Design of Concrete Structures with Stress Fields

1 Introduction and Theoretical Basis.- 1.1 Introductory Remarks.- 1.2 Fundamentals of the Theory of Plasticity.- 1.2.1 Material Behaviour.- 1.2.2 Limit State Theorems of the Theory of Plasticity.- (a) Static Solution.- (b) Kinematic Solution.- 1.3 Engineering Methods.- 2 Stress Fields for Simple Structures.- 2.1 Introduction.- 2.2 Beams with Rectangular Cross-Section Subjected to Bending and Shear.- 2.2.1 Deep Beams, Concentrated Loads.- 2.2.2 Deep Beams, Several Concentrated Loads.- 2.2.3 Deep Beams, Distributed Load.- 2.2.4 Beams with Medium Slenderness Ratio, Concentrated Loads.- 2.3 Beams with I-Cross-Section Subjected to Bending and Shear.- 2.3.1 Slender Beams, Concentrated Loads.- 2.3.2 Slender Beams, Distributed Load.- 2.3.3 General Case, Practical Design.- 2.3.4 Beams of Variable Depth.- 2.3.5 Compression Flange.- 2.3.6 Tension Flange.- 2.4 Members Subjected to Torsion and Combined Action.- 2.4.1 Introduction.- 2.4.2 Warping Torsion (Open Cross-Sections).- 2.4.3 Circulatory Torsion.- 2.4.4 Circulatory Torsion Combined with Bending and Shear.- 2.5 Brackets.- 2.6 Coupling Beams.- 2.7 Joints of Frames.- 2.7.1 Corner Joint, Compression on the Inside.- 2.7.2 Corner Joint, Tension on the Inside.- 2.7.3 Joints of Frames with Three Connecting Beams.- 2.7.4 Joints of Frames with Four Connecting Beams.- 2.8 Beams with Sudden Changes in Cross-Section.- 2.9 Walls.- 2.9.1 Shear Walls.- 2.9.2 Diaphragms.- 2.10 Three-Dimensional Example.- 3 Material Strengths and other Properties.- 3.1 Reinforcing Steel.- 3.2 Concrete.- 3.2.1 Uniaxial Stress State.- 3.2.2 Three-Dimensional Stress State.- 3.2.3 Concrete with Imposed Cracks.- 3.2.4 Cracks: Aggregate Interlock.- 3.3 Force Transfer Reinforcement - Concrete.- 3.3.1 Anchorage of Reinforcing Bars.- 3.3.2 Splices of Reinforcement.- 3.3.3 Force Deviations.- 4 Additional Considerations for the Development of Stress Fields.- 4.1 Remarks on Plastic Design Applied to Reinforced Concrete.- 4.1.1 Behavior of Statically Indeterminate Beams.- 4.1.2 Selection of the Inclination of the Compression Field in the Web of Beams.- 4.1.3 Redistribution of Internal Forces and Ductility Requirements.- 4.2 Procedure for Developing Stress Fields.- 4.2.1 Introduction.- 4.2.2 Spreading of Force in a Wall Element Loaded in Tension.- 4.2.3 Spreading of Force in a Wall Element Loaded in Compression.- 4.2.4 Further Cases.- 4.3 Impaired Strength through Wide Cracks.- 4.4 Stress Distribution in Highly Stressed Compression Zones.- 4.4.1 Introduction.- 4.4.2 Stress Fields for Beam-Columns.- 4.5 Prestressed Beams.- 4.5.1 Beam with straight cable.- 4.5.2 Beam with curved cable.- 4.5.3 Anchorage zone of pretensioned beams.- 4.5.4 Unbonded prestressed beams.- 5 Plane Stress, Plate and Shell Elements.- 5.1 Plane Stress Elements.- 5.2 Slab Elements.- 5.3 Shell Elements.- 6 Outlook: Computer Programs.- References.