Preface p. ix
Acknowledgements p. xiv
Symbols and notations p. xv
General introduction p. xx
Part I Analysis p. 1
1 Introduction to applied analyses p. 3
1.1 General information, definitions and assumptions p. 3
1.2 Displacement-based formulation of soil-structure interaction p. 6
1.3 Soil idealisations p. 7
1.3.1 Properties of Winkler foundation p. 7
1.3.2 Properties of smooth Homogeneous Elastic Half-Space p. 8
2 Linear-elastic analysis of beams and strips on elastic foundations p. 11
2.1 Introduction to beam and strip analysis - scope and basic assumptions p. 11
2.2 Stiffness analysis of beams and strips resting on Winkler foundations p. 12
2.2.1 Development of element stiffness matrix p. 16
2.2.2 Element fixed-end forces p. 20
2.2.3 Formulation of stiffness equations for the whole beam p. 23
2.2.4 Support conditions p. 27
2.2.5 Solution of governing equations and evaluation of internal forces p. 28
2.2.6 Strip analysis as a modification of the beam treatment p. 29
2.3 Stiffness analysis of beams and strips on smooth homogeneous elastic half-space p. 32
2.3.1 Flexibility coefficients for an elastic half-space in contact with a beam p. 33
2.3.2 Flexibility coefficients for an elastic half-space in contact with a strip p. 36
2.3.3 Global stiffness matrix, governing equations and problem solution p. 37
2.4 Finite-difference analysis of beams and strips based on strain energy p. 38
2.4.1 Equivalent stiffness matrix of the structure p. 41
2.4.2 Stiffness matrices for elastic media in contact with beam p. 49
2.4.3 Equivalent nodal forces p. 53
2.4.4 Solution of governing equations and evaluation of internal forces p. 55
2.5 Examples of beam/strip analysis p. 58
2.6 Application of beam/strip analysis to laterally loaded piles, thin retaining walls and aqueducts p. 72
2.6.1 Elastic analysis of laterally loaded piles p. 72
2.6.2 Bending analysis of base slabs of thin frictionless retaining walls p. 73
2.6.3 Elastic analysis of base slabs of aqueducts p. 75
2.6.4 Examples p. 76
3 Linear-elastic analysis of circular plates on elastic foundations p. 86
3.1 Introduction - scope and basic assumptions p. 86
3.2 Structural idealisation and general formulation of the problem p. 86
3.3 Strain energy of the plate - derivation of stiffness equations p. 91
3.3.1 Curvatures, slopes and bending moments associated with nodal lines p. 91
3.3.2 Bending strain energy expressions for plate rings related to nodal lines and their derivatives p. 101
3.3.3 Plate stiffness coefficients p. 106
3.4 Stiffness matrix of Winkler foundation p. 107
3.5 Flexibility and stiffness matrices for smooth homogeneous elastic half-space p. 109
3.5.1 Flexibility coefficients for an elastic half-space in contact with a circular plate p. 109
3.5.2 Stiffness matrix for an elastic half-space associated with a circular plate p. 112
3.6 Stiffness matrix for elastic nodal restraints p. 112
3.7 Equivalent nodal forces due to loads and environmental changes p. 112
3.7.1 Equivalent nodal forces due to loads applied along nodal lines p. 113
3.7.2 Effects of loads distributed over ring elements bounded by nodal lines p. 113
3.7.3 Equivalent nodal loads due to radial moments applied along nodal lines p. 114
3.7.4 Equivalent nodal loads due to environmental changes p. 115
3.8 Solution of stiffness equations - evaluation of structural response fields p. 120
3.8.1 Radial and circumferential bending moments in sections adjacent to nodal lines p. 120
3.8.2 Estimates of contact pressure under nodal lines p. 123
3.8.3 Radial shear forces in sections adjacent to nodal lines p. 123
3.9 Examples of plate analysis p. 125
4 Linear-elastic analysis of cylindrical tanks under conditions of axial symmetry p. 153
4.1 Introduction - scope and main assumptions p. 153
4.2 General concepts p. 154
4.3 Base plate analysis - structural modelling p. 155
4.3.1 Plate bending behaviour p. 155
4.3.2 Plate in-plane behaviour p. 155
4.4 Wall cylinder analysis - structural modelling p. 160
4.4.1 Constitutive and differential equations - effect of axial forces on hoop forces and flexure p. 160
4.4.2 Wall bending behaviour p. 162
4.4.3 Ring-stiffened walls p. 164
4.4.4 Effects of loads and environmental changes - fixed-end forces p. 167
4.5 Roof structure analysis p. 175
4.5.1 Roof plate treatment p. 175
4.5.2 Axi-symmetric roof shell analysis applying Finite Element Method p. 177
4.6 Integration of individual analyses of tank sub-structures into global solution p. 192
4.6.1 Wall-plate/shell compatibility of displacements conditions p. 193
4.6.2 Global solution of a circular-cylindrical tank problem p. 199
4.7 Examples of tank analysis p. 200
Part 2 Computer software p. 233
5 General information p. 235
5.1 About BPT software p. 235
5.2 Hardware requirements and software installation p. 236
5.3 Data input p. 236
5.4 Output p. 237
5.5 Main units p. 237
5.6 Structural idealisations p. 237
5.6.1 Beam and strip modelling p. 237
5.6.2 Plate and tank's plate modelling p. 238
5.6.3 Tank wall idealisation p. 239
5.6.4 Tank's roof shell idealisation p. 240
5.7 Allowable loads - sign and plotting conventions p. 240
5.7.1 Beams and strips p. 240
5.7.2 Circular plates p. 241
5.7.3 Wall p. 241
5.7.4 Loads on tank's roof shell p. 242
5.8 Data and results file storage p. 243
5.9 Starting BPT p. 244
6 Data input p. 250
6.1 Geometry and material properties data input p. 250
6.1.1 General geometry and material properties data input p. 251
6.1.2 Input of element geometry data p. 252
6.2 Support media data input p. 256
6.2.1 Support general information input p. 256
6.2.2 Support specific data input p. 257
6.3 Load/environmental change data input p. 261
6.3.1 Uniform load and self-weight data input p. 262
6.3.2 Nodal load data input p. 263
6.3.3 Trapezoidal load data input p. 264
6.3.4 Input of data for hydrostatic load on tank p. 265
6.3.5 Data input for environmental change effects p. 265
7 Statical analysis and data/results presentation p. 268
7.1 Analysis p. 268
7.2 Previewing, printing and saving data and results p. 270
7.2.1 Previewing data details p. 271
7.2.2 Viewing results of analysis p. 271
7.3 Plotting structural response diagrams p. 272
7.3.1 Beam/strip structure p. 274
7.3.2 Cylindrical tank structure p. 274
7.3.3 Axi-symmetric circular plate p. 277
References p. 278
Index p. 280