Advanced Methods of Structural Analysis

✍ Scribed by Igor A. Karnovsky, Olga Lebed

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 824
• Edition: 2nd ed. 2021
• Category: Library

✦ Synopsis

This revised and significantly expanded edition contains a rigorous examination of key concepts, new chapters and discussions within existing chapters, and added reference materials in the appendix, while retaining its classroom-tested approach to helping readers navigate through the deep ideas, vast collection of the fundamental methods of structural analysis. The authors show how to undertake the numerous analytical methods used in structural analysis by focusing on the principal concepts, detailed procedures and results, as well as taking into account the advantages and disadvantages of each method and sphere of their effective application. The end result is a guide to mastering the many intricacies of the range of methods of structural analysis. The book differentiates itself by focusing on extended analysis of beams, plane and spatial trusses, frames, arches, cables and combined structures; extensive application of influence lines for analysis of structures; simple and effective procedures for computation of deflections; introduction to plastic analysis, stability, and free and forced vibration analysis, as well as some special topics. Ten years ago, Professor Igor A. Karnovsky and Olga Lebed crafted a must-read book. Now fully updated, expanded, and titled Advanced Methods of Structural Analysis (Strength, Stability, Vibration), the book is ideal for instructors, civil and structural engineers, as well as researches and graduate and post graduate students with an interest in perfecting structural analysis. 

✦ Table of Contents

Preface to the Second Edition
Preface to the First Edition
Contents
Introduction
The Subject and Purposes of the Structural Mechanics
Modeling of Engineering Structures and Principal Assumptions
Design Diagram
Idealization of Material Properties
Load Idealization
The Location of Points at Which Forces Are Applied to the Body
The Nature of Change of Forces in the Process of Their Application
The Nature of the Dependence of Forces on the Deformation of the Structure
Duration of the Influence of Loads on Structures
Idealization of the Structure as a Whole
Types of Structures
Modeling of Structural Members
Features of Some Loads and Their Load Path
Simplest Industrial Building
Specific Loads
Load Combination
Types of Analysis and Particular Assumptions
Fundamental Approaches of Linear Static Analysis
Part I: Statically Determinate Structures
Chapter 1: Kinematical Analysis of Structures
1.1 Classification of Structures by Kinematical Viewpoint
1.2 Generation of Geometrically Unchangeable Structures
1.2.1 Required and Redundant Constraints
1.2.2 Constraint Replacing
1.3 Analytical Criteria of the Instantaneously Changeable Structures
1.4 Degrees of Freedom
1.5 Null Load Method
Problems
Chapter 2: The Simplest Beams: Theory of Influence Lines
2.1 General
2.2 Analytical Method for Construction of Influence Lines
2.2.1 Influence Lines for Reactions
2.2.1.1 Simply Supported Beam
Influence Line for RA
Influence Line for RB
2.2.1.2 Simply Supported Beam with Overhang
2.2.1.3 Cantilevered Beam
The Vertical Reaction RA
The Moment M0 at Support A
2.2.2 Influence Lines for Internal Forces
2.2.2.1 Bending Moment Mk
Load P = 1 is Located to the Left of Section k
Load P = 1 is Located to the Right of Section k
2.2.2.2 Influence Line Qk
2.2.2.3 Discussion
Bending Moment M1 and Shear Force Q1
Shear Force Q2 and Bending Moment M2 (Fig. 2.10)
2.3 Application of Influence Lines for Fixed and Moving Loads
