Draft DRAFT
Lecture Notes in:
STRUCTURAL CONCEPTS AND SYSTEMS
FOR ARCHITECTS
Victor E. Saouma
Dept. of Civil Environmental and Architectural Engineering
University of Colorado, Boulder, CO 80309-0428
,Draft
Contents
1 INTRODUCTION 15
1.1 Science and Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2 Structural Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Structures and their Surroundings . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Architecture & Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Architectural Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6 Architectural Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.7 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.8 Structural Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.9 Load Transfer Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.10 Structure Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.11 Structural Engineering Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.12 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2 LOADS 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Vertical Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Dead Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Live Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
E 2-1 Live Load Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.3 Snow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Lateral Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
E 2-2 Wind Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.2 Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
E 2-3 Earthquake Load on a Frame . . . . . . . . . . . . . . . . . . . . . . . . . 44
E 2-4 Earthquake Load on a Tall Building, (Schueller 1996) . . . . . . . . . . . 45
2.4 Other Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.1 Hydrostatic and Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
E 2-5 Hydrostatic Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.2 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
E 2-6 Thermal Expansion/Stress (Schueller 1996) . . . . . . . . . . . . . . . . . 48
2.4.3 Bridge Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.4.4 Impact Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 Other Important Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5.1 Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5.2 Load Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
,Draft
5.4 Flexure .............................................................................................................................. 112
CONTENTS
5.4.1 Basic Kinematic Assumption; Curvature ......................................................... 112
5.4.2 Stress-Strain Relations ......................................................................................... 113
5
5.4.3 Internal Equilibrium; Section Properties ............................................................ 113
5.4.3.1 ΣFx = 0; Neutral Axis......................................................................... 113
5.4.3.2 ΣM = 0; Moment of Inertia .............................................................. 114
5.4.4 Beam Formula ..................................................................................................... 114
E 5-10 Design Example .................................................................................................... 116
5.4.5 Approximate Analysis......................................................................................... 117
E 5-11 Approximate Analysis of a Statically Indeterminate beam ............................ 117
6 Case Study II: GEORGE WASHINGTON BRIDGE 123
6.1 Theory................................................................................................................................ 123
6.2 The Case Study ................................................................................................................ 126
6.2.1 Geometry .............................................................................................................. 126
6.2.2 Loads ..................................................................................................................... 127
6.2.3 Cable Forces ......................................................................................................... 129
6.2.4 Reactions .............................................................................................................. 129
7 A BRIEF HISTORY OF STRUCTURAL ARCHITECTURE 133
7.1 Before the Greeks ............................................................................................................. 133
7.2 Greeks................................................................................................................................ 133
7.3 Romans .............................................................................................................................. 135
7.4 The Medieval Period (477-1492) ..................................................................................... 136
7.5 The Renaissance .............................................................................................................. 138
7.5.1 Leonardo da Vinci 1452-1519.............................................................................. 138
7.5.2 Brunelleschi 1377-1446 ......................................................................................... 139
7.5.3 Alberti 1404-1472 .................................................................................................. 140
7.5.4 Palladio 1508-1580 ................................................................................................ 140
7.5.5 Stevin .................................................................................................................... 142
7.5.6 Galileo 1564-1642 .................................................................................................. 142
7.6 Pre Modern Period, Seventeenth Century ..................................................................... 144
7.6.1 Hooke, 1635-1703 .................................................................................................. 144
7.6.2 Newton, 1642-1727................................................................................................ 145
7.6.3 Bernoulli Family 1654-1782 ................................................................................. 147
7.6.4 Euler 1707-1783 ..................................................................................................... 147
7.7 The pre-Modern Period; Coulomb and Navier ............................................................. 149
7.8 The Modern Period (1857-Present) ................................................................................ 150
7.8.1 Structures/Mechanics ........................................................................................ 150
7.8.2 Eiffel Tower .......................................................................................................... 150
7.8.3 Sullivan 1856-1924 ................................................................................................ 150
7.8.4 Roebling, 1806-1869.............................................................................................. 151
7.8.5 Maillart ................................................................................................................. 151
7.8.6 Nervi, 1891-1979 ................................................................................................... 152
7.8.7 Khan ...................................................................................................................... 152
7.8.8 et al......................................................................................................................... 153
CONTENTS 7
Victor Saouma Structural Concepts and Systems for Architects
, Draft
12 PRESTRESSED CONCRETE
CONTENTS 1975
12.1 Introduction ...................................................................................................................... 197
12.1.1 Materials .............................................................................................................. 197
12.1.2 Prestressing Forces .............................................................................................. 200
12.1.3 Assumptions ........................................................................................................ 200
12.1.4 Tendon Configuration......................................................................................... 200
12.1.5 Equivalent Load ................................................................................................... 200
12.1.6 Load Deformation ............................................................................................... 202
