Contents -- Preface -- I INTRODUCTION -- 1 THE PURPOSE AND SCOPE OF THEORY OF STRUCTURES -- 1 1 General -- 1.2 The basis of theory of structures -- 1.3 Methods of theory of structures -- 1.4 Statics and structural dynamics -- 1.5 Theory of structures and structural engineering -- 2 BRIEF HISTORICAL BACKGROUND -- II FUNDAMENTALS -- 3 DESIGN OF STRUCTURES -- 3.1 General -- 3.2 Conceptual design -- 3.3 Service criteria agreement and basis of design -- 3.4 Summary -- 3.5 Exercises -- 4 STRUCTURAL ANALYSIS AND DIMENSIONING -- 4.1 General -- 4.2 Actions -- 4.2.1 Actions and action effects -- 4.2.2 Models of actions and representative values -- 4.3 Structural models -- 4.4 Limit states -- 4.5 Design situations and load cases -- 4.6 Verifications -- 4.6.1 Verification concept -- 4.6.2 Design values -- 4.6.3 Verification of structural safety -- 4.6.4 Verification of serviceability -- 4.7 Commentary -- 4.8 Recommendations for the structural calculations -- 4.9 Recommendations for the technical report -- 4.10 Summary -- 4.11 Exercises -- 5 STATIC RELATIONSHIPS -- 5.1 Force systems and equilibrium -- 5.1.1 Terminology -- 5.1.2 Force systems -- 5.1.3 Equilibrium -- 5.1.4 Overall stability -- 5.1.5 Supports -- 5.1.6 Hinges -- 5.1.7 Stress resultants -- 5.2 Stresses -- 5.2.1 Terminology -- 5.2.2 Uniaxial stress state -- 5.2.3 Coplanar stress states -- 5.2.4 Three-dimensional stress states -- 5.3 Differential structural elements -- 5.3.1 Straight bars -- 5.3.2 Bars in single curvature -- 5.4 Summary -- 5.5 Exercises -- 6 KINEMATIC RELATIONSHIPS -- 6.1 Terminology -- 6.2 Coplanar deformation -- 6.3 Three-dimensional deformation state -- 6.4 Summary -- 6.5 Exercises -- 7 CONSTITUTIVE RELATIONSHIPS -- 7.1 Terminology -- 7.2 Linear elastic behaviour -- 7.3 Perfectly plastic behaviour -- 7.3.1 Uniaxial stress state -- 7.3.2 Three-dimensional stress states.

7.3.3 Yield conditions -- 7.4 Time-dependent behaviour -- 7.4.1 Shrinkage -- 7.4.2 Creep and relaxation -- 7.5 Thermal deformations -- 7.6 Fatigue -- 7.6.1 General -- 7.6.2 S-N curves -- 7.6.3 Damage accumulation under fatigue loads -- 7.7 Summary -- 7.8 Exercises -- 8 ENERGY METHODS -- 8.1 Introductory example -- 8.1.1 Statically determinate system -- 8.1.2 Statically indeterminate system -- 8.1.3 Work equation -- 8.1.4 Commentary -- 8.2 Variables and operators -- 8.2.1 Introduction -- 8.2.2 Plane framed structures -- 8.2.3 Spatial framed structures -- 8.2.4 Coplanar stress states -- 8.2.5 Coplanar strain state -- 8.2.6 Slabs -- 8.2.7 Three-dimensional continua -- 8.2.8 Commentary -- 8.3 The principle of virtual work -- 8.3.1 Virtual force and deformation variables -- 8.3.2 The principle of virtual deformations -- 8.3.3 The principle of virtual forces -- 8.3.4 Commentary -- 8.4 Elastic systems -- 8.4.1 Hyperelastic materials -- 8.4.2 Conservative systems -- 8.4.3 Linear elastic systems -- 8.5 Approximation methods -- 8.5.1 Introduction -- 8.5.2 The RITZ method -- 8.5.3 The GALERKIN method -- 8.6 Summary -- 8.7 Exercises -- III LINEAR ANALYSIS OF FRAMED STRUCTURES -- 9 STRUCTURAL ELEMENTS AND TOPOLOGY -- 9.1 General -- 9.2 Modelling of structures -- 9.3 Discretised structural models -- 9.3.1 Description of the static system -- 9.3.2 Joint equilibrium -- 9.3.3 Static determinacy -- 9.3.4 Kinematic derivation of the equilibrium matrix -- 9.4 Summary -- 9.5 Exercises -- 10 DETERMINING THE FORCES -- 10.1 General -- 10.2 Investigating selected free bodies -- 10.3 Joint equilibrium -- 10.4 The kinematic method -- 10.5 Summary -- 10.6 Exercises -- 11 STRESS RESULTANTS AND STATE DIAGRAMS -- 11.1 General -- 11.2 Hinged frameworks -- 11.2.1 Hinged girders -- 11.2.2 Hinged arches and frames -- 11.2.3 Stiffened beams with intermediate hinges -- 11.3 Trusses.

