TLFeBOOK
CIVIL
ENGINEERING
FORMULAS
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TLFeBOOK
CIVIL
ENGINEERING
FORMULAS
Tyler G. Hicks, P. E .
International Engineering Associates
Member: American Society of Mechanical Engineers
United States Naval Institute
McGRAW-HILL
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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 Allowable-Stress
Design Approach / 113
Composite Columns / 115

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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Stiffeners on Bridge Girders / 327
Hybrid Bridge Girders / 329
CONTENTS ix
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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

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, 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

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 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.

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

4. Apply the conversion values wherever 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 meas-
urement is becoming comfortable with the names and
magnitudes of the units. Numerical conversion is simple,
once you have set up your own conversion table.
2 CHAPTER ONE
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Be careful, when using formulas containing a numerical
constant, to convert the constant to that for the system you
are using. You can, however, use the formula for the USCS
units (when the formula is given in those units) and then
convert the final result to the SI equivalent using Table 1.3.
For the few formulas given in SI units, the reverse proce-
dure should be used.
CONVERSION FACTORS 3
TABLE 1.1 Commonly Used USCS and SI Units
†
Conversion factor
(multiply USCS unit
by this factor to
USCS unit SI unit SI symbol obtain SI unit)
square foot square meter m
2
0.0929
cubic foot cubic meter m
3
0.2831
pound per

acre foot per day cubic meter per E Ϫ 02
second 1.427641
acre square meter 4.046873 E ϩ 03
cubic foot per cubic meter per
second second 2.831685 E Ϫ 02
†
This table contains only selected values. See the U.S. Department of the
Interior Metric Manual, or National Bureau of Standards, The International
System of Units (SI), both available from the U.S. Government Printing
Office (GPO), for far more comprehensive listings of conversion factors.
‡
The E indicates an exponent, as in scientific notation, followed by a positive
or negative number, representing the power of 10 by which the given con-
version factor is to be multiplied before use. Thus, for the square foot con-
version factor, 9.290304 ϫ 1/100 ϭ 0.09290304, the factor to be used to
convert square feet to square meters. For a positive exponent, as in convert-
ing acres to square meters, multiply by 4.046873 ϫ 1000 ϭ 4046.8.
Where a conversion factor cannot be found, simply use the dimensional
substitution. Thus, to convert pounds per cubic inch to kilograms per cubic
meter, find 1 lb ϭ 0.4535924 kg and 1 in
3
ϭ 0.00001638706 m
3
. Then,
1 lb/in
3
ϭ 0.4535924 kg/0.00001638706 m
3
ϭ 27,680.01, or 2.768 E ϩ 4.
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3
2.359737 E Ϫ 03
British thermal unit, joule, J 1.05587 E ϩ 03
Btu, (mean)
British thermal unit, watt per meter 1.442279 E Ϫ 01
Btu (International kelvin, W/(mиK)
Table)иin/(h)(ft
2
)
(°F) (k, thermal
conductivity)
British thermal unit, watt, W 2.930711 E Ϫ 01
Btu (International
Table)/h
British thermal unit, watt per square 5.678263 E ϩ 00
Btu (International meter kelvin,
Table)/(h)(ft
2
)(°F) W/(m
2
иK)
(C, thermal
conductance)
British thermal unit, joule per kilogram, 2.326000
*
E ϩ 03
Btu (International J/kg
Table)/lb
CONVERSION FACTORS 5
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2
5.067075 E Ϫ 10
day second, s 8.640000
*
E ϩ 04
day (sidereal) second, s 8.616409 E ϩ 04
degree (angle) radian, rad 1.745329 E Ϫ 02
degree Celsius kelvin, K T
K
ϭ t
C
ϩ 273.15
degree Fahrenheit degree Celsius, °C t
C
ϭ (t
F
Ϫ 32)/1.8
degree Fahrenheit kelvin, K T
K
ϭ (t
F
ϩ 459.67)/1.8
degree Rankine kelvin, K T
K
ϭ T
R
/1.8
(°F)(h)(ft
2
)/Btu kelvin square 1.761102 E Ϫ 01

2
9.290304
†
E Ϫ 02
square foot per hour, square meter per 2.580640
†
E Ϫ 05
ft
2
/h (thermal second, m
2
/s
diffusivity)
square foot per square meter per 9.290304
†
E Ϫ 02
second, ft
2
/s second, m
2
/s
cubic foot, ft
3
(volume cubic meter, m
3
2.831685 E Ϫ 02
or section modulus)
cubic foot per minute, cubic meter per 4.719474 E Ϫ 04
ft
3