Preface |
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iv | |
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1 Geometric Stability and Types of Structures |
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1 | (21) |
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1.1 Classifications of Structural Members and Connections |
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1 | (4) |
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1.2 Introduction to Geometrically Stable and Unstable Systems |
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5 | (1) |
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1.3 Rigid Degrees of Freedom and Constraints |
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6 | (3) |
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1.4 Rules for Constructing Geometrically Stable Systems |
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9 | (7) |
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9 | (2) |
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11 | (1) |
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12 | (2) |
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1.4.4 The Simply-Supported Rule |
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14 | (2) |
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1.5 Examples of Geometric-Stability Analysis |
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16 | (6) |
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2 Internal Forces in Statically Determinate Structures |
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22 | (23) |
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2.1 Analysis of Beams and Frames |
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22 | (14) |
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2.1.1 Properties of Moment Diagrams |
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22 | (2) |
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2.1.2 Constructions of Moment Diagrams by the Superposition Method in Segments |
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24 | (5) |
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2.1.3 Calculations of Internal Forces through Moment Diagrams |
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29 | (1) |
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30 | (6) |
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2.2 Analysis of Trusses and Composite Structures |
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36 | (4) |
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36 | (1) |
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2.2.2 Analysis of Statically Determinate Trusses |
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36 | (3) |
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2.2.3 Analysis of Statically Composite Structures |
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39 | (1) |
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2.3 Analysis of Statically Determinate Arches |
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40 | (5) |
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2.3.1 Comparison of Internal Forces in Arches and the Corresponding Beams |
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40 | (2) |
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2.3.2 The Ideal Axis of Parabolic Arch |
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42 | (3) |
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3 Deflections of Statically Determinate Structures |
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45 | (17) |
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3.1 Virtual-Work Principle for Rigid Bodies and Its Applications |
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45 | (6) |
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3.1.1 Work and Virtual Work |
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45 | (1) |
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3.1.2 Principle of Virtual Displacements for Rigid Bodies |
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46 | (3) |
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3.1.3 Principle of Virtual Forces for Rigid Bodies |
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49 | (2) |
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3.2 Principle of Virtual Forces for Elastic Structures |
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51 | (2) |
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3.3 Deflections Caused by External Loads |
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53 | (9) |
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3.3.1 Calculation of Structural Displacements to Loads by the Unit-Load Method |
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53 | (3) |
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3.3.2 Graphic Multiplication and Its Applications |
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56 | (6) |
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62 | (23) |
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4.1 Statically Indeterminate Structures |
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62 | (1) |
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4.2 General Procedure of the Force Method |
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63 | (3) |
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4.3 Analysis of Statically Indeterminate Structures under Loads |
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66 | (2) |
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4.4 Symmetric Structures and Their Half-Structures |
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68 | (10) |
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4.4.1 Symmetry of Structures, Loads and Responses |
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68 | (3) |
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4.4.2 Half-Structures of Symmetric Structures |
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71 | (7) |
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4.5 Analysis of Statically Indeterminate Structures Having Thermal Changes, Fabrication Errors and Support Settlements |
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78 | (2) |
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4.6 Deflections of Statically Indeterminate Structures |
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80 | (5) |
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85 | (27) |
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5.1 Beams with Support Displacements and Slope-Deflection Equations |
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85 | (2) |
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5.2 Displacement Method for Analyzing Frames under Nodal Loads |
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87 | (6) |
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5.2.1 The Procedure Using Slope-Deflection Equations |
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87 | (1) |
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5.2.2 The Procedure Directly Using Primary Systems |
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88 | (1) |
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5.2.3 Unknown Degrees of Freedom of the Displacement Method |
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89 | (4) |
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5.3 The Analysis of Frames Under In-Span Loading |
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93 | (5) |
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93 | (2) |
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5.3.2 Processing of In-Span Loads and Nodal Equivalent Loads |
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95 | (3) |
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5.4 Examples of Frames with In-Span Loads |
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98 | (5) |
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5.5 Moment Distribution Approach |
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103 | (9) |
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5.5.1 Moment Distribution Approach for SDOF Structures |
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103 | (2) |
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5.5.2 Moment Distribution Approach for MDOF Beams |
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105 | (7) |
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6 Influence Lines for Statically Determinate Structures |
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112 | (12) |
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112 | (1) |
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6.2 Influence Lines for Beams |
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112 | (3) |
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6.2.1 Constructing Influence Lines by the Principle of Virtual Displacements |
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113 | (2) |
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6.3 Influence Lines for Trusses |
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115 | (1) |
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6.4 Maximum Response at a Specific Point |
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116 | (3) |
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6.4.1 Maximum Response at a Point under Live Loads |
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116 | (1) |
