Fundamentals of Structural Mechanics, Dynamics, and Stability

✍ Scribed by A.I. Rusakov

• Publisher: CRC Press
• Year: 2020
• Tongue: English
• Leaves: 627
• Edition: 1
• Category: Library

✦ Synopsis

This book will examine structural mechanics from a fundamental point of view, and allow students to use logical inference and creative reasoning to solve problems versus rote memorization, which is what most textbooks in the field currently offer. It will present theory and also emphasize the relevant mathematical concepts as related to structural mechanics in each chapter. It will include problems, examples, and case studies throughout, and present simulation technique employed in structural engineering software. It will explain the Finite Element Method for elastic bodies, trusses, frames, and more, and present other modern methods of structural analysis.

• Presents the material from the general (theory and fundamentals) to the particular (specific applications).
• Emphasizes the relevant mathematical concepts as related to structural mechanics in each chapter.
• Presents analysis of ductile structures and modern methods in analysis of stability and dynamics.
• Explains the Finite Element Method for elastic bodies, trusses, frames, and more.
• Includes numerous worked examples and case studies throughout.

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✦ Table of Contents

Cover
Half-Title
Title
Copyright
Contents
About the Author
Introduction
SECTION I Basic Concepts
Chapter 1 Kinematic Analysis Basics in Structural Mechanics
1.1 Basic Terms: Geometrical Stability and Instability of Systems; Discs, Constraints, Degrees of Freedom
1.2 Number of Constraints as Criterion of System Stability and Determinacy
Supplement to Chapter
Kinematic Analysis of Plane Systems by Examples
SECTION II Influence Lines
Chapter 2 Movable Loads on a Beam
2.1 Classification of Bar Systems
2.2 Influence Lines and Particular Case of Beams; Properties of Influence Lines
2.3 Analysis of the Stress-Strain State of Girders by Using a Beam with Indirect Load Application
Supplement to Chapter
Reduction of Loads from Vehicle on Bridge to Plane System of Forces
Chapter 3 Theoretical Basics of Calculations via Influence Lines
3.1 Determination of Design Position of Live Load Series for Given Influence Line
3.2 Bridge Design Live Loads Specified by Design Regulations
3.2.1 Highway Bridges
3.2.2 Railroad Bridges
SECTION III Three-Hinged Arches
Chapter 4 Arches: General Info and Diagrams of Internal Forces
4.1 Concept of Arches and Calculation of Support Reactions for Three-Hinged Arches
4.2 Analytical Calculation of Internal Forces and the Rational Axis of A THREE-HINGED ARCH
Chapter 5 Three-Hinged Arches under Live Static Load
5.1 Analytical Technique of Influence Line Construction and Nil Point Method
5.2 Kern Moments and Normal Stresses
SECTION IV Hinged Beams
Chapter 6 Hinged Beams
6.1 Concept of a Hinged Beam and Its Kinematic Analysis; Interaction Scheme
6.2 Static Method of Influence Line Construction
6.3 Kinematic Method of Influence Line Construction
SECTION V Statically Determinate Trusses
Chapter 7 Preliminaries on Trusses
Introduction from Linear Algebra
7.1 Classification of Trusses
7.2 Stability and Determinacy of Trusses
7.3 Conversion of a Load Exerted upon a Member of a Statically Determinate Truss to Its Joints
Chapter 8 Internal Forces in Statically Determinate Trusses
8.1 Method of Moment Point
8.2 Method of Projections and Method of Joints; Zero-Force Members
8.3 Method of Substitute Members
8.4 Method of Load Conversion for Analysis of Trusses with Secondary Truss Members
Chapter 9 Influence Lines for Internal Forces and Support Reactions in Trusses
9.1 Construction of Influence Lines for Internal Forces in Truss Girders Using the Static Method
9.2 Method of Substitute Members for Construction of Influence Lines and Utilization of the Kinematic Method
Chapter 10 Space Statically Determinate Trusses
10.1 Space Connections and Geometrical Stability
10.2 Equations of Statics in Space
10.3 Methods of Determination of Internal Forces in Space Trusses
Supplement to Chapter
Representation of a Complete Set of Statics Equations for a Rigid Body in the Form of Equations of Axial Moment Equilibrium
SECTION VI Energy Methods in Deflection Analysis