2.3.1 Fixed Loads
2.3.1.1 Concentrated Loads
2.3.1.2 Uniformly Distributed Load
2.3.1.3 Couple
2.3.1.4 Nonuniform Distributed Load
Summary
2.3.2 Moving Loads
2.3.2.1 Influence Line Forms a Triangle
2.3.2.2 Influence Line Forms a Polygon
2.3.3 Envelope Diagrams of Internal Forces
2.3.3.1 The Beam is Loaded by Single Moving Load P (Fig. 2.16a)
2.3.3.2 The Beam is Loaded by Set of Connected Moving Loads P
2.3.4 Absolute Maximum of Bending Moment
2.4 Indirect Load Application
2.5 Kinematical Method for Construction of Influence Lines
2.5.1 Influence Line for Bending Moment at Section k, IL(Mk)
2.5.2 Influence Line for Shear Force at Section k, IL(Qk)
2.5.3 Conclusion
2.6 Combining of Fixed and Moving Load Approaches
2.7 Properties of Influence Lines
Problems
Chapter 3: Multispan Hinged Beams and Frames
3.1 Generation of Multispan Hinged Beams
3.2 Interaction Diagrams and Load Path
3.3 Fixed Load Method for Beams
3.4 Influence Lines for Reactions and Internal Forces
3.4.1 Static Approach
3.4.1.1 Influence Line for RD
3.4.1.2 Influence Lines for Shear Qk, and Bending Moment Mk at Section k
3.4.1.3 Influence Lines for Shear Qn, and Bending Moment Mn at Section n
3.4.1.4 Influence Lines for Shear Qs, and Bending Moment Ms at Section s
3.4.1.5 Summary
3.4.2 Kinematical Approach
3.4.2.1 Influence Line for RA
3.4.2.2 Influence Line for RB
3.4.2.3 Influence Line for Mi
3.4.3 Indirect Load Application
3.4.3.1 Influence Line for RA (Fig. 3.11c)
3.4.3.2 Influence Line for Mk (Fig. 3.11d)
3.4.3.3 Discussion
3.5 Fixed Load Method for Frames
Summary
Problems
Chapter 4: Plane Trusses
4.1 General
4.1.1 Classification of the Plane Trusses
4.1.2 Assumptions and Design Diagram
Discussion
4.2 The Generation of Statically Determinate Trusses
4.2.1 Simple Trusses
4.2.2 Compound Trusses
4.2.3 Complex Trusses
4.3 Simple Trusses: Fixed Loads
4.3.1 Analytical Methods of Analysis
4.3.1.1 Method of Joint Isolation
4.3.1.2 Method of Through Sections (Ritter´s Method)
4.3.1.3 Special Cases
4.3.2 Maxwell-Cremona Diagram
4.4 Simple Trusses: Influence Line Method-Static Approach
4.5 Trusses with Subdivided Panels
4.5.1 Main and Auxiliary Trusses and Load Path
4.5.1.1 Kinematical Analysis
4.5.2 Single-Tiered Auxiliary Trusses
4.5.3 Two-Tiered Auxiliary Trusses
Discussion
4.6 Special Types of Trusses
4.6.1 Three-Hinged Trusses
4.6.2 Trusses with a Hinged Chain
4.6.2.1 Reaction of Supports and Internal Forces
4.6.2.2 Discussion
4.7 Kinematical Method for Construction of Influence Lines
4.8 Complex Trusses
4.8.1 Substitution Bar Method
Discussion
4.8.2 Closed Section Method
4.8.3 Summary
Problems
Chapter 5: Space Frameworks
5.1 General Assumptions
5.2 Classification of the Space Frameworks
5.2.1 Method of Formation
5.2.2 Three-Dimensional Engineering Rod Structures
5.3 Space Framework Supports
5.4 Kinematical Analysis of Space Frameworks
5.4.1 Attached and Released Frameworks
5.4.1.1 Spatial Trusses Attached to Supports
5.4.1.2 Spatial Trusses Separated from Supports
5.4.2 Improper Connections of 3-D Structures
5.4.3 Meshwork Structures
5.4.3.1 Cauchy Theorem
5.5 Static Analysis of 3-D Structures
5.5.1 General
5.5.1.1 Zero Rod Cases
5.5.1.2 Method of Sections
5.5.2 Meshwork Structures
5.5.3 Compound Space Frameworks
5.5.4 Complex Space Frameworks: The Rod Replacement Method
Discussion
5.5.5 Schwedler Dome
5.5.5.1 Design Diagram of Dome
5.5.5.2 Kinematical Analysis
5.5.5.3 Features of Schwedler Structure
5.5.5.4 Decomposing of Space Framework to Plane Trusses
Problems
Chapter 6: Three-Hinged Arches
6.1 Preliminary Remarks
6.1.1 Design Diagram of Three-Hinged Arch
6.1.2 Peculiarities of the Arches
