Civil_Engineering_Reference_Manual_for_the_PE_Exam_Fifteenth_Edition.pdf

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1SPGFTTJPOBM1VCMJDBUJPOT *ODt#FMNPOU $BMJGPSOJB
Civil
Engineering
Reference
Manual
for the PE Exam
Fifteenth Edition
Michael R. Lindeburg, PE
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Topics
Topic I: Background and Support
Topic II: Water Resources
Topic III: Environmental
Topic IV: Geotechnical
Topic V: Structural
Topic VI: Transportation
Topic VII: Construction
Topic VIII: Systems, Management, and Professional
Topic IX: Support Material
Support
Material
Background
and
Support
Water
Resources
Environmental
Geotechnical
Structural
Transportation
Construction
Systems,
Mgmt,
and
Professional
P P I * w w w . p p i 2 p a s s . c o m
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Where do I find practice problems
to test what I’ve learned in this Reference Manual?
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Practice Problems for the Civil Engineering PE Exam: A Companion to the
Civil Engineering Reference Manual5IJTQVCMJDBUJPOQSPWJEFTZPVXJUINPSF
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Practice Problems for the Civil Engineering PE Exam NBZCFPCUBJOFEGSPN11*
BUQQJQBTTDPNPSGSPNZPVSGBWPSJUFSFUBJMFS
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Table of Contents
Appendices Table of Contents . . . . . . . . . . . . . . vii
Preface to the Fourteenth Edition . . . . . . . . . . . xi
Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . xv
Codes and Standards . . . . . . . . . . . . . . . . . . . . xvii
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Topic I: Background and Support
Systems of Units . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
Engineering Drawing Practice . . . . . . . . . . . . . . . 2-1
Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
Linear Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1
Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1
Analytic Geometry . . . . . . . . . . . . . . . . . . . . . . . 7-1
Differential Calculus . . . . . . . . . . . . . . . . . . . . . . 8-1
Integral Calculus . . . . . . . . . . . . . . . . . . . . . . . . . 9-1
Differential Equations . . . . . . . . . . . . . . . . . . . . .10-1
Probability and Statistical Analysis of Data . . . . .11-1
Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . .12-1
Energy, Work, and Power . . . . . . . . . . . . . . . . . .13-1
Topic II: Water Resources
Fluid Properties. . . . . . . . . . . . . . . . . . . . . . . . . .14-1
Fluid Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . .15-1
Fluid Flow Parameters. . . . . . . . . . . . . . . . . . . . .16-1
Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . .17-1
Hydraulic Machines . . . . . . . . . . . . . . . . . . . . . . .18-1
Open Channel Flow . . . . . . . . . . . . . . . . . . . . . . .19-1
Meteorology, Climatology, and Hydrology. . . . . . .20-1
Groundwater . . . . . . . . . . . . . . . . . . . . . . . . . . . .21-1
Inorganic Chemistry. . . . . . . . . . . . . . . . . . . . . . .22-1
Organic Chemistry. . . . . . . . . . . . . . . . . . . . . . . .23-1
Combustion and Incineration . . . . . . . . . . . . . . . .24-1
Water Supply Quality and Testing . . . . . . . . . . . .25-1
Water Supply Treatment and Distribution . . . . . .26-1
Topic III: Environmental
Cellular Biology. . . . . . . . . . . . . . . . . . . . . . . . . .27-1
Wastewater Quantity and Quality . . . . . . . . . . . .28-1
Wastewater Treatment: Equipment and
Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . .29-1
Activated Sludge and Sludge Processing . . . . . . . .30-1
Municipal Solid Waste . . . . . . . . . . . . . . . . . . . . .31-1
Pollutants in the Environment . . . . . . . . . . . . . . .32-1
Storage and Disposition of Hazardous Materials . .33-1
Environmental Remediation . . . . . . . . . . . . . . . . .34-1
Topic IV: Geotechnical
Soil Properties and Testing . . . . . . . . . . . . . . . . .35-1
Shallow Foundations . . . . . . . . . . . . . . . . . . . . . .36-1
Rigid Retaining Walls . . . . . . . . . . . . . . . . . . . . .37-1
Piles and Deep Foundations . . . . . . . . . . . . . . . . .38-1
Excavations. . . . . . . . . . . . . . . . . . . . . . . . . . . . .39-1
Special Soil Topics. . . . . . . . . . . . . . . . . . . . . . . .40-1
Topic V: Structural
Determinate Statics . . . . . . . . . . . . . . . . . . . . . . .41-1
Properties of Areas . . . . . . . . . . . . . . . . . . . . . . .42-1
Material Testing . . . . . . . . . . . . . . . . . . . . . . . . .43-1
Strength of Materials . . . . . . . . . . . . . . . . . . . . . .44-1
Basic Elements of Design . . . . . . . . . . . . . . . . . . .45-1
Structural Analysis I . . . . . . . . . . . . . . . . . . . . . .46-1
Structural Analysis II. . . . . . . . . . . . . . . . . . . . . .47-1
Properties of Concrete and Reinforcing Steel . . . . .48-1
Concrete Proportioning, Mixing, and Placing . . . .49-1
Reinforced Concrete: Beams . . . . . . . . . . . . . . . . .50-1
Reinforced Concrete: Slabs . . . . . . . . . . . . . . . . . .51-1
Reinforced Concrete: Short Columns. . . . . . . . . . .52-1
Reinforced Concrete: Long Columns . . . . . . . . . . .53-1
Reinforced Concrete: Walls and Retaining Walls . .54-1
Reinforced Concrete: Footings . . . . . . . . . . . . . . .55-1
Prestressed Concrete . . . . . . . . . . . . . . . . . . . . . .56-1
Composite Concrete and Steel Bridge Girders . . . .57-1
Structural Steel: Introduction . . . . . . . . . . . . . . . .58-1
Structural Steel: Beams . . . . . . . . . . . . . . . . . . . .59-1
Structural Steel: Tension Members . . . . . . . . . . . .60-1
Structural Steel: Compression Members . . . . . . . .61-1
Structural Steel: Beam-Columns . . . . . . . . . . . . . .62-1
Structural Steel: Built-Up Sections . . . . . . . . . . . .63-1
Structural Steel: Composite Beams . . . . . . . . . . . .64-1
Structural Steel: Connectors. . . . . . . . . . . . . . . . .65-1
Structural Steel: Welding . . . . . . . . . . . . . . . . . . .66-1
Properties of Masonry . . . . . . . . . . . . . . . . . . . . .67-1
Masonry Walls . . . . . . . . . . . . . . . . . . . . . . . . . .68-1
Masonry Columns . . . . . . . . . . . . . . . . . . . . . . . .69-1
Topic VI: Transportation
Properties of Solid Bodies. . . . . . . . . . . . . . . . . . . 70-1
Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71-1
Kinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72-1
Roads and Highways: Capacity Analysis . . . . . . . . 73-1
Bridges: Condition and Rating . . . . . . . . . . . . . . . 74-1
Highway Safety . . . . . . . . . . . . . . . . . . . . . . . . . . 75-1
Flexible Pavement Design . . . . . . . . . . . . . . . . . . 76-1
Rigid Pavement Design . . . . . . . . . . . . . . . . . . . . 77-1
Plane Surveying. . . . . . . . . . . . . . . . . . . . . . . . . . 78-1
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Horizontal, Compound, Vertical, and
Spiral Curves. . . . . . . . . . . . . . . . . . . . . . . . . . 79-1
Topic VII: Construction
Construction Earthwork. . . . . . . . . . . . . . . . . . . .80-1
Construction Staking and Layout . . . . . . . . . . . . .81-1
Building Codes and Materials Testing. . . . . . . . . .82-1
Construction and Job Site Safety . . . . . . . . . . . . .83-1
Topic VIII: Systems, Management, and
Professional
Electrical Systems and Equipment . . . . . . . . . . . .84-1
Instrumentation and Measurements . . . . . . . . . . .85-1
Project Management, Budgeting, and
Scheduling. . . . . . . . . . . . . . . . . . . . . . . . . . . .86-1
Engineering Economic Analysis . . . . . . . . . . . . . .87-1
Professional Services, Contracts, and
Engineering Law . . . . . . . . . . . . . . . . . . . . . . .88-1
Engineering Ethics. . . . . . . . . . . . . . . . . . . . . . . .89-1
Engineering Licensing in the United States . . . . . .90-1
Topic IX: Support Material
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G-1
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I-1
vi C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L
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Appendices
Table of Contents
1.A Conversion Factors . . . . . . . . . . . . . . . . . . . . . A-1
1.B Common SI Unit Conversion Factors . . . . . . . . A-3
7.A Mensuration of Two-Dimensional Areas . . . . . . A-7
7.B Mensuration of Three-Dimensional Volumes . . . A-9
9.A Abbreviated Table of Indefinite Integrals . . . . A-10
10.A Laplace Transforms . . . . . . . . . . . . . . . . . . . . A-11
11.A Areas Under the Standard Normal Curve . . . . A-12
11.B Chi-Squared Distribution . . . . . . . . . . . . . . . . A-13
11.C Values of tC for Student’s t-Distribution . . . . . A-14
11.D Values of the Error Function and
Complementary Error Function . . . . . . . . . A-15
14.A Properties of Water at Atmospheric Pressure
(customary U.S. units) . . . . . . . . . . . . . . . . A-16
14.B Properties of Ordinary Liquid Water
(SI units). . . . . . . . . . . . . . . . . . . . . . . . . . A-17
14.C Viscosity of Water in Other Units
14.D Properties of Air at Atmospheric Pressure
14.E Properties of Air at Atmospheric Pressure
(SI units). . . . . . . . . . . . . . . . . . . . . . . . . . A-22
14.F Properties of Common Liquids . . . . . . . . . . . . A-23
14.G Viscosities Versus Temperature of
Hydrocarbons, Lubricants, Fuels, and Heat
Transfer Fluids . . . . . . . . . . . . . . . . . . . . . A-24
14.H Properties of Uncommon Fluids . . . . . . . . . . . A-25
14.I Vapor Pressure of Various Hydrocarbons and
Water (Cox Chart) . . . . . . . . . . . . . . . . . . A-26
14.J Specific Gravity of Hydrocarbons . . . . . . . . . . A-27
14.K Viscosity Conversion Chart (Approximate
Conversions for Newtonian Fluids) . . . . . . . A-28
14.L Viscosity Index Chart: 0–100 VI. . . . . . . . . . . A-29
16.A Area, Wetted Perimeter, and Hydraulic Radius
of Partially Filled Circular Pipes. . . . . . . . . A-30
16.B Dimensions of Welded and Seamless Steel Pipe
16.C Dimensions of Welded and Seamless Steel Pipe
(SI units). . . . . . . . . . . . . . . . . . . . . . . . . . A-35
16.D Dimensions of Rigid PVC and CPVC Pipe
