Seismic Design and Analysis of Tanks

Gian Michele Calvi, PhD, is a Full Professor of Structural Engineering at the IUSS Pavia and adjunct professor at North Carolina State University in the Department of Civil, Construction, and Environmental Engineering, He is also the founder of the EU-CENTRE Foundation for Training and Research in Earthquake Engineering and is currently the Director of the Internatonal Association of Earthquake Engineering. Roberto Nascimbene, PhD, is an Associate Professor of Structural Engineering at the IUSS Pavia and adjunct professor at University of Pavia in the Department of Civil Engineering and Architecte. He is also a "National committee member" in European UNI/CT 021/SC 03 "Steel Structures" and member of the Project Team SC8.T5 - Evolution of EN 1998-4 and EN 1998-6 "M/515 phase 3 or 4". .

Preface xi Acknowledgments xiii Introduction xv 1 Appealing shell structures 1 1.1 Beams and arches . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Plates and vaults . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Rectangular and cylindrical tanks . . . . . . . . . . . . . . . . . . 12 1.4 Seismic behaviour of tanks . . . . . . . . . . . . . . . . . . . . . 23 1.5 Field observation of damage to tanks induced by seismic events 38 1.6 Design consideration . . . . . . . . . . . . . . . . . . . . . . . . . 48 1.7 A simplified description of seismic response of tanks . . . . . . . 57 1.8 Discussion on existing codes . . . . . . . . . . . . . . . . . . . . . 60 1.9 Content of the book . . . . . . . . . . . . . . . . . . . . . . . . . 66 2 Above ground anchored rigid tanks 67 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.2 Circular vertical anchored tanks . . . . . . . . . . . . . . . . . . . 68 2.2.1 Impulsive pressure component . . . . . . . . . . . . . 71 2.2.2 Convective pressure component . . . . . . . . . . . . 81 2.2.3 Effects of vertical component of the seismic action . 89 vii 2.2.4 Effects of tank inertia . . . . . . . . . . . . . . . . . . 92 2.2.5 Periods of vibration . . . . . . . . . . . . . . . . . . . 93 2.2.6 Effects of liquid viscosity . . . . . . . . . . . . . . . . 99 2.2.7 Effects of inhomogeneous liquids . . . . . . . . . . . 102 2.2.8 Convective wave displacement and pressure . . . . . 111 2.2.9 Combination of pressures and behavior factor . . . . 118 2.2.10 Tank forces and stresses . . . . . . . . . . . . . . . . 124 2.2.11 Effects of rocking motion . . . . . . . . . . . . . . . . 131 2.3 Rectangular anchored tanks . . . . . . . . . . . . . . . . . . . . . 136 2.3.1 Impulsive and convective pressure components . . . 136 2.3.2 Periods of vibration . . . . . . . . . . . . . . . . . . . 141 2.3.3 Convective wave displacement . . . . . . . . . . . . . 143 2.3.4 Tank forces and stresses . . . . . . . . . . . . . . . . 143 3 Above ground unanchored rigid tanks 149 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 3.2 Vertical cylindrical tanks . . . . . . . . . . . . . . . . . . . . . . . 153 3.2.1 Axial membrane stress in shell wall . . . . . . . . . . 161 3.2.2 Shell uplift . . . . . . . . . . . . . . . . . . . . . . . . 165 3.2.3 Radial membrane stress at base . . . . . . . . . . . . 167 3.2.4 Plastic rotation at base . . . . . . . . . . . . . . . . . 168 3.3 Rectangular tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 4 Elevated tanks 175 viii 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 4.2 Single lumped-mass model . . . . . . . . . . . . . . . . . . . . . . 182 4.3 Two uncoupled mass model . . . . . . . . . . . . . . . . . . . . . 186 4.4 Two coupled masses model . . . . . . . . . . . . . . . . . . . . . 190 5 Flexible tanks 201 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 5.2 Impulsive pressure component . . . . . . . . . . . . . . . . . . . . 205 5.2.1 Vertical cylindrical tanks . . . . . . . . . . . . . . . . 205 5.2.2 Rectangular tanks . . . . . . . . . . . . . . . . . . . . 219 5.3 Effects of vertical component of the seismic action . . . . . . . 226 5.4 Periods of vibration . . . . . . . . . . . . . . . . . . . . . . . . . . 231 5.5 Combination of pressures . . . . . . . . . . . . . . . . . . . . . . 246 5.6 Tank forces and stresses . . . . . . . . . . . . . . . . . . . . . . . 255 5.6.1 Vertical cylindrical tanks . . . . . . . . . . . . . . . . 257 5.6.2 Rectangular tanks . . . . . . . . . . . . . . . . . . . . 270 5.7 Effects of rocking motion . . . . . . . . . . . . . . . . . . . . . . 272 6 Other peculiar principles 277 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 6.2 Effects of soil-structure interaction . . . . . . . . . . . . . . . . . 278 6.3 Flow-dampening devices . . . . . . . . . . . . . . . . . . . . . . . 288 6.4 Base-isolation devices . . . . . . . . . . . . . . . . . . . . . . . . 302 6.5 Underground rigid tanks . . . . . . . . . . . . . . . . . . . . . . . 313 ix 6.6 Horizontal tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 6.7 Conical tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 7 General design principles 333 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 7.2 Requirements for steel tanks . . . . . . . . . . . . . . . . . . . . 334 7.2.1 Base plate . . . . . . . . . . . . . . . . . . . . . . . . 335 7.2.2 Sidewall . . . . . . . . . . . . . . . . . . . . . . . . . . 339 7.2.3 Openings . . . . . . . . . . . . . . . . . . . . . . . . . 348 7.2.4 Roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 7.2.5 Foundation . . . . . . . . . . . . . . . . . . . . . . . . 362 7.2.6 Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . 373 7.2.7 Buckling limit state . . . . . . . . . . . . . . . . . . . 406 7.3 Requirements for concrete tanks . . . . . . . . . . . . . . . . . . 423 7.3.1 Serviceability limit state . . . . . . . . . . . . . . . . 425 7.3.2 Ultimate limit state . . . . . . . . . . . . . . . . . . . 435 7.3.3 Detailing and particular rules . . . . . . . . . . . . . . 436 A Dimensionless design charts 463 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 B Codes, Manuals, Recommendations, Guidelines, Reports 471 B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486