12.2 Flexural Stresses ...............................................................................................................202
E 12-1 Prestressed Concrete I Beam .............................................................................. 204
12.3 Case Study: Walnut Lane Bridge ................................................................................... 206
12.3.1 Cross-Section Properties ....................................................................................... 206
12.3.2 Prestressing ......................................................................................................... 208
12.3.3 Loads ..................................................................................................................... 209
12.3.4 Flexural Stresses ................................................................................................. 209
13 ARCHES and CURVED STRUCTURES 211
13.1 Arches ................................................................................................................................ 211
13.1.1 Statically Determinate ....................................................................................... 214
E 13-1 Three Hinged Arch, Point Loads. (Gerstle 1974) ............................................ 214
E 13-2 Semi-Circular Arch, (Gerstle 1974) .................................................................... 215
13.1.2 Statically Indeterminate .................................................................................... 217
E 13-3 Statically Indeterminate Arch, (Kinney 1957) ................................................. 217
13.2 Curved Space Structures ................................................................................................. 220
E 13-4 Semi-Circular Box Girder, (Gerstle 1974) ......................................................... 220
13.2.1 Theory ................................................................................................................... 222
13.2.1.1 Geometry .............................................................................................. 222
13.2.1.2 Equilibrium.......................................................................................... 223
E 13-5 Internal Forces in an Helicoidal Cantilevered Girder, (Gerstle 1974) ............ 224
14 BUILDING STRUCTURES 229
14.1 Introduction ...................................................................................................................... 229
14.1.1 Beam Column Connections ................................................................................. 229
14.1.2 Behavior of Simple Frames ................................................................................. 229
14.1.3 Eccentricity of Applied Loads ............................................................................. 230
14.2 Buildings Structures ......................................................................................................... 233
14.2.1 Wall Subsystems ................................................................................................. 233
14.2.1.1 Example: Concrete Shear Wall ........................................................... 233
14.2.1.2 Example: Trussed Shear Wall ............................................................. 235
14.2.2 Shaft Systems ...................................................................................................... 236
14.2.2.1 Example: Tube Subsystem ................................................................. 236
14.2.3 Rigid Frames........................................................................................................ 237
14.3 Approximate Analysis of Buildings ................................................................................ 238
14.3.1 Vertical Loads ...................................................................................................... 239
14.3.2 Horizontal Loads .................................................................................................. 241
14.3.2.1 Portal Method ...................................................................................... 241
E 14-1 Approximate Analysis of a Frame subjected to Vertical and Horizontal Loads243
14.4 Lateral Deflections ........................................................................................................... 253
Victor Saouma Structural Concepts and Systems for Architects
Lecture Notes in:
STRUCTURAL CONCEPTS AND SYSTEMS
FOR ARCHITECTS
Victor E. Saouma
Dept. of Civil Environmental and Architectural Engineering
University of Colorado, Boulder, CO 80309-0428
,Draft
Contents
1 INTRODUCTION 15
1.1 Science and Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2 Structural Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Structures and their Surroundings . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Architecture & Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Architectural Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6 Architectural Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.7 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.8 Structural Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.9 Load Transfer Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.10 Structure Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.11 Structural Engineering Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.12 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2 LOADS 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Vertical Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Dead Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Live Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
E 2-1 Live Load Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.3 Snow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Lateral Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
E 2-2 Wind Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.2 Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
E 2-3 Earthquake Load on a Frame . . . . . . . . . . . . . . . . . . . . . . . . . 44
E 2-4 Earthquake Load on a Tall Building, (Schueller 1996) . . . . . . . . . . . 45
2.4 Other Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.1 Hydrostatic and Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
E 2-5 Hydrostatic Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.2 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
E 2-6 Thermal Expansion/Stress (Schueller 1996) . . . . . . . . . . . . . . . . . 48
2.4.3 Bridge Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.4.4 Impact Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 Other Important Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5.1 Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5.2 Load Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
,Draft
5.4 Flexure .............................................................................................................................. 112
CONTENTS
5.4.1 Basic Kinematic Assumption; Curvature ......................................................... 112
5.4.2 Stress-Strain Relations ......................................................................................... 113
5
5.4.3 Internal Equilibrium; Section Properties ............................................................ 113
5.4.3.1 ΣFx = 0; Neutral Axis......................................................................... 113
5.4.3.2 ΣM = 0; Moment of Inertia .............................................................. 114
5.4.4 Beam Formula ..................................................................................................... 114
E 5-10 Design Example .................................................................................................... 116
5.4.5 Approximate Analysis......................................................................................... 117
E 5-11 Approximate Analysis of a Statically Indeterminate beam ............................ 117
6 Case Study II: GEORGE WASHINGTON BRIDGE 123
6.1 Theory................................................................................................................................ 123
6.2 The Case Study ................................................................................................................ 126
6.2.1 Geometry .............................................................................................................. 126
6.2.2 Loads ..................................................................................................................... 127
6.2.3 Cable Forces ......................................................................................................... 129
6.2.4 Reactions .............................................................................................................. 129
