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E-raamat: Design Principles and Analysis of Thin Concrete Shells, Domes and Folders

(Ariel University, Israel),
  • Formaat: 182 pages
  • Ilmumisaeg: 16-Nov-2015
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498726658
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Design Principles and Analysis of Thin Concrete Shells, Domes and FoldersSuurem pilt
  • Formaat: 182 pages
  • Ilmumisaeg: 16-Nov-2015
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498726658
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One of the main goals of a good and effective structural design is to decrease, as far as possible, the self-weight of structures, because they must carry the service load. This is especially important for reinforced concrete (RC) structures, as the self-weight of the material is substantial. For RC structures it is furthermore important that the whole structure or most of the structural elements are under compression with small eccentricities. Continuous spatial concrete structures satisfy the above-mentioned requirements. It is shown in this book that a span of a spatial structure is practically independent of its thickness and is a function of its geometry. It is also important to define which structure can be called a spatial one. Such a definition is given in the book and based on this definition, five types of spatial concrete structures were selected: translation shells with positive Gaussian curvature, long convex cylindrical shells, hyperbolic paraboloid shells, domes, and long folders.

To demonstrate the complex research, results of experimental, analytical, and numerical evaluation of a real RC dome are presented and discussed. The book is suitable for structural engineers, students, researchers and faculty members at universities.

