Fundamentals of Structural Analysis

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Fundamentals of Structural Analysis


TABLE   OF   CONTENTS

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 
  2.2  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  81
  3.2  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  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
  6.8  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  267
  7.2  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  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
  11.7  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  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
  12.8  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  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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