16.E Dimensions of Large Diameter, Nonpressure,
PVC Sewer and Water Pipe
16.F Dimensions and Weights of Concrete Sewer Pipe
16.G Dimensions of Cast-Iron and Ductile Iron Pipe
Standard Pressure Classes
16.H Dimensions of Ductile Iron Pipe
Special Pressure Classes
16.I Standard ASME/ANSI Z32.2.3
Piping Symbols . . . . . . . . . . . . . . . . . . . . . A-46
16.J Dimensions of Copper Water Tubing
16.K Dimensions of Brass and Copper Tubing
16.L Dimensions of Seamless Steel Boiler (BWG)
Tubing (customary U.S. units) . . . . . . . . . A-49
17.A Specific Roughness and Hazen-Williams Constants
for Various Water Pipe Materials . . . . . . . . A-50
17.B Darcy Friction Factors (turbulent flow) . . . . . A-51
17.C Water Pressure Drop in Schedule-40
Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . A-55
17.D Equivalent Length of Straight Pipe for
Various (Generic) Fittings . . . . . . . . . . . . . A-56
17.E Hazen-Williams Nomograph (C = 100) . . . . . . A-57
17.F Corrugated Metal Pipe. . . . . . . . . . . . . . . . . . A-58
18.A International Standard Atmosphere . . . . . . . . A-59
18.B Properties of Saturated Steam by Temperature
18.C Properties of Saturated Steam by Pressure
18.D Properties of Superheated Steam
18.E Properties of Saturated Steam by Temperature
(SI units). . . . . . . . . . . . . . . . . . . . . . . . . . A-70
18.F Properties of Saturated Steam by Pressure
(SI units). . . . . . . . . . . . . . . . . . . . . . . . . . A-70
18.G Properties of Superheated Steam (SI units) . . . A-72
19.A Manning’s Roughness Coefficient (design use) . A-73
19.B Manning Equation Nomograph. . . . . . . . . . . . A-74
19.C Circular Channel Ratios. . . . . . . . . . . . . . . . . A-75
19.D Critical Depths in Circular Channels. . . . . . . . A-76
19.E Conveyance Factor, K . . . . . . . . . . . . . . . . . . A-77
19.F Conveyance Factor, K0
. . . . . . . . . . . . . . . . . A-79
20.A Rational Method Runoff C-Coefficients . . . . . . A-81
20.B Random Numbers . . . . . . . . . . . . . . . . . . . . . A-82
22.A Atomic Numbers and Weights of the
Elements . . . . . . . . . . . . . . . . . . . . . . . . . . A-65
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22.B Periodic Table of the Elements
(referred to carbon-12) . . . . . . . . . . . . . . . . A-84
22.C Water Chemistry CaCO3 Equivalents . . . . . . . A-85
22.D Saturation Concentrations of Dissolved Oxygen in
Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-87
22.E Names and Formulas of Important
Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . A-88
22.F Approximate Solubility Product
Constants at 25!
C . . . . . . . . . . . . . . . . . . . A-89
22.G Dissociation Constants of Acids at 25!
C . . . . . A-92
22.H Dissociation Constants of Bases at 25!
C . . . . . A-93
24.A Heats of Combustion for Common
Compounds . . . . . . . . . . . . . . . . . . . . . . . . A-94
24.B Approximate Properties of Selected Gases. . . . A-95
25.A National Primary Drinking Water
Regulations . . . . . . . . . . . . . . . . . . . . . . . . A-96
26.A Properties of Chemicals Used in Water
Treatment . . . . . . . . . . . . . . . . . . . . . . . . A-103
29.A Selected Ten States’ Standards . . . . . . . . . . . A-104
35.A USCS Soil Boring, Well, and Geotextile
Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . A-106
37.A Active Components for Retaining Walls
(straight slope backfill). . . . . . . . . . . . . . . A-108
37.B Active Components for Retaining Walls
(broken slope backfill) . . . . . . . . . . . . . . . A-109
37.C Curves for Determining Active and Passive Earth
Pressure Coefficients, ka and kp (with inclined
wall face, !, wall friction, , and
horizontal backfill) . . . . . . . . . . . . . . . . . . A-110
37.D Curves for Determining Active and Passive
Earth Pressure Coefficients, ka and kp
(with vertical face, wall friction, , and
sloping backfill, #) . . . . . . . . . . . . . . . . . . A-111
40.A Boussinesq Stress Contour Chart
(infinitely long and square footings) . . . . . A-112
40.B Boussinesq Stress Contour Chart
(uniformly loaded circular footings). . . . . . A-113
42.A Centroids and Area Moments of Inertia for Basic
Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . A-114
43.A Typical Properties of Structural Steel, Aluminum,
and Magnesium . . . . . . . . . . . . . . . . . . . . A-115
43.B Typical Mechanical Properties of Representative
Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . A-116
43.C Typical Mechanical Properties of Thermoplastic
Resins and Composites (room temperature,
after post-mold annealing) . . . . . . . . . . . . A-119
44.A Elastic Beam Deflection Equations . . . . . . . . A-120
44.B Stress Concentration Factors . . . . . . . . . . . . A-124
45.A Properties of Weld Groups . . . . . . . . . . . . . . A-125
47.A Elastic Fixed-End Moments . . . . . . . . . . . . . A-126
47.B Indeterminate Beam Formulas . . . . . . . . . . . A-128
47.C Moment Distribution Worksheet. . . . . . . . . . A-133
48.A ASTM Standards for Wire Reinforcement . . . A-134
52.A Reinforced Concrete Interaction Diagram,
$ = 0.60 (round, 4 ksi concrete,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-135
52.B Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-136
52.C Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-137
52.D Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-138
52.E Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-139
52.F Reinforced Concrete Interaction Diagram,
$ = 0.60 (square, 4 ksi concrete,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-140
52.G Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-141
52.H Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-142
52.I Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-143
52.J Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-144
52.K Reinforced Concrete Interaction Diagram,
$ = 0.60 (uniplane, 4 ksi concrete,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-145
52.L Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-146
52.M Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-147
52.N Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-148
52.O Reinforced Concrete Interaction Diagram,
60 ksi steel) . . . . . . . . . . . . . . . . . . . . . . . A-149
58.A Common Structural Steels . . . . . . . . . . . . . . A-150
58.B Properties of Structural Steel at High
Temperatures . . . . . . . . . . . . . . . . . . . . . A-151
59.A Values of Cb for Simply-Supported Beams . . . A-152
68.A Section Properties of Masonry Horizontal
Cross Sections . . . . . . . . . . . . . . . . . . . . . A-153
68.B Section Properties of Masonry Vertical
Cross Sections . . . . . . . . . . . . . . . . . . . . . A-155
68.C Ungrouted Wall Section Properties . . . . . . . . A-157
68.D Grouted Wall Section Properties. . . . . . . . . . A-158
69.A Column Interaction Diagram
(compression controls, g = 0.4) . . . . . . . . . A-159
69.B Column Interaction Diagram
69.C Column Interaction Diagram
viii C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L
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69.D Column Interaction Diagram
(tension controls, g = 0.4) . . . . . . . . . . . . A-162
69.E Column Interaction Diagram
69.F Column Interaction Diagram
70.A Mass Moments of Inertia . . . . . . . . . . . . . . . A-165
76.A Axle Load Equivalency Factors for Flexible
Pavements (single axles and pt of 2.5) . . . . A-166
76.B Axle Load Equivalency Factors for Flexible
Pavements (tandem axles and pt of 2.5). . . A-167
76.C Axle Load Equivalency Factors for Flexible
Pavements (triple axles and pt of 2.5) . . . . A-168
77.A Axle Load Equivalency Factors for Rigid
Pavements (single axles and pt of 2.5) . . . . A-169
77.B Axle Load Equivalency Factors for Rigid
Pavements (double axles and pt of 2.5) . . . A-170
77.C Axle Load Equivalency Factors for Rigid
Pavements (triple axles and pt of 2.5) . . . . A-171
78.A Oblique Triangle Equations . . . . . . . . . . . . . A-172
84.A Polyphase Motor Classifications and
Characteristics. . . . . . . . . . . . . . . . . . . . . A-173
84.B DC and Single-Phase Motor Classifications
and Characteristics . . . . . . . . . . . . . . . . . A-174
85.A Thermoelectric Constants
for Thermocouples . . . . . . . . . . . . . . . . . . A-175
87.A Standard Cash Flow Factors . . . . . . . . . . . . A-177
87.B Cash Flow Equivalent Factors . . . . . . . . . . . A-178
A P P E N D I C E S T A B L E O F C O N T E N T S ix
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Preface to the Fifteenth Edition
As I mentioned in the preface to the fourteenth edition,
I am chagrined to admit that I never read a single pre-
face while I was in college. Out of the prefaces of 100 or
so textbooks written by witty, clever, dedicated, and
famous experts, I never read a single word. Since then,
I have added hundreds of additional books to my
library, and I have only read a few of their prefaces. I
certainly have never written to an author and said,
“Hey, I loved your preface.” Nor have I ever received
such a communication about any book that I have
written. So, why does a book even need a preface?
The preface usually explains (a) why the author wanted
to write the book, (b) why the book turned out the way
it did, and (c) how the book differs from the previous
edition. Whereas subsequent chapters after the preface
constitute a book’s brain, the preface constitutes a book’s
heart and soul. You do not have to read its preface for a
book to have utility. The real “value” is in the subsequent
chapters. However, if you want a special connection with
the book, if you want to get inside the author’s head, if
you want to feel what you are learning, you should start
by reading its preface.
New books are written for a variety of reasons; new
editions less so. Typically, new editions are written
to replace old editions that have become somehow
inadequate. Although I have read some that come close,
authors do not intentionally write books to be inade-
quate when they are first published; instead, their books
just evolve into obsolescence and inadequacy over time.
Now and then, however, the reason behind publishing a
new edition is more complex.
