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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