6.1.3 Geometric Parameters of Circular and Parabolic Arches
6.1.3.1 Circular Arch
6.1.3.2 Parabolic Arch
6.2 Internal Forces
6.2.1 Concept of Substitute Beam
6.2.1.1 Analysis of Formulae (6.8) and (6.10)
6.2.2 Numerical Example
6.2.3 Maximum Economy Arches
6.3 Influence Lines for Reactions and Internal Forces
6.3.1 Influence Lines for Reactions
6.3.2 Influence Lines for Internal Forces
6.3.2.1 Bending Moment
6.3.2.2 Shear Force
6.3.2.3 Axial Force
6.3.2.4 Features of the Influence Lines for Internal Forces
6.3.3 Application of Influence Lines
6.3.3.1 Reactions of Supports
6.3.3.2 Internal Forces in Section k
6.4 Nil Point Method for Construction of Influence Lines
6.4.1 Bending Moment
6.4.2 Shear Force
6.4.3 Axial Force
6.5 Special Types of Arches
6.5.1 Askew Arch
6.5.1.1 Reactions and Bending Moment at Section k
6.5.1.2 Influence Lines for Thrust and Bending Moment Mk
6.5.2 Parabolic Arch with Complex Tie
6.5.2.1 Reactions and Bending Moment at Section k
6.5.2.2 Influence Lines for Thrust and Bending Moment at Section k
Problems
Chapter 7: Cables
7.1 Preliminary Remarks
7.1.1 Direct and Inverse Problems
7.1.2 Fundamental Relationships
7.2 Cable with Neglected Self-Weight
7.2.1 Cables Subjected to Concentrated Load
7.2.1.1 Thrust-Shape Problem
7.2.1.2 Length-Thrust Problem
7.2.2 Cable Subjected to Uniformly Distributed Load
7.2.2.1 Thrust-Shape Problem
7.2.2.2 Length-Thrust Problem
Approximate Solution of Length Determination
Exact Solution of the Length Determination
7.3 Effect of Arbitrary Load on the Thrust and Sag
7.4 Cable with Self-Weight
7.4.1 Fundamental Relationships
7.4.2 Cable with Supports Located at the Same Level
7.4.3 Cable with Supports Located on Different Elevations
7.4.3.1 Saddle Point Within the Span
7.4.3.2 Saddle Point Outside of the Span
7.5 Comparison of Parabolic and Catenary Cables
7.6 Effect of Axial Stiffness
7.6.1 Elastic Cable with Concentrated Load
7.6.2 Elastic Cable with Uniformly Distributed Load
Problems
Chapter 8: Deflections of Elastic Structures
8.1 Introduction
8.2 Double Integration Method
Conclusion
8.3 Initial Parameter Method
8.3.1 Universal Equation of Elastic Curve of a Beam
8.3.2 Beam Subjected to Settlement of Supports
8.3.3 Beams with Intermediate Hinge
8.4 Conjugate Beam Method
Summary
Short History (Bernshtein 1957)
8.5 Strain Energy Methods
8.5.1 Fundamental Concepts
8.5.1.1 The Work Performed by External Forces in Terms of External Forces and Displacements
8.5.1.2 The Work Performed by External Forces in Terms of Internal Forces
8.5.2 Work-Energy Principle
Summary
8.5.3 Castigliano´s Theorem
Short Historical Remarks
8.5.4 Principle of Least Work (Menabrea Principle)
Strain Energy Methods: Summary
Short Historical Remarks
8.6 Maxwell-Mohr Method (Dummy Load Method)
8.6.1 Deflections Due to Fixed Loads
8.6.2 Deflections Due to Change of Temperature
Summary
8.7 Displacement Due to Settlement of Supports and Errors of Fabrication
Discussion
8.8 Graph Multiplication Method
Discussion
8.9 Elastic Load Method
Discussion
Summary
8.10 Reciprocal Theorems
8.10.1 Reciprocal Work Theorem (Betti´s Theorem)
8.10.2 Reciprocal Unit Displacement Theorem (Maxwell´s Theorem)
8.10.3 Reciprocal Unit Reaction Theorem (Rayleigh´s First Theorem)
8.10.4 Reciprocal Unit Displacement and Reaction Theorem (Rayleigh´s Second Theorem)
8.11 Summary
Problems
Part II: Statically Indeterminate Structures
Chapter 9: The Force Method
9.1 Fundamental Idea of the Force Method
9.1.1 Degree of Redundancy, Primary Unknowns, and Primary System
9.1.2 Compatibility Equation in Simplest Case
9.2 Canonical Equations of Force Method
9.2.1 The Concept of Unit Displacements
9.2.2 Coefficients and Free Terms of Canonical Equations
