Structural Analysis

Energy Methods in Structural Analysis......Page 4
General Introduction......Page 5
1.1 Introduction......Page 6
1.2 Classification of Structures......Page 7
1.3 Equations of Static Equilibrium......Page 12
1.4 Static Indeterminacy......Page 15
1.5 Kinematic Indeterminacy......Page 21
1.6 Kinematically Unstable Structure......Page 24
1.8 Force-Displacement Relationship......Page 25
Suggested Text Books for Further Reading......Page 27
Energy Methods in Structural Analysis......Page 29
Principle of Superposition,Strain Energy......Page 30
2.2 Principle of Superposition......Page 31
2.3 Strain Energy......Page 36
2.3.1 Strain energy under axial load......Page 40
2.3.2 Strain energy due to bending......Page 42
2.3.3 Strain energy due to transverse shear......Page 45
2.3.4 Strain energy due to torsion......Page 47
Summary......Page 49
Energy Methods in Structural Analysis......Page 50
Instructional Objectives......Page 51
3.2 Castigliano’s First Theorem......Page 52
3.3 Castigliano’s Second Theorem......Page 61
Summary......Page 62
Energy Methods in Structural Analysis......Page 63
Theorem of Least Work......Page 64
4.2 Theorem of Least Work......Page 65
4.3 Maxwell–Betti Reciprocal theorem......Page 74
Energy Methods in Structural Analysis......Page 78
Virtual Work......Page 79
5.2 Principle of Virtual Work......Page 80
5.3 Principle of Virtual Displacement......Page 81
5.5 Unit Load Method......Page 82
5.6 Unit Displacement Method......Page 91
Summary......Page 92
Energy Methods in Structural Analysis......Page 93
Engesser’s Theorem and Truss Deflections by Virtual Work Principles......Page 94
6.2 Crotti-Engesser Theorem......Page 95
6.3.2 Temperature Loading......Page 97
6.4 Procedure for calculating truss deflection......Page 98
Summary......Page 106
Analysis of Statically Indeterminate Structures by the Matrix Force Method......Page 107
The Force Method of Analysis:An Introduction......Page 108
7.2 Simple Example......Page 111
7.3 Summary......Page 118
Summary......Page 125
Analysis of Statically Indeterminate Structures by the Matrix Force Method......Page 126
The Force Method of Analysis: Beams......Page 127
8.2 Formalization of Procedure......Page 128
Summary......Page 138
Analysis of Statically Indeterminate Structures by the Matrix Force Method......Page 139
The Force Method of Analysis:Beams (Continued)......Page 140
9.1 Introduction......Page 141
9.2 Support Displacements......Page 143
9.3 Temperature Stresses......Page 144
Summary......Page 152
Analysis of Statically Indeterminate Structures by the Matrix Force Method......Page 153
The Force Method of Analysis: Trusses......Page 154
10.1 Introduction......Page 155
Summary......Page 169
Analysis of Statically Indeterminate Structures by the Matrix Force Method......Page 170
The Force Method of Analysis: Frames......Page 171
11.1 Introduction......Page 172
11.2 Support settlements......Page 183
Summary......Page 191
Analysis of Statically Indeterminate Structures by the Matrix Force Method......Page 192
The Three-Moment Equations-I......Page 193
12.2 Three-moment equation......Page 194
12.3 Alternate derivation......Page 198
Summary......Page 209
Analysis of Statically Indeterminate Structures by the Matrix Force Method......Page 210
The Three-Moment Equations-Ii......Page 211
13.2 Derivation of Three-Moment Equation......Page 212
Summary......Page 226
Analysis of Statically Indeterminate Structures by the Displacement Method......Page 227
The Slope-Deflection Method: An Introduction......Page 228
Degrees of freedom......Page 229
14.2 Slope-Deflection Equations......Page 231
14.3 Application of Slope-Deflection Equations to Statically Indeterminate Beams.......Page 235
Summary......Page 244
Analysis of Statically Indeterminate Structures by the Displacement Method......Page 246
