Fundamentals of Structural Analysis

Chapter 1  Introduction

1.1  Overview of the Text
1.2  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 Code
2.7  Natural Hazards

Chapter 3  Statics of Structures—Reactions

3.1  Introduction  81
3.2  Forces  82
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  131
4.2  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  175
5.2  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  235
6.2  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
6.9  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  267
7.2  Double Integration Method  268
7.3  Moment-Area Method  275
7.5  Conjugate Beam Method  297
7.6  Design Aids for Beams  305

Chapter 8   Work-Energy Methods for Computing Deﬂections

8.1  Introduction  319
8.2  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  377
9.2  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  423
10.2  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  467
11.2  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
11.8  Analysis of Multistory Frames  508
11.9  Nonprismatic Members  509

Chapter 12  Influence Lines for Moving Loads

12.1  Introduction  529
12.2  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
12.9  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  605
13.2  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  661
14.2  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  685
15.2  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  717
16.2  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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