9.3 Analysis of Redundant Beams
9.3.1 Canonical Equation of the Force Method
Summary
9.3.2 The Three-Moment Equation (Clapeyron Theorem)
9.3.2.1 Special Cases
9.3.2.2 Discussion
9.3.2.3 Summary
9.3.2.4 Short Historical Remarks
9.3.3 Focal Ratios Method
Summary
9.3.4 Redundant Beam with Intermediate Hinge
9.4 Redundant Plane Frames
9.4.1 Frames of the First Degree of Redundancy
9.4.2 Frames of the Second and More Degree of Redundancy
Discussion
9.4.3 Frame with Closed Contour. Elastic Center
Discussion
9.4.4 Frame with Elastically Compliant Supports and Joints
9.5 Redundant Trusses
9.5.1 Externally Redundant Truss
Discussion
9.5.2 Internally Redundant Truss
9.5.3 Some Properties of Redundant Trusses
9.6 Redundant Arches
9.6.1 Parabolic Two-Hinged Arch
9.6.2 Circular Arch with Clamped Supports
9.6.3 Analysis of Parabolic Arch on the Basis of Modified Design Diagram
Discussion
9.7 Combined Redundant Structures
9.8 Deflections of Statically Indeterminate Structures
9.9 Settlements of Supports
9.9.1 Internal Forces due to the Settlements of Supports
Discussion
9.9.2 Displacements Due to the Settlements of Supports. Modified Approach
9.10 Temperature Changes
9.10.1 General
9.10.2 Redundant Beams
Discussion
9.10.3 Redundant Trusses
Discussion
9.10.4 Redundant Frames
9.11 Some Features of Redundant Structures
9.12 Comparison of the Redundant and Statically Determinate Structures
Problems
Additional Problems
Chapter 10: The Displacement Method
10.1 Fundamental Idea of the Displacement Method
10.1.1 Kinematical Indeterminacy
10.1.2 Primary System and Primary Unknowns
10.1.3 Compatibility Equation: Concept of Unit Reaction
10.2 Canonical Equations of Displacement Method
10.2.1 Compatibility Equations in General Case
10.2.2 Calculation of Unit Reactions
10.2.3 Properties of Unit Reactions
10.2.4 Procedure for Analysis
10.2.4.1 Continuous Beams
10.2.4.2 Beam with Intermediate Hinge
10.2.4.3 Discussion
10.2.4.4 Summary
10.3 Comparison of the Force and Displacement Methods
10.3.1 Properties of Canonical Equations
10.3.2 Variations of Design Diagrams and Choice of Methods of Analysis
10.4 Sidesway Frames with Absolutely Rigid Crossbars
10.5 Special Types of Exposures
10.5.1 Settlements of Supports
Discussion
10.5.2 Errors of Fabrication
Discussion
10.6 Analysis of Symmetrical Structures: Combined Method
10.6.1 Symmetrical and Antisymmetrical Loading
10.6.2 Concept of Half-Structure
Problems
Chapter 11: Mixed Method
11.1 Fundamental Idea of the Mixed Method
11.1.1 General
11.1.2 Mixed Indeterminacy, Primary Unknowns, and Primary System
11.2 Canonical Equations of the Mixed Method
11.2.1 The Matter of Unit Coefficients and Canonical Equations
11.2.2 Calculation of Coefficients and Free Terms
11.2.3 Computation of Internal Forces
Problems
Chapter 12: Influence Lines Method
12.1 Construction of Influence Lines by the Force Method
12.1.1 General
12.1.2 Continuous Beams
12.1.2.1 Primary System
12.1.2.2 Influence Line for Primary Unknown X1
12.1.2.3 Influence Line for Bending Moment Mk
12.1.2.4 Influence Line for Shear Force Qk
12.1.2.5 Statically Indeterminate Primary System
12.1.3 Hingeless Nonuniform Arches
12.1.3.1 Unit Coefficients
12.1.3.2 Reactions of Support A
12.1.3.3 Bending Moment at Crown C
12.1.3.4 Discussion
12.1.4 Statically Indeterminate Trusses
12.1.4.1 Construction of Function δP1
12.1.4.2 Influence Line for Primary Unknown X1
12.1.4.3 Summary
12.2 Construction of Influence Lines by the Displacement Method
12.2.1 General
12.2.2 Continuous Beams
12.2.2.1 Influence Line for Primary Unknown Z1
12.2.2.2 Influence Line for Bending Moment Mk
12.2.2.3 Influence Line for Shear Force Qk