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6.4.2 Maximum Response at a Point under a Set of Concentrated Moving Loads |
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117 | (2) |
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6.5 Moment Envelopes and Absolute Maximum Moments of Members |
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119 | (5) |
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6.5.1 Definition of Moment Envelope |
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119 | (1) |
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6.5.2 Moment Envelopes of Beams under Moving Loads |
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120 | (4) |
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7 Matrix Displacement Analysis |
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124 | (35) |
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7.1 An Introductory Example |
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124 | (5) |
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7.1.1 A Beam Element Type with Two Degree-of-Freedoms (DOFs) -- Beam 1 |
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124 | (1) |
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7.1.2 Pre-processing -- Discretizing and Digitizing of the Continuous Beam |
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125 | (1) |
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7.1.3 Calculate the Element Stiffness Matrices of the Continuous Beam |
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126 | (1) |
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7.1.4 Assembling Stiffness Equation of the Structure by the Direct Stiffness Method |
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126 | (2) |
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7.1.5 Solving and Post-processing |
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128 | (1) |
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7.1.6 MATLAB Codes -- Beam 1 Package |
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129 | (1) |
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7.2 Boundary Conditions and the Beam Element with Six DOFs |
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129 | (13) |
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7.2.1 Analyzing an Unrestrained Continuous Beam by Beam2 Element |
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129 | (5) |
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7.2.2 Post-Imposing of Boundary Conditions and Support Settlements |
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134 | (8) |
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7.3 Frames Subjected to Nodal Loading -- Change of Coordinates |
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142 | (10) |
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142 | (1) |
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7.3.2 Change of Coordinates |
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142 | (2) |
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7.3.3 Element Stiffness Matrices in Global Coordinates and the Assembling Rules |
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144 | (1) |
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7.3.4 Analysis of the Frames Subjected to Nodal Loads |
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145 | (7) |
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7.4 Frames Subjected to In-span Loads and Equivalent Nodal Loads |
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152 | (7) |
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7.4.1 The Equivalent Nodal Loads |
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152 | (4) |
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7.4.2 The Stiffness Equation of the Structure |
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156 | (1) |
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7.4.3 The End Displacement and Forces of the Structure |
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157 | (2) |
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159 | (72) |
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8.1 Introduction to Structural Dynamics |
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159 | (8) |
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8.1.1 What is Structural Dynamics? |
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159 | (1) |
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8.1.2 Models for Dynamic Analysis |
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160 | (2) |
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8.1.3 Equations of Motion and Initial Conditions |
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162 | (2) |
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8.1.4 Free Vibrations and Dynamic Properties |
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164 | (1) |
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8.1.5 Dynamic Responses to External Excitations |
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165 | (2) |
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167 | (1) |
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167 | (24) |
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8.2.1 Stiffness Method: The Dynamic-Equilibrium Procedure |
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167 | (3) |
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8.2.2 Stiffness Method: The Virtual Constraint Approach |
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170 | (6) |
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8.2.3 Flexibility Method to Formulate Equations of Motion |
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176 | (3) |
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8.2.4 Stiffness Method: The Matrix Displacement Approach and Static Condensation |
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179 | (9) |
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8.2.5 Damping in Structures |
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188 | (3) |
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8.3 Dynamic Properties of Structures |
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191 | (16) |
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8.3.1 Vibrations of SDOF Systems: Natural Frequency and Damping Ratio |
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191 | (7) |
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8.3.2 Undamped Free Vibrations of MDOF Systems: Normal Modes |
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198 | (4) |
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8.3.3 Properties of Modes |
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202 | (3) |
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8.3.4 Rayleigh Damping Matrix |
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205 | (2) |
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8.4 Analysis of Dynamic Responses Using the Mode Superposition Method |
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207 | (14) |
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8.4.1 Transient Responses of Uncoupled MDOF Systems to Combined Excitations |
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207 | (5) |
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8.4.2 Steady-State Responses of Uncoupled MDOF Systems to Combined Excitations |
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212 | (3) |
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8.4.3 Responses of Coupled MDOF Systems: Mode Superposition Method |
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215 | (6) |
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8.5 Analysis of the Dynamic Response Using the MATLAB ODE Solver: "ode45" |
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221 | (1) |
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8.6 Steady-State Responses to Separable Excitations |
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222 | (5) |
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224 | (1) |
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8.6.2 Peak Responses to Separable Excitations and Modal Combination Rules |
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225 | (2) |
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8.7 Appendix for Structural Dynamics |
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227 | (4) |
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8.7.1 Steady-State Responses to Space-time Coupled Excitations |
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227 | (4) |
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9 Limit Loads of Structures |
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231 | (14) |
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231 | (4) |
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9.2 Theorems of Plasticity |
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235 | (1) |
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9.3 Applications of the Upper Bound Theorem |
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236 | (4) |
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9.4 Limit Analysis by Linear Programing |
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240 | (5) |
Appendix |
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245 | (2) |
Index |
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247 | |