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D-CAD Technologies Development Centre forApplied Dynamics |
Machine Foundation Design Competency Centre for Frame and Block Foundation Rotary, Reciprocating, Impact Machines and Vibration Isolation |
About the Book
Table of Contents
Foreword
Preface
Acknowledgement
CONTENTS
1 Indeterminacy of Structures
1.1 Introduction 1
1.2 Static Indeterminacy 4
1.2.1 Static Indeterminacy of Planar Pin- Jointed Structures 6
1.2.2 Static Indeterminacy of Pin-Jointed Space Structures 9
1.2.3 Degree of Static Indeterminacy of Beams and Rigid
Frames-Planar Structures 9
1.2.4 Static Indeterminacy of Rigid Space Frames 11
1.3 Henderson and Bickley Method 12
1.3.1 Characteristics of a Tree Structure 12
1.3.2 Rigid Jointed Structures 12
1.3.3 Pin-jointed Structures 15
1.3.4 Mixed Systems 16
1.4 Static Indeterminacy using the Concept of a Ring 17
1.5 Kinematic Indeterminacy of Structures 19
1.5.1 Determination of Kinematic Indeterminacy or
Degrees of Freedom of Structures 22
2 Principle of Virtual Work
2.1 Introduction 25 2.2 Principle of Virtual Work 26 2.3 Principle of Virtual Work Applied to Rigid Bodies 26 2.4 Principle of Virtual Work Applied to Elastic Bodies 27 2.5 Expressions for External and Internal Work 28 2.5.1 Work Done by External Forces (WE) 28 2.5.2 Work Done by Internal Forces (WI) 29 2.6 Virtual Work Transformation 37 2.7 Unit Load Theorem 37 2.8 Application of Unit Load Theorem to Determine Deflections 39 2.8.1 Pin-Jointed Structures 39 2.8.2 Beams and Frames 48 2.8.3 Evaluation of Integrals for the Determination of Deflections 56 2.9 Maxwell-Betti's Reciprocal Theorem 68 2.10 Maxwell's Theorem 71 [Top]
3 Flexibility Method of Structural Analysis
3.1 Introduction 75
3.2 Procedure of Analysing Beams and Frames by Flexibility Method 75
3.3 General Procedure of Flexibility Method in Matrix Notation 81
3.3.1 Analysis for a Number of Applied Load Cases 82
3.4 Analysis of Beams by Flexibility Method 83
3.4.1 Settlement of Supports 92
3.5 Analysis of Frames by Flexibility Method 99
3.6 Use of Symmetry and Anti-symmetry 113
3.6.1 Symmetrical Loading 114
3.6.2 Anti-symmetrical Loading 118
3.6.3 Superposition of Loading Systems 121
3.7 Lack of Fit 123
3.8 Three Moment Equation Applied to Continuous Beams 126
3.9 Column Analogy Method - an Application of Flexibility Method 136
3.9.1 Elastic Centre and Analogous Column 136
3.9.2 Sign Conventions 142
3.9.3 Other Support Conditions 142
3.10 Unsymmetrical Frames 144
3.11 Choice of the Primary Structure 144
3.12 Analysis of Statically Indeterminate Pin-jointed Structures 167
[Top]
4 Stiffness Method
4.1 Introduction 179
4.2 Stiffness Method Applied to Skeletal Structures 179
4.2.1 Determination of Fixed End Forces for a Beam Element Subjected to
Various Types of External Loads 183
4.3 Force Displacement Relationship for a Linear Beam Element with
Axial Deformations 187
4.3.1 u1 0 and all Other Displacement Components Being Zero 187
4.3.2 v1 0 and all Other Components are Equal to Zero 188
4.3.3 1 0 and all Other Displacement Components are Zero 190
4.4 Sign Conventions 192
4.5 Analysis of Continuous Beams by Stiffness Method 193
4.6 Analysis of Beams with Settlement of Supports 208
4.7 Analysis of Non-sway Frames 215
4.8 Analysis of Orthogonal Sway Frames 226
4.9 Symmetrical Structures Subjected to Symmetrical or Anti-symmetrical
Loading 241
4.10 Non-orthogonal Sway Frames 247
4.10.1 Determination of Relative Displacement between the Ends of
Frame Members 246
4.11 Analysis of Multistorey Frames 259
4.12 Settlement of Supports of Rigid Frames 264
4.13 Matrix Formulation of Stiffness Method 267
4.13.1 Continuous Beams 268
4.13.2 Settlement of Beam Supports 277
4.13.3 Non-sway Frame 280
4.13.4 Orthogonal Sway Frames 286
4.13.5 Non-orthogonal Sway Frames 293
4.14 Effect of Prescribed Displacements at the Coordinates 302
4.15 Finite Element Method 304
4.15.1 Steps of Analysis 305
4.15.2 Stiffness Matrix in Global Coordinates 306
4.15.3 Coordinate Transformation Matrix [ T ] 307
4.16 K of a Beam Element 308
4.17 Assemblage of Element Stiffness Matrices 310
4.18 Boundary Conditions 313
[Top]
5 Moment Distribution Method
5.1 Introduction 321
5.2 Flexural Stiffness of a Prismatic Member 322