The Slope-Deflection Method: Beams (Continued)......Page 247
15.1 Introduction......Page 248
Summary......Page 260
Analysis of Statically Indeterminate Structures by the Displacement Method......Page 261
The Slope-Deflection Method: Frames Without Sidesway......Page 262
16.1 Introduction......Page 263
Summary......Page 284
Analysis of Statically Indeterminate Structures by the Displacement Method......Page 285
The Slope-Deflection Method: Frames with Sidesway......Page 286
17.1 Introduction......Page 287
Summary......Page 305
Analysis of Statically Indeterminate Structures by the Displacement Method......Page 306
The Moment-Distribution Method: Introduction......Page 307
18.2 Basic Concepts......Page 308
Summary......Page 320
ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY THE DISPLACEMENT METHOD......Page 321
THE MOMENT-DISTRIBUTION METHOD: STATICALLY INDETERMINATE BEAMS WITH SUPPORT SETTLEMENTS......Page 322
19.1 Introduction......Page 323
Summary......Page 336
Analysis of Statically Indeterminate Structures by the Displacement Method......Page 337
The Moment-Distribution Method: Frames without Sidesway......Page 338
20.1 Introduction......Page 339
Summary......Page 347
Analysis of Statically Indeterminate Structures by the Displacement Method......Page 348
The Moment-Distribution Method: Frames with Sidesway......Page 349
21.2 Procedure......Page 350
Summary......Page 373
Analysis of Statically Indeterminate Structures by the Displacement Method......Page 374
The Multistory Frames with Sidesway......Page 375
22.1 Introduction......Page 376
22.2 Slope-deflection method......Page 380
22.3 Moment-distribution method......Page 386
Summary......Page 397
Analysis of Statically Indeterminate Structures by the Direct Stiffness Method......Page 398
The Direct Stiffness Method: An Introduction......Page 399
23.1 Introduction......Page 400
23.2 A simple example with one degree of freedom......Page 405
23.3 Two degrees of freedom structure......Page 408
Summary......Page 421
Analysis of Statically Indeterminate Structures by the Direct Stiffness Method......Page 422
The Direct Stiffness Method: Truss Analysis......Page 423
24.1 Introduction......Page 424
24.2 Local and Global Co-ordinate System......Page 426
24.3 Member Stiffness Matrix......Page 427
Displacement Transformation Matrix......Page 429
Force transformation matrix......Page 432
Member Global Stiffness Matrix......Page 433
24.5 Analysis of plane truss.......Page 435
Summary......Page 444
Analysis of StaticallyIndeterminateStructures by the DirectStiffness Method......Page 445
The Direct StiffnessMethod: Truss Analysis(Continued)......Page 446
25.1 Introduction......Page 447
25.2 Inclined supports......Page 459
Summary......Page 468
Analysis of StaticallyIndeterminateStructures by the DirectStiffness Method......Page 469
Instructional Objectives......Page 470
26.2 Temperature Effects and Fabrication Errors......Page 471
Summary......Page 488
Analysis of Statically Indeterminate Structures by the Direct Stiffness Method......Page 489
The Direct Stiffness Method: Beams......Page 490
27.1 Introduction.......Page 491
27.2 Beam Stiffness Matrix.......Page 493
27.3 Beam (global) Stiffness Matrix.......Page 498
27.4 Formation of load vector.......Page 500
27.5 Solution of equilibrium equations......Page 502
Summary......Page 505
Analysis of Statically Indeterminate Structures by the Direct Stiffness Method......Page 506
The Direct Stiffness Method: Beams (Continued)......Page 507
28.1 Introduction......Page 508
Summary......Page 520
Analysis of StaticallyIndeterminateStructures by the DirectStiffness Method......Page 521
The Direct StiffnessMethod: Beams(Continued)......Page 522
29.2 Support settlements......Page 523
29.3 Effect of temperature change......Page 525
Summary......Page 536
