Design Principles and Analysis of Thin Concrete Shells, Domes and Folders

182 Pages·2015·6.168 MB·\182

by  Iakov Iskhakov (Author), Yuri Ribakov (Author)

Design Principles and Analysis
of Thin Concrete Shells,
Domes and Folders
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Design Principles and Analysis
of Thin Concrete Shells,
Domes and Folders
Iakov Iskhakov and Yuri Ribakov
Ariel University, Israel
p,
A SCIENCE PUBLISHERS BOOK
GL--Prelims with new title page.indd ii 4/25/2012 9:52:40 AM
GL--Prelims with new title page.indd ii 4/25/2012 9:52:40 AM
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Preface
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 defi ne, which structure can be called a spatial one. Such
a defi nition is given in the book and based on this defi nition, fi ve 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.
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Contents
Preface v
Introduction xiii
1. General Concepts of Differential Geometry and Surface Theory 1
1.1 Main concepts of differential geometry 1
1.1.1 Plane curves in different systems of coordinates 1
1.1.2 Local elements of a curve 2
1.1.3 Concave and convex curves bending point 4
1.1.4 Curvature and radius of curvature 4
1.1.5 Spatial curves 6
1.2 Concepts in the theory of surfaces 7
1.2.1 Surface equation 7
1.2.2 Geometry of continuous surfaces 8
1.2.3 Equations of revolution surfaces 9
1.2.4 Equations of translation surfaces 9
1.2.5 Surface curved coordinate system 11
1.3 Surface curvature 12
1.3.1 Differential of a curve 12
1.3.2 Length of a curved line and surface area 12
1.3.3 The surface curvature 13
1.3.4 Coeffi cients of the second quadratic shape of the 16
surface
1.3.5 Shallow surface 17
1.4 Numerical examples in geometry of shells 17
1.4.1 Translation shell 17
1.4.2 Simple hyperboloid 19
1.4.3 Long cylindrical shell 19
1.4.4 Saddle-shaped shell 20
1.4.5 Ellipsoid of revolution 21
1.4.6 Dome 23
1.4.7 Cylindrical shell 25
viii Design Principles and Analysis of Thin Concrete Shells, Domes and Folders
2. Structural Principles in Design of Spatial Concrete Structures 27
2.1 General 27
2.1.1 Defi nition of a spatial structure 27
2.1.2 Types of spatial structures and their structural elements 29
2.1.3 Openings in shells 32
2.2 Reinforcement schemes in shells and folders 34
2.2.1 Reinforcement types; using pre-stressed concrete; local 34
bending moments
2.2.2 Reinforcement schemes by calculation 34
2.2.3 Constructive reinforcement in shells, domes and folders 36
3. Elements of Elastic Shells’ Theory 39
3.1 Internal forces and deformations of thin-walled shells 39
3.1.1 Two groups of internal forces 39
3.1.2 Local bending 41
3.1.3 Normal and bending deformations in translation 42
shallow shells
3.2 Equilibrium equations of the shell element 45
3.2.1 Components of the defl ections’ vector 45
3.2.2 Equilibrium equations of a thin-walled shallow 46
shell element
3.2.3 Boundary conditions 47
4. Convex Translation Shells 49
4.1 Reinforced concrete shells with steel trusses 49
4.1.1 General 49
4.1.2 The shell structure 50
4.1.3 Supports of trusses 52
4.1.4 Supporting of shells by row of columns 54
4.1.5 Recommendations for shell construction 55
4.1.6 The design loads and materials’ consumption 55
4.1.7 Example of a shell supported on row of columns 56
4.1.8 Example of roofi ng shell with reinforced concrete arc 57
diaphragms
4.2 Calculation of internal membrane forces in shallow 58
rectangular shells
4.2.1 Function of stresses 58
4.2.2 Calculation of rectangular shells with infi nitely stiff edge 59
elements
4.2.3 Special case—square shell 63
4.2.4 Buckling of convex thin-walled shallow shells 65
4.2.5 Calculation of shells by local bending moment 68
Contents ix
4.3 Numerical examples for translation shells 71
4.3.1 Square shell 71
4.3.2 Rectangular shell 73
4.3.3 Calculation of N forces in the upper truss belt 76
xy
5. Long Convex Cylindrical Shells 79
5.1 Reinforced concrete shell structures 79
5.1.1 General 79
5.1.2 Constructive requirements to shell dimensions 80
5.1.3 A cylindrical shell of the 2E terminal at the Charles 82
de Gaulle Airport
5.2 Calculation of internal forces in a long cylindrical shell 83
5.2.1 Cylindrical shell with infi nitely stiff edge element 83
5.2.2 Membrane forces diagrams 85
5.2.3 Bending moments in the transverse direction of 86
the shell
5.2.4 Local bending near the diaphragms 86
5.2.5 Calculating the shell buckling capacity 87
5.3 Calculating a long cylindrical shell as a simple supported 88
beam
5.3.1 General 88
5.3.2 Cylindrical shell with fi nite stiffness of edge elements 89
5.4 Numerical examples for calculating long cylindrical shells 93
5.4.1 A cylindrical shell as a simple supported beam: 93
calculating the reinforcement section area in the edge
element
5.4.2 Cylindrical shell with infi nitely stiff edge element 94
5.4.3 Calculating the buckling load for a covering shell 95
6. Hyperbolic Paraboloid Shells 99
6.1 Saddle shells 99
6.1.1 Saddle surface equation 99
6.1.2 Calculation of the shell 100
6.2 Hyperbolic shells 100
6.2.1 Simple hyperboloid 100
6.2.2 Calculation of a simple hyperboloid 102
6.2.3 Composite hyperboloid 103
6.2.4 General approaches for calculating composite hypars 106
6.3 Numerical examples for hypars 108
6.3.1 Simple hypar—calculating the internal forces and the 108
reinforcement section
6.3.2 Composite hypar—calculating the edge element and the 109
thrust force