5.2.1 Absolute Stiffness of a Member in Flexure 322
5.2.2 Flexural Stiffness of a Member when its far end is hinged 323
5.2.3 Flexural Stiffness of a Member when its far end is partially
restrained 324
5.3 Distribution Factors 324
5.4 Carry-over Factors 327
5.5 Scheme of Moment Distribution 327
5.6 Moment Distribution Applied to Beams using Modified Stiffness 332
5.7 Analysis of continuous Beams with Settlement of Supports 339
5.8 Analysis of Non-sway Orthogonal Frames 344
5.9 Settlement of Frame Supports 350
5.10 Analysis of Orthogonal Sway Frames 351
5.10.1 Determination of Lateral Force P Corresponding to Above
Calculated Sway Moments 365
5.10.2 Determination of Force P Corresponding to the above Calculated
Sway Moments 368
5.11 Use of Symmetry and Anti-symmetry 369
5.11.1 Determination of Lateral Force P Required to Induce the
Calculated Sway Moments 378
5.12 Analysis of Non-Orthogonal Frames 379
5.12.1 Determination of Lateral Force P Responsible For the Above
Calculated Sway Moments 387
5.12.2 Determination of Restraining Forces R2 and R4 389
5.13 Analysis of Multi-storey Frames 397
5.13.1 Determination of Restraining Force Vector {R} 401
5.14 Cantilever or "NO-SHEAR" Moment Distribution 406
[Top]
6 Multistorey Frames Subjected to Lateral Loads 6.1 Introduction 413 6.2 Approximate Methods 414 6.2.1 Portal Method of Analysing Multi-storey Frame Structures 416 6.2.2 Cantilever Method of Analysing Multi-storey Frame Structures 420 6.3 Substitute Frame Method 426 6.3.1 Open Type Frame Structure 429 6.3.2 Modified Substitute Frame 432 6.4 The Principle of Multiples 435 6.5 Analysis of Frames with Hinged Supports 440 6.6 General Application of Modified Substitute Frame 445 [Top] 7 Influence Lines for Indeterminate Structures 7.1 Introduction 451 7.2 Muller-Breslau Pripciple 451 7.3 Influence Lines for Beams 455 7.4 Influence Lines for Frames 472 7.5 Influence Lines for Multi-storey Frames 482 [Top] 8 Plastic Analysis of Structures 8.1 Introduction 485 8.2 Fully Plastic Section 486 8.3 Fully Plastic Moment 487 8.4 Plastic Behaviour of a Simple Beam 489 8.5 Proportional Loading 491 8.6 Plastic Analysis of Continuous Beams 497 8.7 Plastic Analysis of Orthogonal Frames 504 8.8 Plastic Analysis of Non-orthogonal Frames 509 8.9 Effect of Axial Load 512 8.10 Limitations 514 [Top]
9 Dynamic Analysis of Structures 9.1 Introduction 515 9.2 Equation of Motion of an Un-damped Single Degree of Freedom (SDOF) System 516 9.2.1 Free Vibrations of an Un-damped SDOF System 518 9.2.2 Importance of Dynamic Analysis 520 9.3 Response of an Un-damped SDOF System Subjected to a General Type of Load-time Function 522 9.3.1 Response of an Un-damped SDOF System to a Pulsating Force 529 9.4 Resonance 531 9.5 Damping 533 9.6 Damped Response of a SDOF System 533 9.6.1 Damped Free Vibrations of a SDOF System 534 9.6.2 Damped Forced Vibrations 535 9.6.3 Damped Response of a SDOF System to a Harmonic Excitation 535 9.7 Analysis of Structures Subjected to Ground Motion Caused by Earthquakes 537 9.8 Energy Method of Finding Natural Frequency, p, of a Structure 542 9.8.1 Rayleigh's Principle 544 9.8.2 Selection of the Principal Mode Shape 546 9.8.3 Code Basis 548 9.9 Dynamic Response of Multi-degree of Freedom (MDOF) Linear Systems 549 9.10 Dynamic Analysis of Multi-storey Shear Type Buildings 549 9.10.1 Natural Frequencies and Normal Modes of a Shear Building 552 9.11 Seismic Design 553 9.11.1 Seismic Coefficient 554 9.11.2 Determination of Seismic Design Loads 555 9.11.3 Base Shear 559 9.11.4 Distribution of Seismic Forces over the Height of Building 559 9.11.5 Proportion of Base Shear Applied at Each Floor Level 560 9.11.6 Lateral Force Applied at Each Floor Level 560 9.11.7 Forces in Each Element of the Administrative Building 561 9.11.8 Determination of Centre of Mass and the Centre of Rigidity at Each Floor Level 562 9.11.9 Seismic Lateral Loading 570 9.11.10 Distribution of Seismic Loads to Various Elements 570 9.11.11 Direction East or West 571 9.12 Distribution of Seismic Loads to Various Elements 571 9.12.1 Determination of Total Torque Resisted by the Typical Floor Elements 571 9.12.2 Direction North or South 574 [Top] 10 Exercises 577 11 Appendix 585 12 References 589 13 Index 591