For example, sometimes a perfectly good book can
become suddenly obsolete due to an external event. This
book has had many “sudden” new editions (and this
fifteenth edition is no exception), which were triggered
by some change to the civil PE exam. Typical exam
changes that have required publishing a new edition of
this book include revisions to the codes and standards
on which the civil PE exam is based, as well as changes
to the exam’s body of knowledge, format, administra-
tion, and emphasis on (i.e., number of questions for)
each subject.
Other times, new editions are driven by an author’s
desire to add new material or to improve preexisting
material. Sometimes they are driven by a need to incor-
porate accumulated corrections.
This fifteenth edition of the Civil Engineering Reference
Manual represents a complex agglomeration of the
reasons mentioned: revisions to exam codes and stan-
dards, addition of new and improved material, and
changes in how the exam is administered.
The reasons this fifteenth edition turned out the way that
it did are as complex as the reasons why it was written in
the first place. First, like its predecessors, this edition was
developed in an ethical and professional manner, which
means that only the NCEES published outline of exam
subjects guided me when I wrote this edition. It may
seem strange to you that a book designed to help you
pass the civil PE exam would not be based on the actual
exam content; however, though not associated with
NCEES in any way, both PPI and I share its passion
for exam security. Therefore, no actual exam content is
present in this book.
Second, as a professional engineer, I understand it is my
responsibility to protect the public, while still helping
qualified applicants to prepare for their future careers as
engineers. To help you review and learn the engineering
concepts necessary to pass the civil PE exam (and thus,
go on to protect the public), PPI went far beyond indus-
try standards in getting content checked and reviewed,
edited, and proofread.
Finally, this book is the way that it is because I wrote it
to be the kind of textbook I would want to help me learn
the concepts needed to pass the civil PE exam. You will
not have to go very far to find someone who will tell you
that this book goes beyond the subjects covered on the
civil PE exam. This is true. I have my own idea of what
engineering concepts the civil PE exam should cover,
and I have woven those concepts into this book. You
may disagree with this practice. Indeed, history has
shown that my expectations of what an engineer with
a minimum of four years of experience should know are
very high. (You would probably have to read trade and
industry publications every day to have the knowledge
that I want you to have when you take your civil PE
exam.) However, I have incorporated those concepts
because I do not just want you to review or learn “some
engineering” from this book. Instead, I actually want
you to be a better engineer for having read it. Think of
passing your exam as icing on the cake of being a great
engineer.
Regardless of why I wrote this edition, or why this edition
turned out the way that it did, inevitably, PPI’s Custo-
mer Care (what PPI calls “Customer Service”) depart-
ment will need to answer the pre-purchase questions
such as, “What has changed?” and “Do I really need to
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purchase this book?” and “I have the 12th edition. Can I
use it?” This department also has to deal with irate
customers who purchased the previous edition 25 months
ago and swear they would have waited if they had known
that Michael R. Lindeburg was writing a new edition.
(Hey, everyone: I’m always writing a new edition. But,
only the publisher knows when it is coming out.)
To answer those questions and to help the Customer
Care department answer such questions, I am writing
this script: “Yes. You absolutely need to get this new
edition. The author did not write it for nothing. He
wrote it because the exam changed. He wrote it because
it is better. He wrote it because it is more helpful, easier
to understand, more complete, and better organized.
This edition differs from the 10th (or 11th, or 12th,
etc.) edition in several hundred thousand ways. No, a
zillion ways. You will not know everything that has
changed, but you will benefit from the changes. You
do not use obsolete technology like a buggy whip,
leaded fuel, a rotary-dial phone, carbon paper, or an
IBM Selectric typewriter any more, do you? Instead,
you drive a motorized car, use unleaded fuel, talk
“hands-free” on your cell phone, send emails (from this
same phone!), and type on your personal laptop or
tablet. Still not convinced you need this edition? Let
me put it another way: You would not study for your
driver’s license test using a 1968 copy of your state’s
DMV driver handbook, would you? No, you would not.
So, why then, would you take a book based on obsolete
material into the most important exam of your career?
Do not be penny-wise and pound-foolish. In fact, do not
be foolish, period. You need this fifteenth edition.”
To satisfy the marketing department, which inevitably
wants to know what has changed since the fourteenth
edition, I will say: “This book is completely consistent
with the NCEES exam content and breadth-and-depth
format, and it is equally representative of the codes and
standards NCEES has adopted for the exam. In fact, the
largest replacement of content that took place in this
edition occurred in order to make material consistent
with NCEES-adopted codes and standards.” (The
actual codes and standards used by this book are listed
in this book’s “Codes Used to Prepare This Book” sec-
tion of the front matter.)
In addition to the 15 new appendices and the usual slate
of reader-suggested improvements, updates, and inevi-
table errata, this fifteenth edition incorporates changes
in structural design. For example, the concrete chapters
were updated to the 2011 ACI 318; the steel chapters
were updated to the 2011 AISC fourteenth edition; the
masonry chapters were updated to the 2012 IBC and the
2011 ACI 530/530.1, including deleting the one-third
allowable stress increase for wind and seismic loads;
and the traffic and transportation chapters were
updated to the 2012 Highway Capacity Manual. A lot
of new material has been added from AASHTO’s first-
ever 2010 Highway Safety Manual, which is now listed
by NCEES as a civil PE exam standard/code reference.
Four structural chapters have been augmented with
additional material from the 2012 AASHTO LRFD
Bridge Design Specifications. Statistics on new content
are listed in Sidebar S1 at the end of this preface.
The geotechnical chapters reflect NCEES’s reliance on
specific editions and/or parts of Minimum Design Loads
for Buildings and Other Structures (ASCE/SEI7), and
Occupational Safety and Health Standards for the Con-
struction Industry (OSHA 1926).
The structural chapters reflect NCEES’s reliance on spe-
cific editions and releases of Building Code Requirements
for Structural Concrete (ACI 318); Building Code
Requirements and Specification for Masonry Structures
(ACI 530/530.1); Steel Construction Manual (AISC Man-
ual); Minimum Design Loads for Buildings and Other
Structures (ASCE/SEI7); International Building Code
(IBC); National Design Specification for Wood Construc-
tion ASD/LRFD (NDS); PCI Design Handbook: Precast
and Prestressed Concrete (PCI); and AASHTO LRFD
Bridge Design Specifications (AASHTO LRFD).
For concrete, solutions based on ACI 318 App. C may
not be used on the exam. This book provides solutions
using only ACI 318 Chap. 9 (the so-called unified)
methods.
For steel, you may still use either load and resistance
factor design (LRFD) or allowable stress design (ASD)
methods on the exam. Therefore, this book presents
both solving methods in parallel so regardless of which
method you choose to study, you will be supported.
For masonry, only ASD may be used on the exam, with
the exception that the strength design (SD) method
covered in ACI 530 Sec. 3.3.5 is the only method per-
mitted to be used for slender walls with out-of-plane
loads. This book provides ASD solutions, followed by
SD solutions for additional reference.
As with the fourteenth edition, this book contains a
chapter covering some bridge topics. Bridge rating is
not specifically identified by NCEES as an exam sub-
ject, although bits and pieces of bridge design, analysis,
and construction are implicit in other civil engineering
activities that are covered on the exam. Given the great
likelihood of future transportation funding shortfalls,
even with the ongoing dedicated and noble efforts of
our state departments of transportation, I feel that all
professional engineers should be able to speak about the
U.S. transportation infrastructure. This bridges chapter
is a stub that I intend to continue to flesh out in future
editions according to my own observations.
The transportation chapters reflect NCEES’s reliance
on specific editions of A Policy on Geometric Design of
Highways and Streets (AASHTO Green Book);
AASHTO Guide for Design of Pavement Structures
(AASHTO GDPS-4-M); AASHTO Roadside Design
Guide; Mechanistic-Empirical Pavement Design Guide:
A Manual of Practice (AASHTO MEPDG); Guide for
the Planning, Design, and Operation of Pedestrian
Facilities (AASHTO Pedestrian); Highway Safety
xii C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L
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Manual (HSM); AI The Asphalt Handbook (MS-4); NRC
Highway Capacity Manual (HCM); Manual on Uniform
Traffic Control Devices (MUTCD); Design and Control
of Concrete Mixtures; and Hydraulic Design of Highway
Culverts.
The construction chapters reflect NCEES’s reliance on
specific editions of ACI 318; Guide to Formwork for Con-
crete (ACI 347); Formwork for Concrete (ACI SP-4);
AISC Manual, Design Loads on Structures During Con-
struction (ASCE 37); NDS, CMWB Standard Practice for
Bracing Masonry Walls Under Construction; and Occupa-
tional Safety and Health Standards for the Construction
Industry (OSHA 1926). Still, the majority of what NCEES
considers to be “construction” was already present in this
book and continues to be covered in other chapters. Earth-
work, foundations, slope stability, compaction, temporary
structures, and other geotechnical subjects are in their
own chapters, as are formwork, engineering economics,
construction law, and many other construction subjects.
Although there is no single chapter titled “Construction”
that contains everything NCEES thinks you should know,
this book presents the construction topic to the same
degree of detail as other topics—regardless of where you
read it.
Sidebar S.1 contains the statistics of what distinguishes
this edition from the previous editions.
Sidebar S.1 New Edition Statistics
chapters with new material, 11
new equations, 21
new tables, 8
new appendices, 15
new figures, 12
new index entries, 275
You and I are associates in the same honorable profes-
sion, and we are also members of the same species. In
those regards, we exist to help each other. Helping you
review and learn the subjects in the chapters that follow
was always foremost in my mind. With every word that
I wrote, I wanted to help you conduct an ethical review
that would make both of us proud. This book is proof
that I have been here for you. Now, you should go do
your best to serve humanity. That starts by passing the
PE exam.
P R E F A C E T O T H E F I F T E E N T H E D I T I O N xiii
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Acknowledgments
Every new edition is a lot of work, for someone. Some-
times, as when new content is needed, the work of bring-
ing out a new edition falls to the author; sometimes the
work falls to the publisher’s editorial and production
staff, as when existing content is reformatted and reor-
ganized; and sometimes the work falls to one or more
subject matter experts, as when specialized knowledge is
required to integrate changes in standards, codes, and
federal legislation. Sometimes, one player shoulders a
disproportionate share of the load; sometimes one player
gets off easier than another.
This fifteenth edition was one of those new editions where
a lot of people contributed. If anything, the author got off
the easiest (my hand is up). Yes, there is new content.