7 A BRIEF HISTORY OF STRUCTURAL ARCHITECTURE 133
7.1 Before the Greeks ............................................................................................................. 133
7.2 Greeks................................................................................................................................ 133
7.3 Romans .............................................................................................................................. 135
7.4 The Medieval Period (477-1492) ..................................................................................... 136
7.5 The Renaissance .............................................................................................................. 138
7.5.1 Leonardo da Vinci 1452-1519.............................................................................. 138
7.5.2 Brunelleschi 1377-1446 ......................................................................................... 139
7.5.3 Alberti 1404-1472 .................................................................................................. 140
7.5.4 Palladio 1508-1580 ................................................................................................ 140
7.5.5 Stevin .................................................................................................................... 142
7.5.6 Galileo 1564-1642 .................................................................................................. 142
7.6 Pre Modern Period, Seventeenth Century ..................................................................... 144
7.6.1 Hooke, 1635-1703 .................................................................................................. 144
7.6.2 Newton, 1642-1727................................................................................................ 145
7.6.3 Bernoulli Family 1654-1782 ................................................................................. 147
7.6.4 Euler 1707-1783 ..................................................................................................... 147
7.7 The pre-Modern Period; Coulomb and Navier ............................................................. 149
7.8 The Modern Period (1857-Present) ................................................................................ 150
7.8.1 Structures/Mechanics ........................................................................................ 150
7.8.2 Eiffel Tower .......................................................................................................... 150
7.8.3 Sullivan 1856-1924 ................................................................................................ 150
7.8.4 Roebling, 1806-1869.............................................................................................. 151
7.8.5 Maillart ................................................................................................................. 151
7.8.6 Nervi, 1891-1979 ................................................................................................... 152
7.8.7 Khan ...................................................................................................................... 152
7.8.8 et al......................................................................................................................... 153
CONTENTS 7
Victor Saouma Structural Concepts and Systems for Architects
, Draft
12 PRESTRESSED CONCRETE
CONTENTS 1975
12.1 Introduction ...................................................................................................................... 197
12.1.1 Materials .............................................................................................................. 197
12.1.2 Prestressing Forces .............................................................................................. 200
12.1.3 Assumptions ........................................................................................................ 200
12.1.4 Tendon Configuration......................................................................................... 200
12.1.5 Equivalent Load ................................................................................................... 200
12.1.6 Load Deformation ............................................................................................... 202
12.2 Flexural Stresses ...............................................................................................................202
E 12-1 Prestressed Concrete I Beam .............................................................................. 204
12.3 Case Study: Walnut Lane Bridge ................................................................................... 206
12.3.1 Cross-Section Properties ....................................................................................... 206
12.3.2 Prestressing ......................................................................................................... 208
12.3.3 Loads ..................................................................................................................... 209
12.3.4 Flexural Stresses ................................................................................................. 209
13 ARCHES and CURVED STRUCTURES 211
13.1 Arches ................................................................................................................................ 211
13.1.1 Statically Determinate ....................................................................................... 214
E 13-1 Three Hinged Arch, Point Loads. (Gerstle 1974) ............................................ 214
E 13-2 Semi-Circular Arch, (Gerstle 1974) .................................................................... 215
13.1.2 Statically Indeterminate .................................................................................... 217
E 13-3 Statically Indeterminate Arch, (Kinney 1957) ................................................. 217
13.2 Curved Space Structures ................................................................................................. 220
E 13-4 Semi-Circular Box Girder, (Gerstle 1974) ......................................................... 220
13.2.1 Theory ................................................................................................................... 222
13.2.1.1 Geometry .............................................................................................. 222
13.2.1.2 Equilibrium.......................................................................................... 223
E 13-5 Internal Forces in an Helicoidal Cantilevered Girder, (Gerstle 1974) ............ 224
14 BUILDING STRUCTURES 229
14.1 Introduction ...................................................................................................................... 229
14.1.1 Beam Column Connections ................................................................................. 229
14.1.2 Behavior of Simple Frames ................................................................................. 229
14.1.3 Eccentricity of Applied Loads ............................................................................. 230
14.2 Buildings Structures ......................................................................................................... 233
14.2.1 Wall Subsystems ................................................................................................. 233
14.2.1.1 Example: Concrete Shear Wall ........................................................... 233
14.2.1.2 Example: Trussed Shear Wall ............................................................. 235
14.2.2 Shaft Systems ...................................................................................................... 236
14.2.2.1 Example: Tube Subsystem ................................................................. 236
14.2.3 Rigid Frames........................................................................................................ 237
14.3 Approximate Analysis of Buildings ................................................................................ 238
14.3.1 Vertical Loads ...................................................................................................... 239
14.3.2 Horizontal Loads .................................................................................................. 241
14.3.2.1 Portal Method ...................................................................................... 241
E 14-1 Approximate Analysis of a Frame subjected to Vertical and Horizontal Loads243
14.4 Lateral Deflections ........................................................................................................... 253
Victor Saouma Structural Concepts and Systems for Architects
