Structural Modeling And Analysis

by Clive L. Dym

• ISBN13: 9780521020077
• ISBN10: 0521020077
• Format: Paperback
• Copyright: 2005-09-15
• Publisher: Cambridge University Press

Summary

The study of structural analysis and design is a central subject in civil, aeronautical and mechanical engineering. This book presents a modern and unified introduction to structural analysis, with a strong emphasis on how structures actually behave. The unifying theme is the application of energy methods, developed without the formal mathematics of the calculus of variations. The energy approach makes it possible to articulate the logical relationship between equilibrium and compatibility; emphasise the unity of structural analysis, particularly for indeterminate structures; and identify the roles of idealization and discretization in structural modelling. Thus, energy methods also serve as a prelude to the main ideas behind modern computational approaches to structural analysis and design. As an aid to upper-level undergraduate students in mastering this material, the text includes numerous worked examples, as well as homework problems.

Table of Contents

List of Photos
Preface
Acknowledgments
Structural Mechanics: The Big Picture	2	(28)
Structures and one-dimensional structural elements
The conceptual ``elements'' of structural mechanics
Loads
Reactions
Internal forces
Stresses
Strains
Displacements and deflections
Equilibrium
Constitutive laws
Compatibility
Structural analysis and structural design
Design criteria, codes, specifications, and loads
Design for stiffness and design for strength
Some behavioral design criteria
Design specifications and codes and fabrication specifications
Design specifications and design loads
Structural Models and Modeling	30	(28)
Modeling structural elements: bars, beams, arches, frames, surfaces
One-dimensional basic structural elements
Two-dimensional basic structural elements
Stress resultants for one-dimensional structural elements
Modeling structural supports
Indeterminate structures, redundancy, load paths, stability
On counting the degree of indeterminacy
On indeterminacy and why redundancy matters
Two important aspects of structural stability
Modeling structural loading and structural materials
Modeling structural loading
Modeling structural materials
Modeling: on approximating magnitudes; the role of dimensions
Modeling: idealization and discretization
Elementary Discrete Structural Models: Energy Approaches	58	(14)
Minimum potential energy and equilibrium for a simple spring
Minimum potential energy and equilibrium for discrete structures
Compatibility and total potential energy modeling of structures
Virtual work in discrete modeling of structures
Problems
Bars: Axially Loaded Members	72	(24)
Stress, strain, and Hooke's law for axially loaded members
Strain energy and work--energy for axially loaded members
Total potential energy principle for axially loaded members
Exact and approximate solutions for bars and rods
An exact solution for the centrally loaded bar
Trigonometric series approximations for the centrally loaded bar
Polynomial approximations for the centrally loaded bar
Castigliano's theorems for bars and rods
The force approach and the displacement approach
Problems
Trusses: Assemblages of Bars	96	(16)
Classical truss analysis; the methods of joints and of sections
On trusses (again)
The method of joints
The method of sections
Castigliano's second theorem and trusses as assemblages of bars
Castigliano's second theorem, unit loads, and virtual work
Castigliano's second theorem for internally indeterminate trusses
Matrix formulation of Castigliano's second theorem
Problems
Energy Principles for Calculating Displacements and Forces	112	(26)
Recapitulation and review
Work--energy relationships and methods
Work--energy in the force (flexibility) paradigm
Work--energy in the displacement (stiffness) paradigm
Matrix formulation of work--energy relations
Minimum total potential energy principle
Minimum total potential energy in three dimensions
Virtual work and reciprocity in three dimensions
Minimum total complementary energy principle
Complementary virtual work in three dimensions
Minimum total complementary energy in three dimensions
Some comments on the energy methods
The Castigliano theorems
Direct and indirect approaches, and approximate solutions
The force (flexibility) -- displacement (stiffness) duality
Problems
Beams: Transversely Loaded Members	138	(30)
A brief review of engineering beam theory
Deriving engineering beam theory with potential energy
Kinematic assumptions of engineering beam theory
Stresses and stress resultants for engineering beam theory
Strain and potential energies for engineering beam theory
Minimum potential energy for engineering beam theory
Some typical boundary conditions for engineering beams
Using the total potential energy principle for beam analysis
The indirect approach and exact solutions
Boundary conditions and indeterminate beams
Discretization and the direct displacement approach
Further observations on determinate and indeterminate beams
Validating and estimating in elementary beam theory
Validating the assumptions of elementary beam theory
On the magnitudes of beam deflections and stresses
Problems
Calculating Beam Deflections	168	(26)
Castigliano's theorems for beams
First theorem versus second theorem
Castigliano's second theorem for beam deflections
Consistent deformation and least work for indeterminate beams
Calculating and using beam deflections
Deflections and flexibility and stiffness coefficients
Using flexibility coefficients for indeterminate beams
Stiffness coefficients for beams as springs and beams on springs
Deflections via unit loads and virtual work
Problems
Frames: Assemblages of Beams	194	(30)
Modeling stored energy in frames assembled of beamlike elements
Calculating the deflections of frames
Symmetry and antisymmetry in frame analysis
Inflection points in frames
Inflection points in laterally loaded portal frames
Inflection points in vertically loaded portal frames
Some comments on inflection points
Approximate methods for frames
The portal approximation
Approximating vertically loaded beams in frames
Some comments on frame modeling and approximation
Problems
Force and Displacement Methods	224	(25)
Recapitulation and overview
Force (flexibility) methods: matrix formulation
General formulation
Some discretization aspects of the flexibility method for frames
Assembling discrete elements in the flexibility method for frames
Displacement (stiffness) methods: matrix formulation
General formulation
Some discretization aspects of the stiffness method for frames
Assembling discrete elements in the stiffness method for frames
On the flexibility method and the stiffness method
Problems
Appendix: A Short Introduction to Matrix Manipulation	249	(6)
Bibliography	255	(4)
Index	259