Structural Analysis of Plane Frames – Solved Examples with Force and Displacement Methods
Structural Analysis of Plane Frames – Solved Examples with Force and Displacement Methods
Isabella Giorgia Colombo , Matteo Colombo , Marco di Prisco , Anna Magri , Paolo Martinelli , Letizia Mazzoleni , Giulio Zani
Contents
1 Short Notes on Kinematic Analysis . 1
1.1 Redundancy 1
1.2 Centre of Instantaneous Rotation (CIR) . 1
2 Solution of Simple Reference Cases 7
2.1 Problem A(I): Inclined Rod . 7
2.2 Problem A(II): Inclined Rod 19
2.3 Problem B(I): Extensional Spring 27
2.4 Problem B(II): Extensional Spring . 35
2.5 Problem C(I): Rotational Spring . 42
2.6 Problem C(II): Rotational Spring 53
2.7 Problem D(I): Thermal Variation 59
2.8 Problem D(II): Thermal Variation 65
2.9 Problem E(I): Symmetry and Anti-symmetry 71
2.10 Problem E(II): Symmetry and Anti-symmetry . 75
2.11 Problem E(III): Symmetry and Anti-symmetry 82
2.12 Problem F(I): Imposed Displacement/Rotation . 92
2.13 Problem F(II): Imposed Displacement/Rotation 98
2.14 Problem G(I): Infinitely Rigid Bending Rod . 103
2.15 Problem G(II): Infinitely Rigid Bending Rod 106
2.16 Problem H: Concentrated Load 111
2.17 Problem I: Statically Determined Portion . 116
2.18 Problem J: Unusual Restraints . 122
2.19 Problem K(I): Distributed Loads/Moments 127
2.20 Problem K(II): Distributed Loads/Moments . 132
2.21 Problem L: Rod with Finite Axial Stiffness 137
3 Solution of Complex Frames 143
3.1 Worked Example 1 143
3.2 Worked Example 2 158
3.3 Worked Example 3 164
3.4 Worked Example 4 172
ixx Contents
3.5 Worked Example 5 179
3.6 Worked Example 6 185
3.7 Worked Example 7 191
3.8 Worked Example 8 197
3.9 Worked Example 9 203
3.10 Worked Example 10 . 210
3.11 Worked Example 11 . 216
3.12 Worked Example 12 . 222
3.13 Worked Example 13 . 228
3.14 Worked Example 14 . 233
3.15 Worked Example 15 . 238
3.16 Worked Example 16 . 245
3.17 Worked Example 17 . 253
3.18 Worked Example 18 . 259
3.19 Worked Example 19 . 265
3.20 Worked Example 20 . 272
3.21 Worked Example 21 . 279
3.22 Worked Example 22 . 285
3.23 Worked Example 23 . 290
3.24 Worked Example 24 . 295
3.25 Worked Example 25 . 299
3.26 Worked Example 26 . 307
3.27 Worked Example 27 . 313
3.28 Worked Example 28 . 319
3.29 Worked Example 29 . 325
3.30 Worked Example 30 . 331
Appendix A . 337
Appendix B . 343
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