Structural Analysis Fundamentals

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Half Title
Title Page
Copyright Page
Table of Contents
Introduction to Structural Analysis Fundamentals
Preface to Structural Analysis Fundamentals
Notations
The SI System of Units of Measurements
Authors
Chapter 1 Structural analysis modeling
	1.1 Introduction
	1.2 Types of structures
		1.2.1 Cables and arches
	1.3 Load path
	1.4 Deflected shape
	1.5 Structural idealization
	1.6 Idealization examples: grid analogy
	1.7 Framed structures
		1.7.1 Computer programs
	1.8 Non-framed or continuous structures
	1.9 Connections and support conditions
	1.10 Loads and load idealization
		1.10.1 Thermal effects
	1.11 Stresses and deformations
	1.12 Normal stress
		1.12.1 Normal stresses in plane frames and beams
		1.12.2 Examples of deflected shapes and bending moment diagrams
		1.12.3 Deflected shapes and bending moment diagrams due to temperature variation
	1.13 Comparisons: beams, arches, and trusses
	1.14 Strut-and-tie models in reinforced concrete design
		1.14.1 B- and D-regions
		1.14.2 Statically indeterminate strut-and-tie models
	1.15 Structural design
	1.16 General
	References
	Problems
Chapter 2 Statically determinate structures
	2.1 Introduction
	2.2 Equilibrium of a body
	2.3 Internal forces: sign convention and diagrams
	2.4 Verification of internal forces
	2.5 General
	Problems
	Notes
Chapter 3 Introduction to the analysis of statically indeterminate structures
	3.1 Introduction
	3.2 Statical indeterminacy
	3.3 Expressions for degree of indeterminacy
		3.3.1 Plane frames having pin connections
	3.4 General methods of analysis of statically indeterminate structures
	3.5 Kinematic indeterminacy
	3.6 Principle of superposition
	3.7 General
	Problems
	Note
Chapter 4 Force method of analysis
	4.1 Introduction
	4.2 Description of method
	4.3 Released structure and coordinate system
		4.3.1 Use of a coordinate represented by a single arrow or a pair of arrows
	4.4 Analysis for environmental effects
		4.4.1 Deflected shapes due to environmental effects
	4.5 Analysis for different loadings
	4.6 Five steps of the force method
	4.7 Moving loads on continuous beams and frames
	4.8 Influence lines
		4.8.1 Müller-Breslau’s principle
	4.9 Maximum effect of moving load
	4.10 General
	Reference
	Problems
Chapter 5 Displacement method of analysis
	5.1 Introduction
	5.2 Description of method
	5.3 Degrees of freedom and coordinate system
		Remarks
	5.4 Five steps of displacement method
	5.5 Properties of flexibility and stiffness matrices
	5.6 Stiffness matrix for a prismatic member of space and plane frames
	5.7 Relation between flexibility and stiffness matrices
	5.8 Analysis for different loadings
	5.9 Effect of nonlinear temperature variation
	5.10 Effect of shrinkage and creep
	5.11 Effect of prestressing
	5.12 Condensation of stiffness matrices
	5.13 Analysis of symmetrical structures by displacement method
	5.14 General
	Problems
	Note
Chapter 6 Time-dependant displacements in structural concrete
	6.1 Introduction
	6.2 Long-term displacements in structural concrete
		6.2.1 Creep of concrete
		6.2.2 Relaxation of prestressing
		6.2.3 Immediate strain parameters
		6.2.4 Long-term strain parameters
		6.2.5 Cracking
		6.2.6 Strain–displacement relationship
	6.3 Long-term deflection of reinforced concrete floors
	6.4 Use of linear computer programs
		6.4.1 Assumptions and limitations
		6.4.2 Two computer runs
	6.5 Multi-stage construction
	6.6 General
	References
	Problems
Chapter 7 Strain energy and virtual work
	7.1 Introduction
	7.2 Strain energy
	7.3 Normal and shear stresses in beams
		7.3.1 Normal stress in plane sections
		7.3.2 Strain energy due to shear
		7.3.3 Strain energy due to torsion
		7.3.4 Total strain energy
	7.4 Basic equations of elasticity
		7.4.1 Plane stress and plane strain
		7.4.2 Bending of plates
		7.4.3 Three-dimensional solid
	7.5 Differential equations for deformations
		7.5.1 Beam in bending
		7.5.2 Plates in bending
	7.6 Virtual work principle
	7.7 Unit-load and unit-displacement theorems
		7.7.1 Symmetry of flexibility and stiffness matrices
	7.8 General
Chapter 8 Virtual work applications
	8.1 Introduction
	8.2 Displacement calculation by virtual work
		8.2.1 Definite integral of product of two functions
	8.3 Displacements required in the force method
	8.4 Displacement of statically indeterminate structures
	8.5 Truss deflection
	8.6 Equivalent joint loading
	8.7 Deflection of beams and frames
	8.8 Effect of temperature variation