Preface v
Introduction xiii
1 General Concepts of Differential Geometry and Surface Theory 1(26)
1.1 Main concepts of differential geometry
1(6)
1.1.1 Plane curves in different systems of coordinates
1(1)
1.1.2 Local elements of a curve
2(2)
1.1.3 Concave and convex curves bending point
4(1)
1.1.4 Curvature and radius of curvature
4(2)
1.1.5 Spatial curves
6(1)
1.2 Concepts in the theory of surfaces
7(5)
1.2.1 Surface equation
7(1)
1.2.2 Geometry of continuous surfaces
8(1)
1.2.3 Equations of revolution surfaces
9(1)
1.2.4 Equations of translation surfaces
9(2)
1.2.5 Surface curved coordinate system
11(1)
1.3 Surface curvature
12(5)
1.3.1 Differential of a curve
12(1)
1.3.2 Length of a curved line and surface area
12(1)
1.3.3 The surface curvature
13(3)
1.3.4 Coefficients of the second quadratic shape of the surface
16(1)
1.3.5 Shallow surface
17(1)
1.4 Numerical examples in geometry of shells
17(10)
1.4.1 Translation shell
17(2)
1.4.2 Simple hyperboloid
19(1)
1.4.3 Long cylindrical shell
19(1)
1.4.4 Saddle-shaped shell
20(1)
1.4.5 Ellipsoid of revolution
21(2)
1.4.6 Dome
23(2)
1.4.7 Cylindrical shell
25(2)
2 Structural Principles in Design of Spatial Concrete Structures 27(12)
2.1 General
27(7)
2.1.1 Definition of a spatial structure
27(2)
2.1.2 Types of spatial structures and their structural elements
29(3)
2.1.3 Openings in shells
32(2)
2.2 Reinforcement schemes in shells and folders
34(5)
2.2.1 Reinforcement types; using pre-stressed concrete; local bending moments
34(1)
2.2.2 Reinforcement schemes by calculation
34(2)
2.2.3 Constructive reinforcement in shells, domes and folders
36(3)
3 Elements of Elastic Shells' Theory 39(10)
3.1 Internal forces and deformations of thin-walled shells
39(6)
3.1.1 Two groups of internal forces
39(2)
3.1.2 Local bending
41(1)
3.1.3 Normal and bending deformations in translation shallow shells
42(3)
3.2 Equilibrium equations of the shell element
45(4)
3.2.1 Components of the deflections' vector
45(1)
3.2.2 Equilibrium equations of a thin-walled shallow shell element
46(1)
3.2.3 Boundary conditions
47(2)
4 Convex Translation Shells 49(30)
4.1 Reinforced concrete shells with steel trusses
49(9)
4.1.1 General
49(1)
4.1.2 The shell structure
50(2)
4.1.3 Supports of trusses
52(2)
4.1.4 Supporting of shells by row of columns
54(1)
4.1.5 Recommendations for shell construction
55(1)
4.1.6 The design loads and materials' consumption
55(1)
4.1.7 Example of a shell supported on row of columns
56(1)
4.1.8 Example of roofing shell with reinforced concrete arc diaphragms
57(1)
4.2 Calculation of internal membrane forces in shallow rectangular shells
58(13)
4.2.1 Function of stresses
58(1)
4.2.2 Calculation of rectangular shells with infinitely stiff edge elements
59(4)
4.2.3 Special case—square shell
63(2)
4.2.4 Buckling of convex thin-walled shallow shells
65(3)
4.2.5 Calculation of shells by local bending moment
68(3)
4.3 Numerical examples for translation shells
71(8)
4.3.1 Square shell
71(2)
4.3.2 Rectangular shell
73(3)
4.3.3 Calculation of Nxy forces in the upper truss belt
76(3)
5 Long Convex Cylindrical Shells 79(20)
5.1 Reinforced concrete shell structures
79(4)
5.1.1 General
79(1)
5.1.2 Constructive requirements to shell dimensions
80(2)
5.1.3 A cylindrical shell of the 2E terminal at the Charles de Gaulle Airport
82(1)
5.2 Calculation of internal forces in a long cylindrical shell
83(5)
5.2.1 Cylindrical shell with infinitely stiff edge element
83(2)
5.2.2 Membrane forces diagrams
85(1)
5.2.3 Bending moments in the transverse direction of the shell
86(1)
5.2.4 Local bending near the diaphragms
86(1)
5.2.5 Calculating the shell buckling capacity
87(1)
5.3 Calculating a long cylindrical shell as a simple supported beam
88(5)
5.3.1 General
88(1)
5.3.2 Cylindrical shell with finite stiffness of edge elements
89(4)
5.4 Numerical examples for calculating long cylindrical shells
93(6)
5.4.1 A cylindrical shell as a simple supported beam: calculating the reinforcement section area in the edge element
93(1)
5.4.2 Cylindrical shell with infinitely stiff edge element
94(1)
5.4.3 Calculating the buckling load for a covering shell
95(4)
6 Hyperbolic Paraboloid Shells 99(12)
6.1 Saddle shells
99(1)
6.1.1 Saddle surface equation
99(1)
6.1.2 Calculation of the shell
100(1)
6.2 Hyperbolic shells
100(8)
6.2.1 Simple hyperboloid
100(2)
6.2.2 Calculation of a simple hyperboloid
102(1)
6.2.3 Composite hyperboloid
103(3)
6.2.4 General approaches for calculating composite hypars
106(2)
6.3 Numerical examples for hypars
108(3)
6.3.1 Simple hypar—calculating the internal forces and the reinforcement section
108(1)
6.3.2 Composite hypar—calculating the edge element and the thrust force
109(2)
7 Shells of Revolution—Domes 111(26)
7.1 World-famous dome structures
111(9)
7.1.1 Millennium dome in London
111(1)
7.1.2 Aqua Park dome in Moscow
112(2)
7.1.3 Geodetic dome of the Ice Park in Eilat
114(4)
7.1.4 Reinforced concrete elliptic-shape shell in Switzerland
118(2)
7.2 Statically determined spherical shells
120(8)
7.2.1 General
120(1)
7.2.2 Calculation of membrane forces
121(4)
7.2.3 Total thrust forces in a pre-cast dome
125(1)
7.2.4 Tensile force in the supporting ring
125(1)
7.2.5 Local bending moments
126(1)
7.2.6 Critical buckling load
127(1)
7.2.7 Example of a statically determined dome
127(1)
7.3 A dome with elastic support along its perimeter
128(3)
7.4 Numerical examples for domes
131(6)
7.4.1 Hemispherical statically determined dome
131(1)
7.4.2 Calculation of the local bending moment
132(1)
7.4.3 Calculation of the supporting ring of a pre-cast dome
133(1)
7.4.4 Calculation of the elastic connection between the dome and the supporting ring
134(1)
7.4.5 Calculation of the dome critical buckling load
135(2)
8 Investigations of a Full-Scale RC Dome Under Vertical Vibrations 137(12)
8.1 General
137(1)
8.2 Analytical investigation of long span shells due to out of phase supports' vibrations
138(4)
8.3 Vibration testing of the RC dome
142(3)
8.4 Analytical investigation of RC domes vertical vibrations
145(2)
8.5 Finite elements analysis of the dome natural vibration period
147(2)
9 Long Reinforced Concrete Folders 149(10)
9.1 Constructive requirements
149(1)
9.1.1 General
149(1)
9.1.2 Main dimensions
150(1)
9.2 The folder action in the long direction
150(5)
9.2.1 Approximate calculation of a folder using an equivalent section
150(2)
9.2.2 Exact calculation of a folder with a triangular section
152(2)
9.2.3 Example for calculating a folder as an ordinary simple supported beam
154(1)
9.3 Considering the folder plates flexibility
155(4)
9.3.1 Transverse bending moments in plates
155(1)
9.3.2 Example: calculating a folder in transverse direction
156(1)
9.3.3 In-plane flexibility of plates in longitudinal direction
157(1)
9.3.4 Example of calculating the folder plates in longitudinal direction
158(1)
9.3.5 Bending of plates
158(1)
References 159(2)
Appendix. List of Symbols 161(4)
Index 165
Iskhakov, Iakov; Ribakov, Yuri
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