Structural Analysis : A Unified Classical and Matrix Approach, Seventh Edition

963 Pages·2017·26.419 MB·English

by  Ghali, Amin, Neville, Adam

Structural Analysis: A unified
classical and matrix approach
Now in its seventh edition, this book is used internationally in six languages by students,
lecturers and engineers, because of the level of clarity and thorough selection of contents,
honed in successive editions. With new solved examples and problems and an expanded set
of computer programs, the text comprises more than 160 worked examples and 425 prob-
lems with answers. There are added sections and chapters. The fundamentals of dynamic
analysis of structures are now presented in three chapters including the response of struc-
tures to earthquakes. Throughout the text, the analysis of three-dimensional spatial struc-
tures is considered.
The book contains basic procedures of structural analysis that should be covered in first
courses, teaching modeling structures as beams, trusses, plane or space frames and grids or
assemblages of finite elements. A companion set of computer programs, with their source
code and executable files, assist in thorough understanding and applying the procedures.
Advanced topics are presented in the same text for use in higher courses and practice and
to inspire beginners.
Amin Ghali is Professor Emeritus in the Civil Engineering Department of the University of
Calgary, Canada.
Adam Neville was Principal and Vice-Chancellor of University of Dundee, Scotland.

Structural Analysis: A unified
classical and matrix approach
7th edition
A. Ghali
Structural Engineering Consultant
Professor Emeritus of Civil Engineering
University of Calgary
A. M. Neville
Civil Engineering Consultant
Formerly Principal and Vice-Chancellor
University of Dundee
CRC Press
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Contents
Preface to the Seventh Edition xxi
Notation xxv
The SI System of Units of Measurement xxvii
Imperial equivalents of SI units xxiii
1 Structural analysis modeling 1
1.1 Introduction 1
1.2 Types of structures 2
1.2.1 Cables and arches 8
1.3 Load path 11
1.4 Deflected shape 15
1.5 Structural idealization 16
1.6 Framed structures 16
1.6.1 Computer programs 19
1.7 Non-framed or continuous structures 19
1.8 Connections and support conditions 20
1.9 Loads and load idealization 21
1.9.1 Thermal effects 22
1.10 Stresses and deformations 23
1.11 Normal stress 25
1.11.1 Normal stresses in plane frames and beams 26
1.11.2 Examples of deflected shapes and bending moment diagrams 29
1.11.3 Deflected shapes and bending moment
diagrams due to temperature variation 30
1.12 Comparisons: beams, arches and trusses 31
Example 1.1: Load path comparisons: beam, arch and truss 32
Example 1.2: Three-hinged, two-hinged, and totally fixed arches 34
1.13 Strut-and-tie models in reinforced concrete design 37
1.13.1 B- and D-regions 38
Example 1.3: Strut-and-tie model for a wall supporting an eccentric load 40
1.13.2 Statically indeterminate strut-and-tie models 40
1.14 Structural design 41
1.15 General 42
v
vi Contents
2 Statically determinate structures 47
2.1 Introduction 47
2.2 Equilibrium of a body 49
Example 2.1: Reactions for a spatial body: a cantilever 50
Example 2.2: Equilibrium of a node of a space truss 52
Example 2.3: Reactions for a plane frame 53
Example 2.4: Equilibrium of a joint of a plane frame 53
Example 2.5: Forces in members of a plane truss 54
2.3 Internal forces: sign convention and diagrams 54
2.4 Verification of internal forces 57
Example 2.6: Member of a plane frame: V and M-diagrams 59
Example 2.7: Simple beams: verification of V and M-diagrams 60
Example 2.8: A cantilever plane frame 60
Example 2.9: A simply-supported plane frame 61
Example 2.10: M-diagrams determined without calculation of reactions 62
Example 2.11: Three-hinged arches 63
2.5 Effect of moving loads 64
2.5.1 Single load 64
2.5.2 Uniform load 64
2.5.3 Two concentrated loads 65
Example 2.12: Maximum bending moment diagram 67
2.5.4 Group of concentrated loads 68
2.5.5 Absolute maximum effect 69
2.6 Influence lines for simple beams and trusses 71
Example 2.13: Simple beam with two moving loads 71
Example 2.14: Maximum values of M and V using influence lines 73
2.7 General 74
Problems 75
3 Introduction to the analysis of statically indeterminate structures 85
3.1 Introduction 85
3.2 Statical indeterminacy 85
3.3 Expressions for degree of indeterminacy 89
Example 3.1: Computer analysis of a space truss 93
3.3.1 Plane frames having pin connections 94
3.4 General methods of analysis of statically indeterminate structures 95
3.5 Kinematic indeterminacy 96
3.6 Principle of superposition 100
3.7 General 102
4 Force method of analysis 107
4.1 Introduction 107
4.2 Description of method 107
Example 4.1: Structure with degree of indeterminacy = 2 108
Contents vii
4.3 Released structure and coordinate system 111
4.3.1 Use of coordinate represented by a single arrow or a pair of arrows 112
4.4 Analysis for environmental effects 112
4.4.1 Deflected shapes due to environmental effects 114
Example 4.2: Deflection of a continuous
beam due to temperature variation 114
4.5 Analysis for different loadings 115
4.6 Five steps of force method 115
Example 4.3: A stayed cantilever 116
Example 4.4: A beam with a spring support 118
Example 4.5: Simply-supported arch with a tie 118