However, the biggest content changes were updates to
the structural and transportation chapters. Regarding
those changes, this book is the beneficiary of Akash
Rao, PE, LEED AP BD+C; Kent A. Harries; Joshua
T. Frohman, PE; Alfredo Cely, PE; Norman R. Voigt,
PE, PLS; and Ralph Arcena. Mr. Rao developed content
for the structural chapters in accordance with AASHTO
LRFD Bridge Design Specifications (AASHTO LRFD),
sixth edition; National Design Specification for Wood
Construction ASD/LRFD (NDS), 2012 edition; Steel
Construction Manual (AISC), fourteenth edition; and
Building Code Requirements for Structural Concrete
(ACI 318), 2011 edition. Mr. Harries reviewed and
revised content for the structural chapters to be consis-
tent with AASHTO LRFD. Mr. Frohman developed
content for Chap. 75, Highway Safety, in accordance
with Highway Safety Manual (HSM), first edition.
Mr. Cely and Mr. Voight contributed their time and
engineering expertise to Chap. 75 by reviewing the
added HSM content. I would also like to thank Mr. Arcena
for meticulously checking calculations throughout this
edition.
Now, I would like to introduce you to the “I could not
have done it without you” crew. The talented team at
PPI that produced this edition is the same team that
produced the new edition of Practice Problems for the
Civil Engineering PE Exam, and the team members
deserve just as many accolades here as I gave them in
the Acknowledgments of that book. As it turns out,
producing two new books is not twice as hard as pro-
ducing one new book. Considering all of the connections
between the two books, producing this edition is greatly
complicated by the need for consistency with and cross-
references to the Practice Problems. Producing a set of
interrelated books is not a task for the faint of heart.
At PPI, the task of making the vision of a new edition
into a reality fell to a Product Development and Imple-
mentation Department team that consisted of Sam
Webster, editorial manager; Serena Cavanaugh, acquisi-
tions editor; Nicole Evans, associate project manager;
Tracy Katz, lead editor; Thomas Bliss, David Chu, Tyler
Hayes, Sierra Cirimelli-Low, Julia Lopez, Scott Marley,
Ellen Nordman, and Ian A. Walker, copy editors; Tom
Bergstrom, production associate and technical illustrator;
Kate Hayes, production associate; Cathy Schrott, pro-
duction services manager; and Sarah Hubbard, director
of product development and implementation. I wish to
thank Jenny Lindeburg King, associate editor-in-chief,
for her instrumental role in ensuring this edition met
PPI’s quality standards.
I also wish to recognize and honor Kate Hayes, who
retired from PPI in October of 2015. Kate is a 20-year
employee whose fingers have competently transposed,
formed, programmed, and paginated all of my books.
However, this fifteenth edition of the Civil Engineering
Reference Manual will be her last Michael R. Lindeburg
book—at least for a little while. I am grateful for and
humbled by her attitude toward and dedication to the
PPI cause, and I am amazed at her professionalism. But,
her legacy is not defined by the hundreds of new books,
new editions, and reprints that she has worked on over
the past two decades. It is not even defined by the
millions of engineers, architects, surveyors, interior
designers, and other building and construction profes-
sionals on whose careers she has had an impact. Her
true, lasting legacy is defined by the relationships she
formed with PPI’s coworkers, past and present, who
have found her to be respectful, helpful, caring, and
infinitely delightful to work and play with. What a role
model! What an inspiration! What a friend! I miss her
already. I am looking forward to the day when PPI
pushes a project in her direction (to be worked on in
the comfort of her sofa, of course).
This edition incorporates the comments, questions, sug-
gestions, and errata submitted by many people who have
used the previous edition for their own preparations. As
an author, I am humbled to know that these individuals
have read the previous edition in such detail as to notice
typos, illogic, and other errata, and that they subse-
quently took the time to share their observations with
me. Their suggestions have been incorporated into this
edition, and their attention to detail will benefit you and
all future readers. The following is a partial list (in
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alphabetical order) of some of those who have improved
this book through their comments.
Alex Bachowski; Mike Berkey; Robert Bernard;
Laura Buchanan; Rebecca Carmine; Waqar
Cheema; Redi Gjecka; Jacqueline Gonsalves; Joel
Hinnenkamp; Peter Kauffmann; Paul Lefebvre;
Yarrow Murphy; Dominic Pontarolo; Aliasgar
Rangwala; Jeffrey Rodgers; Ken Sanoski; Sean
Shigenaga; Ahmed Thabet; Julian Vaduva; and
Bernard Vannoy
This edition shares a common developmental heritage
with all of its previous editions. There are hundreds of
additional people that I mentioned by name in the
acknowledgments of those books. They are not forgot-
ten, and their names will live on in the tens of thou-
sands of old editions that remain in widespread
circulation. For this edition, though, there is not a
single contributor that I intentionally excluded. Still,
I could have slipped up and forgotten to mention you. I
hope you will let me know if you should have been
credited, but were inadvertently left out. I would
appreciate the opportunity to list your name in the
next printing of this edition.
Near the end of the acknowledgments, after mentioning
many people who contributed to the book and, there-
fore, could be blamed for a variety of types of errors, it is
common for an author to say something like, “I take
responsibility for all of the errors you find in this book.”
Or, “All of the mistakes are mine.” This is certainly true,
given the process of publishing, since the author sees
and approves the final version before his or her book
goes to the printer. You would think that after more
than 35 years of writing, I would have figured out how
to write something without making a mistake and how
to proofread without missing those blunders that are so
obvious to readers. However, such perfection continues
to elude me. So, yes, the finger points straight at me.
All I can say instead is that I will do my best to respond
to any suggestions and errata that you report through
PPI’s website, ppi2pass.com/errata. I would love to
see your name in the acknowledgments for the next
edition.
Thank you, everyone!
xvi C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L
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Codes and Standards
The information that was used to write and update
this book was based on the exam specifications at the
time of publication. However, as with engineering
practice itself, the PE exam is not always based on the
most current codes or cutting-edge technology. Simi-
larly, codes, standards, and regulations adopted by state
and local agencies often lag issuance by several years. It
is likely that the codes that are most current, the codes
that you use in practice, and the codes that are the basis
of your exam will all be different.
PPI lists on its website the dates and editions of the
codes, standards, and regulations on which NCEES has
announced the PE exams are based. It is your respon-
sibility to find out which codes are relevant to your exam.
CONSTRUCTION DESIGN STANDARDS
ACI 318: Building Code Requirements for Structural
Concrete, 2011. American Concrete Institute, Farming-
ton Hills, MI.
ACI 347: Guide to Formwork for Concrete, 2004. Amer-
ican Concrete Institute, Farmington Hills, MI. (as an
appendix of ACI SP-4, Seventh ed.)
ACI SP-4: Formwork for Concrete, Seventh ed., 2005.
American Concrete Institute, Farmington Hills, MI.
AISC: Steel Construction Manual, Fourteenth ed., 2011.
American Institute of Steel Construction, Inc.,
Chicago, IL.
ASCE 37: Design Loads on Structures During Con-
struction, 2002. American Society of Civil Engineers,
Reston, VA.
CMWB: Standard Practice for Bracing Masonry Walls
Under Construction, 2012. Council for Masonry Wall
Bracing, Mason Contractors Association of America,
Lombard, IL.
MUTCD-Pt 6: Manual on Uniform Traffic Control
Devices—Part 6, Temporary Traffic Control, 2009.
U.S. Department of Transportation, Federal Highway
Administration, Washington, DC.
NDS: National Design Specification for Wood Construc-
tion ASD/LRFD, 2012 ed. American Wood Council,
Washington, DC.
OSHA 1926: Occupational Safety and Health Regula-
tions for the Construction Industry (U.S. Federal ver-
sion). U.S. Department of Labor, Washington, DC.
GEOTECHNICAL DESIGN STANDARDS
ASCE/SEI7: Minimum Design Loads for Buildings and
Other Structures, 2010. American Society of Civil Engi-
neers, Reston, VA.
sion). U.S. Department of Labor, Washington, DC.
STRUCTURAL DESIGN STANDARDS
AASHTO LRFD: AASHTO LRFD Bridge Design Spec-
ifications, Sixth ed., 2012. American Association of
State Highway and Transportation Officials, Washing-
ton, DC.
ACI 3181
: Building Code Requirements for Structural
Concrete, 2011. American Concrete Institute, Farming-
ton Hills, MI.
ACI 530/530.12
: Building Code Requirements and Spec-
ification for Masonry Structures (and companion com-
mentaries), 2011. The Masonry Society, Boulder, CO;
American Concrete Institute, Detroit, MI; and Struc-
tural Engineering Institute of the American Society of
Civil Engineers, Reston, VA.
AISC: Steel Construction Manual, Fourteenth ed.,
2011. American Institute of Steel Construction, Inc.,
Chicago, IL.
ASCE/SEI7: Minimum Design Loads for Buildings and
Other Structures, 2010. American Society of Civil Engi-
neers, Reston, VA.
AWS D1.1/D1.1M3
: Structural Welding Code—Steel,
Twenty-second ed., 2010. American Welding Society,
Miami, FL.
AWS D1.2/D1.2M4
: Structural Welding Code—Alumi-
num, Sixth ed., 2014. American Welding Society,
Miami, FL.
1
ACI 318 App. C does not apply to the Civil PE structural depth
exam.
2
Only the Allowable Stress Design (ASD) method may be used on the
exam, except that ACI 530 Sec. 3.3.5 (strength design) may be used for
walls with out-of-plane loads.
3
AWS D1.1, AWS D1.2, and AWS D1.4 are listed in the Codes,
Standards, and Documents subsection of NCEES’s Civil PE structural
depth exam specifications.
4
See Ftn. 3.
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AWS D1.4/D1.4M5
: Structural Welding Code—
Reinforcing Steel, Seventh ed., 2011. American Welding
Society, Miami, FL.
IBC: 2012 International Building Code (without sup-
plements). International Code Council, Inc., Falls
Church, VA.
NDS6
: National Design Specification for Wood Con-
struction ASD/LRFD, 2012 ed., and National Design
Specification Supplement, Design Values for Wood Con-
struction, 2012 ed. American Wood Council, Washing-
ton, DC.
OSHA 19107
: Occupational Safety and Health Standards
(U.S. Federal version). U.S. Department of Labor,
Washington, DC.
sion) Subpart E, Personal Protective and Life Saving
Equipment, 1926.95–1926.107; Subpart M, Fall Protec-
tion, 1926.500–1926.503, App. A–E; Subpart Q, Con-
crete and Masonry Construction, 1926.700–1926.706,
with App. A; and Subpart R, Steel Erection,
1926.750–1926.761, with App. A–H. U.S. Department
of Labor, Washington, DC.
