Units and Unit Conversions

Chapter 1 Mathematics

Analytic Geometry

Straight Line

Distance Formula

Quadratic Equation

Trigonometry

Law of Sines and Law of Cosines

Trigonometric Identities

Conic Sections

Eccentricity

Generalized Equation of Conic Sections

Circle

Ellipse

Hyperbola

Parabola

Mensuration: Regular Polygon

Mensuration

Mensuration: Area of a Parallelogram

Volume of Solids

Vectors

Dot Product

Cross Product

Complex Numbers

Roots of Complex Equations

Matrix Algebra

Cofactor

Classical Adjoint

Determinant

Polynomials of Higher Order—Interrelationships of Roots

Second-Order Polynomial (Quadratic)

Third-Order Polynomial (Cubic)

Fourth-Order Polynomial (Quartic)

Newton’s Method of Root Extraction

Differential Calculus

Limits

The Derivative

L’Hôpital’s Rule

Tests for Maxima and Minima

Chain Rule for Derivatives

Derivative of an Exponent

Derivative of a Product of Several Functions

Derivative of a Quotient of Two Functions

Curvature

Taylor’s Series

Integral Calculus

Standard Integrals

Integration by Parts

Integration by Substitution

Integration by Separable Variables

Numerical Integration: Euler’s Rule, Trapezoidal Rule, and Simpson’s Rule

Partial Fractions

Ordinary Differential Equation with Constant Coefficients

Homogeneous Differential Equations

First-Order Linear Homogeneous Differential Equation with Constant Coefficients

First-Order Linear Nonhomogeneous Differential Equation with Constant Coefficients

Second-Order Linear Homogeneous Differential Equation with Constant Coefficients

Nonhomogeneous Linear Ordinary Differential Equation: Particular Solution

Chapter 2 Probability and Statistics

Permutations and Combinations

Laws of Probability

Independent Events

Conditional Probability—Related Events

Bayes’ Theorem

Measures of Central Tendency

Mean

Variance

Combinations of Random Variables

Sample Mean and Sample Variance

Median

Probability Functions

Discrete Random Variable

Continuous Random Variable

Normal (Gaussian) Distribution

Student’s t-Distribution

Confidence Intervals

Binomial Distribution

Expected Value

Discrete Variable

Continuous Variable

Use of Expected Value in Decision Making

Hypothesis Testing

Test on Means of Normal Distribution—Variance Known

Linear Regression

Chapter 3 Computational Tools

Number Systems

Binary (Base 2)

Octal (Base 8)

Decimal (Base 10)

Hexadecimal (Base 16)

Spreadsheets as an Analysis and Design Tool

Copying Formulas

Some Useful Functions in EXCEL

Structured Programming

Declaration

Initialization

Counters

Loops

IF ELSE Expressions

Sum

Logical Tests

Chapter 4 Ethics and Professional Practice

Code of Ethics

National Society of Professional Engineers Code of Ethics

National Council of Examiners for Engineering and Surveying Rules

NSPE Rules of Practice

Professional Obligations (as Listed in the NSPE Code of Ethics)

Intellectual Property

Professional Liability

Licensure

Engineering Intern

Portfolio Review

Examination(s)

Certification of Professional Competence

General versus Specific Types of Licensure

Sustainability and Sustainable Design

Indicators of Sustainability

Index of Sustainable Economic Welfare

Chapter 5 Engineering Economics

Types of Cash Flow

Year-End Accounting Convention

Minimum Attractive Rate of Return

Nonannual Compounding

Present Worth

Principal in a Sinking Fund

Capitalized Cost

Equivalent Uniform Annual Cost

Depreciation

Straight-Line Method

Modified Accelerated Cost Recovery System

Tax Issues

Bonds

Break-Even Analysis

Return on Investment

Benefit-Cost Analysis

Uncertainty (Expected Value and Risk)

Chapter 6 Statics

Vectors

Definitions

Resultant of a System of Forces (2D)

Moment of a Force

Moment about a Point

Moment about a Line (Axis)

Equivalent Force Systems

Equilibrium of Rigid Bodies

Representation of Distributed Loads

Rigid Frames: Degrees of Freedom, Determinacy, and Stability

Inclined Support

Ideal Truss—Stability and Determinacy

Truss Member Forces: Method of Joints

Truss Member Forces: Method of Sections

Identification of Zero-Force Members

Truss Deflection: Method of Virtual Work

Influence Line for Truss Member Force

Centroid of an Area by Integration

Centroid of a Compound Area—Weighted Average

Various Section Properties

Moment of Inertia (I)

Polar Moment of Inertia (J)