Analysis of Statically Indeterminate Structures by the Direct Stiffness Method......Page 537
The Direct Stiffness Method: Plane Frames......Page 538
30.2 Member Stiffness Matrix......Page 539
30.3.1 Displacement transformation matrix......Page 541
30.3.2 Force displacement matrix......Page 543
30.3.3 Member global stiffness matrix......Page 545
Summary......Page 559
Cables and Arches......Page 560
31.1 Introduction......Page 562
31.3 Cable subjected to uniform load.......Page 564
Summary......Page 574
Cables and Arches......Page 575
Instructional Objectives:......Page 576
32.1 Introduction......Page 577
32.2 Type of arches......Page 579
32.3 Analysis of three-hinged arch......Page 581
Summary......Page 591
Cables and Arches......Page 592
Two-Hinged Arch......Page 593
33.2 Analysis of two-hinged arch......Page 594
33.2.1 Symmetrical two hinged arch......Page 596
33.2.2 Temperature effect......Page 600
Summary......Page 609
Cables and Arches......Page 611
Symmetrical Hingeless Arch......Page 612
34.2 Analysis of Symmetrical Hingeless Arch......Page 613
34.3 Temperature stresses......Page 616
34.4 Elastic centre method......Page 621
34.4.1Temperature stresses......Page 623
Summary......Page 630
Approximate Methods for Indeterminate Structural Analysis......Page 631
Indeterminate Trusses and Industrial Frames......Page 632
35.1 Introduction......Page 633
35.2 Indeterminate Trusses: Parallel-chord trusses with two diagonals in each panel.......Page 634
35.3 Industrial frames and portals......Page 646
Summary......Page 658
Approximate Methods for Indeterminate Structural Analysis......Page 659
Building Frames......Page 660
36.1 Introduction......Page 661
36. 2 Analysis of Building Frames to Vertical Loads......Page 664
36.3 Analysis of Building Frames to lateral (horizontal) Loads......Page 670
36.3.1 Portal method......Page 672
36.3.2 Cantilever method......Page 675
Summary......Page 680
Influence Lines......Page 681
37.1 Introduction......Page 682
37.3 Construction of Influence Lines......Page 683
37.3.2 Sign Conventions......Page 684
37.4 Numerical Examples......Page 685
37.5.1 Concentrated load......Page 694
37.5.2 Uniformly Distributed Load......Page 695
37.6 Numerical Example......Page 696
Suggested Text Books for Further Reading......Page 698
Influence Lines......Page 699
Influence Linesfor Beams......Page 700
38.1 Müller Breslau Principle for Qualitative Influence Lines......Page 701
38.2.1 UDL longer than the span......Page 704
38.3.1 UDL longer than the span......Page 706
38.3.2 UDL shorter than the span......Page 707
Suggested Text Books for Further Reading......Page 708
Influence Lines......Page 710
Influence Lines for Beams(Contd.)......Page 711
39.2 Maximum shear at sections in a beam supporting two concentrated loads......Page 712
39.3 Maximum moment at sections in a beam supporting two concentrated loads......Page 714
39.4 Maximum end shear in a beam supporting a series of moving concentrated loads......Page 715
39.4.1 Numerical Example......Page 717
39.5 Maximum shear at a section in a beam supporting a series of moving concentrated loads......Page 718
39.5.1 Numerical Example......Page 719
39.6 Maximum Moment at a section in a beam supporting a series of moving concentrated loads......Page 720
39.6.1 Numerical Example......Page 721
39.7 Absolute maximum moment in s beam supporting a series of moving concentrated loads.......Page 723
39.7.1 Numerical Examples......Page 725
39.8 Envelopes of maximum influence line values......Page 727
Suggested Text Books for Further Reading......Page 728
Influence Lines......Page 729
Influence Lines for Simple Trusses......Page 730
40.2 Bridge Truss Floor System......Page 731
40.3 Influence lines for truss support reaction......Page 732
40.4.1 Numerical Examples......Page 733
40.5 Closing Remarks......Page 736
Suggested Text Books for Further Reading......Page 737