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 contains the conversion factors needed to switch from one system to the other. For engineers unfamiliar with either
system of units, the author suggests the following steps for
becoming acquainted with the unknown system:
1. Prepare a list of measurementscommonly used in your
daily work.
2. Insert, opposite each known unit,the unit from the other
system. Table 1.1 shows such a list of USCS units with
corresponding SI units and symbols prepared by a civil
engineer who normally uses the USCS. The SI units
shown in Table 1.1 were obtained from Table 1.3 by the
engineer.
3. Find, from a table of conversion factors,such as Table 1.3,
the value used to convert from USCS to SI units. Insert
each appropriate value in Table 1.2 from Table 1.3.
4. Apply the conversion valueswherever necessary for the
formulas in this book.
5. Recognize—here and now—that the most difficult
aspect of becoming familiar with a new system of measurement is becoming comfortable with the names and
magnitudes of the units. Numerical conversion is simple,
once you have set up your own conversion table.
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CIVIL
ENGINEERING
FORMULAS
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CIVIL
ENGINEERING
FORMULAS
Tyler G. Hicks, P.E.
International Engineering Associates
Member: American Society of Mechanical Engineers
United States Naval Institute
McGRAWHILL
New York Chicago San Francisco Lisbon London
Madrid Mexico City Milan New Delhi San Juan
Seoul Singapore Sydney Toronto
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Copyright © 2002 by The McGrawHill 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.
0071395423
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This is a copyrighted work and The McGrawHill Companies, Inc. (“McGrawHill”) and its licen
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DOI: 10.1036/0071395423
ab
McGrawHill
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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
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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 AllowableStress
Design Approach / 113
Composite Columns / 115
Elastic Flexural Buckling of Columns / 118
Allowable Design Loads for Aluminum Columns / 121
UltimateStrength 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
FoundationStability Analysis / 139
AxialLoad 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 OneWay Slabs / 151
Design Methods for Beams, Columns, and Other Members / 153
Properties in the Hardened State / 167
vi CONTENTS
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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
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Compaction Equipment / 275
Formulas for Earthmoving / 276
Scraper Production / 278
Vibration Control in Blasting / 280
Chapter 9. Building and Structures Formulas 283
LoadandResistance Factor Design for Shear in Buildings / 284
AllowableStress Design for Building Columns / 285
LoadandResistance Factor Design for Building Columns / 287
AllowableStress Design for Building Beams / 287
LoadandResistance Factor Design for Building Beams / 290
AllowableStress 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 SuspensionCable
Formulas 321
Shear Strength Design for Bridges / 322
AllowableStress Design for Bridge Columns / 323
LoadandResistance Factor Design for Bridge Columns / 324
AllowableStress Design for Bridge Beams / 325
Stiffeners on Bridge Girders / 327
Hybrid Bridge Girders / 329
CONTENTS ix
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LoadFactor 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
AllowableStress 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
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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
OpenChannel 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 SedimentDelivery 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
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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, professionalengineer license examination
candidates, concrete specialists, timberstructure 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 openchannel 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
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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
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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 McGrawHill Companies. Fred
was an editor on EngineeringNews 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.
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The author also thanks Larry Hager, Senior Editor, Pro
fessional Group, The McGrawHill 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
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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!
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CHAPTER 1
CONVERSION
FACTORS FOR
CIVIL
ENGINEERING
PRACTICE
40816 HICKS Mcghp Chap_01 Second Pass 7/3/2001
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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