PCI: PCI Design Handbook: Precast and Prestressed
Concrete, Seventh ed., 2010. Precast/Prestressed Con-
crete Institute, Chicago, IL.
TRANSPORTATION DESIGN STANDARDS
AASHTO GDPS: AASHTO Guide for Design of Pave-
ment Structures (GDPS-4-M), 1993, and 1998 supple-
ment. American Association of State Highway and
Transportation Officials, Washington, DC.
AASHTO Green Book: A Policy on Geometric Design
of Highways and Streets, Sixth ed., 2011. American
Association of State Highway and Transportation Offi-
cials, Washington, DC.
AASHTO: Guide for the Planning, Design, and Opera-
tion of Pedestrian Facilities, First ed., 2004. American
Association of State Highway and Transportation Offi-
cials, Washington, DC.
HSM: Highway Safety Manual, First ed., 2010. Ameri-
can Association of State Highway and Transportation
Officials, Washington, DC.
AASHTO MEPDG: Mechanistic-Empirical Pavement
Design Guide: A Manual of Practice, Interim ed.,
2008. American Association of State Highway and
Transportation Officials, Washington, DC.
AASHTO: Roadside Design Guide, Fourth ed., 2011.
American Association of State Highway and Transpor-
tation Officials, Washington, DC.
AI: The Asphalt Handbook (MS-4), Seventh ed., 2007.
Asphalt Institute, Lexington, KY.
FHWA: Hydraulic Design of Highway Culverts, Hydrau-
lic Design Series no. 5, Publication no. FHWA-HIF-12-
026, Third ed., 2012. U.S. Department of Transportation,
Federal Highway Administration, Washington, DC.
HCM: Highway Capacity Manual, 2010 ed. Transporta-
tion Research Board, National Research Council,
Washington, DC.
MUTCD: Manual on Uniform Traffic Control Devices,
2009 (including Revisions 1 and 2, May 2012). U.S.
Department of Transportation, Federal Highway
Administration, Washington, DC.
PCA: Design and Control of Concrete Mixtures, Fifteenth
ed., 2011. Portland Cement Association, Skokie, IL.
5
See Ftn. 3.
6
Only the ASD method may be used for wood design on the exam.
7
Part 1910 is listed in the Codes, Standards, and Documents subsec-
tion of NCEES’s Civil PE structural depth exam specifications.
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Introduction
PART 1: HOW YOU CAN USE THIS
BOOK
QUICKSTART
If you never read the material at the front of your books
anyway, if you are in a hurry to begin, and you only
want to read one paragraph, here it is:
Most chapters in this book are independent. Start
with any one and look through it. Use the index
extensively. Decide if you are going to work prob-
lems in that topic. If so, solve as many problems
in that topic as time allows. Do not stop studying
until the exam. Start right now! Quickly! Good
luck.
However, if you want to begin a thorough review, you
should probably try to find out everything there is to
know about the National Council of Examiners for Engi-
neering and Surveying (NCEES) Civil PE exam. The
rest of this Introduction is for you.
IF YOU ARE A PRACTICING ENGINEER
If you are a practicing engineer and have obtained this
book as a general reference handbook, it will probably
sit in your bookcase until you have a specific need.
However, if you are preparing for the PE exam in civil
engineering, the following suggestions may help.
. Find out the current edition of this book. You might
be reading this book long after it was published.
Newer editions mean that the codes, stan-
dards, and regulations on which the exam is
based are not represented in the older edition,
that the exam body of knowledge has changed,
and/or the exam format and policies have
changed. Older editions are no longer appropriate
for the current exam, and it is not reasonable for you
to expect an older edition to serve your needs when it
is out of date.
. Be reasonable in what you expect from this book.
Much like any textbook, this book is a compilation
of material designed to help you learn certain sub-
jects—in this case, subjects on the exam. This book
does not contain “everything” that you need to know
to pass the exam, particularly the afternoon part of
the exam. (PPI has published reference manuals
specifically for the afternoon parts.) You will need
to assemble a library of other references. This book is
not a substitute for the experience, general knowl-
edge, and judgment that engineers are expected to
demonstrate on the exam. This book will help you
learn subjects. It will not help you pass the exam if
you go into the exam unprepared or unqualified.
. Become intimately familiar with this book. This
means knowing the order of the chapters, the approx-
imate locations of important figures and tables, what
appendices are available, and so on.
. Use the subject title tabs along the side of each page.
The tab names correspond to the exam organization.
. Use Table 1 and Table 2 of this Introduction to learn
which subjects in this book are not specific exam
subjects. Some chapters in this book are supportive
and do not cover specific exam topics. However,
these chapters provide background and support for
the other chapters.
. Some engineers read every page in a chapter. Some
merely skim through a chapter and its appendices. In
either case, you must familiarize yourself with the
subjects before starting to solve practice problems.
. Identify and obtain a set of 10–30 solved practice
problems for each of the exam subjects. I have writ-
ten an accompanying book, Practice Problems for the
Civil Engineering PE Exam, for this purpose. Other
resources include the Civil PE Practice exam, books
in the Six-Minute Solutions series, and the Civil PE
Exam Cafe, all published by PPI. You may use prob-
lem sets from your old textbooks, college notes, or
review course if they are more convenient. Regardless
of the resources you use, you should know that you
will encounter two types of practice problems. Some
problems look like exam problems. They are short
and have multiple-choice answers. These types of
problems are good for familiarizing yourself with the
exam format. However, they are not very effective at
exposing you to the integration of multiple concepts
in problem solving, for familiarizing you with this
book, and for making sure you have seen all of the
“gotchas” that are possible in a subject. To address
those requirements, you will need some longer prob-
lems. Practice Problems for the Civil Engineering PE
Exam contains both types of problems.
. Most of the problems in Practice Problems for the Civil
Engineering PE Exam are presented in both custom-
ary U.S. units (also known as the “U.S. Customary
System” or “USCS,” “English units,” inch-pound units,”
and “British units”) and the International System of
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Units (SI). Initially, work through the problems in U.S.
units. (All structural engineering problems on the
exam use U.S. units.) If you have time at the end of
your review, start over and solve all of the problems in
SI units.
. Set a reasonable limit on the time you spend on each
subject. It is not necessary to solve an infinite num-
ber of practice problems. The number of practice
problems you attempt will depend on how much
time you have and how skilled you are in the subject.
. If it is not already your habit, practice carrying units
along in all calculations. Many errors are caused by,
and many incorrect exam answer options are based
on, common mistakes with units. Pounds do not
work in F ¼ ma; and ft3
/sec does not cancel gpm.
When working in U.S. units, you will find equations
in this book in which the quantity g=gc appears. For
calculations at standard gravity, the numerical value
of this fraction is 1.00. Therefore, it is necessary to
incorporate this quantity only in calculations with a
nonstandard gravity or when you are being meticu-
lous with units.
. Use the solutions to your practice problems to check
your work. If your answer is not correct, figure out
why.
. To minimize time spent in searching for often-used
formulas and data, prepare a one-page summary of
all the important formulas and information in each
subject area. You can then use these summaries
during the exam instead of searching in this book.
You may want to consider Quick Reference for the
Civil Engineering PE Exam, which PPI has pub-
lished for this type of use.
. Use the index extensively. Every significant term,
law, theorem, and concept has been indexed in every
conceivable way—backward and forward—using
fuzzy logic synonyms in anticipation of frantic exam
searches. If you do not recognize a term used, look
for it in the index. Many engineers bring a separate
copy of the index with them to the exam.
. Some subjects appear in more than one chapter.
(Construction engineering is a good example of a
subject that resists single-chapter organization.)
Use the index liberally to learn all there is to know
about a particular subject.
IF YOU ARE AN INSTRUCTOR
The first two editions of this book consisted of a series of
handouts prepared for the benefit of my PE review
courses. These editions were intended to be compilations
of all the long formulas, illustrations, and tables of data
that I did not have time to put on the chalkboard. You
can use this edition in the same way.
If you are teaching a review course for the PE exam,
you can use the material in this book as a guide to
prepare your lectures.
I have always tried to overprepare my students. For
that reason, the homework problems (i.e., example
problems in this book and practice problems in Practice
Problems for the Civil Engineering PE Exam) are often
more difficult and more varied than actual exam ques-
tions. Also, you will appreciate the fact that it is more
efficient to cover several procedural steps in one problem
than to ask simple “one-liners” or definition questions.
That is the reason that the example and homework
problems are often harder and longer than actual exam
problems.
To do all the homework for some chapters requires
approximately 15 to 20 hours. If you are covering one
or more chapters per week, that is a lot of homework.
“Capacity assignment” is the goal in my review courses.
If you assign 20 hours of homework and a student is able
to put in only 10 hours that week, that student will have
worked to his or her capacity. After the PE exam, that
student will honestly say that he or she could not have
prepared any more than he or she did in your course.
For that reason, you have to assign homework on the
basis of what is required to become proficient in the
subjects of your lecture. You must resist assigning only
the homework that you think can be completed in an
arbitrary number of hours.
Homework assignments in my review courses are not
individually graded. Instead, students are permitted to
make use of existing solutions to learn procedures and
techniques to the problems in their homework set, such
as those in Practice Problems for the Civil Engineering
PE Exam book, which contains solutions to all practice
problems. However, each student must turn in a com-
pleted set of problems for credit each week. Though I do
not correct the homework problems, I address comments
or questions emailed to me, posted on the course forum,
or written on the assignments.
I believe that students should start preparing for the
PE exam at least six months before the exam date.
However, most wait until three or four months before
getting serious. Because of that, I have found that a 13-
or 14-week format works well for a live PE review
course. It is a little rushed, but the course is over before
everyone gets bored with my jokes. Each week, there is
a three-hour meeting, which includes a lecture and a
short break. Table 1 outlines a course format that
might work for you. If you can add more course time,
your students will appreciate it. Another lecture cover-
ing water resources or environmental engineering
would be wonderful. However, I do not think you can
cover the full breadth of material in much less time or
in fewer weeks.
I have tried to order the subjects in a logical, progressive
manner, keeping my eye on “playing the high-probability
subjects.” I cover the subjects that everyone can learn
(e.g., fluids and soils) early in the course.
