ADVANCED STRUCTURAL ANALYSIS Contents Introduction Part1 Statically determinate structures 1 Kinematical analysis of structures Classification of structures by kinematical Viewpoint Generation of geometrically unchangeable structures Analytical criteria of the instantaneously Changeable structures Degrees of freedom Problems 2 General theory of influence lines Analytical method for construction of influence Lines Influence lines for reactions Influence lines for fixed and Moving loads Fixed loads Moving loads Indirect load application Combining of fixed and and moving load approaches Properties of influence lines Problems 3 Multispan beams and trusses Multispan beams and trusses Multispan statically determinate beams Generation of multispan statically Determinate hinged beams Interaction schemes and load path Influence lines for multispan hinged Beams Summary The generation of statically determinate trusses Simple trusses Compound trusses Complex trusses Simple trusses Trusses with subdivided panels Main and auxiliary trusses and load path Baltimore and subdivided warren trusses Special types of trusses Three-hinged trusses Trusses with a hinged chain Complex trusses Summary Problems 4 Three-hinged arches Preliminary remarks Design diagram of three-hinged arch Peculiarities of the arches Geometric parameters of circular And parabolic arches Internal forces Influence lines for reactions and internal forces Influence lines for reactions Influence lines for internal forces Application of influence lines Nil point method for construction of influence Lines Bending moment Shear force Axial force Special types of arches Askew arch Parabolic arch with complex tie Problems 5 Cables Preliminary remarks Direct and inverse problems Fundamental relationships Cable with neglected self-weight Cable subjected to concentrated load Cable subjected to uniformly distributed Load Effect of arbitrary load on the thrust and sag Cable with self-weight Fundamental relationships Cable with supports located at the same Level Cable with support located On the different elevations Comparison of parabolic and catenary cables Effect of axial stiffness Elastic cable with concentrated load Elastic cable with uniformly distributed Load Problem 6 Deflection of elastic structures Introduction Initial parameters method Maxwell- mohr method Deflections due to fixed loads Deflections due to change of temperature Summary Displacement due to settlement of supports And errors of fabrication Graph multiplication method Elastic loads method Reciprocal theorems Theorem of reciprocal works Theorem of reciprocal unit Displacements Maxwell theorem Theorem of reciprocal unit displacements Maxwell theorem Theorem of reciprocal unit reactions Rayleigh first theorem Theorem of reciprocal unit displacements And reactions (Rayleigh second theorem) Summary…… Problems Part II Statically indeterminate structures 7 The force method Fundamental idea of the force method Degree of redundancy, primary unknowns And primary system Compatibility equation in simplest case Canonical equations of force method The concept of unit displacements Calculation of coefficients and free terms Of canonical equations Analysis of statically indeterminate structures Continuous beams Analysis of statically indeterminate Frames Analysis of statically indeterminate Trusses Analysis of statically indeterminate arches Computation of deflections of redundant structures Settlements of supports Temperature changes Problems 8 The displacement method Fundamental idea of the displacement method Kinematical indeterminacy Primary system and primary unknowns Compatibility equation. Concept of unit Reaction Canonical equations of displacement method Compatibility equations in general case Calculation of unit reactions Properties of unit reactions Procedure for analysis Comparison of the force and displacement methods Properties of canonical equations Sideway frames with absolutely rigid crossbars Special types of exposures Settlements of supports Errors of fabrication Analysis of symmetrical structures Symmetrical and antisymmetrical loading Concept of half-structure Problems 9 Mixed method Fundamental idea of the mixed method Mixed indeterminacy and primary Unknowns Primary system Canonical equations of the mixed method The matter of unit coefficients And canonical equations Calculation of coefficients and free terms Computation of internal forces 10 Influence Lines method Construction of influence lines by the force Method Continuous beams Hingeless nonuniform arches Statically indeterminate trusses Construction of influence lines By the displacement method Continuous beams Redundant frames Comparison of the force and displacements Methods Kinematical method for construction of influence Lines