Circular storage tanks and silos
Ghali, A.
Circular storage tanks and silos - Ed.2 - London & New York Routledge 2010 - xviii, 330,ip.
Contents Preface m second edition xi Preface to first edition xiii The SI system of units ami British equivalent xv Notation xvii PART I Analysis 1 1 Introduction to the analysis of circular tanks 3 1.1 Scope 3 1.2 Basic assumptions 4 1.3 General methods of structural analysis 4 1.4 The displacement method 5 1.5 The force method 7 1.6 Flexibility and stiffness matrices 8 1.7 Moment distribution 9 1.7.1 Norarion and sign convention 10 1.7.2 Steps of analysis 11 1.8 Adjusted stiffness and flexibility coefficients 11 1.9 General 13 2 Circular walls of constant thickness 15 2.1 Introduction 15 2.2 Beam-on-elastic-foundation analogy 15 2.3 General solution of the differential equation of the deflection of a wall of constant thickness 18 2.4 Characteristic parameters 20 2.5 Stiffness and flexibility matrices 21 2.6 End-rotational stiffness and carry-over factor 24 2.7 Fixed-end forces 25 2.7.1 Uniform or linearly varying load 25 2.7.2 Concentrated load 26 2.7.3 Couple 28 2.8 Semi-infinite beam on elastic foundation and simplified equations for long cylinders 29 2.9 Classification of beams on elastic foundation and circular walls as long or shoit 32 2.10 Examples 32 Example 2.1 Circular wall hinged at the bottom 32 Example 2.2 Circular wall, on bearing pads 34 Example 2.3 Circular wall, with thickness change 35 2.11 General 39 3 Circular walls of varying thickness 40 3.1 Introduction 40 3.2 Finite-difference equations 41 3.3 Boundary conditions and reactions 45 3.4 Generation of simultaneous equations 47 3.5 Sudden change in thickness 47 3.6 Examples 48 Example 3.1 Circular wall, on bearing pads, with linearly varying load 48 Example 3.2 Circular wall, with bottom edge cncastrc and top edge hinged 50 3.7 Flexibility and stiffness of circular walls of variable thickness 52 3.8 Effect of temperature 53 3.9 General 57 4 Design tables and examples of their use 58 4.1 Introduction 58 4.2 Description of design tables 58 4.3 Variables 61 4.4 Arbitrary edge conditions 61 4.5 Examples 62 Example 4.1 Circular wall of varying thickness, on bearing pads, with trapezoidal normal load 62 Example 4.2 Circular wall, with circumferential prestressing tendons 64 Example 4.3 Reinforced tank, on rigid found a (ion 67 Example 4.4 Circular wall, with variable thickness, subjected to temperature rise varying linearly through the thickness 72 4.6 Long cylinders 79 Example 4.5 Circular wall, fixed at the base and free at the top 81 4.7 Poisson's ratio 82 4.8 Beams on elastic foundations 82 4.9 General 84 5 Finite-element analysis 85 5.1Introduction 85 5.2 Nodal displacements and nodal forces 85 5.3 Transformation of stiffness matrix 89 5.4 Displacement interpolations 89 5.5 Stress resultants 90 5.6 Stiffness matrix of individual element 91 5.7 Analysis for effect of temperature 92 5.8 Assemblage of stiffness matrices and load vectors 93 5.9 Nodal forces 95 5.10 Examples 96 Example 5.1 Cylindrical wall, with uniform radial force on bottom edge 96 Example 5,2 Cylindrical wall, bottom edge encastre and top edge free, with temperature rise 98 Example 5.3 Circular plate, with outer edge eneastre, subjected to uniform load 99 Example 5.4 Circular cylinder, monolithic with spherical dome 100 6 Time-dependent effects 102 6.1 Introduction 102 6.2 Creep and shrinkage of concrete 102 6.3 Relaxation of prestressed steel 106 6.4 Basic equations for stress and strain distributions in a homogeneous section 106 6.5 Time-dependent stress and strain in a section 109 6.5.1 Special case.- section subjected to axial force only 112 Example 6.1 Time-dependent stresses in a prvstressed section: effect of presence of' non-prestressed steel 114 6.6 Normal force N and bending moment M due to prestressing 115 6.6.1 Circumferential prestressing 116 6.6.2 Vertical prestressing of a circular-cylindrical wall 117 Example 6.2 Internal forces due to vertical prestressing of a circular wall 118 6.7 Time-dependent internal forces 119 Example 6.3 Time-dependent internal forces in a cylindrical wall on elastomeric pads 122 Example 6-4 Time-dependent internal forces in a cylindrical tank wall monolithic with base 126 7 Thermal stresses 131 7.1 introduction 131 7.2 Effects of temperature variation in a cylindrical wall 133 7.3 Linear temperature variation through wall thickness 135 7.4 Thermal internal forces in deep tanks and silos 135 7.4.1 Bottom edge encastre and top edge free 136 7.4.2 Bottom edge hinged and top edge free 136 7.4.3 Bottom edge free to slide and rotate and top edge free 136 Example 7.1 Thermal stresses in a cylindrical concrete wall 137 7.5 Internal forces due to shrinkage of concrete 142 Example 