Chapter 11 Foundations of Energy Approach in Displacement Analysis of Elastic Systems
11.1 Properties of Elastic Systems; Strain Energy of Bar Systems
11.2 Generalized Force and Displacement; Theorems of Reciprocal Works and Reciprocal Displacements
11.3 Reciprocal Work Calculation and Mohr Integral
Supplements to Chapter
Strain Energy of Elastic Systems
Castigliano’s Second Theorem
Chapter 12 Reactions of Constraints in Elastic Systems
12.1 Representation of Internal Forces by Reactions of Constraints and Displacement in the Direction of the Removed Constraint
12.2 Rayleigh First Theorem and Calculation of Reactions Due to Displacements in Constraints
12.3 Rayleigh’s Second Theorem and Calculation of Reactions Due to Loading upon a System
SECTION VII Force Method
Chapter 13 Theoretical Basics of Force Method
13.1 Analysis of Static Indeterminacy of Bar Systems
13.2 Force Method and Canonical Equations
13.3 Graph Multiplication Technique
Chapter 14 Simplification Ways of Analysis of Statically Indeterminate Systems
14.1 Conception of Canonical Equations’ Decomposition and Taking into Account Requirement for Decomposition during Construction of Primary Systems
14.2 Decomposition by Means of Linear Transformation of Redundant Forces
14.3 Verification of Calculations in the Force Method
14.4 Example of Construction of a Bending Moment Diagram for a Frame by the Force Method
14.5 Technique and Example of Construction of Shear and Axial Forces’ Diagrams for Frames
Chapter 15 Force Method for Structures Subjected to Temperature Changes and Support Settlements
15.1 Temperature Displacements in Bar Systems; Force Method in Case of Temperature Changes
15.2 Structure Analysis by the Force Method in the Case of Support Settlements
Chapter 16 Force Method for Construction of Influence Lines and Analysis of Space Systems
16.1 Analytical Method of Construction of Influence Lines
16.2 Kinematic Method of Construction of Influence Lines
16.3 Construction of Influence Lines for Statically Indeterminate Trusses
16.4 Analysis of Space Systems by Force Method
Supplement to Chapter
Peculiarities of Analysis of Space Truss by Force Method
SECTION VIII Displacement Method and Mixed Method
Chapter 17 Flexibility Matrix and Stiffness Matrix: Initial Info about Displacement Method
Introduction from Linear Algebra
17.1 Flexibility Matrix and Stiffness Matrix; Existence of Stiffness Matrix
17.2 Impact of Displacements upon Elastic System; Active Connections
17.3 Theoretical Basics of Displacement Method; Theses of Method in Analysis of Frames
Supplement to Chapter
Independence Conditions Imposed on Displacements in Directions of Removed Constraints in Stable Systems
Chapter 18 Actualization of Displacement Method
18.1 Canonical Equations and General Formulas for Calculation of Reactions and Construction of Diagrams; Determination of Reactions by Static Method
18.2 Verification of Calculations in Displacement Method
18.3 Mixed Method of Analysis of Statically Indeterminate Frames
SECTION IX Plastic Behavior of Structures
Chapter 19 Load and Resistance Factor Design and Models of Ductile Bar’s Collapse
19.1 Basic Provisions of Load and Resistance Factor Design; LRFD Method versus Allowable Stress Design Method
19.2 Ultimate Limit States of Statically Determinate Elastoplastic Member
Chapter 20 Principles of Plastic Design of Statically Indeterminate Structures
20.1 Principles of Modeling Loading Process in Analysis of Elastic Perfectly Plastic Statically Indeterminate Structure; Examples of Connections’ Loss and Recovery
20.2 Method of Sequential Identification of Lost and Restored Connections; Static Principle of Plastic Analysis
Chapter 21 Theoretical Basics and Kinematic Method of Elastoplastic Structures’ Analysis
21.1 Static Theorem of Structural Analysis and Proof of Static Principle
21.2 Assumed Collapse Mechanism and Strengthened System; Kinematic Theorem of Structural Analysis
21.3 Kinematic Method of Calculation of Bearing Capacity
21.4 Calculation of Continuous Beams by Kinematic Method
Supplements to Chapter
About the Existence of the Assumed Collapse Mechanism
Substantiation of Hypothesis about Collapse Mechanisms of a Continuous Beam
Chapter 22 Features in Plastic Analysis of Statically Indeterminate Beams and Frames
