Static and Dynamic Analysis of Structures

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.