12.2.2.4 Discussion
12.2.3 Redundant Frames
Discussion
12.3 Comparison of the Force and Displacement Methods
Notes
12.4 Kinematical Method (Müller-Breslau Principle)
12.4.1 General
12.4.2 Continuous Beams: Analytical Solution
12.4.3 Continuous Beams: Models of Influence lines
Summary
Problems
Chapter 13: Matrix Stiffness Method
13.1 Basic Idea and Concepts
13.1.1 Finite Elements
13.1.2 Global and Local Coordinate Systems
13.1.3 Displacements of Joints and Degrees of Freedom
13.2 Auxiliary Diagrams
13.2.1 Joint-Load (J-L) Diagram
13.2.2 Displacement-Load (Z-P) Diagram
13.2.3 Internal Forces-Deformation (S-e) Diagram
Summary
13.3 Initial Matrices
13.3.1 Vector of External Joint Loads
13.3.2 Vector of Internal Unknown Forces
Summary
13.4 Resolving Equations
13.4.1 Static Equations and Static Matrix
13.4.2 Geometrical Equations and Deformation Matrix
13.4.3 Physical Equations and Stiffness Matrix in Local Coordinates
13.5 Set of Formulas and Procedure for Analysis
13.5.1 Stiffness Matrix in Global Coordinates
13.5.2 Unknown Displacements and Internal Forces
13.5.3 Matrix Procedures
13.6 Analysis of Continuous Beams
13.6.1 Fixed Loads
13.6.2 Settlements of Supports
13.6.3 Moving Load (Construction of Influence Lines)
13.6.3.1 Load P = 1 in the First Span
13.6.3.2 Load P = 1 in the Second Span
13.6.3.3 Load P = 1 in the Third Span
13.7 Analysis of Redundant Frame
13.8 Analysis of Redundant Trusses
13.9 Stiffness Matrices: Expanded Forms
13.9.1 Truss Element (Pinned-Pinned Element)
13.9.2 Beam Elements
13.9.3 More General Case of a Finite Element
13.10 Summary
Remarks Concerning Analysis of the Bending Structures by MSM
Problems
Part III: Special Topics
Chapter 14: Plastic Behavior of Structures
14.1 Idealized Stress-Strain Diagrams
14.2 Direct Method of Plastic Analysis
14.2.1 Elastic Analysis
14.2.2 Plastic Analysis
14.3 Fundamental Methods of Plastic Analysis
14.3.1 Kinematical Method
14.3.2 Static Method
14.3.3 Summary
14.4 Plastic Analysis of Continuous Beams
14.4.1 Static Method
14.4.2 Kinematical Method
Discussion
14.5 Plastic Analysis of Frames
14.5.1 Beam Failure
14.5.2 Sidesway Failure
14.5.3 Combined Failure
14.5.4 Limit Combination Diagram
Problems
Chapter 15: Stability of Elastic Systems
15.1 Fundamental Concepts
15.2 Stability of Structures with Finite Number of Degrees of Freedom
15.2.1 Structures with One Degree of Freedom
Discussion
15.2.2 Structures with Two or More Degrees of Freedom
15.3 Stability of Columns with Rigid and Elastic Supports
15.3.1 The Double Integration Method
15.3.1.1 Uniform Clamped-Free Column
15.3.1.2 Uniform Columns with Elastic Supports
15.3.2 Initial Parameters Method
15.3.2.1 Limiting Cases
15.3.2.2 Discussion
15.3.3 Euler´s Solution and Paradox of Critical Load
15.4 Stability of Continuous Beams and Frames
15.4.1 Unit Reactions of the Beam-Columns
Some Features of the Solution
15.4.2 Displacement Method
Special cases
Special Cases
15.4.3 Modified Approach of the Displacement Method
15.5 Stability of Arches
15.5.1 Introduction
15.5.1.1 Forms of the Loss of Stability of the Arches
15.5.2 Circular Arches under Hydrostatic Load
15.5.3 Complex Arched Structure: Arch with Elastic Supports
15.5.4 Parabolic Arch under Gravity Load
Arches with Variable Cross Sections
Problems
Chapter 16: Dynamics of Elastic Systems: Free Vibration
16.1 Fundamental Concepts
16.1.1 Kinematics of Vibrating Processes
16.1.2 Forces Which Arise at Vibrations
16.1.3 Degrees of Freedom
16.1.4 Purpose of Structural Dynamics
16.2 Systems with Finite Number of Degrees of Freedom: Force Method
16.2.1 Differential Equations of Free Vibration in Displacements
16.2.2 Frequency Equation
