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 CONTENTS 5 5.4 Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.4.1 Basic Kinematic Assumption; Curvature . . . . . . . . . . . . . . . . . . . 112 5.4.2 Stress-Strain Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4.3 Internal Equilibrium; Section Properties . . . . . . . . . . . . . . . . . . . 113 5.4.3.1 (cid:6)F = 0; Neutral Axis. . . . . . . . . . . . . . . . . . . . . . . . 113 x 5.4.3.2 (cid:6)M = 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 Ei(cid:11)el 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 Victor Saouma Structural Concepts and Systems for Architects Draft CONTENTS 7 12 PRESTRESSED CONCRETE 197 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.1.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.1.2 Prestressing Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 12.1.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 12.1.4 Tendon Con(cid:12)guration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 De(cid:13)ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Victor Saouma Structural Concepts and Systems for Architects Draft List of Figures 1.1 Types of Forces in Structural Elements (1D) . . . . . . . . . . . . . . . . . . . . . 18 1.2 Basic Aspects of Cable Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3 Basic Aspects of Arches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4 Types of Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5 Variations in Post and Beams Con(cid:12)gurations . . . . . . . . . . . . . . . . . . . . 22 1.6 Di(cid:11)erent Beam Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7 Basic Forms of Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.8 Examples of Air Supported Structures . . . . . . . . . . . . . . . . . . . . . . . . 25 1.9 Basic Forms of Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1 Approximation of a Series of Closely Spaced Loads . . . . . . . . . . . . . . . . . 30 2.2 Snow Map of the United States, ubc . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Loads on Projected Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.4 Vertical and Normal Loads Acting on Inclined Surfaces . . . . . . . . . . . . . . 34 2.5 Wind Map of the United States, (UBC 1995) . . . . . . . . . . . . . . . . . . . . 35 2.6 E(cid:11)ect of Wind Load on Structures(Schueller 1996) . . . . . . . . . . . . . . . . . 36 2.7 Approximate Design Wind Pressure p for Ordinary Wind Force Resisting Building Structures 39 2.8 Vibrations of a Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.9 Seismic Zones of the United States, (UBC 1995) . . . . . . . . . . . . . . . . . . 41 2.10 Earth and Hydrostatic Loads on Structures . . . . . . . . . . . . . . . . . . . . . 47 2.11 Truck Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.12 Load Placement to Maximize Moments . . . . . . . . . . . . . . . . . . . . . . . . 51 2.13 Load Life of a Structure, (Lin and Stotesbury 1981) . . . . . . . . . . . . . . . . 51 2.14 Concept of Tributary Areas for Structural Member Loading . . . . . . . . . . . . 52 2.15 One or Two Way actions in Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.16 Load Transfer in R/C Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.17 Two Way Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.18 Example of Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.1 Stress Strain Curves of Concrete and Steel . . . . . . . . . . . . . . . . . . . . . . 58 3.2 Standard Rolled Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.3 Residual Stresses in Rolled Sections . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4 Residual Stresses in Welded Sections . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.5 In(cid:13)uence of Residual Stress on Average Stress-Strain Curve of a Rolled Section . 60 3.6 Concrete microcracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.7 W and C sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.8 prefabricated Steel Joists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Draft LIST OF FIGURES 11 7.12 Experimental Set Up Used by Hooke . . . . . . . . . . . . . . . . . . . . . . . . . 145 7.13 Isaac Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 7.14 Philosophiae Naturalis Principia Mathematica, Cover Page . . . . . . . . . . . . 146 7.15 Leonhard Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7.16 Coulomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 7.17 Nervi’s Palazetto Dello Sport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 8.1 Magazzini Generali; Overall Dimensions, (Billington and Mark 1983) . . . . . . . 158 8.2 Magazzini Generali; Support System, (Billington and Mark 1983) . . . . . . . . . 158 8.3 Magazzini Generali; Loads (Billington and Mark 1983) . . . . . . . . . . . . . . . 159 8.4 Magazzini Generali; Beam Reactions, (Billington and Mark 1983) . . . . . . . . . 