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TLFeBOOK 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.i CIVIL ENGINEERING FORMULAS 40816_FM_pi-xvii 10/22/01 12:37 PM Page i TLFeBOOK This page intentionally left blank. TLFeBOOK 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.iii 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 40816_FM_pi-xvii 10/22/01 12:37 PM Page iii TLFeBOOK Copyright © 2002 by The McGraw-Hill Companies. All rights reserved. Manufactured in the United States of America. 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McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COM- PLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPER- LINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MER- CHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licen- sors do not warrant or guarantee that the functions contained in the work will meet your require- ments or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licen- sors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw- Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise. DOI: 10.1036/0071395423 ab 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 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.v 9 . t n - 40816_FM_pi-xvii 10/22/01 12:37 PM Page v Copyright 2002 The McGraw-Hill Companies. Click Here for Terms of Use.TLFeBOOK T C C R D U W U W U W U W F F S C S B L S C C W C G S B B C C 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.vi 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 40816_FM_pi-xvii 10/22/01 12:37 PM Page vi TLFeBOOK C F S V C L A L A L A S B C B P L C W D F C N P C F S A L A S H 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 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.viii 40816_FM_pi-xvii 10/22/01 12:37 PM Page viii 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 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.ix 3 7 40816_FM_pi-xvii 10/22/01 12:37 PM Page ix TLFeBOOK F O W P T F C O M H N W F P E M C G W F E V H 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 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.x 40816_FM_pi-xvii 10/22/01 12:37 PM Page x TLFeBOOK Fluid Jets / 409 Orifice Discharge into Diverging Conical Tubes / 410 Water Hammer / 412 Pipe Stresses Perpendicular to the Longitudinal Axis / 412 Temperature Expansion of Pipe / 414 Forces Due to Pipe Bends / 414 Culverts / 417 Open-Channel Flow / 420 Manning’s Equation for Open Channels / 424 Hydraulic Jump / 425 Nonuniform Flow in Open Channels / 429 Weirs / 436 Flow Over Weirs / 438 Prediction of Sediment-Delivery Rate / 440 Evaporation and Transpiration / 442 Method for Determining Runoff for Minor Hydraulic Structures / 443 Computing Rainfall Intensity / 443 Groundwater / 446 Water Flow for Firefighting / 446 Flow from Wells / 447 Economical Sizing of Distribution Piping / 448 Venturi Meter Flow Computation / 448 Hydroelectric Power Generation / 449 Index 451 CONTENTS xi 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.xi 5 1 40816_FM_pi-xvii 10/22/01 12:37 PM Page xi TLFeBOOK This page intentionally left blank. TLFeBOOK PREFACE This handy book presents more than 2000 needed formulas for civil engineers to help them in the design office, in the field, and on a variety of construction jobs, anywhere in the world. These formulas are also useful to design drafters, structural engineers, bridge engineers, foundation builders, field engineers, professional-engineer license examination candidates, concrete specialists, timber-structure builders, and students in a variety of civil engineering pursuits. The book presents formulas needed in 12 different spe- cialized branches of civil engineering—beams and girders, columns, piles and piling, concrete structures, timber engi- neering, surveying, soils and earthwork, building struc- tures, bridges, suspension cables, highways and roads, and hydraulics and open-channel flow. Key formulas are pre- sented for each of these topics. Each formula is explained so the engineer, drafter, or designer knows how, where, and when to use the formula in professional work. Formula units are given in both the United States Customary System (USCS) and System International (SI). Hence, the text is usable throughout the world. To assist the civil engineer using this material in worldwide engineering practice, a com- prehensive tabulation of conversion factors is presented in Chapter 1. In assembling this collection of formulas, the author was guided by experts who recommended the areas of 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.xiii 40816_FM_pi-xvii 10/22/01 12:37 PM Page xiii Copyright 2002 The McGraw-Hill Companies. Click Here for Terms of Use.TLFeBOOK AM t a H a w F p w a L N e p F a s f e w p t 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.xiv greatest need for a handy book of practical and applied civil engineering formulas. Sources for the formulas presented here include the var- ious regulatory and industry groups in the field of civil engi- neering, authors of recognized books on important topics in the field, drafters, researchers in the field of civil engineer- ing, and a number of design engineers who work daily in the field of civil engineering. These sources are cited in the Acknowledgments. When using any of the formulas in this book that may come from an industry or regulatory code, the user is cautioned to consult the latest version of the code. Formulas may be changed from one edition of a code to the next. In a work of this magnitude it is difficult to include the latest formulas from the numerous constant- ly changing codes. Hence, the formulas given here are those current at the time of publication of this book. In a work this large it is possible that errors may occur. Hence, the author will be grateful to any user of the book who detects an error and calls it to the author’s attention. Just write the