22.1 Analysis of Continuous Beams by Method of Adjusting Bending Moments to Ultimate Values
22.2 Basic Provisions of the Method of Combining Mechanisms in Analysis of Frames; Example of Portal Frame
22.3 Implementation of the Method of Combining Mechanisms for Multi-Story and Multi-Bay Latticed Frames; Frame with Gabled Roof
SECTION X Finite Element Method in Analysis of Elastic Structures
Chapter 23 Finite Element Method Exemplified in Elastic Plane Body
23.1 Essence of Finite Element Method and Calculation of Strain Energy of Finite Element
23.2 Strain Energy of an Elastic Body in Approximation of FEM; Stiffness Matrices of Free Body and Structure-Body
23.3 FEM Equations and Physical Meaning of Stiffness Matrix
Remark
23.4 Rules of Finite Element Model Construction; Example of Analysis
Supplements to Chapter
Differentiation of Quadratic Form
Perfectly Rigid Bodies as Part of a Structure
Chapter 24 Quadrilateral Finite Element of Plane Body
24.1 Approximation of Displacement Field by Square FE of Plane Body; Shape Functions of Displacement Field
24.2 Quadrilateral Convex FE of a Plane Body: Shape Functions of FE and Natural CS
24.3 Stiffness Matrix of Quadrilateral FE of Plane Body
Supplement to Chapter
Image of Template Square Box upon Generalized Quadrilateral
Chapter 25 Stiffness Method and Its Implementation for Analysis of Trusses
25.1 Degrees of Freedom and Stiffness Matrix of Free Bar System
25.2 The Stages of Calculation in Stiffness Method; Member of Truss as Finite Element
25.3 Stiffness Method for Truss Analysis: Structure Stiffness Equations; Case of Inclined Supports
25.4 Example of Truss Analysis by Stiffness Method
Chapter 26 Stiffness Method for Analysis of Frames and Generalization of FEM for an Arbitrary Elastic System
26.1 Particularities of Frame Analysis by Stiffness Method: Reduction of Intermediate Loads to Nodes; Bending Member of Frame as Finite Element
26.2 Basic Provisions of FEM for Analysis of Arbitrary Elastic Structure
26.3 Example of Frame Analysis
Supplements to Chapter
Stiffness Matrices of Bending Members in Global CS
FE Model of Reinforced-Concrete Skeleton of Residential House (Brief Description)
SECTION XI Stability of Elastic Systems
Chapter 27 Theoretical Basics of Structure Stability Analysis
27.1 Problem of Elastic Structure Stability and Static Approach to Analysis of Stability
27.2 Energy Approach to Analysis of Stability
27.3 Analysis of Frame’s Stability by Rayleigh Method
Chapter 28 Methods of Structure Stability Analysis
28.1 Bubnov-Galerkin Method and Buckling Analysis
28.2 Introduction to Displacement Method
Supplement to Chapter
Symmetry of Unit Reaction Matrix
Chapter 29 Investigation of Frames’ Buckling by Means of Displacement Method
29.1 Determination of SSS of Beam-Column Using Initial Parameters Method
29.2 Theoretical Provisions of Calculation of Reactions Developed by Additional Supports in a Primary System
29.3 Procedure of Calculation of Reactions Developed by Additional Supports and Example of Analysis by Displacement Method
SECTION XII Dynamics of Elastic Systems
Chapter 30 Free Vibration of Systems with a Single Degree of Freedom
30.1 Basic Concepts of Structural Dynamics; D’Alembert Principle and Static Approach to Solving the Problems of Structural Dynamics
30.2 Energy Approach in Solving the Problems of Dynamics; Motion Equation for Single DOF System with Energy Dissipation
30.3 Free Vibration of System; Logarithmic Decrement
Supplements to Chapter
Characteristics of Energy Model of Elastic Structure
Solving Equations of a Single-DOF System’s Free Vibration
Chapter 31 A Dynamic Factor and Problem of Finding Natural Frequencies
31.1 Forced Vibration and Dynamic Magnification Factor
31.2 Free Vibration of Systems with a Finite Number of DOFs
Supplement to Chapter
Constructing a Fundamental Set of Solutions for System of Second Order Linear Differential Equations
Chapter 32 Forced Vibration of Systems with a Finite Number of DOFs
32.1 Dynamic Force Method for Vibration Analysis of Frames
32.2 Motion of Elastic Systems under Arbitrary Loading and without Energy Losses
32.3 Analysis of an Elastic System’s Motion Taking into Account Energy Dissipation
Supplement to Chapter
Taking into Account Initial Motion of System in the Modal Expansion Method
Bibliography
Index