كتاب Mechanics of Elastic Structures with Inclined Members

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Mechanics of Elastic Structures with Inclined Members
- Analysis of Vibration, Buckling
and Bending of X-Braced Frames
and Conical Shells
Chin Hao Chang

ويتناول الموضوعات الأتية :

1 Two Methods for Analysis of Continuum Mechanics
of Elastic Structures 1
1.1 Longitude Vibration of a Bar 1
1.1.1 Formulation – By Equation of Motion 1
1.1.2 Solutions 2
1.1.3 An Example – A Fixed-Free Bar   3
1.1.4 Orthogonality of Normal Functions – Clebsch’s
Theorem [34]   3
1.1.5 Transient and Forced Vibrations   4
1.2 Transverse Vibration of a Beam    5
1.2.1 Formulation – By Energy Method – Hamilton’s
Principle [23]   5
1.2.2 An Example – A Fixed-Free Beam 7
2 Vibrations of Inclined Bars
with End Constraint 9
2.1 One-Dimensional Model of Inclined Members    9
2.2 Formulation for Vibrations of Inclined Bars 10
2.3 Normal Functions and Frequency Equations 12
2.3.1 Inclined Bars with Hinged – “Hinged” Ends 12
2.3.2 Inclined Bars with Bottom Hinged and Top “Clamped” 15
2.3.3 Inclined Bars with Bottom Clamped
and Top “Hinged” 16
2.3.4 Inclined Bars with Bottom Clamped
and Top Clamped in Rotation 17
2.4 Orthogonality of the Normal Functions    19
3 Vibrations of Frames with Inclined Members   21
3.1 Formulation    21
3.2 Vibrations of Two-Bar Frames 23
3.2.1 Frames with All Joints Hinged 24
X Contents
3.2.2 Frames with Two Ends Fixed and Central Joint Hinged 27
3.2.3 Frames with All Joints Rigidly Connected 28
3.2.4 Frames with Two Ends Hinged
and Central Joint Rigidly Connected 30
3.3 Vibrations of Three-Bar Frames    31
3.4 Orthogonality of the Normal Functions    33
4 Vibrations of X-Braced Portal Frames    35
4.1 Free Vibration 35
4.2 Forced Vibration 42
5 Vibrations of X-Braced Multi-Story Frames    47
5.1 Formulation    47
5.2 Free Vibration 49
5.3 Vibrations due to Horizontal Forces
and Ground Motion   49
5.4 Numerical Examples   51
5.4.1 Natural Frequencies of 2- to 5-Story Frames 51
5.4.2 Modes of Free Vibrations of Two 3-Story Frames 55
5.4.3 Forced Vibrations of a 3-Story Frame 56
5.4.4 Response to Horizontal Ground Vibrations
for 3-, 4- and 5-Story Frames 57
5.4.5 Comparison with a Rectangular Unbraced Frame 58
5.5 Discussion 59
6 Effect of Rotatory Inertia and Shear Deformation
on Vibration of Inclined Bars with End Constraint   63
6.1 Formulation    63
6.2 Solutions 65
6.2.1 Inclined Bars with Hinged – “Hinged” Ends 66
6.2.2 Inclined Bars with Bottom Hinged-Top “Clamped” 69
6.2.3 Inclined Bars with Bottom Clamped-Top “Hinged” 70
6.2.4 Inclined Bars with Bottom Clamped-Top Clamped
in Rotation 71
7 Out-of-Plane Vibrations of Plane Frames 75
7.1 Formulation    75
7.2 Free Vibration 78
7.3 Forced Vibration 80
7.4 Numerical Examples   85
7.5 Discussion 87
Contents XI
8 Buckling of Inclined Columns 93
8.1 Large Deflection Theory for Buckling of Inclined Columns 94
8.2 Solutions 97
8.2.1 Inclined Columns with Two Ends Simply Supported    97
8.2.2 Inclined Columns with Lower End Fixed
and Upper End “Hinged”    101
8.2.3 Inclined Columns with Lower End Hinged
and Upper End Fixed in Rotation   103
8.2.4 Inclined Columns with Lower End Fixed
and Upper End Fixed in Rotation   103
8.3 Eigenvalue Method    104
8.4 Effect of Angle Change 108
8.5 Comparison with Conventional Approach   109
8.5.1 Mises Truss 110
8.5.2 For an Inclined Column 111
9 Inclined Girders with End Constraint Subjected
to Normal Loads 113
9.1 Formulation and Solutions    115
9.2 Effect of Angle Change 120
9.3 Comparison of Beam-Column Solutions   124
9.3.1 AISC Formula 124
9.3.2 Cheong’s Beam-Column Formula   125
10 A Boundary-Layer Solution Verified by Buckling
of a Rectangular Plate   127
10.1 Basic Equations for Buckling of a Plate
and Boundary-Layer Solution 127
10.2 Comparison of Analytic Solutions
with Experimental Results    130
11 Buckling of Conical Shells under a Single Axial Load 133
11.1 Formulation of Large Deflection Theory for Buckling
of Conical Shells 133
11.2 Membrane and Bending Solutions   136
11.3 Deformation    138
11.4 Effect of Angle Change 141
11.5 Discussion of the Results 142
12 Conical Shells of Linearly Varying Thickness Subjected
to Normal Loads 145
12.1 Basic and Characteristic Equations 145
12.2 Asymptotic Solutions 151
12.3 Particular Solutions due to Lateral Normal Loads 154
XII Contents
12.4 An Example – A Semi-Circular Cone Subjected
to Normal Loads 156
13 Asymptotic Solutions of Conical Shells
of Constant Thickness   163
13.1 Basic Equations 163
13.2 Membrane Solutions   165
13.3 Solutions of Bending Effect   167
13.4 A Particular Solution 170
13.5 Numerical Examples   171
13.5.1 The Semi-Circular Cone Studied in Chap 12    171
13.5.2 A Cantilever Complete Cone 171
13.6 Appendix 177
14 Membrane Vibrations of Conical Shells   179
14.1 Basic Equations for Membrane Vibrations 179
14.2 Vibrations in the Meridional Direction    180
14.3 Solutions for Free Vibrations 181
14.4 Numerical Examples   183
14.4.1 Cones with the Small End Fixed (S-fixed)
and Large End Free (L-free) 183
14.4.2 Cones with the Small End Free, (S-free)
and Large End Fixed (L-fixed) 184
14.4.3 Cones with Both Ends Free (Free-free)    185
14.4.4 Cones with Both Ends Fixed (Fixed-fixed) 186
14.5 Forced and Transient Vibrations    186
14.6 Axisymmetric Torsional Vibrations 188
14.7 Solutions and Frequency Equations for Four Cases 189
Appendix Elements of Matrix [Aij] of (4.7)   193
References 197
Index 201

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كتاب Mechanics of Elastic Structures with Inclined Members 761752

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