## Structural Analysis

Structural Stell

1 Introduction to Structural Analysis
CLASSIFICATION OF STRUCTURES
2.7 Hydrostatic and Soil Pressures

Plane and Space Trusses

5.1 Axial Force, Shear, and Bending Moment
5.2 Shear and Bending Moment Diagrams
5.3 Qualitative Deflected Shapes
5.4 Relationships between Loads, Shears, and Bending Moments
5.5 Static Determinacy, Indeterminacy, and Instability of Plane Frames
5.6 Analysis of Plane Frames

6 Deflections of Beams: Geometric Methods 226
6.1 Di¤erential Equation for Beam Deflection 227
6.2 Direct Integration Method 230
6.3 Superposition Method 233
6.4 Moment-Area Method 234
6.5 Bending Moment Diagrams by Parts 248
6.6 Conjugate-Beam Method 253
Summary 269
Problems 269
7 Deflections of Trusses, Beams, and Frames: Work–Energy Methods 275
7.1 Work 276
7.2 Principle of Virtual Work 278
7.3 Deflections of Trusses by the Virtual Work Method 282
7.4 Deflections of Beams by the Virtual Work Method 293
7.5 Deflections of Frames by the Virtual Work Method 301
7.6 Conservation of Energy and Strain Energy 312
7.7 Castigliano’s Second Theorem 316
7.8 Betti’s Law and Maxwell’s Law of Reciprocal Deflections 325
Summary 326
Problems 328
8 Influence Lines 337
8.1 Influence Lines for Beams and Frames by Equilibrium
Method 338
8.2 Mu¨ eller-Breslau’s Principle and Qualitative Influence Lines 353
8.3 Influence Lines for Girders with Floor Systems 367
8.4 Influence Lines for Trusses 377
8.5 Influence Lines for Deflections 389
Summary 392
Problems 393
9 Application of Influence Lines 401
9.1 Response at a Particular Location Due to a Single Moving
9.2 Response at a Particular Location Due to a Uniformly
9.3 Response at a Particular Location Due to a Series of Moving
9.4 Absolute Maximum Response 415
Summary 421
Problems 422
10 Analysis of Symmetric Structures 425
10.1 Symmetric Structures 426
10.3 Behavior of Symmetric Structures under Symmetric and
10.4 Procedure for Analysis of Symmetric Structures 447
Summary 455
Problems 456
PART THREE ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES 459
11 Introduction to Statically Indeterminate Structures 461
11.2 Analysis of Indeterminate Structures 465
Summary 470
12 Approximate Analysis of Rectangular Building Frames 471
12.1 Assumptions for Approximate Analysis 472
12.2 Analysis for Vertical Loads 475
12.3 Analysis for Lateral Loads—Portal Method 481
12.4 Analysis for Lateral Loads—Cantilever Method 497
Summary 504
Problems 505
13 Method of Consistent Deformations—Force Method 508
13.1 Structures with Single Degree of Indeterminacy 509
13.2 Internal Forces and Moments as Redundants 531
13.3 Structures with Multiple Degrees of Indeterminacy 544
13.4 Support Settlements, Temperature Changes and Fabrication
Errors 568
Summary 577
Problems 578
14 Three-Moment Equation and the Method of Least Work 586
14.1 Derivation of Three-Moment Equation 587
14.2 Application of Three-Moment Equation 592
14.3 Method of Least Work 599
Summary 606
Problems 607
15 Influence Lines for Statically Indeterminate Structures 609
15.1 Influence Lines for Beams and Trusses 610
15.2 Qualitative Influence Lines by Mu¨ ller-Breslau’s Principle 627
Summary 631
Problems 632
16 Slope-Deflection Method 635
16.1 Slope-Deflection Equations 636
16.2 Basic Concept of the Slope-Deflection Method 644
16.3 Analysis of Continuous Beams 651
16.4 Analysis of Frames without Sidesway 673
16.5 Analysis of Frames with Sidesway 681
Summary 702
Problems 702
17 Moment-Distribution Method 707
17.1 Definitions and Terminology 708
17.2 Basic Concept of the Moment-Distribution Method 717
17.3 Analysis of Continuous Beams 725
17.4 Analysis of Frames without Sidesway 741
17.5 Analysis of Frames with Sidesway 744
Summary 761
Problems 762
18 Introduction to Matrix Structural Analysis 767
18.1 Analytical Model 768
18.2 Member Sti¤ness Relations in Local Coordinates 772
18.3 Coordinate Transformations 780
18.4 Member Sti¤ness Relations in Global Coordinates 786
18.5 Structure Sti¤ness Relations 787
18.6 Procedure for Analysis 795
Summary 813
Problems 814
Appendix A Areas and Centroids of Geometric Shapes 817
Appendix B Review of Matrix Algebra 821
B.1 Definition of a Matrix 821
B.2 Types of Matrices 822
B.3 Matrix Operations 824
B.4 Solution of Simultaneous Equations by the Gauss-Jordan
Method 831
Problems 835
Appendix C Computer Software 837
Starting the Computer Software 837
Inputting Data 837
Results of the Analysis 844
Problems 849

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