159 8.5 Magazzini Generali; Shear and Moment Diagrams (Billington and Mark 1983) . . 160 8.6 Magazzini Generali; Internal Moment, (Billington and Mark 1983) . . . . . . . . 160 8.7 Magazzini Generali; Similarities Between The Frame Shape and its Moment Diagram, (Billington and Mark 1983)161 8.8 Magazzini Generali; Equilibrium of Forces at the Beam Support, (Billington and Mark 1983)161 8.9 Magazzini Generali; E(cid:11)ect of Lateral Supports, (Billington and Mark 1983) . . . 162 9.1 Load Life of a Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 9.2 Normalized Gauss Distribution, and Cumulative Distribution Function . . . . . . 166 9.3 Frequency Distributions of Load Q and Resistance R . . . . . . . . . . . . . . . . 167 9.4 De(cid:12)nition of Reliability Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 9.5 Probability of Failure in terms of (cid:12) . . . . . . . . . . . . . . . . . . . . . . . . . . 168 10.1 Lateral Bracing for Steel Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 10.2 Failure of Steel beam; Plastic Hinges . . . . . . . . . . . . . . . . . . . . . . . . . 175 10.3 Failure of Steel beam; Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . 175 10.4 Failure of Steel beam; Lateral Torsional Buckling . . . . . . . . . . . . . . . . . . 176 10.5 Stress distribution at di(cid:11)erent stages of loading . . . . . . . . . . . . . . . . . . . 176 10.6 Stress-strain diagram for most structural steels . . . . . . . . . . . . . . . . . . . 177 10.7 Nominal Moments for Compact and Partially Compact Sections . . . . . . . . . . 179 11.1 Failure Modes for R/C Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 11.2 Internal Equilibrium in a R/C Beam . . . . . . . . . . . . . . . . . . . . . . . . . 185 11.3 Cracked Section, Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 11.4 Whitney Stress Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 11.5 Reinforcement in Continuous R/C Beams . . . . . . . . . . . . . . . . . . . . . . 194 12.1 Pretensioned Prestressed Concrete Beam, (Nilson 1978) . . . . . . . . . . . . . . 198 12.2 Posttensioned Prestressed Concrete Beam, (Nilson 1978) . . . . . . . . . . . . . . 198 12.3 7 Wire Prestressing Tendon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 12.4 Alternative Schemes for Prestressing a Rectangular Concrete Beam, (Nilson 1978)201 12.5 Determination of Equivalent Loads . . . . . . . . . . . . . . . . . . . . . . . . . . 201 12.6 Load-De(cid:13)ection Curve and Corresponding Internal Flexural Stresses for a Typical Prestressed Concrete Beam, (Nilson 1978)202 12.7 Flexural Stress Distribution for a Beam with Variable Eccentricity; Maximum Moment Section and Support Section, (Nilson 1978)203 12.8 Walnut Lane Bridge, Plan View . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 12.9 Walnut Lane Bridge, Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . 208 13.1 Moment Resisting Forces in an Arch or Suspension System as Compared to a Beam, (Lin and Stotesbury 1981)212 13.2 Statics of a Three-Hinged Arch, (Lin and Stotesbury 1981) . . . . . . . . . . . . 212 Victor Saouma Structural Concepts and Systems for Architects Draft List of Tables 1.1 Structural Engineering Coverage for Architects and Engineers . . . . . . . . . . . 26 1.2 tab:secae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1 Unit Weight of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2 Weights of Building Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3 Average Gross Dead Load in Buildings . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4 Minimum Uniformly Distributed Live Loads, (UBC 1995) . . . . . . . . . . . . . 32 2.5 Wind Velocity Variation above Ground . . . . . . . . . . . . . . . . . . . . . . . . 36 2.6 C Coe(cid:14)cients for Wind Load, (UBC 1995) . . . . . . . . . . . . . . . . . . . . . 37 e 2.7 Wind Pressure Coe(cid:14)cients C , (UBC 1995) . . . . . . . . . . . . . . . . . . . . . 37 q 2.8 Importance Factors for Wind and Earthquake Load, (UBC 1995) . . . . . . . . . 38 2.9 Approximate Design Wind Pressure p for Ordinary Wind Force Resisting Building Structures 38 2.10 Z Factors for Di(cid:11)erent Seismic Zones, ubc . . . . . . . . . . . . . . . . . . . . . . 42 2.11 S Site Coe(cid:14)cients for Earthquake Loading, (UBC 1995) . . . . . . . . . . . . . . 42 2.12 Partial List of R for Various Structure Systems, (UBC 1995) . . . . . . . . . . 43 W 2.13 Coe(cid:14)cients of Thermal Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.1 Properties of Major Structural Steels . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2 Properties of Reinforcing Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3 Joist Series Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.4 Joist Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1 Equations of Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.2 Static Determinacy and Stability of Trusses . . . . . . . . . . . . . . . . . . . . . 