Brief Introduction to the Book................................... III
About the Authors............................................ V
Preface..................................................... VII
Notations................................................... XV
CHAPTER 1
Introduction................................................. 1
1.1 Research Object and Tasks of StructuralAnalysis................ 2
1.1.1 Research Object.................................... 2
1.1.2 Tasks............................................ 3
1.2 Computational Models of Structures.......................... 4
1.2.1 Simplification of Structural Systems..................... 5
1.2.2 Simplification of Members............................ 5
1.2.3 Simplification of Joints............................... 6
1.2.4 Simplification of the Supports......................... 7
1.2.5 Simplification of MaterialProperties..................... 8
1.2.6 Simplification of Loads............................... 8
1.3 Classification of Member Structures andLoads .................. 10
1.3.1 Classification of Member Structures..................... 10
1.3.2 Classification of Loads............................... 11
1.4 A Brief History of the Development ofStructural Analysis ......... 12
1.4.1 Energy Principles and Energy Methods.................. 13
1.4.2 Force Method and Displacement Method................. 15
1.4.3 Matrix Displacement Method and FiniteElement Method .... 18
1.5 A Brief Introduction to Important Figuresin Structural Analysis .... 20
CHAPTER 2
Kinematic Analysis of Plane Member Systems....................... 27
2.1 Several Concepts of Kinematic Analysis....................... 28
2.1.1 Degree of Freedom and Constraint...................... 28
2.1.2 Instantaneously Changeable System and Constantly Changeable System................................. 30
2.1.3 Instantaneous Hinge................................. 31
2.2 Basic Construction Rules of Plane Geometrically Unchangeable Systems............................................... 32
2.2.1 The Rule of Pin-Joined Member System.................. 32
2.2.2 The Rule of Two Rigid Discs.......................... 33
2.2.3 The Rule of Three Rigid Discs......................... 34
2.3 Computational Degree of Freedom of PlaneMember Systems ....... 39
2.3.1 Computational Degree of Freedom of RigidDisc System ...... 40
2.3.2 Computational Degree of Freedom of theHinged System ..... 42
2.3.3 Computational Degree of Freedom of theMixed System ...... 44
2.4 Geometrical Stability and StaticDeterminacy of Systems .......... 45
Problems................................................... 46
CHAPTER 3
Analysis of Statically Determinate Structures........................ 49
3.1 Single-Span Statically Determinate Beams..................... 50
3.1.1 Single-Span Statically Determinate Beamsand Internal Forces........................................... 50
3.1.2 Relations Between Loads and InternalForces .............. 52
3.1.3 Method of Segmental Superposition..................... 54
3.2 Multi-Span Statically Determinate Beams...................... 57
3.3 Statically Determinate Plane Trusses......................... 62
3.3.1 Characteristics and Classification ofTrusses ............... 62
3.3.2 Method of Joints................................... 64
3.3.3 Method ofSections.................................. 67
3.3.4 Combined Application of the Method ofJoints and the Method of Sections........................... 69
3.4 Statically Determinate PlaneFrames.......................... 71
3.4.1 Characteristics of Frames............................. 71
3.4.2 Calculation of Support Reactions....................... 71
3.4.3 Internal Force Analysis and DrawingInternal Force Diagram of Frames.................................. 75
3.4.4 Quick Drawing of Moment Diagrams ofStatically Determinate Frames................................. 84
3.5 Statically Determine Composite Structures..................... 86
3.6 Three-Hinged Arches..................................... 92
3.6.1 Support Reactions and Internal ForceCalculation of Three-Hinged Arches.............................. 93
3.6.2 Rational Axes of Three-Hinged Arches................... 99
3.7 General Properties of Statically Determinate Structures ........... 104
Problems................................................... 106
CHAPTER 4
Principle of Virtual Work and Deflectio Calculation .................. 113
4.1 Overview of Deflection Calculation........................... 113
4.1.1 Concept of Structural Displacements.................... 113
4.1.2 Purpose of Deflection Calculation....................... 115