I leave the subjects that only daily practitioners should
attempt (e.g., concrete, steel, and highway capacity) to
the end.
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Table 1 Typical PE Exam Review Course Format
meeting subject covered chapters
1 Introduction to the Exam, Engineering Economics 90, 87
2 Fluids, Conduit Flow, and Pumps 14–18
3 Open Channel Flow 19
4 Hydrology 20–21
5 Water Supply 25–26
6 Wastewater and the Environment 28–30, 31–34
7 Soils, Foundations, Settlement, and Retaining Walls 35–40
8 Surveying and Concrete Mixing 78, 49
9 Highway Design and Traffic Analysis 73, 75, 79
10 Construction Engineering 80–83
11 Mechanics of Materials 41–47
12 Concrete Design 48–50
13 Steel Design 59, 61–62
Lecture coverage of some exam subjects is necessarily
brief; other subjects are not covered at all. These omis-
sions are intentional; they are not the result of schedul-
ing omissions. Why? First, time is not on our side in a
review course. Second, some subjects rarely contribute
to the exam. Third, some subjects are not well-received
by the students. For example, I have found that very
few people try to become proficient in bridges, timber,
and masonry if they do not already work in those areas.
Most nonstructural civil engineers stick with the non-
structural basics: fluids, soils, surveying, water supply,
and wastewater. Most structural engineers stick with
structural subjects. Unless you have six months in which
to teach your PE review, your students’ time can be
better spent covering other subjects.
All the skipped chapters and any related practice prob-
lems are presented as floating assignments to be made
up in the students’ “free time.”
I strongly believe in exposing my students to a realistic
sample exam, but I no longer administer an in-class
mock exam. Since the review course usually ends only
a few days before the real PE exam, I hesitate to make
students sit for several hours in the late evening to take
a “final exam.” Rather, I distribute and assign a take-
home practice exam at the first meeting of the review
course.
If the practice exam is to be used as an indication of
preparedness, caution your students not to look at the
practice exam prior to taking it. Looking at the practice
exam, or otherwise using it to direct their review, will
produce unwarranted specialization in subjects con-
tained in the practice exam.
There are many ways to organize a PE review course,
depending on your available time, budget, intended
audience, facilities, and enthusiasm. However, all good
course formats have the same result: The students
struggle with the workload during the course, and then
they breeze through the exam after the course.
PART 2: EVERYTHING YOU EVER
WANTED TO KNOW ABOUT THE
PE EXAM
WHAT IS THE FORMAT OF THE PE EXAM?
The NCEES PE exam in civil engineering consists of two
four-hour sessions separated by a one-hour lunch period.
The morning “breadth” session is taken by all examinees.
There are five afternoon “depth” modules: construction,
geotechnical, structural, transportation, and water
resources and environmental. (The depth modules may
be referred to as “discipline-specific,” or DS, modules,
borrowing a term from the FE exam.) You must be
approved by your state licensing board before you can
register for the exam using the “MyNCEES” system on
the NCEES website. You select your depth module when
you register for the exam. At the exam, you will receive
an exam booklet for the depth module you selected dur-
ing registration. Switching modules is not possible. Your
answer sheet will be scored based on the module you
selected during registration.
Both the morning and afternoon sessions contain 40 ques-
tions in multiple-choice (i.e., “objective”) format. As this
is a “no-choice” exam, you must answer all questions in
each session correctly to receive full credit. There are no
optional questions.
WHAT SUBJECTS ARE ON THE PE EXAM?
NCEES has published a description of subjects on the
exam. Irrespective of the published exam structure, the
exact number of questions that will appear in each sub-
ject area cannot be predicted reliably.
There is no guarantee that any single subject will occur
in any quantity. One of the reasons for this is that some
of the questions span several disciplines. You might
consider a pump selection question to come from the
subject of fluids, while NCEES might categorize it as
engineering economics.
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Table 2 Detailed Analysis of Tested Subjects
MORNING SESSION
(40 multiple-choice questions)
Project planning: quantity take-off methods; cost estimating; project schedules; activity identification and sequencing
Means and methods: construction loads; construction methods; temporary structures and facilities
Soil mechanics: lateral earth pressure; soil consolidation; effective and total stresses; bearing capacity; foundation settlement; slope
stability; shear (e.g., forces and stresses); axial (e.g., forces and stresses); combined stresses; deflection; beams; columns; slabs;
footings; retaining walls
Structural mechanics: dead and live loads; trusses; bending (e.g., moments and stresses); shear (e.g., forces and stresses); axial (e.g.,
forces and stresses); combined stresses; deflection; beams; columns; slabs; footings; retaining walls
Hydraulics and hydrology: open-channel flow; stormwater collection and drainage (e.g., culvert, stormwater inlets, gutter flow,
street flow, storm sewer pipes); storm characteristics (e.g., storm frequency, rainfall measurement, and distribution); runoff
analysis (e.g., rational and SCS/NRCS methods, hydrographic application, runoff time of concentration); detention/retention
ponds; pressure conduit (e.g., single pipe, force mains, Hazen-Williams, Darcy Weisbach, major and minor losses); energy and/or
continuity equation (e.g., Bernoulli)
Geometrics: basic circular curve elements (e.g., middle ordinate, length, chord, radius); basic vertical curve elements; traffic volume
(e.g., vehicle mix, flow, and speed)
Materials: soil classification and boring log interpretations; soil properties (e.g., strength, permeability, compressibility, phase
relationships); concrete (e.g., nonreinforced, reinforced); structural steel; material test methods and specification conformance;
compaction
Site development: excavation and embankment (e.g., cut and fill); construction site layout and control; temporary and permanent
soil erosion and sediment control (e.g., construction erosion control and permits, sediment transport, channel/outlet protection);
impact of construction on adjacent facilities; safety (e.g., construction, roadside, work zone)
AFTERNOON SESSIONS
(40 multiple-choice questions)*
CIVIL/CONSTRUCTION DEPTH EXAM
Earthwork construction and layout (6): excavation and embankment (e.g., cut and fill); borrow pit volumes; site layout and control;
earthwork mass diagrams and haul distance; site and subsurface investigations
Estimating quantities and costs (6): quantity take-off methods; cost estimating; cost analysis for resource selection; work
measurement and productivity
Construction operations and methods (7): lifting and rigging; crane stability; dewatering and pumping; equipment operations (e.g.,
selection, production, economics); deep foundation installation
Scheduling (5): construction sequencing; activity time analysis; critical path method (CPM) analysis; resource scheduling and
leveling; time-cost trade-off
Material quality control and production (6): material properties and testing (e.g., soils, concrete, asphalt); weld and bolt installation;
quality control process (QA/QC); concrete proportioning and placement; concrete maturity and early strength evaluation
Temporary structures (7): construction loads, codes, and standards; formwork; falsework and scaffolding; shoring and reshoring;
bracing and anchorage for stability; temporary support of excavation
Health and safety (3): OSHA regulations and hazard identification/abatement; safety management and statistics; work zone and
public safety
CIVIL/GEOTECHNICAL DEPTH EXAM
Site characterization (5): interpretation of available existing site data and proposed site development data (e.g., aerial photography,
geologic and topographic maps, GIS data, as-built plans, planning studies and reports); subsurface exploration planning;
geophysics (e.g., GPR, resistivity, seismic methods); drilling techniques (e.g., hollow stem auger, cased boring, mud rotary, air
rotary, rock coring, sonic drilling); sampling techniques (e.g., split-barrel sampling, thin-walled tube sampling, handling and
storage); in situ testing (e.g., standard penetration testing, cone penetration testing, pressure meter testing, dilatometer testing,
field vane shear); description and classification of soils (e.g., Burmeister, Unified Soil Classification System, AASHTO, USDA);
rock classification and characterization (e.g., recovery, rock quality designation, RMR, weathering, orientation); groundwater
exploration, sampling, and characterization
Soil mechanics, laboratory testing, and analysis (5): index properties and testing; strength testing of soil and rock; stress-strain
testing of soil and rock; permeability testing properties of soil and rock; effective and total stresses
*The numbers in parentheses reflect the approximate number of questions for a given exam topic.