Product of Inertia

Friction

Belt Friction

Screw Thread

Chapter 7 Dynamics

Kinematics

Particle Kinematics

Rigid Body Kinematics

Kinetics

Particle Kinetics

Constant Length of String Concept

Rigid Body Kinetics

Principle of Impulse and Momentum

Impact

Coefficient of Restitution

Elastic versus Plastic Impact

Principle of Work and Energy

Work

Gravitational Potential Energy

Elastic Potential Energy

Kinetic Energy

Chapter 8 Mechanics of Materials

Shear Force and Bending Moment Diagrams

Shear Force Diagram

Bending Moment Diagram

Normal Stress and Strain

Hooke’s Law

Elastic versus Inelastic Behavior

Poisson’s Ratio

Shear Stress

Generalized Hooke’s Law

Typical Stress-Strain Curve for Mild Steel

Ductility

Elasto-Plastic Model

Bending Stress

Elastic Section Modulus

Plastic Section Modulus

Combined Axial and Bending Stress

Shear Stress due to Transverse Load

Beam Deflection—The Elastic Curve

Direct Integration Method

Unit Load Method

Beam Deflection Equations

Torsion

Shear Stress due to Torsion—Circular Sections

Shear Stress due to Torsion—Thin-Walled Sections

Thermal Stress and Strain

Mohr’s Circle: Normal (s) and Shear (t) Stress Combination

Principal Stresses

Composite Materials

Composite Section Undergoing Axial Force

Composite Section Undergoing Flexure

Stability of Axially Loaded Columns—Euler Buckling

Chapter 9 Materials

Concrete Mix Design

Absolute Volume Method

Asphalt Mix Design: Volumetric Relationships

Unit Volume Approach to Calculating Asphalt Properties

Common Material Tests

Asphalt: Particle Size Analysis (AASHTO T30/ASTM D5444)

Asphalt: Moisture Susceptibility Test (AASHTO T283/ASTM D4867)

Asphalt: Specific Gravity and Absorption of Coarse Aggregate (AASHTO T85/ASTM C127)

Asphalt Binder Content Test (AASHTO T308/ASTM D6307)

Voids in Mineral Aggregate (VMA) (AASHTO T166 and T209/ASTM D2726 and D2041)

Steel: Tensile Test

Concrete: Compression Test

Concrete: Split Cylinder Test

Third Point Loading Test of a Beam (Flexure)

Engineering Materials and Their Properties

Unit Weight

Steel: Tensile Strength

Concrete: Compressive Strength

Modulus of Elasticity

Poisson’s Ratio

Thermal Expansion

Composites

Chapter 10 Fluid Mechanics

Fluid Properties

Density

Surface Tension

Capillary Action

Viscosity

Laminar versus Turbulent Flow

Relationship between Average Velocity and Maximum Velocity

Static Pressure on Submerged Surfaces

Static Pressure on Plane Area of Arbitrary Shape

Static Pressure on Compound Area (Curved or Multiple Linear Segments)

Fluid Dynamics

Conservation of Mass

Conservation of Energy

Conservation of Momentum

Energy Grade Line and Hydraulic Grade Line

Fluid Power

Dynamic Similarity

Flow Measurement Devices

Pitot Tube

Orifice Meter

Venturi Meter

Flow Measurement with Weirs

Sharp-Crested Weirs

Triangular Weirs

Chapter 11 Hydraulics and Hydrologic Systems

Hydrologic Balance

Precipitation

Rainfall Intensity

Intensity-Duration-Frequency Curves

Time of Concentration

Hydrograph

Hydrograph Separation

Unit Hydrograph

Runoff Estimation by Natural Resources Conservation Service Curve Number

Procedure for the NRCS Method

Rational Method for Predicting Runoff

Water Distribution Systems

Inflow and Infiltration

Closed Conduit Hydraulics

Darcy-Weisbach Equation

Laminar Flow

Hydraulic Radius and Hydraulic Diameter

Hazen-Williams Equation

Head Loss in Circular Conduits

Minor Losses

Equivalent Length

Pipe Networks

Two-Node Network

Pumps

System Curve

Pump Curves

Cavitation

Circular Pipe Head Loss

Open Channel Flow Fundamentals

Rectangular Open Channels

Critical Depth of Flow in Open Channels

Alternate Depths

Velocity in Open Channels

Hydraulic Parameters of Straight-Sided Open Channels

Hydraulic Parameters of Circular Open Channels

Momentum in Open Channels

Hydraulic Jump

Groundwater Distribution

Groundwater Dewatering

Chapter 12 Structural Analysis

Structural Determinacy and Stability

Determinacy and Stability of Trusses, Frames, and Beams

Trusses

Frames

Beams

Load Path and Tributary Area

Floor System: Load Path

Analysis of Trusses

Load Types

Dead Loads

Live Loads

Snow Loads

Seismic Loads

Moving Loads: Influence Lines

Deflection

Truss Deflection

Frame Deflection

Introduction to Indeterminate Structural Analysis

Compatibility

Indeterminate Trusses

Displacement Methods: Slope Deflection and Moment Distribution

Chapter 13 Structural Design

Reinforced Concrete Design

Basic Provisions of ACI 318-2011

Reinforcement

Strength Design Approach

Analysis and Design of Reinforced Concrete Beams in Flexure

Analysis and Design of Reinforced Concrete Columns

Steel Design

Load and Resistance Factor Design

Analysis and Design of Beams (Flexure)