16.2.3 Mode Shapes of Vibration and Modal Matrix
16.3 Systems with Finite Number of Degrees of Freedom: Displacement Method
16.3.1 Differential Equations of Free Vibration in Reactions
16.3.2 Frequency Equation
16.3.3 Mode Shape of Vibrations and Modal Matrix
16.3.4 Comparison of the Force and Displacement Methods
16.4 Structures with Infinite Number of Degrees of Freedom
16.4.1 Differential Equation of Transversal Vibration of the Beam
16.4.1.1 Boundary Conditions
16.4.1.2 Initial Conditions
16.4.2 Fourier Method
16.4.3 Krylov-Duncan Method
16.4.3.1 Properties of Krylov-Duncan Functions (16.24)
16.4.4 Initial Parameters Method
16.4.5 Transfer Matrices Method
16.4.5.1 Transfer Matrix of Uniform Beam with Distributed Mass
16.4.5.2 Transfer Matrix of Uniform Massless Beam
16.4.5.3 Mathematical Model of a Complex Structure
16.4.6 Displacement Method
16.4.7 Missed (Unaccounted) Frequencies
Problems
Chapter 17: Dynamics of Elastic Systems: Forced Vibration
17.1 Structures with One Degree of Freedom
17.1.1 Differential Equations: Two Classical Approaches
17.1.1.1 Force Method
17.1.1.2 Displacement Method
17.1.2 Types of Excitations
17.1.3 Duhamel Integral and Some Special Types of Excitation
17.1.4 Harmonic Excitation: Equivalent Design Diagram
17.1.4.1 Equivalent Design Diagram
17.1.5 Kinematical Excitation
17.2 Structures with Finite Number of Degrees of Freedom: The Force Method
17.2.1 Resolving Equation of the Force Method
17.2.2 Harmonic Excitation: Reciprocal Theorems
17.2.3 Impulsive Excitation
17.2.4 General Case of Excitation
17.3 Structures with Finite Number of Degrees of Freedom: Initial Parameters Method
17.3.1 Resolving Equations
17.3.2 Steady-State Vibrations
17.4 Structures with Finite Number of Degrees of Freedom: Displacement Method
17.4.1 The Steady-State Vibration
17.4.2 Group Unknowns Method
17.5 Structures with Distributed Parameters
17.5.1 Initial Parameter Method
17.5.2 Displacement Method
17.5.3 Bolotin Approximate Method
Problems
Structures with Finite Number of Degrees of Freedom
Kinematical Excitation
Forced Excitations
Structures with Infinite Numbers Degrees of Freedom
Chapter 18: Special Topics of Structural Dynamics
18.1 Timoshenko-Ehrenfest Beam Theory
18.2 Flexural Vibration of Compressed Beam
18.2.1 Fundamental Equations
18.2.2 Galef´s Formula
18.3 Traveling Load
18.3.1 General
18.3.2 Quasi-Static Loading
18.3.3 Critical Velocity of Moving Load
18.4 Parametric Vibration
18.4.1 Dynamic Stability of Simply Supported Column
18.4.2 Ince-Strutt Diagram
18.5 Vibration Protection
18.5.1 Vibration Protection Methods
18.5.2 Dynamic Absorber
18.5.3 Lumped Vibration Absorber of the Beams
Chapter 19: Nonlinear Structural Analysis
19.1 Introduction and Types of Nonlinearities
19.1.1 Types of Nonlinearities
19.2 Compressed Rods with Lateral Loading
19.2.1 Double Integration Method
19.2.2 Initial Parameters Method
19.2.2.1 Free-Clamped Beam: Precise Solution
19.2.3 P-Delta Analysis
19.3 Static Nonlinearity
19.3.1 Features of the Problem
19.3.2 Transversal Vibration of a Rod
19.4 Physical Nonlinearity
19.4.1 Features of the Problem
19.4.2 Transversal Free Vibration of Uniform Beam
19.5 Geometrical Nonlinearity
19.5.1 General
19.5.2 Stability of a Flexible Rod
Problems
Chapter 20: Conclusion: Once More About Modeling of Structures
20.1 Some Problems of Structural Modeling
20.2 Common Modeling Problems
20.3 Differences Between Structural Analysis and Direct Design
Chapter 21: Fundamental Developments in the History of Structural Mechanics
Appendix
Tabulated Data for Standard Uniform Beams
Bibliography
General Textbooks and Manuals
Handbooks
Related List of Literature
History
Index
Index