(continued)
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Table 2 Detailed Analysis of Tested Subjects (continued)
Field materials testing, methods, and safety (3): excavation and embankment, borrow source studies, laboratory and field
compaction; trench and construction safety; geotechnical instrumentation (e.g., inclinometer, settlement plates, piezometer,
vibration monitoring)
Earthquake engineering and dynamic loads (2): liquefaction analysis and mitigation techniques; seismic site characterization,
including site classification using ASCE/SEI7; pseudo-static analysis and earthquake loads
Earth structures (4): slab on grade; ground improvement (e.g., grouting, soil mixing, preconsolidation/wicks, lightweight
materials); geosynthetic applications (e.g., separation, strength, filtration, drainage, reinforced soil slopes, internal stability of
MSE); slope stability and slope stabilization; earth dams, levees, and embankments; landfills and caps (e.g., interface stability,
drainage systems, lining systems); pavement structures (rigid, flexible, or unpaved), including equivalent single-axle load
(ESAL), pavement thickness, subgrade testing, subgrade preparation, maintenance and rehabilitation treatments; settlement
Groundwater and seepage (3): seepage analysis/groundwater flow; dewatering design, methods, and impact on nearby structures;
drainage design/infiltration; grouting and other methods of reducing seepage
Problematic soil and rock conditions (3): Karst; collapsible, expansive, and sensitive soils; reactive/corrosive soils; frost
susceptibility
Earth retaining structures (ASD or LRFD) (5): lateral earth pressure; load distribution; rigid retaining wall stability analysis (e.g.,
CIP, gravity, external stability of MSE, crib, bin); flexible retaining wall stability analysis (e.g., soldier pile and lagging, sheet
pile, secant pile, tangent pile, diaphragm walls, temporary support of excavation, braced and anchored walls); cofferdams;
underpinning (e.g., effects on adjacent construction); ground anchors, tie-backs, soil nails, and rock anchors for foundations and
slopes
Shallow foundations (ASD or LRFD) (5): bearing capacity; settlement, including vertical stress distribution
Deep foundations (ASD or LRFD) (5): single-element axial capacity (e.g., driven pile, drilled shaft, micropile, helical screw piles,
auger cast piles); lateral load and deformation analysis; single-element settlement; downdrag; group effects (e.g., axial capacity,
settlement, lateral deflection); installation methods/hammer selection; pile dynamics (e.g., wave equation, high-strain dynamic
testing, signal matching); pile and drilled-shaft load testing; integrity testing methods (e.g., low-strain impact integrity testing,
ultrasonic cross-hole testing, coring, thermal integrity testing)
CIVIL/STRUCTURAL DEPTH EXAM
Analysis of Structures (14)
Loads and load applications (4): dead loads; live loads; construction loads; wind loads; seismic loads; moving loads (e.g., vehicular,
cranes); snow, rain, ice; impact loads; earth pressure and surcharge loads; load paths (e.g., lateral and vertical); load
combinations; tributary areas
Forces and load effects (10): diagrams (e.g., shear and moment); axial (e.g., tension and compression); shear; flexure; deflection;
special topics (e.g., torsion, buckling, fatigue, progressive collapse, thermal deformation, bearing)
Design and Details of Structures (20)
Materials and material properties (5): concrete (e.g., plain, reinforced, cast-in-place, precast, pretensioned, post-tensioned); steel
(e.g., structural, reinforcing, cold-formed); timber; masonry (e.g., brick veneer, CMU)
Component design and detailing (15): horizontal members (e.g., beams, slabs, diaphragms); vertical members (e.g., columns, bearing
walls, shear walls); systems (e.g., trusses, braces, frames, composite construction); connections (e.g., bearing, bolted, welded,
embedded, anchored); foundations (e.g., retaining walls, footings, combined footings, slabs, mats, piers, piles, caissons, drilled
shafts)
Codes and Construction (6)
Codes, standards, and guidance documents (4): International Building Code (IBC); Building Code Requirements for Structural
Concrete (ACI 318); Building Code Requirements and Specification for Masonry Structures (ACI 530/530.1); PCI Design
Handbook: Precast and Prestressed Concrete (PCI); Steel Construction Manual (AISC); National Design Specification for Wood
Construction ASD/LRFD (NDS); AASHTO LRFD Bridge Design Specifications (AASHTO LRFD); Minimum Design Loads for
Buildings and Other Structures (ASCE/SEI7); Structural Welding Code—Steel (AWS D1.1); Structural Welding Code—
Aluminum (AWS D1.2); Structural Welding Code—Reinforcing Steel (AWS D1.4); Occupational Safety and Health Standards
(OSHA 1910); Safety and Health Regulations for Construction (OSHA 1926)
Temporary structures and other topics (2): special inspections; submittals; formwork; falsework and scaffolding; shoring and
reshoring; concrete maturity and early strength evaluation; bracing; anchorage; OSHA regulations; safety management
(continued)
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Table 2 Detailed Analysis of Tested Subjects (continued)
CIVIL/TRANSPORTATION DEPTH EXAM
Traffic engineering (capacity analysis and transportation planning) (11): uninterrupted flow (e.g., level of service, capacity); street
segment interrupted flow (e.g., level of service, running time, travel speed); intersection capacity (e.g., at grade, signalized,
roundabout, interchange); traffic analysis (e.g., volume studies, peak hour factor, speed studies, modal split); trip generation and
traffic impact studies; accident analysis (e.g., conflict analysis, accident rates, collision diagrams); nonmotorized facilities (e.g.,
pedestrian, bicycle); traffic forecast; highway safety analysis (e.g., crash modification factors, Highway Safety Manual)
Horizontal design (4): basic curve elements (e.g., middle ordinate, length, chord, radius); sight distance considerations;
superelevation (e.g., rate, transitions, method, components); special horizontal curves (e.g., compound/reverse curves, curve
widening, coordination with vertical geometry)
Vertical design (4): vertical curve geometry; stopping and passing sight distance (e.g., crest curve, sag curve); vertical clearance
Intersection geometry (4): intersection sight distance; interchanges (e.g., freeway merge, entrance and exit design, horizontal design,
vertical design); at-grade intersection layout, including roundabouts
Roadside and cross-section design (4): forgiving roadside concepts (e.g., clear zone, recoverable slopes, roadside obstacles); barrier
design (e.g., barrier types, end treatments, crash cushions); cross-section elements (e.g., lane widths, shoulders, bike lane,
sidewalks); Americans with Disabilities Act (ADA) design considerations
Signal design (3): signal timing (e.g., clearance intervals, phasing, pedestrian crossing timing, railroad preemption); signal warrants
Traffic control design (3): signs and pavement markings; temporary traffic control
Geotechnical and pavement (4): design traffic analysis (e.g., equivalent single-axle load (ESAL); sampling and testing (e.g.,
subgrade resilient modulus, CBR, R-values, field tests); mechanistic design procedures (e.g., flexible and rigid pavement);
pavement evaluation and maintenance measures (e.g., skid, roughness, structural capacity, rehabilitation treatments);
settlement and compaction; soil stabilization techniques; excavation, embankment, and mass balance
Drainage (2): hydrology (e.g., rational method, hydrographs, SCS/NRCS method); culvert design, including hydraulic energy
dissipation; stormwater collection systems (e.g., inlet capacities, pipe flow); gutter flow; open-channel flow; runoff detention/
retention/water quality mitigation measures
Alternatives analysis (1): economic analysis (e.g., present worth, lifecycle costs)
CIVIL/WATER RESOURCES AND ENVIRONMENTAL DEPTH EXAM
Analysis and design (4): mass balance; hydraulic loading; solids loading (e.g., sediment loading, sludge); hydraulic flow
measurement
Hydraulics–closed conduit (5): energy and/or continuity equation (e.g., Bernoulli, momentum equation); pressure conduit (e.g.,
single pipe, force mains, Hazen-Williams, Darcy-Weisbach, major and minor losses); pump application and analysis, including
wet wells, lift stations, and cavitation; pipe network analysis (e.g., series, parallel, and loop networks)
Hydraulics–open channel (5): open-channel flow; hydraulic energy dissipation; stormwater collection and drainage (e.g., culvert,
stormwater inlets, gutter flow, street flow, storm sewer pipes); subcritical and supercritical flow
Hydrology (7): storm characteristics (e.g., storm frequency, rainfall measurement, and distribution); runoff analysis (e.g., rational
and SCS/NRCS methods); hydrograph development and applications, including synthetic hydrographs; rainfall intensity,
duration, and frequency; time of concentration; rainfall and stream gauging stations; depletions (e.g., evaporation, detention,
percolation, and diversions); stormwater management (e.g., detention ponds, retention ponds, infiltration systems, and swales)
Groundwater and wells (3): aquifers; groundwater flow; well analysis–steady state
Wastewater collection and treatment (6): wastewater collection systems (e.g., lift stations, sewer networks, infiltration, inflow,
smoke testing, maintenance, and odor control); wastewater treatment processes; wastewater flow rates; preliminary treatment;
primary treatment; secondary treatment (e.g., physical, chemical, and biological processes); nitrification/denitrification;
phosphorus removal; solids treatment, handling, and disposal; digestion; disinfection; advanced treatment (e.g., physical,
chemical, and biological processes)
Water quality (3): stream degradation; oxygen dynamics; total maximum daily load (TMDL) (e.g., nutrient contamination, DO,
load allocation); biological contaminants; chemical contaminants, including bioaccumulation
Drinking water distribution and treatment (6): drinking water distribution systems; drinking water treatment processes; demands;
storage; sedimentation; taste and odor control; rapid mixing (e.g., coagulation); flocculation; filtration; disinfection, including
disinfection byproducts; hardness and softening
Engineering economics analysis (1): economic analysis (e.g., present worth, lifecycle costs, comparison of alternatives)
xxiv C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L
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Table 2 describes the subjects in detail. Most examinees
find the list to be formidable in appearance. The problem
counts in Table 2 are according to NCEES, but these
problem counts are approximate. NCEES adds,
The exam is developed with questions that will
require a variety of approaches and methodolo-
gies, including design, analysis, and application.
Some problems may require knowledge of engi-
neering economics. The knowledge areas speci-
fied as examples of kinds of knowledge are not
exclusive or exhaustive categories.
As Table 2 shows, the subjects in morning and after-
noon sessions overlap. However, the depth of required
knowledge is not the same within and between sessions.
Therefore, Table 2 provides some guidance as to just
“what” each of these subjects means.
WHAT IS THE TYPICAL QUESTION FORMAT?
Almost all of the questions are standalone—that is, they
are completely independent. However, NCEES allows
that some sets of questions may start with a statement
of a “situation” that will apply to (typically) two to five
following questions. Such grouped questions are increas-
ingly rare, however.
Each of the questions will have four answer options
labeled “A,” “B,” “C,” and “D.” If the answer options are
numerical, they will be displayed in increasing value. One
of the answer options is correct (or, will be “most nearly
correct,” as described in the following section). The
remaining answer options are incorrect and may consist
of one or more “logical distractors,” the term used by
NCEES to designate incorrect options that look correct.
NCEES intends the questions to be unrelated. Ques-
tions are independent or start with new given data. A
mistake on one of the questions should not cause you to
get a subsequent question wrong. However, considerable
time may be required to repeat previous calculations
with a new set of given data.
HOW MUCH “LOOK-UP” IS REQUIRED ON
THE EXAM?
Since the questions are multiple-choice in design, all
required data will appear in the situation statement.
Since the exam would be unfair if it was possible to
arrive at an incorrect answer after making valid assump-
tions or using plausible data, you will not generally be
required to come up with numerical data that might
affect your success on the problem. There will also be
superfluous information in the majority of questions.
WHAT DOES “MOST NEARLY” REALLY
MEAN?
One of the more disquieting aspects of these questions
is that the available answer choices are seldom exact.
Answer choices generally have only two or three
significant digits. Exam questions ask, “Which answer
choice is most nearly the correct value?” or they
instruct you to complete the sentence, “The value is
approximately . . .” A lot of self-confidence is required
to move on to the next question when you do not find
an exact match for the answer you calculated, or if you
have had to split the difference because no available
answer option is close.
NCEES has described it like this:
Many of the questions on NCEES exams require
calculations to arrive at a numerical answer.
Depending on the method of calculation used, it
is very possible that examinees working correctly
will arrive at a range of answers. The phrase
“most nearly” is used to accommodate answers
that have been derived correctly but that may be
slightly different from the correct answer choice
given on the exam. You should use good engi-
neering judgment when selecting your choice of
answer. For example, if the question asks you to
calculate an electrical current or determine the
load on a beam, you should literally select the
answer option that is most nearly what you cal-
culated, regardless of whether it is more or less
than your calculated value. However, if the ques-
tion asks you to select a fuse or circuit breaker to
protect against a calculated current or to size a
beam to carry a load, you should select an answer
option that will safely carry the current or load.
