[Will @ummi-mn* FORM uLAs “Tyler G. Hlcks, P.E.
CIVIL ENGINEERING FORMULAS
ABOUT THE AUTHOR Tyler G. Hicks, P.E., is a consulting engineer and a successful engi- neering book author. He has worked in plant design and operation in a variety of industries, taught at several engineering schools, and lectured both in the United States and abroad. Mr. Hicks holds a bachelor’s degree in Mechanical Engineering from Cooper Union School of Engineering in New York. He is the author of more than 100 books in engineering and related fields.
CIVIL ENGINEERING FORMULAS Tyler G. Hicks, P.E. International Engineering Associates Member: American Society of Mechanical Engineers United States Naval Institute
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CONTENTS Preface xi Acknowledgments xiii How to Use This Book xv Chapter 1. Conversion Factors for Civil Engineering Practice 1 Chapter 2. Beam Formulas 11 Continuous Beams / 11 Ultimate Strength of Continuous Beams / 46 Beams of Uniform Strength / 52 Safe Loads for Beams of Various Types / 53 Rolling and Moving Loads / 53 Curved Beams / 65 Elastic Lateral Buckling of Beams / 69 Combined Axial and Bending Loads / 72 Unsymmetrical Bending / 73 Eccentric Loading / 73 Natural Circular Frequencies and Natural Periods of Vibration of Prismatic Beams / 74 Torsion in Structural Members / 76 Strain Energy in Structural Members / 76 Fixed-End Moments in Beams / 79 Chapter 3. Column Formulas 81 General Considerations / 81 Short Columns / 81 Eccentric Loads on Columns / 83 Columns of Special Materials / 88 Column Base Plate Design / 90 American Institute of Steel Construction Allowable-Stress Design Approach / 91 Composite Columns / 92 Elastic Flexural Buckling of Columns / 94 Allowable Design Loads for Aluminum Columns / 96 Ultimate Strength Design Concrete Columns / 97 Design of Axially Loaded Steel Columns / 102 v
vi CONTENTS Chapter 4. Piles and Piling Formulas 105 Allowable Loads on Piles / 105 Laterally Loaded Vertical Piles / 105 Toe Capacity Load / 107 Groups of Piles / 107 FoundationStability Analysis / 109 Axial-Load Capacity of Single Piles / 112 Shaft Settlement / 112 Shaft Resistance in Cohesionless Soils / 113 Chapter 5. Concrete formulas 115 Reinforced Concrete / 115 Water/Cementitious Materials Ratio / 115 Job Mix Concrete Volume / 116 Modulus of Elasticity of Concrete / 116 Tensile Strength of Concrete / 117 Reinforcing Steel / 117 Continuous Beams and One-Way Slabs / 117 Design Methods for Beams, Columns, and Other Members / 118 Properties in the Hardened State / 127 Tension Development Lengths / 128 Compression Development Lengths / 128 Crack Control of Flexural Members / 128 Required Strength / 129 Deflection Computations and Criteria for Concrete Beams / 130 Ultimate-Strength Design of Rectangular Beams with Tension Reinforcement Only / 130 Working-Stress Design of Rectangular Beams with Tension Reinforcement Only / 133 Ultimate-Strength Design of Rectangular Beams with Compression Bars / 135 WorkingStress Design of Rectangular Beams with Compression Bars / 136 Ultimate-Strength Design of I- and T-beams / 138 Working-Stress Design of I- and Tbeams / 138 Ultimate-Strength Design for Torsion / 140 Working-Stress Design for Torsion / 141 Flat-Slab Construction / 142 Flat-Plate Construction / 142 Shear in Slabs / 145 Column Moments / 146 Spirals / 147 Braced and Unbraced Frames / 147 Shear Walls / 148 Concrete Gravity Retaining Walls / 150 Cantilever Retaining Walls / 153 Wall Footings / 155
CONTENTS vii Chapter 6. Timber Engineering Formulas 157 Grading of Lumber / 157 Size of Lumber / 157 Bearing / 159 Beams / 159 Columns / 160 Combined Bending and Axial Load / 161 Compression at Angle to Grain / 161 Recommendations of the Forest Products Laboratory / 162 Compression on Oblique Plane / 163 Adjustment Factors for Design Values / 164 Fasteners for Wood / 169 Adjustment of Design Values for Connections with Fasteners / 171 Roof Slope to Prevent Ponding / 172 Bending and Axial Tension / 173 Bending and Axial Compression / 173 Solid Rectangular or Square Columns with Flat Ends / 174 Chapter 7. Surveying Formulas 177 Units of Measurement / 177 Theory of Errors / 178 