7.2 Shrinkage stresses in a cylindrical concrete wall 142 7.6 Significance of linear analysis 145 8 Optimum design of prestressing 146 8.1 Introduction 146 8.2 Trapezoidal distribution of circumferential prestressing 146 Example 8.1 Trapezoidal distribution of circumferential prestressing; cylindrical wall encastre at the bottom edge 148 8.3 Improved distribution of circumferential prestressing 149 Example 8.2 Improved distribution of circumferential prestressing 150 8.4 Design objectives 153 8.5 Design of circumferential prestress distribution 154 Example 8.3 Design for distribution of circumferential prestressing 156 9 Effects of cracking of concrete 161 9.1 Introduction 161 9.2 Stress and strain in a cracked section 161 9.3 Decompression forces 162 9.4 Equilibrium equations 163 9.5 Rectangular section analysis 165 9.6 Tension stiffening 166 9.7 Crack width 167 Example 9.1 Analysis of cracked prestressed section 169 9.8 Time-dependent strain and stress in cracked sections 173 9.9 Influence of cracking on internal forces 173 10 Control of cracking in concrete tanks and silos 176 10.1 Introduction 176 10.2 Causes of cracking 177 10.3 Tensile strength of concrete 177 10.4 Force-induced cracking 178 10.4.1 Effect of prestressing 381 Example 10.1 Hoop force versus elongation for a circular reinforced concrete ring 182 10.5 Displacement-induced cracking 184 10.6 Cracking by bending: force-induced and displacement-induced 186 10.7 Motives for crack control 187 1O.8 Means of controlling cracking 188 10.9 Minimum reinforcement to avoid yielding of reinforcement 188 10.10 Amount of reinforcement to limit crack width:displacement-induced cracking 191 Example 10.2 Reinforcement required to limit the width of cracks caused by temperature variation 192 10.11 Change in steel stress at cracking 193 PART II Design tables 197 11 Tables for analysis of circular walls of thickness varying linearly from top to bottom 199 12 Tables for analysis of circular walls of thickness constant in upper part and varying linearly in lower three-tenths of height 260 Appendix: Stiffness and fixed-end forces for circular and annular plates 320 A.1 Governing differentia! equation 320 A.2 Stiffness and fixed-end moments of eircular plates 321 A.3 Stiffness of annular piates 322 A.4 Fixed-end forces of annular plates 326 A.5 Approximate analysis for annular plates 327 Index 328
0419235604
690.53 / GHA
Circular storage tanks and silos - Ed.2 - London & New York Routledge 2010 - xviii, 330,ip.
Contents Preface m second edition xi Preface to first edition xiii The SI system of units ami British equivalent xv Notation xvii PART I Analysis 1 1 Introduction to the analysis of circular tanks 3 1.1 Scope 3 1.2 Basic assumptions 4 1.3 General methods of structural analysis 4 1.4 The displacement method 5 1.5 The force method 7 1.6 Flexibility and stiffness matrices 8 1.7 Moment distribution 9 1.7.1 Norarion and sign convention 10 1.7.2 Steps of analysis 11 1.8 Adjusted stiffness and flexibility coefficients 11 1.9 General 13 2 Circular walls of constant thickness 15 2.1 Introduction 15 2.2 Beam-on-elastic-foundation analogy 15 2.3 General solution of the differential equation of the deflection of a wall of constant thickness 18 2.4 Characteristic parameters 20 2.5 Stiffness and flexibility matrices 21 2.6 End-rotational stiffness and carry-over factor 24 2.7 Fixed-end forces 25 2.7.1 Uniform or linearly varying load 25 2.7.2 Concentrated load 26 2.7.3 Couple 28 2.8 Semi-infinite beam on elastic foundation and simplified equations for long cylinders 29 2.9 Classification of beams on elastic foundation and circular walls as long or shoit 32 2.10 Examples 32 Example 2.1 Circular wall hinged at the bottom 32 Example 2.2 Circular wall, on bearing pads 34 Example 2.3 Circular wall, with thickness change 35 2.11 General 39 3 Circular walls of varying thickness 40 3.1 Introduction 40 3.2 Finite-difference equations 41 3.3 Boundary conditions and reactions 45 3.4 Generation of simultaneous equations 47 3.5 Sudden change in thickness 47 3.6 Examples 48 Example 3.1 Circular wall, on bearing pads, with linearly varying load 48 Example 3.2 Circular wall, with bottom edge cncastrc and top edge hinged 50 3.7 Flexibility and stiffness of circular walls of variable thickness 52 3.8 Effect of temperature 53 3.9 General 57 4 Design tables and examples of their use 58 4.1 Introduction 58 4.2 Description of design tables 58 4.3 Variables 61 4.4 Arbitrary edge conditions 61 4.5 Examples 62 Example 4.1 Circular wall of varying thickness, on bearing pads, with trapezoidal normal load 62 Example 4.2 Circular wall, with circumferential prestressing tendons 64 Example 4.3 Reinforced tank, on rigid found a (ion 67 Example 4.4 Circular wall, with variable