Static and Dynamic Analysis of Structures

This book is concerned with the static and dynamic analysis of structures. Specifi­ cally, it uses the stiffness formulated matrix methods for use on computers to tackle some of the fundamental problems facing engineers in structural mechanics. This is done by covering the Mechanics of Structures, its rephrasing in terms of the Matrix Methods, and then their Computational implementation, all within a cohesivesetting. Although this book is designed primarily as a text for use at the upper-undergraduate and beginning graduate level, many practicing structural engineers will find it useful as a reference and self-study guide. Several dozen books on structural mechanics and as many on matrix methods are currently available. A natural question to ask is why another text? An odd devel­ opment has occurred in engineering in recent years that can serve as a backdrop to why this book was written. With the widespread availability and use of comput­ ers, today's engineers have on their desk tops an analysis capability undreamt of by previous generations. However, the ever increasing quality and range of capabilities of commercially available software packages has divided the engineering profession into two groups: a small group of specialist program writers that know the ins and outs of the coding, algorithms, and solution strategies; and a much larger group of practicing engineers who use the programs. It is possible for this latter group to use this enormous power without really knowing anything of its source.

Contenu

1 Background and Scope.- 1.1 Structural Analysis.- 1.2 Types of Structures Considered.- 1.3 Mechanics of Structures.- 1.4 Degrees of Freedom.- 1.5 Time Varying Loads.- 1.6 Computers and Algorithms.- 1.7 Systems of Units.- Exercises.- 2 Rod Structures.- 2.1 Rod Theory.- 2.2 Rod Element Stiffness Matrix.- 2.3 Structural Stiffness Matrix.- 2.4 Boundary Conditions.- 2.5 Member Distributions and Reaction.- 2.6 Distributed Loads.- Problems.- Exercises.- 3 Beam Structures.- 3.1 Beam Theory.- 3.2 Beam Element Stiffness Matrix.- 3.3 Structural Stiffness Matrix.- 3.4 Equivalent Loads.- 3.5 Elastic Supports.- 3.6 Member Loads and Reactions.- Problems.- Exercises.- 4 Truss and Frame Analysis.- 4.1 Truss Analysis.- 4.2 Plane Frame Analysis.- 4.3 Space Frames.- 4.4 Determining the Rotation Matrix.- 4.5 Special Considerations.- 4.6 Substructuring.- Problems.- Exercises.- 5 Structural Stability.- 5.1 Elastic Stability.- 5.2 Stability of Truss Structures.- 5.3 Matrix Formulation for Truss Stability.- 5.4 Beams with Axial Forces.- 5.5 Beam Buckling.- 5.6 Matrix Analysis of Stability of Beams.- 5.7 Stability of Space Frames.- Problems.- Exercises.- 6 General Structural Principles I.- 6.1 Work and Strain Energy.- 6.2 Linear Elastic Structures.- 6.3 Virtual Work.- 6.4 Stationary Potential Energy.- 6.5 Ritz Approximate Analysis.- 6.6 The Finite Element Method.- 6.7 Stability Reconsidered.- Problems.- Exercises.- 7 Computer Methods I.- 7.1 Computers and Data Storage.- 7.2 Structural Analysis Programs.- 7.3 Node Renumbering.- 7.4 Solving Simultaneous Equations.- 7.5 Solving Eigenvalue Problems.- Problems.- Exercises.- 8 Dynamics of Elastic Systems.- 8.1 Harmonic Motion and Vibration.- 8.2 Complex Notation.- 8.3 Damping.- 8.4 Forced Response.- Problems.- Exercises.- 9 Vibration of Rod Structures.- 9.1 Rod Theory.- 9.2 Structural Connections.- 9.3 Exact Dynamic Stiffness Matrix.- 9.4 Approximate Matrix Formulation.- 9.5 Matrix Form of Dynamic Problems.- Problems.- Exercises.- 10 Vibration of Beam Structures.- 10.1 Spectral Analysis of Beams.- 10.2 Structural Connections.- 10.3 Exact Matrix Formulation.- 10.4 Approximate Matrix Formulation.- 10.5 Beam Structures Problems.- Problems.- Exercises.- 11 Modal Analysis of Frames.- 11.1 Dynamic Stiffness for Space Frames.- 11.2 Modal Matrix.- 11.3 Transformation to Principal Coordinates.- 11.4 Forced Damped Motion.- 11.5 The Modal Model.- 11.6 Dynamic Structural Testing.- 11.7 Structural Modification.- Problems.- Exercises.- 12 General Structural Principles II.- 12.1 Elements of Analytical Dynamics.- 12.2 Hamilton's Principle.- 12.3 Approximate Structural Theories.- 12.4 Lagrange's Equation.- 12.5 The Ritz Method.- 12.6 Ritz Method Applied to Discrete Systems.- 12.7 Rayleigh Quotient.- Problems.- Exercises.- 13 Computer Methods II.- 13.1 Finite Differences.- 13.2 Direct Integration Methods.- 13.3 Newmark's Method.- 13.4 Complete Solution of Eigensystems.- 13.5 Generalized Jacobi Method.- 13.6 Subspace Iteration.- 13.7 Selecting a Dynamic Solver.- Problems.- Exercises.- A Matrices and Linear Algebra.- A.1 Matrix Notation.- A.2 Matrix Operations.- A.3 Vector and Matrix Norms.- A.4 Determinants.- A.5 Solution of Simultaneous Equations.- A.6 Eigenvectors and Eigenvalues.- A.7 Vector Spaces.- B Spectral Analysis.- B.1 Continuous Fourier Transform.- B.2 Periodic Functions: Fourier series.- B.3 Discrete Fourier Transform.- B.4 Fast Fourier Transform Algorithm.- C Computer Source Code.- C.1 Compiling the Source Code.- C.2 Manual and Tutorial.- C.3 Source Code for STADYN.- C.4 Source Code from MODDYN.- References.