Structural and Stress Analysis, Theories, Tutorials, and examples, 2008
مطالب
1 Introduction 1
1.1 Forces and moments 1
1.2 Types of force and deformation 3
1.2.1 Force 3
1.2.2 Deformation 3
1.3 Equilibrium system 3
1.3.1 The method of section 3
1.3.2 The method of joint 4
1.4 Stresses 5
1.4.1 Normal stress 5
1.4.2 Shear stress 6
1.5 Strains 7
1.6 Strain–stress relation 7
1.7 Generalized Hooke’s law 8
1.8 Strength, stiffness and failure 10
1.9 Key points review 11
1.10 Basic approach for structural analysis 12
1.11 Conceptual questions 13
1.12 Mini test 14
2 Axial tension and compression 16
2.1 Sign convention 16
2.2 Normal (direct) stress 16
2.3 Stresses on an arbitrarily inclined plane 17
2.4 Deformation of axially loaded members 18
2.4.1 Members of uniform sections 18
2.4.2 Members with step changes 18
2.5 Statically indeterminate axial deformation 19
2.6 Elastic strain energy of an axially
loaded member 20
2.6.1 Strain energy U in an axially loaded member 20
2.6.2 Strain energy density, U0 20
2.7 Saint-Venant’s principle and stress concentration 20
2.8 Stresses caused by temperature 21
2.9 Key points review 22
2.10 Recommended procedure of solution 23
2.11 Examples 23
2.12 Conceptual questions 31
2.13 Mini test 33
3 Torsion 36
3.1 Sign convention 36
3.2 Shear stress 37
3.3 Angle of twist 38
3.4 Torsion of rotating shafts 38
3.5 Key points review 39
3.6 Recommended procedure of solution 39
3.7 Examples 40
3.8 Conceptual questions 49
3.9 Mini test 51
4 Shear and bending moment 53
4.1 Definition of beam 54
4.2 Shear force and bending moment 54
4.3 Beam supports 54
4.4 Sign convention 54
4.4.1 Definition of positive shear 54
4.4.2 Definition of positive bending moment 55
4.5 Relationships between bending moment, shear force and
applied load 56
4.6 Shear force and bending moment diagrams 57
4.7 Key points review 57
4.8 Recommended procedure of solution 58
4.9 Examples 58
4.10 Conceptual questions 75
4.11 Mini test 77
5 Bending stresses in symmetric beams 80
5.1 Normal stresses in beams 81
5.2 Calculation of second moment of inertia 82
5.3 Shear stresses in beams 84
5.4 Key points review 85
5.5 Recommended procedure of solution 86
5.6 Examples 87
5.7 Conceptual questions 102
5.8 Mini test 105
6 Deflection of beams under bending 107
6.1 Sign convention 108
6.2 Equation of beam deflection 108
6.2.1 The integration method 108
6.2.2 The superposition method 109
6.2.3 Macaulay’s method (step function method) 110
6.3 Key points review 112
6.4 Examples 113
6.4.1 Examples of the integration method 113
6.4.2 Examples of the superposition method 118
6.4.3 Examples of Macaulay’s method 123
6.5 Conceptual questions 127
6.6 Mini test 128
7 Complex stresses 130
7.1 Two-dimensional state of stress 131
7.1.1 Sign convention of stresses 132
7.1.2 Analytical method 133
7.1.3 Graphic method 137
7.2 Key points review 138
7.2.1 Complex stress system 138
7.2.2 Mohr’s circle 139
7.3 Examples 139
7.4 Conceptual questions 148
7.5 Mini test 149
8 Complex strains and strain gauges 151
8.1 Strain analysis 154
8.2 Strain measurement by strain gauges 155
8.3 Key points review 156
8.3.1 Complex strain system 156
8.3.2 Strain measurement by strain gauges 157
8.4 Examples 157
8.5 Conceptual questions 164
8.6 Mini test 164
9 Theories of elastic failure 166
9.1 Maximum principal stress criterion 167
9.2 Maximum shear stress criterion (Tresca theory) 169
9.3 Distortional energy density (von Mises theory) criterion 169
9.4 Special forms of Tresca and von Mises criterions 170
9.5 Key points review 171
9.6 Recommended procedure of solution 171
9.7 Examples 171
9.8 Conceptual questions 176
9.9 Mini test 176
10 Buckling of columns 178
10.1 Euler formulas for columns 179
10.1.1 Euler formula for columns with pinned ends 179
10.1.2 Euler formulas for columns with other ends 180
10.2 Limitations of Euler formulas 181
10.3 Key points review 182
10.4 Examples 183
10.5 Conceptual questions 192
10.6 Mini test 193
11 Energy method 195
11.1 Work and strain energy 195
11.1.1 Work done by a force 195
11.1.2 Strain energy 196
11.2 Solutions based on energy method 196
11.2.1 Castigliano’s first theorem 197
11.2.2 Castigliano’s second theorem 197
11.3 Virtual work and the principle of virtual work 197
11.3.1 Virtual work 197
11.3.2 The principle of virtual work 198
11.3.3 Deflection of a truss system 199
11.4 Key points review 200
11.5 Examples 200
11.6 Conceptual questions 212
11.7 Mini test 212
Structural and Stress Analysis, Theories, Tutorials, and examples, 2008