Problems 11 Matrix stiffness method Basic idea and concepts Finite elements Global and local coordinate systems Displacement of joints and degrees of freedom Ancillary diagrams Joint-load (j-l) diagram Displacement-load (z-p) diagram Internal forces-deformation (s-e) Diagram Initial matrices Vector of external joint loads Vector of internal unknown forces Resolving equations Statics equations and static matrix Geometrical equations and deformation Matrix Physical equations and stiffness matrix In local coordinates Set of formulas and procedure for analysis Stiffness matrix in global coordinates Unknown displacements and internal Forces Matrix procedures Analysis of continuous beams Analysis of redundant frames Analysis of statically indeterminate trusses Summary Problems Part III Special topics 12 .Plastics behavior of structures Idealized stress-strain diagrams Direct method of plastic analysis Fundamental methods of plastics analysis Kinematical method Static method Limit plastic analysis of continuous beams Static method Kinematical method Limit plastic analysis of frames Beams failure Sidesway failure Combined failure Limit combination diagram Problems 13 Stability of elastic systems Fundamental concepts Stability of structures with finite number degrees Of freedom Structures with one degree of freedom Structures with two or more degree Of freedom Stability of columns with rigid and elastic Supports The double integration method Initial parameters method Stability of continuous beams and frames Unit reactions of the beam-columns Displacement method Modified approach of the displacement Method Stability of arches Circular arches under hydrostatic load Complex arched structure: Arch with elastic supports Compressed roads with lateral loading Double integration method Initial parameters method P-delta analysis of the frames Graph multiplication method For beam-columns Problems 14 Dynamics of elastic systems Fundamental concepts Kinematics of vibrating processes Forces which arise at vibrations Degrees of freedom Purpose of structural dynamics Assumptions Free vibrations of systems with finite number Degree of freedom: force method Differential equations of free vibration in displacements Frequency equation Mode shapes vibration and model matrix Free vibrations of systems with finite number Degrees of freedom: displacement method Differential equations of free vibration In reactions Frequency equation Mode shape vibrations and model matrix Comparison of the force and displacement Methods Free vibrations of one-span beams with uniformly Distributed mass Differential equation of transversal vibration Of the beam Fourier method Krylov-duncan method Problems Appendix Bibliography Index
ADVANCED STRUCTURAL ANALYSIS
Contents
Introduction
Part1 Statically determinate structures
1 Kinematical analysis of structures
Classification of structures by kinematical
Viewpoint
Generation of geometrically unchangeable structures
Analytical criteria of the instantaneously
Changeable structures
Degrees of freedom
Problems
2 General theory of influence lines
Analytical method for construction of influence
Lines
Influence lines for reactions
Influence lines for fixed and
Moving loads
Fixed loads
Indirect load application
Combining of fixed and and moving load approaches
Properties of influence lines
3 Multispan beams and trusses
Multispan beams and trusses
Multispan statically determinate beams
Generation of multispan statically
Determinate hinged beams
Interaction schemes and load path
Influence lines for multispan hinged
Beams
Summary
The generation of statically determinate trusses
Simple trusses
Compound trusses
Complex trusses
Trusses with subdivided panels
Main and auxiliary trusses and load path
Baltimore and subdivided warren trusses
Special types of trusses
Three-hinged trusses
Trusses with a hinged chain
4 Three-hinged arches
Preliminary remarks
Design diagram of three-hinged arch
Peculiarities of the arches
Geometric parameters of circular
And parabolic arches
Internal forces
Influence lines for reactions and internal forces
Influence lines for internal forces
Application of influence lines
Nil point method for construction of influence
Bending moment
Shear force
Axial force
Special types of arches
Askew arch
Parabolic arch with complex tie
5 Cables
Direct and inverse problems
Fundamental relationships
Cable with neglected self-weight
Cable subjected to concentrated load
Cable subjected to uniformly distributed
Load
Effect of arbitrary load on the thrust and sag
Cable with self-weight
Cable with supports located at the same
Level
Cable with support located
On the different elevations
Comparison of parabolic and catenary cables
Effect of axial stiffness
Elastic cable with concentrated load
Elastic cable with uniformly distributed