		8.8.1 Computer analysis for effect of temperature
	8.9 Stiffness matrix of plane frame member considering shear, bending, and axial deformations
	8.10 Transformation of stiffness and flexibility matrices
	8.11 Stiffness matrix of plane frame member with respect to eccentric coordinates
	8.12 General
	Problems
Chapter 9 Application of displacement method: Moment distribution
	9.1 Introduction
	9.2 End-rotational stiffness and carryover moment
	9.3 Process of moment distribution
	9.4 Moment distribution procedure for plane frames without joint translation
	9.5 Adjusted end-rotational stiffnesses
	9.6 Adjusted fixed-end moments
	9.7 General
	References
	Problems
Chapter 10 Effects of axial forces on flexural stiffness
	10.1 Introduction
	10.2 Stiffness of a prismatic member subjected to an axial force
	10.3 Effect of axial compression
	10.4 Effect of axial tension
	10.5 Linear analysis considering effect of axial force
	10.6 Fixed-end moments for a prismatic member subjected to an axial force
		10.6.1 Uniform load
		10.6.2 Concentrated load
	10.7 Elastic stability of frames
	10.8 Elastic stability of frames: general solution
	10.9 Eigenvalue problem
	10.10 General
	Problems
Chapter 11 Analysis of shear wall structures
	11.1 Introduction
	11.2 Stiffness of a shear wall element
	11.3 Stiffness matrix of a beam with rigid end parts
	11.4 Analysis of a plane frame with shear walls
	11.5 Simplified approximate analysis of a building as a plane structure
	11.6 Shear walls with openings
	11.7 Three-dimensional analysis
	11.8 Outrigger-braced high-rise buildings
		11.8.1 Location of the outriggers
	11.9 General
	References
	Problems
Chapter 12 Methods of finite differences and finite-elements
	12.1 Introduction
	12.2 Representation of derivatives by finite differences
	12.3 Beam on elastic foundation
	12.4 Boundary conditions by finite differences
	12.5 Stress resultants and reaction: finite difference relationship to deflection
	12.6 Axisymmetrical circular cylindrical shell: idealization as beam on elastic foundation
	12.7 Finite-element analysis of shells of revolution
		12.7.1 Nodal displacements and nodal forces
		12.7.2 Stiffness matrix transformation
		12.7.3 Displacement interpolation
		12.7.4 Stress resultants
		12.7.5 Element stiffness
		12.7.6 Effect of temperature
		12.7.7 Nodal forces due to distributed loads
		12.7.8 Assemblage of stiffness matrices and nodal forces
	12.8 Finite-element analysis: five steps (of displacement method)
	12.9 Displacement interpolation
		12.9.1 Straight bar element
		12.9.2 Quadrilateral element subjected to in-plane forces
	12.10 Stiffness and stress matrices for displacement-based elements
	12.11 Element load vectors
		12.11.1 Analysis of effects of temperature variation
	12.12 General
	References
	Problems
	Note
Chapter 13 Finite-element analysis
	13.1 Introduction
	13.2 Derivation of shape functions
	13.3 Shells as assemblage of flat elements
		13.3.1 Rectangular shell element
		13.3.2 Fictitious stiffness coefficients
	13.4 Convergence conditions
	13.5 Lagrange interpolation
	13.6 Coordinates of grid nodes
	13.7 Shape functions for two- and three-dimensional isoparametric elements
	13.8 Stiffness matrix and load vector of isoparametric elements
	13.9 Consistent load vectors for rectangular plane element
	13.10 Constant-strain triangle
	13.11 Interpretation of nodal forces
	13.12 Triangular plane-stress and plane-strain elements
		13.12.1 Linear-strain triangle
	13.13 Triangular plate-bending elements
	13.14 Numerical integration
	13.15 General
	References
	Problems
	Notes
Chapter 14 Plastic analysis of plane frames
	14.1 Introduction
	14.2 Ultimate moment
	14.3 Plastic behavior of a simple beam
	14.4 Ultimate strength of fixed-ended and continuous beams and frames
	14.5 Location of plastic hinge under distributed load
	14.6 Plastic analysis by computer
	14.7 Effect of axial force on plastic moment resistance
	14.8 General
	Problems
Chapter 15 Yield-line analysis of reinforced concrete slabs
	15.1 Introduction
	15.2 Fundamentals of yield-line theory
		15.2.1 Convention of representation
		15.2.2 Ultimate moment of a slab equally reinforced in two perpendicular directions
	15.3 Energy method
	15.4 Orthotropic slabs
	15.5 Equilibrium of slab parts
		15.5.1 Nodal forces
	15.6 Equilibrium method
	15.7 Irregular slabs
	15.8 General
	References
	Problems
	Notes
Chapter 16 Structural dynamics
	16.1 Introduction
	16.2 Lumped mass idealization
	16.3 Consistent mass matrix
	16.4 Undamped vibration: single-degree-of-freedom system
