isolated members 218 3.1.3. Alternative effective length expressions 219 3.1.4. Columns with beam restraints 222 3.2. Method of means 227 3.2.1. General 227 3.2.2. Method of means – typical steps 227 3.2.3. Application of the method of means 230 3.3. Global buckling of unbraced or partially braced systems 236 3.3.1.General considerations 236 3.3.2. Flexibility factors 240 3.3.3. System instability and “system” effective lengths 243 3.3.4. Instability of partially braced column – example 248 3.3.5. Instability of partially braced frame – example 251 3.3.6. Sway buckling of unbraced multistory frames 256 3.4. Story sway and moment magnification 262 3.4.1. General 262 3.4.2. Partially braced column – example 264 3.4.3. Partially braced frame – example 266 3.4.4. Sway magnifier prediction of frames with single curvature regions 268 3.4.5. Iterative elastic analysis method 271 3.4.6. Global magnifiers for sway and moments 272 Appendix 1. Cardano’s Method 279 A1.1. Introduction 279 A1.2. Roots of a cubic function – method of resolution 280 A1.2.1. Canonical form 280 A1.2.2. Resolution – one real and two complex roots 281 A1.2.3. Resolution – two real roots 283 A1.2.4. Resolution – three real roots 283 A1.3. Roots of a cubic function – synthesis 285 A1.3.1. Summary of Cardano’s method 285 A1.3.2. Resolution of a cubic equation – example 286 A1.4. Roots of a quartic function – principle of resolution 287 Appendix 2. Steel Reinforcement Table 289 Bibliography 291 Index 305