thickness, subjected to temperature rise varying linearly through the thickness 72 4.6 Long cylinders 79 Example 4.5 Circular wall, fixed at the base and free at the top 81 4.7 Poisson's ratio 82 4.8 Beams on elastic foundations 82 4.9 General 84 5 Finite-element analysis 85 5.1Introduction 85 5.2 Nodal displacements and nodal forces 85 5.3 Transformation of stiffness matrix 89 5.4 Displacement interpolations 89 5.5 Stress resultants 90 5.6 Stiffness matrix of individual element 91 5.7 Analysis for effect of temperature 92 5.8 Assemblage of stiffness matrices and load vectors 93 5.9 Nodal forces 95 5.10 Examples 96 Example 5.1 Cylindrical wall, with uniform radial force on bottom edge 96 Example 5,2 Cylindrical wall, bottom edge encastre and top edge free, with temperature rise 98 Example 5.3 Circular plate, with outer edge eneastre, subjected to uniform load 99 Example 5.4 Circular cylinder, monolithic with spherical dome 100 6 Time-dependent effects 102 6.1 Introduction 102 6.2 Creep and shrinkage of concrete 102 6.3 Relaxation of prestressed steel 106 6.4 Basic equations for stress and strain distributions in a homogeneous section 106 6.5 Time-dependent stress and strain in a section 109 6.5.1 Special case.- section subjected to axial force only 112 Example 6.1 Time-dependent stresses in a prvstressed section: effect of presence of' non-prestressed steel 114 6.6 Normal force N and bending moment M due to prestressing 115 6.6.1 Circumferential prestressing 116 6.6.2 Vertical prestressing of a circular-cylindrical wall 117 Example 6.2 Internal forces due to vertical prestressing of a circular wall 118 6.7 Time-dependent internal forces 119 Example 6.3 Time-dependent internal forces in a cylindrical wall on elastomeric pads 122 Example 6-4 Time-dependent internal forces in a cylindrical tank wall monolithic with base 126 7 Thermal stresses 131 7.1 introduction 131 7.2 Effects of temperature variation in a cylindrical wall 133 7.3 Linear temperature variation through wall thickness 135 7.4 Thermal internal forces in deep tanks and silos 135 7.4.1 Bottom edge encastre and top edge free 136 7.4.2 Bottom edge hinged and top edge free 136 7.4.3 Bottom edge free to slide and rotate and top edge free 136 Example 7.1 Thermal stresses in a cylindrical concrete wall 137 7.5 Internal forces due to shrinkage of concrete 142 Example 7.2 Shrinkage stresses in a cylindrical concrete wall 142 7.6 Significance of linear analysis 145 8 Optimum design of prestressing 146 8.1 Introduction 146 8.2 Trapezoidal distribution of circumferential prestressing 146 Example 8.1 Trapezoidal distribution of circumferential prestressing; cylindrical wall encastre at the bottom edge 148 8.3 Improved distribution of circumferential prestressing 149 Example 8.2 Improved distribution of circumferential prestressing 150 8.4 Design objectives 153 8.5 Design of circumferential prestress distribution 154 Example 8.3 Design for distribution of circumferential prestressing 156 9 Effects of cracking of concrete 161 9.1 Introduction 161 9.2 Stress and strain in a cracked section 161 9.3 Decompression forces 162 9.4 Equilibrium equations 163 9.5 Rectangular section analysis 165 9.6 Tension stiffening 166 9.7 Crack width 167 Example 9.1 Analysis of cracked prestressed section 169 9.8 Time-dependent strain and stress in cracked sections 173 9.9 Influence of cracking on internal forces 173 10 Control of cracking in concrete tanks and silos 176 10.1 Introduction 176 10.2 Causes of cracking 177 10.3 Tensile strength of concrete 177 10.4 Force-induced cracking 178 10.4.1 Effect of prestressing 381 Example 10.1 Hoop force versus elongation for a circular reinforced concrete ring 182 10.5 Displacement-induced cracking 184 10.6 Cracking by bending: force-induced and displacement-induced 186 10.7 Motives for crack control 187 1O.8 Means of controlling cracking 188 10.9 Minimum reinforcement to avoid yielding of reinforcement 188 10.10 Amount of reinforcement to limit crack width:displacement-induced cracking 191 Example 10.2 Reinforcement required to limit the width of cracks caused by temperature variation 192 10.11 Change in steel stress at cracking 193 PART II Design tables 197 11 Tables for analysis of circular walls of thickness varying linearly from top to bottom 199 12 Tables for analysis of circular walls of thickness constant in upper part and varying linearly in lower three-tenths of height 260 Appendix: Stiffness and fixed-end forces for circular and annular plates 320 A.1 Governing differentia! equation 320 A.2 Stiffness and fixed-end moments of eircular plates 321 A.3 Stiffness of annular piates 322 A.4 Fixed-end forces of annular plates 326 A.5 Approximate analysis for annular plates 327 Index 328
0419235604
690.53 / GHA