Typically, this requires selecting a value that is
closest to but larger than the current or load.
The difference is significant. Suppose you were asked to
calculate “most nearly” the volumetric pure water flow
required to dilute a contaminated stream to an accept-
able concentration. Suppose, also, that you calculated
823 gpm. If the answer options were (A) 600 gpm,
(B) 800 gpm, (C) 1000 gpm, and (D) 1200 gpm, you
would go with answer option (B), because it is most
nearly what you calculated. If, however, you were asked
to select a pump or pipe with the same rated capacities,
you would have to go with option (C) because an
800 gpm pump would not be sufficient. Got it?
HOW MUCH MATHEMATICS IS NEEDED FOR
THE EXAM?
There are no pure mathematics questions (algebra,
geometry, trigonometry, etc.) on the exam. However,
you will need to apply your knowledge of these subjects
to the exam questions.
Generally, only simple algebra, trigonometry, and geom-
etry are needed on the PE exam. You will need to use
the trigonometric, logarithm, square root, exponentia-
tion, and similar buttons on your calculator. There is no
need to use any other method for these functions.
Except for simple quadratic equations, you will prob-
ably not need to find the roots of higher-order equations.
I N T R O D U C T I O N xxv
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For second-order (quadratic) equations, NCEES does
not care if you find roots by factoring, completing the
square, using the quadratic equation, or using your
calculator’s root finder. Occasionally, it will be conve-
nient to use the equation-solving capability of your
calculator. However, other solution methods exist.
There is essentially no use of calculus on the exam.
Rarely, you may need to take a simple derivative to find
a maximum or minimum of some simple algebraic func-
tion. Even rarer is the need to integrate to find an aver-
age, moment of inertia, statical moment, or shear flow.
There is essentially no need to solve differential equa-
tions. Questions involving radioactive decay, seismic
vibrations, control systems, chemical reactions, and
fluid mixing have appeared from time to time. However,
these applications are extremely rare, have typically
been first-order, and could usually be handled without
having to solve differential equations.
Basic statistical analysis of observed data may be neces-
sary. Statistical calculations are generally limited to
finding means, medians, standard deviations, variances,
percentiles, and confidence limits. Since the problems
are multiple-choice, you will not have to draw a histo-
gram, although you might have to interpret one. Usu-
ally, the only population distribution you need to be
familiar with is the normal curve. Probability, reliabil-
ity, hypothesis testing, and statistical quality control
are not explicit exam subjects, though their concepts
may appear peripherally in some problems. Although
the term “least squares” may appear in surveying prob-
lems, you will not have to use linear or nonlinear regres-
sion and other curve-fitting techniques to correlate data.
Quantitative optimization methods, such as linear,
dynamic, and integer programming, generally associated
with the field of operations research, are not exam sub-
jects. However, elements of simple queuing theory are
integrated into some traffic and transportation subjects,
so you should have a basic familiarity with the terminol-
ogy of queues.
The PE exam is concerned with numerical answers, not
with proofs or derivations. You will not be asked to prove
or derive formulas, use deductive reasoning, or validate
theorems, corollaries, or lemmas.
Inasmuch as first assumptions can significantly affect the
rate of convergence, problems requiring trial-and-error
solutions are unlikely. Rarely, a calculation may require
an iterative solution method. Generally, there is no need
to complete more than two iterations. You will not need
to program your calculator to obtain an “exact” answer,
nor will you generally need to use complex numerical
methods.
STRAIGHT TALK: STRUCTURAL TOPICS
There are four specialized structural subjects that require
special consideration in your review: masonry, timber,
bridge, and seismic design. These subjects appear
regularly (i.e., on every exam). (Yes, there are simple
seismic design questions on the NCEES Civil PE exam!)
Even if you do not intend to work in the Civil PE
structural depth module, you will have to know a little
something about these subjects for the morning breadth
session.
Bridge, timber, and seismic design are specialized struc-
tural fields that are covered in separate PPI publications.
These publications are Timber Design for the Civil and
Structural PE Exams, and Seismic Design of Building
Structures.
MASONRY: ASD AND SD
The masonry chapters in this book are introductions to
basic concepts and the most common design applica-
tions. Exam questions often go far beyond wall and
column design. If you intend to be ready for any masonry
question, I recommend that you supplement your study
of these chapters. For masonry, only allowable stress
design (ASD) solving methods may be used on the exam,
with the exception that the strength design (SD) method
may be used for walls with out-of-plane loads (ACI 530
Sec. 3.3.5). However, because the SD method is still
reliable for masonry construction, and it is used in indus-
try practice, this book provides both ASD and SD meth-
ods for your additional (and post-exam) reference.
Where design methods differ, this book presents the
ASD method first.
STEEL: ASD AND LRFD
Either ASD or load and resistance factor design (LRFD)
methods may be used, as there will be “parallel” ques-
tions adapted to both. It is not necessary to learn both
systems of design. This book provides both ASD and
LRFD solving methods in parallel.
CONCRETE: ACI 318 CHAP. 9 AND APP. C
For concrete, ACI 318 App. C may not be used on the
structural depth exam. Only ACI 318 Chap. 9 methods
may be used.
WHICH BUILDING CODE?
Building codes may be needed, but only to a limited
extent (e.g., for wind and seismic loadings). Since the
PE exam is a national exam, you are not required to use
a regional building code. NCEES has adopted the IBC
as the basis of its code-related questions. The code edi-
tion (year, version, etc.) tested is a thorny issue, how-
ever. The exam can be years behind the most recently
adopted code, and many years behind the latest codes
being published and distributed.
Occasionally, the International Code Council will
modify, augment, and delete parts of the primary
standard. For example, IBC contains provisions that
differ slightly from those in ACI 530. While this is a
xxvi C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L
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valid practical concern, NCEES is aware of the differ-
ences, and questions that have ambiguous correct
answers are rare on the exam.
HOW ABOUT ENGINEERING ECONOMICS?
For most of the early years of engineering licensing,
questions on engineering economics appeared frequently
on the exams. This is no longer the case. However, in its
outline of exam subjects, NCEES notes: “Some ques-
tions may require knowledge of engineering economics.”
What this means is that engineering economics might
appear in several questions on the exam, or the subject
might be totally absent. While the degree of engineering
economics knowledge may have decreased somewhat,
the basic economic concepts (e.g., time value of money,
present worth, nonannual compounding, comparison of
alternatives, etc.) are still valid test subjects.
If engineering economics is incorporated into other ques-
tions, its “disguise” may be totally transparent. For
example, you might need to compare the economics of
buying and operating two blowers for remediation of a
hydrocarbon spill—blowers whose annual costs must be
calculated from airflow rates and heads. Also, you may
need to use engineering economics concepts and tables
in problems that do not even mention “dollars” (e.g.,
when you need to predict future water demand, popula-
tion growth, or traffic volume).
WHAT ABOUT PROFESSIONALISM AND
ETHICS?
For many decades, NCEES has considered adding pro-
fessionalism and ethics questions to the PE exam. How-
ever, these subjects are not part of the test outline, and
there has yet to be an ethics question in the exam. Con-
struction engineering questions dealing with obligations
related to contracts, bidding, estimating, inspection, and
regulations sometimes get pretty close to the subject of
professional practice. However, you will not encounter
the phrase “ethical obligation” in the exam.
IS THE EXAM TRICKY?
Other than providing superfluous data, the PE exam is
not a “tricky exam.” The exam does not overtly try to
get you to fail. Examinees manage to fail on a regular
basis with perfectly straightforward questions. The
exam questions are difficult in their own right. NCEES
does not need to provide misleading or conflicting state-
ments. However, you will find that commonly made
mistakes are represented in the available answer choices.
Thus, the alternative answers (known as distractors)
will be logical.
Questions are generally practical, dealing with common
and plausible situations that you might experience in
your job. You will not be asked to design a structure for
reduced gravity on the moon, to design a mud-brick
road, to analyze the effects of a nuclear bomb blast on
a structure, or to use bamboo for tension reinforcement.
DOES NCEES WRITE EXAM QUESTIONS
AROUND THIS BOOK?
Only NCEES knows what NCEES uses to write its
exam questions. However, it is irrelevant, because this
book is not intended to (1) be everything you need to
pass the exam, (2) expose exam secrets or exam ques-
tions, or (3) help you pass when you do not deserve to
pass. NCEES knows about this book, but worrying
about NCEES writing exam questions based on infor-
mation that is or is not in this book means you are
placing too much dependency on this book. This book,
for example, will teach you how to use aspects of many
standards and codes. Expecting that this book will
replace those standards and codes is unrealistic. This
book will provide instruction in certain principles.
Expecting that you will not need to learn anything else
is unrealistic. This book presents many facts, defini-
tions, and numerical values. Expecting that you will
not need to know other facts, definitions, and numerical
values is unrealistic. What NCEES uses to write exam
questions will not have any effect on what you need to
do to prepare for the exam.
WHAT MAKES THE QUESTIONS DIFFICULT?
Some questions are difficult because the pertinent the-
ory is not obvious. There may be only one acceptable
procedure, and it may be heuristic (or defined by a code)
such that nothing else will be acceptable. Many highway
capacity questions are this way.
Some questions are difficult because the data needed is
hard to find. Some data just is not available unless you
happen to have brought the right reference book. Many
of the structural questions are of this nature. There is no
way to solve most structural steel questions without the
AISC Manual. Designing an eccentrically loaded con-
crete column without published interaction diagrams is
nearly impossible to do in six minutes. If you did not
bring OSHA regulations to the exam, you are not going
to be able to answer many safety questions.
Some questions are difficult because they defy the imag-
ination. Three-dimensional structural questions and some
surveying curve questions fit this description. If you can-
not visualize the question, you probably cannot solve it.
Some questions are difficult because the computational
burden is high, and they just take a long time. Pipe
networking questions solved with the Hardy Cross
method fall into this category.
Some questions are difficult because the terminology is
obscure, and you just do not know what the terms
mean. This can happen in almost any subject.
DOES THE PE EXAM USE SI UNITS?
The PE exam in civil engineering primarily uses custom-
ary U.S. units although SI and a variety of other metric
systems are also used. Questions use the units that
I N T R O D U C T I O N xxvii
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