		16.4.1 Forced motion of an undamped single-degree-of-freedom system: harmonic force
		16.4.2 Forced motion of an undamped single-degree-of-freedom system: general dynamic forces
	16.5 Viscously damped vibration: single-degree-of-freedom system
		16.5.1 Viscously damped free vibration
		16.5.2 Viscously damped forced vibration – harmonic loading: single-degree-of-freedom system
		16.5.3 Viscously damped forced vibration – general dynamic loading: single-degree-of-freedom system
	16.6 Undamped free vibration of multi-degree-of-freedom systems
		16.6.1 Mode orthogonality
		16.6.2 Normalized mode matrix
	16.7 Modal analysis of damped or undamped multi-degree-of-freedom systems
		16.7.1 Modal damping ratio: Rayleigh damping
	16.8 Single- or multi-degree-of-freedom systems subjected to ground motion
	16.9 Substitute single-degree-of-freedom system
	16.10 Substitute single-degree-of-freedom system for structures having numerous degrees-of-freedom
	16.11 Generalized single-degree-of-freedom system
		16.11.1 Cantilever idealization of a tower with variable cross section
		16.11.2 Cantilever with distributed mass
	16.12 General
	References
	Problems
Chapter 17 Response of structures to earthquakes
	17.1 Introduction
	17.2 Single-degree-of-freedom system
	17.3 Multi-degree-of-freedom system
		17.3.1 Damping ratio
	17.4 Time-stepping analysis
	17.5 Effects of damping and natural period of vibration on response to ground shaking
	17.6 Pseudo-acceleration: static equivalent loading
	17.7 Pseudo-velocity
	17.8 Graphs for pseudo-acceleration and pseudo-velocity
	17.9 Earthquake response spectra
	17.10 Effect of ductility on forces due to earthquakes
	17.11 Comparison of elastic and plastic responses
	17.12 Reduction of equivalent static loading: ductility and over-strength factors
	17.13 Modal spectral analysis of linear systems
	17.14 Mass participation factor
	17.15 Modal combinations
	17.16 Mass lumping
	17.17 Ductility and strength requirement
	17.18 Nonlinear static (pushover) analysis
		17.18.1 P-delta effect
		17.18.2 Modal pushover analysis
		17.18.3 Limitations
	17.19 General
	References
	Problems
Chapter 18 Nonlinear analysis
	18.1 Introduction
	18.2 Geometric stiffness matrix
	18.3 Simple example of geometric nonlinearity
	18.4 Newton–Raphson technique: solution of nonlinear equations
		18.4.1 Modified Newton–Raphson technique
	18.5 Newton–Raphson technique applied to trusses
		18.5.1 Calculations in one iteration cycle
		18.5.2 Convergence criteria
	18.6 Tangent stiffness matrix of a member of plane or space truss
	18.7 Nonlinear buckling
	18.8 Tangent stiffness matrix of a member of plane frame
	18.9 Application of Newton–Raphson technique to plane frames
	18.10 Tangent stiffness matrix of triangular membrane element
	18.11 Analysis of structures made of nonlinear material
	18.12 Iterative methods for analysis of material nonlinearity
	18.13 General
	References
	Problems
Chapter 19 Computer analysis of framed structures
	19.1 Introduction
	19.2 Member local coordinates
		19.2.1 Plane and eccentric grids
	19.3 Band width
	19.4 Input data
	19.5 Direction cosines of element local axes
	19.6 Element stiffness matrices
	19.7 Transformation matrices
	19.8 Member stiffness matrices with respect to global coordinates
	19.9 Assemblage of stiffness matrices and load vectors
	19.10 Displacement support conditions and support reactions
	19.11 Solution of banded equations
	19.12 Member end forces
	19.13 General
	Reference
Chapter 20 Computer programs
	20.1 Introduction
	20.2 Availability of the programs
	20.3 Program components
	20.4 Description of programs
		20.4.1 Group A. Linear analysis programs (basis: Chapter 19)
		20.4.2 Group B. Nonlinear analysis programs
		20.4.3 Group C. Matrix algebra
		20.4.4 Group D. Programs EIGEN1 and EIGEN2
		20.4.5 Group E. Time-dependent analysis programs
		20.4.6 Group F. Programs for analysis of axially symmetric loaded structures
	20.5 Input and output of program PLANEF
	20.6 General
Appendix A Displacements of prismatic members
Appendix B Fixed-end forces of prismatic members
Appendix C End-forces caused by end displacements of prismatic members
Appendix D Reactions and bending moments at supports of continuous beams due to unit displacement of supports
Appendix E Properties of geometrical figures
Appendix F Torsional constant J
Appendix G Values of the integral ∫I Mu Mu dl
Appendix H Forces due to prestressing of concrete members
Answers to problems
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Index