Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
TABLE OF CONTENTS
Chapter 1 Introduction
1.1 Overview of the Text1.2 The Design Process: Relationship of Analysis to Design
1.3 Strength and Serviceability
1.4 Historical Development of Structural Systems
1.5 Basic Structural Elements
1.6 Assembling Basic Elements to Form a Stable Structural System
1.7 Analyzing by Computer
1.8 Preparation of Computations Summary
Chapter 2 Design Loads and Structural Framing
2.1 Building and Design Code2.2 Loads
2.3 Dead Loads and Gravity Framing
2.4 Live Loads
2.5 Snow Loads
2.6 Lateral Load-Resisting Systems
2.7 Natural Hazards
2.8 Wind Loads
2.9 Earthquake Loads
2.10 Tsunami Loads
2.11 Other Loads
2.12 Load Combinations
Chapter 3 Statics of Structures—Reactions
3.1 Introduction 813.2 Forces 82
3.3 Supports 89viii Table of Contents
3.4 Idealizing Structures 93
3.5 Free-Body Diagrams 94
3.6 Equations of Static Equilibrium 96
3.7 Equations of Condition 102
3.8 Influence of Reactions on Stability and Determinacy of Structures 105
3.9 Classifying Structures 113
3.10 Comparison between Determinate and Indeterminate Structures 116
Chapter 4 Trusses
4.1 Introduction 1314.2 Types of Trusses 134
4.3 Analysis of Trusses 135
4.4 Method of Joints 136
4.5 Zero Bars 140
4.6 Method of Sections 142
4.7 Determinacy and Stability 150
4.8 Computer Analysis of Trusses 156
Chapter 5 Beams and Frames
5.1 Introduction 1755.2 Scope of Chapter 180
5.3 Equations for Shear and Moment 181
5.4 Shear and Moment Curves 188
5.5 Principle of Superposition 206
5.6 Sketching the Deflected Shape of a Beam or Frame 210
5.7 Degree of Indeterminacy 215
5.8 Approximate Indeterminate Structural Analysis 218
Chapter 6 Cables and Arches
6.1 Cables 2356.2 Characteristics of Cables 236
6.3 Variation of Cable Force 237
6.4 Analysis of a Cable Supporting Concentrated Gravity Loads 238
6.5 General Cable Theorem 240
6.6 Arches 245
6.7 Types of Arches 245
6.8 Three-Hinged Arches 247Table of Contents ix
6.9 Funicular Shape of an Arch 249
6.10 Funicular Shape for an Arch That Supports a Uniformly Distributed Load 252
Chapter 7 Deflections of Beams and Frames
7.1 Introduction 2677.2 Double Integration Method 268
7.3 Moment-Area Method 275
7.4 Elastic Load Method 293
7.5 Conjugate Beam Method 297
7.6 Design Aids for Beams 305
Chapter 8 Work-Energy Methods for Computing Deflections
8.1 Introduction 3198.2 Work 320
8.3 Strain Energy 322
8.4 Deflections by the Work-Energy Method (Real Work) 325
8.5 Virtual Work: Trusses 326
8.6 Virtual Work: Beams and Frames 343
8.7 Finite Summation 355
8.8 Bernoulli’s Principle of Virtual Displacements 357
8.9 Maxwell-Betti Law of Reciprocal
Chapter 9 Analysis of Indeterminate Structures by the Flexibility Method
9.1 Introduction 3779.2 Concept of a Redundant 378
9.3 Fundamentals of the Flexibility Method 379
9.4 Alternative View of the Flexibility Method (Closing a Gap) 382
9.5 Analysis Using Internal Releases 392
9.6 Support Settlements, Temperature Change, and Fabrication Errors 399
9.7 Analysis of Structures with Several Degrees of Indeterminacy 404
9.8 Beam on Elastic Supports 411
Chapter 10 Analysis of Indeterminate Beams and Frames by the Slope-Deflection Method
10.1 Introduction 42310.2 Illustration of the Slope-Deflection Method 424
10.3 Derivation of the Slope-Deflection Equation 425