94 5.3 Section Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 9.1 Allowable Stresses for Steel and Concrete . . . . . . . . . . . . . . . . . . . . . . 165 9.2 Selected (cid:12) values for Steel and Concrete Structures . . . . . . . . . . . . . . . . . 169 9.3 Strength Reduction Factors, (cid:8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 14.1 Columns Combined Approximate Vertical and Horizontal Loads . . . . . . . . . 254 14.2 Girders Combined Approximate Vertical and Horizontal Loads . . . . . . . . . . 255 Draft Chapter 1 INTRODUCTION 1.1 Science and Technology \There is a fundamental di(cid:11)erence between science and and technology. Engineering or 1 technology is the making of things that did not previously exist, whereas science is the discov- ering of things that have long existed. Technological results are forms that exist only because people want to make them, whereas scienti(cid:12)c results are informations of what exists indepen- dently of human intentions. Technology deals with the arti(cid:12)cial, science with the natural." (Billington 1985) 1.2 Structural Engineering Structural engineers are responsible for the detailed analysis and design of: 2 Architectural structures: Buildings, houses, factories. Theymustworkinclosecooperation with an architect who will ultimately be responsible for the design. Civil Infrastructures: Bridges, dams, pipelines, o(cid:11)shore structures. They work with trans- portation, hydraulic, nuclear and other engineers. For those structures they play the leading role. Aerospace, Mechanical, Naval structures: aeroplanes,spacecrafts,cars,ships,submarines to ensure the structural safety of those important structures. 1.3 Structures and their Surroundings Structural design is a(cid:11)ected by various environmental constraints: 3 1. Major movements: For example, elevator shafts are usually shear walls good at resisting lateral load (wind, earthquake). 2. Sound and structure interact: A dome roof will concentrate the sound (cid:15) A dish roof will di(cid:11)use the sound (cid:15) Draft 1.6 Architectural Design 17 1.6 Architectural Design Architectural design must respect various constraints: 12 Functionality: In(cid:13)uence of the adopted structure on the purposes for which the structure was erected. Aesthetics: The architect often imposes his aesthetic concerns on the engineer. This in turn can place severe limitations on the structural system. Economy: It should be kept in mind that the two largest components of a structure are labors and materials. Design cost is comparatively negligible. Buildings may have di(cid:11)erent functions: 13 Residential: housing, which includes low-rise (up tp 2-3 (cid:13)oors), mid-rise (up to 6-8 (cid:13)oors) and high rise buildings. Commercial: O(cid:14)ces, retail stores, shopping centers, hotels, restaurants. Industrial: warehouses, manufacturing. Institutional: Schools, hospitals, prisons, chruch, government buildings. Special: Towers, stadium, parking, airport, etc. 1.7 Structural Analysis Given an existing structure subjected to a certain load determine internal forces (axial, 14 shear, (cid:13)exural, torsional; or stresses), de(cid:13)ections, and verify that no unstable failure can occur. Thus the basic structural requirements are: 15 Strength: stresses should not exceed critical values: (cid:27) < (cid:27) f Sti(cid:11)ness: de(cid:13)ections should be controlled: (cid:1) < (cid:1) max Stability: buckling or cracking should also be prevented 1.8 Structural Design Given a set of forces, dimension the structural element. 16 Steel/wood Structures Select appropriate section. Reinforced Concrete: Determinedimensionsoftheelementandinternalreinforcement(num- ber and sizes of reinforcing bars). Fornew structures,iterativeprocessbetweenanalysisanddesign. Apreliminarydesignis 17 made using rules of thumbs (best known to Engineers with design experience) and analyzed. Following design, we check for Victor Saouma Structural Concepts and Systems for Architects Draft 1.10 Structure Types 19 Tension & Compression Structures: only, no shear, (cid:13)exure, or torsion. Those are the most e(cid:14)cient types of structures. Cable (tension only): The high strength of steel cables, combined with the e(cid:14)ciency of simple tension, makes cables ideal structural elements to span large distances such as bridges, and dish roofs, Fig. 1.2. A cable structure develops its load carrying Figure 1.2: Basic Aspects of Cable Systems capacity by adjusting its shape so as to provide maximum resistance (form follows function). Care should be exercised in minimizing large de(cid:13)ections and vibrations. Arches (mostly compression) is a \reversed cable structure". In an arch, (cid:13)exure/shear is minimized and most of the load is transfered through axial forces only. Arches are Victor Saouma Structural Concepts and Systems for Architects