author in care of the publisher. The error will be corrected in the next printing. In addition, if a user believes that one or more important formulas have been left out, the author will be happy to consider them for inclusion in the next edition of the book. Again, just write him in care of the publisher. Tyler G. Hicks, P.E. xiv PREFACE 40816_FM_pi-xvii 10/22/01 12:37 PM Page xiv TLFeBOOK ACKNOWLEDGMENTS Many engineers, professional societies, industry associa- tions, and governmental agencies helped the author find and assemble the thousands of formulas presented in this book. Hence, the author wishes to acknowledge this help and assistance. The author’s principal helper, advisor, and contributor was the late Frederick S. Merritt, P.E., Consulting Engineer. For many years Fred and the author were editors on com- panion magazines at The McGraw-Hill Companies. Fred was an editor on Engineering-News Record, whereas the author was an editor on Power magazine. Both lived on Long Island and traveled on the same railroad to and from New York City, spending many hours together discussing engineering, publishing, and book authorship. When the author was approached by the publisher to pre- pare this book, he turned to Fred Merritt for advice and help. Fred delivered, preparing many of the formulas in this book and giving the author access to many more in Fred’s exten- sive files and published materials. The author is most grate- ful to Fred for his extensive help, advice, and guidance. Further, the author thanks the many engineering soci- eties, industry associations, and governmental agencies whose work is referred to in this publication. These organizations provide the framework for safe design of numerous struc- tures of many different types. 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.xv l - - n - n e t r . o o - e . k . l t o . 40816_FM_pi-xvii 10/22/01 12:37 PM Page xv Copyright 2002 The McGraw-Hill Companies. Click Here for Terms of Use.TLFeBOOK T c d s p n T i S o d c c l e d i d a The author also thanks Larry Hager, Senior Editor, Pro- fessional Group, The McGraw-Hill Companies, for his excellent guidance and patience during the long preparation of the manuscript for this book. Finally, the author thanks his wife, Mary Shanley Hicks, a publishing professional, who always most willingly offered help and advice when needed. Specific publications consulted during the preparation of this text include: American Association of State Highway and Transportation Officials (AASHTO) “Standard Specifi- cations for Highway Bridges”; American Concrete Institute (ACI) “Building Code Requirements for Reinforced Con- crete”; American Institute of Steel Construction (AISC) “Manual of Steel Construction,” “Code of Standard Prac- tice,” and “Load and Resistance Factor Design Specifica- tions for Structural Steel Buildings”; American Railway Engineering Association (AREA) “Manual for Railway Engineering”; American Society of Civil Engineers (ASCE) “Ground Water Management”; American Water Works Association (AWWA) “Water Quality and Treat- ment.” In addition, the author consulted several hundred civil engineering reference and textbooks dealing with the topics in the current book. The author is grateful to the writers of all the publications cited here for the insight they gave him to civil engineering formulas. A number of these works are also cited in the text of this book. xvi ACKNOWLEDGMENTS 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.xvi 40816_FM_pi-xvii 10/22/01 12:37 PM Page xvi TLFeBOOK HOW TO USE THIS BOOK The formulas presented in this book are intended for use by civil engineers in every aspect of their professional work— design, evaluation, construction, repair, etc. To find a suitable formula for the situation you face, start by consulting the index. Every effort has been made to present a comprehensive listing of all formulas in the book. Once you find the formula you seek, read any accompa- nying text giving background information about the formula. Then when you understand the formula and its applications, insert the numerical values for the variables in the formula. Solve the formula and use the results for the task at hand. Where a formula may come from a regulatory code, or where a code exists for the particular work being done, be certain to check the latest edition of the appli- cable code to see that the given formula agrees with the code formula. If it does not agree, be certain to use the latest code formula available. Remember, as a design engineer you are responsible for the structures you plan, design, and build. Using the latest edition of any govern- ing code is the only sensible way to produce a safe and dependable design that you will be proud to be associ- ated with. Further, you will sleep more peacefully! 40816 HICKS Mcghp FM Second Pass bcj 7/19/01 p.xvii - s n s , n f y - e - ) - - y y s r - d e e y e 40816_FM_pi-xvii 10/22/01 12:37 PM Page xvii Copyright 2002 The McGraw-Hill Companies. Click Here for Terms of Use.TLFeBOOK This page intentionally left blank. TLFeBOOK CHAPTER 1 CONVERSION FACTORS FOR CIVIL ENGINEERING PRACTICE 40816 HICKS Mcghp Chap_01 Second Pass 7/3/2001 40816_01_p1-14 10/22/01 12:38 PM Page 1 Copyright 2002 The McGraw-Hill Companies. Click Here for Terms of Use.TLFeBOOK c a u c F d Civil engineers throughout the world accept both the United States Customary System (USCS) and the System International (SI) units of measure for both applied and theoretical calculations. However, the SI units are much more widely used than those of the USCS. Hence, both the USCS and the SI units are presented for essentially every formula in this book. Thus, the user of the book can apply the formulas with confidence anywhere in the world. To permit even wider use of this text, this chapter con- tains the conversion factors needed to switch from one sys- tem to the other. For engineer