10.4 Analysis of Structures by the Slope-Deflection Method 431
10.5 Analysis of Structures That Are Free to Sidesway 447
10.6 Kinematic Indeterminacy 457
Chapter 11 Analysis of Indeterminate Beams and Frames by the Moment Distribution
11.1 Introduction 46711.2 Development of the Moment Distribution Method 468
11.3 Summary of the Moment Distribution Method with No Joint Translation 473
11.4 Analysis of Beams by Moment Distribution 474
11.5 Modification of Member Stiffness 482
11.6 Analysis of Frames That Are Free to Sidesway 497
11.7 Analysis of an Unbraced Frame for General Loading 503
11.8 Analysis of Multistory Frames 508
11.9 Nonprismatic Members 509
Chapter 12 Influence Lines for Moving Loads
12.1 Introduction 52912.2 Influence Lines 529
12.3 Construction of Influence Line for Determinate Beams 530
12.4 Müller–Breslau Principle for Determinate Beams 538
12.5 Use of Influence Lines 541
12.6 Influence Lines for Determinate Girders Supporting Floor Systems 544
12.7 Influence Lines for Determinate Trusses 550
12.8 Live Loads for Highway and Railroad Bridges 555
12.9 Increase–Decrease Method 558
12.10 Moment Envelope and Absolute Maximum Live Load Moment 562
12.11 Shear Envelope 567
12.12 Influence Lines for Indeterminate Structures: Introduction 568
12.13 Construction of Influence Lines Using Moment Distribution 569
12.14 Proof of Müller–Breslau Principle 573
12.15 Qualitative Influence Lines for Indeterminate Beams and Frames 578
12.16 Live Load Patterns to Maximize Member Forces in Multistory Buildings 584
12.17 Influence Lines for Indeterminate Trusses 588
Chapter 13 Approximate Analysis of Indeterminate Structures
13.1 Introduction 60513.2 Continuous Beams for Gravity Load 607
13.3 One-bay Rigid Frames for Vertical Load 613
13.4 Trusses with Single Diagonals 617
13.5 Estimating Deflections of Trusses 623
13.6 Trusses with Double Diagonals 625
13.7 Multistory Rigid Frames for Gravity Load 628
13.8 Single-story Rigid Frames for Lateral Load 637
13.9 Multistory Rigid Frames for Lateral Load: Portal Method 640
13.10 Multistory Rigid Frames for Lateral Load: Cantilever Method 648
Chapter 14 Introduction to the General Stiffness Method
14.1 Introduction 66114.2 Comparison between Flexibility and Stiffness Methods 662
14.3 Analysis of an Indeterminate Structure by the General Stiffness Method 666
Chapter 15 Matrix Analysis of Trusses by the Direct Stiffness Method
15.1 Introduction 68515.2 Member and Structure Stiffness Matrices 690
15.3 Construction of a Member Stiffness Matrix for an Individual Truss Bar 691
15.4 Assembly of the Structure Stiffness Matrix 692
15.5 Solution of the Direct Stiffness Method 695
15.6 Member Stiffness Matrix of an Inclined Truss Bar 699
15.7 Coordinate Transformation of a Member Stiffness Matrix 711
Chapter 16 Matrix Analysis of Beams and Frames by the Direct Stiffness Method
16.1 Introduction 71716.2 Structure Stiffness Matrix 719
16.3 The 2 × 2 Rotational Stiffness Matrix for a Flexural Member 720
16.4 The 4 × 4 Member Stiffness Matrix in Local Coordinates 731
16.5 The 6 × 6 Member Stiffness Matrix in Local Coordinates 741
16.6 The 6 × 6 Member Stiffness Matrix in Global Coordinates 750
16.7 Assembly of a Structure Stiffness Matrix—Direct Stiffness Method 752
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