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TLFeBOOK CIVIL ENGINEERING FORMULAS TLFeBOOK This page intentionally left blank. TLFeBOOK CIVIL ENGINEERING FORMULAS Tyler G. Hicks, P. E . International Engineering Associates Member: American Society of Mechanical Engineers United States Naval Institute McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto TLFeBOOK Copyright © 2002 by The McGraw-Hill Companies. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data- base or retrieval system, without the prior written permission of the publisher. 0-07-139542-3 The material in this eBook also appears in the print version of this title: 0-07-135612-3. All trademarks are trademarks of their respective owners. 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DOI: 10.1036/0071395423 abc McGraw-Hill TLFeBOOK CONTENTS Preface xiii Acknowledgments xv How to Use This Book xvii Chapter 1. Conversion Factors for Civil Engineering Practice 1 Chapter 2. Beam Formulas 15 Continuous Beams / 16 Ultimate Strength of Continuous Beams / 53 Beams of Uniform Strength / 63 Safe Loads for Beams of Various Types / 64 Rolling and Moving Loads / 79 Curved Beams / 82 Elastic Lateral Buckling of Beams / 88 Combined Axial and Bending Loads / 92 Unsymmetrical Bending / 93 Eccentric Loading / 94 Natural Circular Frequencies and Natural Periods of Vibration of Prismatic Beams / 96 Copyright 2002 The McGraw-Hill Companies. Click Here for Terms of Use. TLFeBOOK Chapter 3. Column Formulas 99 General Considerations / 100 Short Columns / 102 Eccentric Loads on Columns / 102 Column Base Plate Design / 111 American Institute of Steel Construction Allowable-Stress Design Approach / 113 Composite Columns / 115 Elastic Flexural Buckling of Columns / 118 Allowable Design Loads for Aluminum Columns / 121 Ultimate-Strength Design of Concrete Columns / 124 Chapter 4. Piles and Piling Formulas 131 Allowable Loads on Piles / 132 Laterally Loaded Vertical Piles / 133 Toe Capacity Load / 134 Groups of Piles / 136 Foundation-Stability Analysis / 139 Axial-Load Capacity of Single Piles / 143 Shaft Settlement / 144 Shaft Resistance to Cohesionless Soil / 145 Chapter 5. Concrete Formulas 147 Reinforced Concrete / 148 Water/Cementitious Materials Ratio / 148 Job Mix Concrete Volume / 149 Modulus of Elasticity of Concrete / 150 Tensile Strength of Concrete / 151 Reinforcing Steel / 151 Continuous Beams and One-Way Slabs / 151 Design Methods for Beams, Columns, and Other Members / 153 Properties in the Hardened State / 167 vi CONTENTS TLFeBOOK Compression at Angle to Grain / 220 Recommendations of the Forest Products Laboratory / 221 Compression on Oblique Plane / 223 Adjustments Factors for Design Values / 224 Fasteners for Wood / 233 Adjustment of Design Values for Connections with Fasteners / 236 Roof Slope to Prevent Ponding / 238 Bending and Axial Tension / 239 Bending and Axial Compression / 240 Chapter 7. Surveying Formulas 243 Units of Measurement / 244 Theory of Errors / 245 Measurement of Distance with Tapes / 247 Vertical Control / 253 Stadia Surveying / 253 Photogrammetry / 255 Chapter 8. Soil and Earthwork Formulas 257 Physical Properties of Soils / 258 Index Parameters for Soils / 259 Relationship of Weights and Volumes in Soils / 261 Internal Friction and Cohesion / 263 Vertical Pressures in Soils / 264 Lateral Pressures in Soils, Forces on Retaining Walls / 265 Lateral Pressure of Cohesionless Soils / 266 Lateral Pressure of Cohesive Soils / 267 Water Pressure / 268 Lateral Pressure from Surcharge / 268 Stability of Slopes / 269 Bearing Capacity of Soils / 270 Settlement under Foundations / 271 Soil Compaction Tests / 272 viii CONTENTS TLFeBOOK Compaction Equipment / 275 Formulas for Earthmoving / 276 Scraper Production / 278 Vibration Control in Blasting / 280 Chapter 9. Building and Structures Formulas 283 Load-and-Resistance Factor Design for Shear in Buildings / 284 Allowable-Stress Design for Building Columns / 285 Load-and-Resistance Factor Design for Building Columns / 287 Allowable-Stress Design for Building Beams / 287 Load-and-Resistance Factor Design for Building Beams / 290 Allowable-Stress Design for Shear in Buildings / 295 Stresses in Thin Shells / 297 Bearing Plates / 298 Column Base Plates / 300 Bearing on Milled Surfaces / 301 Plate Girders in Buildings / 302 Load Distribution to Bents and Shear Walls / 304 Combined Axial Compression or Tension and Bending / 306 Webs under Concentrated Loads / 308 Design of Stiffeners under Loads / 311 Fasteners for Buildings / 312 Composite Construction / 313 Number of Connectors Required for Building Construction / 316 Ponding Considerations in Buildings / 318 Chapter 10. Bridge and Suspension-Cable Formulas 321 Shear Strength Design for Bridges / 322 Allowable-Stress Design for Bridge Columns / 323 Load-and-Resistance Factor Design for Bridge Columns / 324 Allowable-Stress Design for Bridge Beams / 325 Stiffeners on Bridge Girders / 327 Hybrid Bridge Girders / 329 CONTENTS ix TLFeBOOK Load-Factor Design for Bridge Beams / 330 Bearing on Milled Surfaces / 332 Bridge Fasteners / 333 Composite Construction in Highway Bridges / 333 Number of Connectors in Bridges / 337 Allowable-Stress Design for Shear in Bridges / 339 Maximum Width/Thickness Ratios for Compression Elements for Highway Bridges / 341 Suspension Cables / 341 General Relations for Suspension Cables / 345 Cable Systems / 353 Chapter 11. Highway and Road Formulas 355 Circular Curves / 356 Parabolic Curves / 359 Highway Curves and Driver Safety / 361 Highway Alignments / 362 Structural Numbers for Flexible Pavements / 365 Transition (Spiral) Curves / 370 Designing Highway Culverts / 371 American Iron and Steel Institute (AISI) Design Procedure / 374 Chapter 12. Hydraulics and Waterworks Formulas 381 Capillary Action / 382 Viscosity / 386 Pressure on Submerged Curved Surfaces / 387 Fundamentals of Fluid Flow / 388 Similitude for Physical Models / 392 Fluid Flow in Pipes / 395 Pressure (Head) Changes Caused by Pipe Size Change / 403 Flow through Orifices / 406 x CONTENTS TLFeBOOK