Problem
6 Deflection of elastic structures
Initial parameters method
Maxwell- mohr method
Deflections due to fixed loads
Deflections due to change of temperature
Displacement due to settlement of supports
And errors of fabrication
Graph multiplication method
Elastic loads method
Reciprocal theorems
Theorem of reciprocal works
Theorem of reciprocal unit Displacements
Maxwell theorem
Theorem of reciprocal unit displacements
Theorem of reciprocal unit reactions
Rayleigh first theorem
And reactions (Rayleigh second theorem)
Summary……
Part II Statically indeterminate structures
7 The force method
Fundamental idea of the force method
Degree of redundancy, primary unknowns
And primary system
Compatibility equation in simplest case
Canonical equations of force method
The concept of unit displacements
Calculation of coefficients and free terms
Of canonical equations
Analysis of statically indeterminate structures
Continuous beams
Analysis of statically indeterminate
Frames
Trusses
Analysis of statically indeterminate arches
Computation of deflections of redundant structures
Settlements of supports
Temperature changes
8 The displacement method
Fundamental idea of the displacement method
Kinematical indeterminacy
Primary system and primary unknowns
Compatibility equation. Concept of unit
Reaction
Canonical equations of displacement method
Compatibility equations in general case
Calculation of unit reactions
Properties of unit reactions
Procedure for analysis
Comparison of the force and displacement methods
Properties of canonical equations
Sideway frames with absolutely rigid crossbars
Special types of exposures
Errors of fabrication
Analysis of symmetrical structures
Symmetrical and antisymmetrical loading
Concept of half-structure
9 Mixed method
Fundamental idea of the mixed method
Mixed indeterminacy and primary
Unknowns
Primary system
Canonical equations of the mixed method
The matter of unit coefficients
And canonical equations
Computation of internal forces
10 Influence Lines method
Construction of influence lines by the force
Method
Hingeless nonuniform arches
Statically indeterminate trusses
Construction of influence lines
By the displacement method
Redundant frames
Comparison of the force and displacements
Methods
Kinematical method for construction of influence
11 Matrix stiffness method
Basic idea and concepts
Finite elements
Global and local coordinate systems
Displacement of joints and degrees of freedom
Ancillary diagrams
Joint-load (j-l) diagram
Displacement-load (z-p) diagram
Internal forces-deformation (s-e)
Diagram
Initial matrices
Vector of external joint loads
Vector of internal unknown forces
Resolving equations
Statics equations and static matrix
Geometrical equations and deformation
Matrix
Physical equations and stiffness matrix
In local coordinates
Set of formulas and procedure for analysis
Stiffness matrix in global coordinates
Unknown displacements and internal
Forces
Matrix procedures
Analysis of continuous beams
Analysis of redundant frames
Analysis of statically indeterminate trusses
Part III Special topics
12 .Plastics behavior of structures
Idealized stress-strain diagrams
Direct method of plastic analysis
Fundamental methods of plastics analysis
Kinematical method
Static method
Limit plastic analysis of continuous beams
Limit plastic analysis of frames
Beams failure
Sidesway failure
Combined failure
Limit combination diagram
13 Stability of elastic systems
Fundamental concepts
Stability of structures with finite number degrees
Of freedom
Structures with one degree of freedom
Structures with two or more degree
Stability of columns with rigid and elastic
Supports
The double integration method
Stability of continuous beams and frames
Unit reactions of the beam-columns
Displacement method
Modified approach of the displacement
Stability of arches
Circular arches under hydrostatic load
Complex arched structure:
Arch with elastic supports
Compressed roads with lateral loading
Double integration method
P-delta analysis of the frames
For beam-columns
14 Dynamics of elastic systems
Kinematics of vibrating processes
Forces which arise at vibrations
Purpose of structural dynamics
Assumptions
Free vibrations of systems with finite number
Degree of freedom: force method
Differential equations of free vibration in displacements
Frequency equation
Mode shapes vibration and model matrix
Degrees of freedom: displacement method
Differential equations of free vibration
In reactions
Mode shape vibrations and model matrix
Comparison of the force and displacement
Free vibrations of one-span beams with uniformly
Distributed mass
Differential equation of transversal vibration
Of the beam
Fourier method
Krylov-duncan method
Appendix
Bibliography
Index
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