11.3.1 Prerequisites and structural topology -- 11.3.2 Methods of calculation -- 11.3.3 Joint equilibrium -- 11.3.4 CREMONA diagram -- 11.3.5 RITTER method of sections -- 11.3.6 The kinematic method -- 11.4 Summary -- 11.5 Exercises -- 12 INFLUENCE LINES -- 12.1 General -- 12.2 Determining influence lines by means of equilibrium conditions -- 12.3 Kinematic determination of influence lines -- 12.4 Summary -- 12.5 Exercises -- 13 ELEMENTARY DEFORMATIONS -- 13.1 General -- 13.2 Bending and normal force -- 13.2.1 Stresses and strains -- 13.2.2 Principal axes -- 13.2.3 Stress calculation -- 13.2.4 Composite cross-sections -- 13.2.5 Thermal deformations -- 13.2.6 Planar bending of curved bars -- 13.2.7 Practical advice -- 13.3 Shear forces -- 13.3.1 Approximation for prismatic bars subjected to pure bending -- 13.3.2 Approximate coplanar stress state -- 13.3.3 Thin-wall cross-sections -- 13.3.4 Shear centre -- 13.4 Torsion -- 13.4.1 Circular cross-sections -- 13.4.2 General cross-sections -- 13.4.3 Thin-wall hollow cross-sections -- 13.4.4 Warping torsion -- 13.5 Summary -- 13.6 Exercises -- 14 SINGLE DEFORMATIONS -- 14.1 General -- 14.2 The work theorem -- 14.2.1 Introductory example -- 14.2.2 General formulation -- 14.2.3 Calculating the passive work integrals -- 14.2.4 Systematic procedure -- 14.3 Applications -- 14.4 MAXWELL's theorem -- 14.5 Summary -- 14.6 Exercises -- 15 DEFORMATION DIAGRAMS -- 15.1 General -- 15.2 Differential equations for straight bar elements -- 15.2.1 In-plane loading -- 15.2.2 General loading -- 15.2.3 The effect of shear forces -- 15.2.4 Creep, shrinkage and thermal deformations -- 15.2.5 Curved bar axes -- 15.3 Integration methods -- 15.3.1 Analytical integration -- 15.3.2 MOHR's analogy -- 15.4 Summary -- 15.5 Exercises -- 16 THE FORCE METHOD -- 16.1 General.