4.2 Principle of Virtual Work for Deformable Structures .............. 116
4.2.1 Principle of Virtual Work for Rigid Body System ........... 116
4.2.2 Application Conditions of Principle of Virtual Work
for Deformable Structures............................ 116
4.2.3 Virtual Work Equation for DeformableStructures .......... 119
4.2.4 Principle of Virtual Forces and Principleof Virtual Displacements..................................... 122
4.3 Unit-Load Method for Structural Deflection Calculation ........... 124
4.4 Deflection Calculation under Loads........................... 127
4.4.1 Formula for Deflection Calculation underLoads ............ 127
4.4.2 Deflection Formulas for Various Structures ................ 128
4.4.3 Examples of Deflection Calculation underLoads............ 130
4.5 Graph Multiplication Method............................... 136
4.5.1 Graph Multiplication Method and ItsApplication Conditions. . 136
4.5.2 Several Specific Problems of ApplyingGraph Multiplication Method.......................................... 137
4.5.3 Examples of Graph Multiplication Method................ 140
4.6 Deflection Calculation under Temperature Change ............... 143
4.7 Reciprocal Theorems of Linearly Elastic Structures ............... 146
4.7.1 Theorem of Reciprocal Works.......................... 146
4.7.2 Theorem of Reciprocal Displacements.................... 148
4.7.3 Theorem of Reciprocal Reactions....................... 149
4.7.4 Theorem of Reciprocal Displacement-Reaction ............. 150
Problems................................................... 151
CHAPTER 5
Force Method................................................ 157
5.1 Determination of Degree of Static Indeterminacy ................ 158
5.1.1 Equilibrium and Geometric Construction Characteristics of Statically Indeterminate Structures.................... 158
5.1.2 Determination of Degree of Indeterminacy and Number of Redundant Constraint Forces........................ 159
5.2 Fundamental Concept of the Force Method..................... 161
5.2.1 Primary Unknowns, Primary System, andBasic Equations of Force Method.................................... 161
5.2.2 Analysis of Structures with MultipleDegrees of Indeterminacy by Force Method................................... 165
5.2.3 Canonical Equations of Force Method................... 167
5.3 Analysis of Statically Indeterminate Framesand Bent Structures .... 169
5.4 Analysis of Statically IndeterminateTrusses and Composite Structures.............................................. 177
5.5 Analysis of Symmetric Structures and Half Structures............. 182
5.5.1 Selection of Symmetric Primary System.................. 184
5.5.2 Determination of Half Structure in Termsof Symmetry ...... 188
5.6 Two-Hinged and HingelessArches............................ 193
5.6.1 Solving Two-Hinged Arch by the Force Method ............ 194
5.6.2 Solving Hingeless Arch by the Force Method .............. 200
5.7 Internal Force Analysis of Structures underSupport Movement or Temperature Change................................... 204
5.7.1 Support Movement.................................. 204
5.7.2 Temperature Change................................ 208
5.8 Deflection Computation of StaticallyIndeterminate Structures ...... 210
5.9 Check for Calculated Results of StaticallyIndeterminate Structures . . 215
5.9.1 Check of Equilibrium Conditions....................... 216
5.9.2 Check of Deformation Conditions....................... 217
Problems................................................... 218
CHAPTER 6
Displacement Method.......................................... 223
6.1 Fundamental Concept of the Displacement Method ............... 224
6.1.1 A Simple Example of Displacement Method............... 224
6.1.2 Primary Unknowns and Basic Equations of Displacement Method.............................. 227
6.1.3 Basic Idea of Calculating FrameStructures by Displacement Method............................. 228
6.1.4 Determination of Primary Unknowns of Displacement Method . 229
6.2 Slope-Deflection Equation of Prismatic Member ................. 232
6.2.1 Calculating Member-End Internal Forcesfrom Member-End Displacements..................................... 234
6.2.2 Calculating Fixed-End Internal Forces from Loads .......... 238
6.3 Analysis of Frames Without Sidesway......................... 241
6.3.1 Selection of Primary Unknowns........................ 241
6.3.2 Establishment of Basic Equations....................... 241
6.4 Analysis of Frames with Sidesway............................ 245