Example 4.6: Compatibility equation for a space truss 121
Example 4.7: Continuous beam: support
settlement and temperature change 122
Example 4.8: Release of a continuous beam as a series of simple beams 125
4.7 Equation of three moments 129
Example 4.9: Beam of Example 4.7 analyzed
by equation of three moments 131
Example 4.10: Continuous beam with overhanging end 132
Example 4.11: Deflection of a continuous beam due to support settlements 134
4.8 Moving loads on continuous beams and frames 135
Example 4.12: Two-span continuous beam 138
4.9 General 139
5 Displacement method of analysis 147
5.1 Introduction 147
5.2 Description of method 147
Example 5.1: Plane truss 148
5.3 Degrees of freedom and coordinate system 151
Example 5.2: Plane frame 152
5.4 Analysis for different loadings 155
5.5 Analysis for environmental effects 156
5.6 Five steps of displacement method 156
Example 5.3: Plane frame with inclined member 157
Example 5.4: A grid 161
5.7 Analysis of effects of displacements at the coordinates 163
Example 5.5: A plane frame: condensation of stiffness matrix 165
5.8 General 166
6 Use of force and displacement methods 173
6.1 Introduction 173
6.2 Relation between flexibility and stiffness matrices 173
Example 6.1: Generation of stiffness matrix of a prismatic member 175
6.3 Choice of force or displacement method 175
viii Contents
Example 6.2: Reactions due to unit settlement
of a support of a continuous beam 176
Example 6.3: Analysis of a grid ignoring torsion 177
6.4 Stiffness matrix for a prismatic member of space and plane frames 179
6.5 Condensation of stiffness matrices 181
Example 6.4: Deflection at tip of a cantilever 183
Example 6.5: End-rotational stiffness of a simple beam 183
6.6 Properties of flexibility and stiffness matrices 184
6.7 Analysis of symmetrical structures by force method 187
Example 6.6: Continuous beam having many
equal spans typically loaded ( Figure 6.6e ) 189
6.8 Analysis of symmetrical structures by displacement method 190
Example 6.7: Single-bay symmetrical plane frame 192
Example 6.8: A horizontal grid subjected to gravity load 193
6.9 Effect of nonlinear temperature variation 195
Example 6.9: Thermal stresses in a continuous beam 199
Example 6.10: Thermal stresses in a portal frame 201
6.10 Effect of shrinkage and creep 204
6.11 Effect of prestressing 205
Example 6.11: Post-tensioning of a continuous beam 206
6.12 General 209
7 Strain energy and virtual work 215
7.1 Introduction 215
7.2 Geometry of displacements 216
7.3 Strain energy 218
7.3.1 Strain energy due to axial force 222
7.3.2 Strain energy due to bending moment 223
7.3.3 Strain energy due to shear 224
7.3.4 Strain energy due to torsion 225
7.3.5 Total strain energy 225
7.4 Complementary energy and complementary work 225
7.5 Principle of virtual work 228
7.6 Unit-load and unit-displacement theorems 230
7.6.1 Symmetry of flexibility and stiffness matrices 231
7.7 Virtual-work transformations 232
Example 7.1: Transformation of a geometry problem 235
7.8 Castigliano’ s theorems 235
7.8.1 Castigliano’ s first theorem 235
7.8.2 Castigliano’ s second theorem 237
7.9 General 239
8 Determination of displacements by virtual work 241
8.1 Introduction 241
8.2 Calculation of displacement by virtual work 241
Contents ix
8.3 Displacements required in the force method 244
8.4 Displacement of statically indeterminate structures 245
8.5 Evaluation of integrals for calculation of
displacement by method of virtual work 247
8.5.1 Definite integral of product of two functions 250
8.5.2 Displacements in plane frames in terms of member end moments 250
8.6 Truss deflection 251
Example 8.1: Plane truss 252
Example 8.2: Deflection due to temperature: statically determinate truss 253
8.7 Equivalent joint loading 254
8.8 Deflection of beams and frames 255
Example 8.3: Simply-supported beam with overhanging end 256
Example 8.4: Deflection due to shear in deep and shallow beams 258
Example 8.5: Deflection calculation using equivalent joint loading 259
Example 8.6: Deflection due to temperature gradient 260
Example 8.7: Effect of twisting combined with bending 262
Example 8.8: Plane frame: displacements due
to bending, axial and shear deformations 263
Example 8.9: Plane frame: flexibility matrix by unit-load theorem 266
Example 8.10: Plane truss: analysis by the force method 267
Example 8.11: Arch with a tie: calculation of
displacements needed in force method 268
Example 8.12: Space truss: Analysis by force method 270
8.9 General 271
9 Further energy theorems 281
9.1 Introduction 281
9.2 Betti’ s and Maxwell’ s theorems 281
9.3 Application of Betti’ s theorem to transformation
of forces and displacements 283
Example 9.1: Plane frame in which axial deformation is ignored 287
9.4 Transformation of stiffness and flexibility matrices 287
Example 9.2: Application of stiffness and flexibility transformations 289
Example 9.3: Stiffness matrix transformation, plane truss member 290
Example 9.4: Transformation of stiffness and
flexibility matrices of a cantilever 292
9.5 Stiffness matrix of assembled structure 293
Example 9.5: Plane frame with inclined member 295
9.6 Potential energy 296
9.7 General 298
10 Displacement of elastic structures by special methods 305
10.1 Introduction 305
10.2 Differential equation for deflection of a beam in bending 305
10.3 Moment– area theorems 307