16.2 Structural behaviour of statically indeterminate systems -- 16.2.1 Overview -- 16.2.2 Statically determinate system -- 16.2.3 System with one degree of static indeterminacy -- 16.2.4 System with two degrees of static indeterminacy -- 16.2.5 In-depth analysis of system with one degree of static indeterminacy -- 16.2.6 In-depth analysis of system with two degrees of static indeterminacy -- 16.3 Classic presentation of the force method -- 16.3.1 General procedure -- 16.3.2 Commentary -- 16.3.3 Deformations -- 16.3.4 Influence lines -- 16.4 Applications -- 16.5 Summary -- 16.6 Exercises -- 17 THE DISPLACEMENT METHOD -- 17.1 Independent bar end variables -- 17.1.1 General -- 17.1.2 Member stiffness relationship -- 17.1.3 Actions on bars -- 17.1.4 Algorithm for the displacement method -- 17.2 Complete bar end variables -- 17.2.1 General -- 17.2.2 Member stiffness relationship -- 17.2.3 Actions on bars -- 17.2.4 Support force variables -- 17.3 The direct stiffness method -- 17.3.1 Incidence transformation -- 17.3.2 Rotational transformation -- 17.3.3 Algorithm for the direct stiffness method -- 17.4 The slope-deflection method -- 17.4.1 General -- 17.4.2 Basic states and member end moments -- 17.4.3 Equilibrium conditions -- 17.4.4 Applications -- 17.4.5 Restraints -- 17.4.6 Influence lines -- 17.4.7 CROSS method of moment distribution -- 17.5 Summary -- 17.6 Exercises -- 18 CONTINUOUS MODELS -- 18.1 General -- 18.2 Bar extension -- 18.2.1 Practical examples -- 18.2.2 Analytical model -- 18.2.3 Residual stresses -- 18.2.4 Restraints -- 18.2.5 Bond -- 18.2.6 Summary -- 18.3 Beams in shear -- 18.3.1 Practical examples -- 18.3.2 Analytical model -- 18.3.3 Multi-storey frame -- 18.3.4 VIERENDEEL girder -- 18.3.5 Sandwich panels -- 18.3.6 Summary -- 18.4 Beams in bending -- 18.4.1 General -- 18.4.2 Analytical model -- 18.4.3 Restraints.

18.4.4 Elastic foundation -- 18.4.5 Summary -- 18.5 Combined shear and bending response -- 18.5.1 General -- 18.5.2 Shear wall frame systems -- 18.5.3 Shear wall connection -- 18.5.4 Dowelled beams -- 18.5.5 Summary -- 18.6 Arches -- 18.6.1 General -- 18.6.2 Analytical model -- 18.6.3 Applications -- 18.6.4 Summary -- 18.7 Annular structures -- 18.7.1 General -- 18.7.2 Analytical model -- 18.7.3 Applications -- 18.7.4 Edge disturbances in cylindrical shells -- 18.7.5 Summary -- 18.8 Cables -- 18.8.1 General -- 18.8.2 Analytical model -- 18.8.3 Inextensible cables -- 18.8.4 Extensible cables -- 18.8.5 Axial stiffness of laterally loaded cables -- 18.8.6 Summary -- 18.9 Combined cable-type and bending response -- 18.9.1 Analytical model -- 18.9.2 Bending-resistant ties -- 18.9.3 Suspended roofs and stress ribbons -- 18.9.4 Suspension bridges -- 18.9.5 Summary -- 18.10 Exercises -- 19 DISCRETISED MODELS -- 19.1 General -- 19.2 The force method -- 19.2.1 Complete and global bar end forces -- 19.2.2 Member flexibility relation -- 19.2.3 Actions on bars -- 19.2.4 Algorithm for the force method -- 19.2.5 Comparison with the classic force method -- 19.2.6 Practical application -- 19.2.7 Reduced degrees of freedom -- 19.2.8 Supplementary remarks -- 19.3 Introduction to the finite element method -- 19.3.1 Basic concepts -- 19.3.2 Element matrices -- 19.3.3 Bar element rigid in shear -- 19.3.4 Shape functions -- 19.3.5 Commentary -- 19.4 Summary -- 19.5 Exercises -- IV NON-LINEAR ANALYSIS OF FRAMED STRUCTURES -- 20 ELASTIC-PLASTIC SYSTEMS -- 20.1 General -- 20.2 Truss with one degree of static indeterminacy -- 20.2.1 Single-parameter loading -- 20.2.2 Dual-parameter loading and generalisation -- 20.3 Beams in bending -- 20.3.1 Moment-curvature diagrams -- 20.3.2 Simply supported beams -- 20.3.3 Continuous beams -- 20.3.4 Frames -- 20.3.5 Commentary.

20.4 Summary.