6.5 Analysis of Symmetric Structures............................ 253
6.6 Primary System in the Displacement Method................... 256
6.6.1 Primary System of the Displacement Method.............. 257
6.6.2 Basic Equations of the Displacement Method .............. 258
6.6.3 Process of Establishing the Basic Equations of the Displacement Method........................... 260
6.6.4 Canonical Equations of Displacemen tMethod ............. 262
6.7 Principle of Potential Energy and Displacement Method ........... 264
6.7.1 Principle of Stationary Potential Energy.................. 264
6.7.2 Linear Elastic Strain Energy of Prismatic Member .......... 266
6.7.3 Principle of Potential Energy and Equilibrium Equation
of Displacement Method.............................. 267
6.8 Rayleigh–Ritz Method.................................... 272
6.9 Moment-Distribution Method and No-Shear Distribution Method .... 274
6.9.1 Basic Principle of the Moment-Distribution Method ......... 275
6.9.2 Computation of Continuous Beams and Frames Without Sidesway Using the Moment-Distribution Method.......... 280
6.9.3 No-Shear Distribution Method......................... 286
6.10 Characteristics of StaticallyIndeterminate Structures ............. 292
Problems................................................... 294
CHAPTER 7
Influence Lines for Structures under Moving Loads .................... 301
7.1 Concepts of Moving Load and Influence Line................... 302
7.2 Equilibrium Method for ConstructingInfluence Lines of Simply Supported Beams........................................ 304
7.3 Influence Lines for Girders and Trusses........................ 309
7.3.1 Influence Lines for Internal Forces of Girders .............. 309
7.3.2 Influence Lines for Axial Forces of Trusses ................ 311
7.4 Kinematic Method for Constructing InfluenceLines of Statically Determinate Structures.................................... 315
7.5 Applications of Influence Lines.............................. 321
7.5.1 Responses Due to Various Kinds of Loads................ 322
7.5.2 Most Unfavorable Position of Moving Loads............... 324
7.5.3 Determination of Critical Position forPolygonal Influence Line............................................. 326
7.5.4 Determination of Critical Position forTriangle Influence Line . . 330
7.6 Kinematic Method for Constructing Influence Lines of Statically Indeterminate Beams..................................... 333
Problems................................................... 341
CHAPTER 8
Matrix Displacement Methods................................... 345
8.1 Fundamental Principle of the MatrixDisplacement Method ........ 346
8.2 Elemental Stiffness Matrix................................. 347
8.2.1 Elemental Stiffness Matrix in LocalCoordinate System ...... 348
8.2.2 Properties of Elemental Stiffness Matrix.................. 350
8.3 Coordinate Transformation of ElementalStiffness Matrix .......... 351
8.3.1 Elemental Stiffness Matrix in the GlobalCoordinate System ... 351
8.3.2 Elemental Stiffness Matrix of ContinuousBeam ............ 355
8.3.3 Elemental Stiffness Matrix of Axial ForceBar.............. 357
8.4 Global Stiffness Matrix of Structure.......................... 360
8.4.1 Element and Node Numberings........................ 360
8.4.2 Direct Stiffness Method for Assembling Global Stiffness Matrix........................................... 362
8.4.3 Imposing Support Conditions.......................... 364
8.4.4 Properties of Global Stiffness Matrix.................... 365
8.4.5 Treatment of Pinned Joints........................... 366
8.5 Equivalent Nodal Loads................................... 366
8.5.1 Basic Equation of Matrix DisplacementMethod ............ 366
8.5.2 Equivalent Nodal Loads of Elements.................... 367
8.5.3 Equivalent Nodal Loads of Structure.................... 369
8.6 Computational Procedures and Examples...................... 372
8.6.1 Example of Truss Analysis............................ 373
8.6.2 Example of Frame Structure........................... 378
8.6.3 Example of Composite Structure....................... 384
8.6.4 Matrix Displacement Method forRectangular Frame
Neglecting Axial Deformation.......................... 388
Problems................................................... 391
Bibliography................................................. 397
Appendix A1. Answers to Problems............................... 399
Appendix A2. Index........................................... 407
Appendix A3. Matlab Program Codes of the MatrixDisplacement Method
for Plane Structural Analysis......................... 409
