Contents-Adv Structural Analysis-AKJ
- 1. Now also available at AMAZON.IN 170 Solved Examples
- 2. Advanced Structural Analysis with Finite Element Method Ashok K. Jain Professor of Civil Engineering Indian Institute of Technology Roorkee ROORKEE and Former Director Malaviya National Institute of Technology JAIPUR Third Edition 2015 Nem Chand & Bros, Roorkee, 247667, U.K., India 170 Solved Examples
- 3. Contents 1. BASIC CONCEPTS 1 - 28 1.1 Introduction 1 1.2 Structural Elements 3 1.3 Statically Determinate vs. Indeterminate Structures 5 1.4 Flexibility Method 8 1.5 Stiffness Method 10 1.6 System Approach vs. Element Approach 13 1.7 Choice of a Method 14 1.8 Degree of Static Indeterminacy 14 1.9 Degree of Kinematic Indeterminacy 15 1.10 Illustrative Examples 16 Problems 28 PART I : FLEXIBILITY METHODS 2. METHOD OF CONSISTENT DEFORMATIONS 31-76 2.1 Introduction 31 2.2 Choice of Redundants 32 2.3 Beams with one Redundant 34 2.4 Beams with two or more Redundants 41 2.5 Reactions due to Yielding of Supports 51 2.6 Frames 54 2.7 Trusses 61 Problems 71 3. THREE MOMENT EQUATION 77-89 3.1 Introduction 77 3.2 Derivation of Three Moment Equation 77 3.3 Beams 81 3.4 Reactions due to Yielding Of Supports 85
- 4. 3.5 Frames 85 Problems 88 4. STRAIN ENERGY METHOD 90-134 4.1 Introduction 90 4.2 Work and Complementary Work 91 4.3 Strain Energy 92 4.4 Energy Theorems 95 4.5 Beams - Illustrative Examples 98 4.6 Frames - Illustrative Examples 103 4.7 Truss 126 Problems 130 (vii) (viii) 5. COLUMN ANALOGY METHOD 135-166 5.1 Introduction 135 5.2 Stress in a Column 135 5.3 Development of the Method 136 5.4 Sign Convention 139 5.5 Analogous Column Sections 139 5.6 Fixed End Moments in Beams of Uniform Cross-Section 141 5.7 Stiffness and Carry Over Factors 145 5.8 Beams with Variable Cross-Section 148 5.9 Portal Frames with One Axis of Symmetry 153 5.10 Closed Frames with One Axis of Symmetry 156 5.11 Portal Frames with No Symmetry 159 Problems 164 6. INFLUENCE COEFFICIENT METHOD 167-199 6.1 Introduction 167 6.2 Sign Convention 168 6.3 Force Diagrams 169 6.4 Graphical Method of Integration 171 6.5 Illustrative Examples 172 Problems 196 7. INFLUENCE LINES 200-208 7.1 Introduction 200 7.2 Muller – Breslau Principle 200 7.3 Illustrative Examples 203 Problems 208 8 ARCHES 209-237 8.1 Introduction 209 8.2 Two-Hinged Arch 210 8.3 Illustrative Examples 213 8.4 Fixed Arch 217 8.5 Symmetrical Fixed Arch 219
- 5. 8.6 Elastic Centre 222 8.7 Illustrative Examples 223 8.8 Influence Lines for a Hinged Arch 232 8.9 Influence Lines for a Fixed Arch 234 Problems 235 PART 2 STIFFNESS METHODS 9. SLOPE-DEFLECTION METHOD 241-300 9.1 Introduction 241 9.2 Development of Slope-Deflection Equations 241 9.3 Equations of Equilibrium 243 9.4 Beams 244 9.5 Frames: No Side Sway 250 (ix) 9.6 Frames: with Side Sway 254 9.7 Frames with Sloping Legs 271 9.8 Effect of Change in Temperature 285 9.9 Flexibility and Stiffness Matrices 289 Problems 296 10. MOMENT DISTRIBUTION METHOD 301-351 10.1 Development of the Method 301 10.2 Distribution Factors 303 10.3 Sign Convention 304 10.4 Beams and Frames with no Side Sway 304 10.5 Beams with Uneven Support Settlement 318 10.6 Frames with Side Sway 321 10.7 Frames with Uneven Support Settlements 328 10.8 Symmetry and Anti-Symmetry 330 10.9 Comments on the Moment Distribution Method 348 Problems 348 11. DIRECT STIFFNESS METHOD – 2D ELEMENTS 352-432 11.1 Development of Stiffness Matrices 352 11.2 Properties of Stiffness Matrices 358 11.3 Transformation of Coordinates 360 11.4 Element Load Vector 363 11.5 Assembly of Global Matrices 364 11.6 Illustrative Examples 373 11.7 Boundary Conditions 383 11.8 Support Reactions 387 11.9 Inclined Roller Support 387 11.10 Summary of Direct Stiffness Method 387 11.11 Beams on Elastic Foundation 389 11.12 Illustrative Examples 390 11.13 Comparison of Flexibility and Stiffness Methods 427 Problems 428 12. DIRECT STIFFNESS METHOD – 3D ELEMENTS 433-461 12.1 Stiffness Matrix- Bar Element 433 12.2 Stiffness Matrix- Beam Element 434
- 6. 12.3 Stiffness Matrix- Grid Element 436 12.4 Stiffness Matrix-Shear Wall element 437 12.5 Stiffness Matrix- Beam with Rigid Ends – 2D 439 12.6 Stepped Members 441 12.7 Transformation Matrix – 3D Bar Element 447 12.8 Transformation Matrix – 3D Beam Element 451 12.9 Constraints and Link Elements 457 12.10 Modeling Bearings and Expansion Joints in Bridges 460 References 461 Problem 461 (x) 13. FINITE ELEMENT METHOD 462-532 13.1 Introduction 462 13.2 Modeling, Discretization and Errors 464 13.3 Steps in Finite Element Method 464 13.4 Interpolation and Shape Functions 465 13.5 Degree of Continuity 466 13.6 Bar Element 466 13.7 Beam Element 468 13.8 Linear Triangle or Constant Strain Triangle 469 13.9 Bi–Linear Rectangle – Q4 473 13.10 Quadratic Rectangle Q8 And Q9 475 13.11 Normalized Coordinates 475 13.12 Rectangular Elements – Lagrange family 476 13.13 Illustrative Examples 478 13.14 Rectangular Elements Serendipity Family 481 13.15 Sequence of Node Numbering 483 13.16 Curved and Isoparametric Elements 484 13.17 Convergence Criteria 485 13.18 Stress-Strain Relations 485 13.19 StrainDisplacement Relations 490 13.20 Equilibrium Equations 492 13.21 Compatibility 492 13.22 Virtual Work 493 13.23 Element Stiffness Matrix – Isoparametric Elements 494 13.24 Transformation of Coordinates 499 13.25 Numerical Integration – Gauss Quadrature 499 13.26 Illustrative Examples 501 13.27 Equivalent Nodal Loads 508 13.28 Consistent Mass Matrix 513 13.29 Illustrative Examples 514 13.30 Application to Field Problems 519 References 529 Problems 529 14. NONLINEAR ANALYSIS: Material Nonlinearity 533-575 14.1 Introduction 533 14.2 Stress-Strain Curve of Steel 533
- 7. 14.3 Theory of Plastic Analysis 534 14.4 Plastic Hinge and Mechanism 537 14.5 Moment-Curvature Relation 539 14.6 Plastic Analysis 540 14.7 Illustrative Examples 542 14.8 Hysteresis Loops 558 14.9 Assumptions 560 14.10 Member Stiffness Matrix 560 14.11 Nonlinear Stiffness Matrix Analysis 562 14.11.1 Incremental Displacement and Load Vectors 566 14.11.2 Modification of the Structural Stiffness Matrix 566 (xi) 14.11.3 Unbalanced Load Vector 567 14.12 Ductility 569 14.13 Illustrative Examples 570 References 574 Problems 574 15. NONLINEAR ANALYSIS : Geometric Nonlinearity 576-594 15.1 Introduction 576 15.2 Geometric Stiffness Matrix - Bar Element 577 15.3 Cable Suspension Systems 579 15.4 P-Delta Effects in Structures 580 15.5 Geometric Stiffness Matrix – Beam Element 581 15.6 Nonlinear Solution Algorithms 584 15.7 Convergence Criteria 587 15.8 Illustrative Examples 588 Reference 593 Problems 593 APPENDIX A – MATRIX ALGEBRA AND MATLAB 595-614 APPENDIX B – SLOPES AND DEFLECTIONS 615-616 APPENDIX C - FIXED END MOMENTS 617-618 INDEX 619-621