Measurement of Distance with Tapes / 179 Vertical Control / 182 Stadia Surveying / 183 Photogrammetry / 184 Chapter 8. Soil and Earthwork Formulas 185 Physical Properties of Soils / 185 Index Parameters for Soils / 186 Relationship of Weights and Volumes in Soils / 186 Internal Friction and Cohesion / 188 Vertical Pressures in Soils / 188 Lateral Pressures in Soils, Forces on Retaining Walls / 189 Lateral Pressure of Cohesionless Soils / 190 Lateral Pressure of Cohesive Soils / 191 Water Pressure / 191 Lateral Pressure from Surcharge / 191 Stability of Slopes / 192 Bearing Capacity of Soils / 192 Settlement under Foundations / 193 Soil Compaction Tests / 193 Compaction Equipment / 195 Formulas for Earthmoving / 196 Scraper Production / 197 Vibration Control in Blasting / 198
viii CONTENTS Chapter 9. Building and Structures Formulas 207 Load-and-Resistance Factor Design for Shear in Buildings / 207 Allowable-Stress Design for Building Columns / 208 Load-and-Resistance Factor Design for Building Columns / 209 Allowable-Stress Design for Building Beams / 209 Load-and-Resistance Factor Design for Building Beams / 211 Allowable-Stress Design for Shear in Buildings / 214 Stresses in Thin Shells / 215 Bearing Plates / 216 Column Base Plates / 217 Bearing on Milled Surfaces / 218 Plate Girders in Buildings / 219 Load Distribution to Bents and Shear Walls / 220 Combined Axial Compression or Tension and Bending / 221 Webs under Concentrated Loads / 222 Design of Stiffeners under Loads / 224 Fasteners in Buildings / 225 Composite Construction / 225 Number of Connectors Required for Building Construction / 226 Ponding Considerations in Buildings / 228 Lightweight Steel Construction / 228 Choosing the Most Economic Structural Steel / 239 Steel Carbon Content and Weldability / 240 Statically Indeterminate Forces and Moments in Building Structures / 241 Roof Live Loads / 244 Chapter 10. Bridge and Suspension-Cable Formulas 249 Shear Strength Design for Bridges / 249 Allowable-Stress Design for Bridge Columns / 250 Load-and-Resistance Factor Design for Bridge Columns / 250 Additional Bridge Column Formulas / 251 Allowable-Stress Design for Bridge Beams / 254 Stiffeners on Bridge Girders / 255 Hybrid Bridge Girders / 256 Load-Factor Design for Bridge Beams / 256 Bearing on Milled Surfaces / 258 Bridge Fasteners / 258 Composite Construction in Highway Bridges / 259 Number of Connectors in Bridges / 261 Allowable-Stress Design for Shear in Bridges / 262 Maximum Width/Thickness Ratios for Compression Elements for Highway Bridges / 263 Suspension Cables / 263 General Relations for Suspension Cables / 267 Cable Systems / 272 Rainwater Accumulation and Drainage on Bridges / 273
CONTENTS ix Chapter 11. Highway and Road Formulas 275 Circular Curves / 275 Parabolic Curves / 277 Highway Curves and Driver Safety / 278 Highway Alignments / 279 Structural Numbers for Flexible Pavements / 281 Transition (Spiral) Curves / 284 Designing Highway Culverts / 285 American Iron and Steel Institute (AISI) Design Procedure / 286 Chapter 12. Hydraulics and Waterworks Formulas 291 Capillary Action / 291 Viscosity / 291 Pressure on Submerged Curved Surfaces / 295 Fundamentals of Fluid Flow / 296 Similitude for Physical Models / 298 Fluid Flow in Pipes / 300 Pressure (Head) Changes Caused by Pipe Size Change / 306 Flow through Orifices / 308 Fluid Jets / 310 Orifice Discharge into Diverging Conical Tubes / 311 Water Hammer / 312 Pipe Stresses Perpendicular to the Longitudinal Axis / 312 Temperature Expansion of Pipe / 313 Forces due to Pipe Bends / 313 Culverts / 315 OpenChannel Flow / 318 Manning’s Equation for Open Channels / 320 Hydraulic Jump / 321 Nonuniform Flow in Open Channels / 323 Weirs / 329 Flow over Weirs / 330 Prediction of Sediment-Delivery Rate / 332 Evaporation and Transpiration / 332 Method for Determining Runoff for Minor Hydraulic Structures / 333 Computing Rainfall Intensity / 333 Groundwater / 334 Water Flow for Fire Fighting / 335 Flow from Wells / 335 Economical Sizing of Distribution Piping / 336 Venturi Meter Flow Computation / 336 Hydroelectric Power Generation / 337 Pumps and Pumping Systems / 338 Hydraulic Turbines / 344 Dams / 348