Design for Shear

Analysis and Design of Steel Compression Members

Analysis and Design of Steel Tension Members

Chapter 14 Geotechnical Engineering

Mineralogy

Igneous Rocks

Weathering

Sedimentary Rocks

Metamorphic Rocks

Clay Minerals

Soil as a Three-Phase System

Fundamental Definitions

Shrinkage and Swell

Effective Stress

Shear Strength (Mohr-Coulomb)

Standard Soil Tests

Liquid Limit Test (ASTM D-4318)

Plastic Limit Test (ASTM D-4318)

Standard Penetration Test

Relative Density

Cone Penetrometer Test

Direct Shear Test

Unconfined Compression Test

Compaction

Triaxial Test Fundamentals

Consolidation

Consolidation Test

Settlement due to Primary Consolidation

Consolidation Rate

Soil Classification

Sieve Sizes

Particle Size Distribution Curves

Hydrometer Analysis

Unified Soil Classification System

AASHTO Soil Classification

Bearing Capacity

Foundation Types

Ultimate Bearing Capacity

Effect of Water Table on Bearing Capacity

Combined Footing

Eccentric Load on a Shallow Footing

Mat Foundations

Deep Foundations

Lateral Earth Pressure

Stability and Strength Checks

Active Earth Pressure

Rankine’s Theory for Earth Pressure

Steps for Evaluating Stability of a Retaining Wall

Slope Stability

Stability of Slopes along a Planar Surface

Permeability of Soils

Darcy’s Law for Seepage

Liquefaction

Laboratory Measurement of Hydraulic Conductivity

Flow Nets

Aquifers

Soil Stabilization

Mechanical Stabilization

Chemical Stabilization

Erosion Control Methods

Geosynthetics

Chapter 15 Transportation

Transportation Planning

Trip Generation

Trip Distribution: Gravity Model

Modal Split by the Logit Model

Design Traffic Volume

Expansion Factors

Travel Speed

Speed–Volume–Density Relationships

Level of Service (LOS) of Freeway Segments

Constant Acceleration and Deceleration

Intersections

Intersection Sight Distance

Change and Clearance Intervals at an Intersection

Pavement Design

Equivalent Single Axle Load

Load Equivalence Factors

Flexible Pavements

Rigid Pavement Design

Highway Design: Horizontal Curves

Highway Design: Superelevation

Coefficient of Side Friction

Highway Design: Spiral Curves

Highway Design: Vertical Curves

Sight Distance

Stopping Sight Distance—AASHTO Recommendations

Sight Distance on Vertical Curves

Stopping Sight Distance on Horizontal Curves

Highway Safety

Accident Rates

Accident Countermeasures

Chapter 16 Environmental Engineering

Main U.S. Environmental Laws

Clean Air Act (1955, amended 1977)

Clean Water Act (1948, amended 1977)

Safe Drinking Water Act

Resource Conservation and Recovery Act (1976, amended 1986)

Surface Water Treatment Rule

Municipal Separate Storm Sewer System

Water Quality–Based Effluent Limits

Water Quality

Biochemical Oxygen Demand

Dilution Purification of Wastewater Streams

Hardness in Water

pH and pOH

Alkalinity

Wastewater Flow Rates from Various Sources

Municipal Wastewater Treatment

Reactors Used for Wastewater Treatment

Reaction Kinetics and Reactor Hydraulics

Physical Unit Operations in Wastewater Treatment

Mixing and Flocculation

Settling of Particles

Primary Sedimentation Tanks

Absorption versus Adsorption

Activated Carbon Adsorption

Coagulation

Chemical Unit Processes in Wastewater Treatment

Chemical Neutralization

Disinfection

Log Inactivation

Biological Wastewater Treatment

Biochemistry, Biology, and Bacteriology

Effect of Temperature and pH

Aerobic versus Anaerobic Biological Treatment

Hydraulic Detention Time

Activated Sludge Process

Air Pollution

Cyclonic Separation

Electrostatic Precipitator

Destruction and Removal Efficiency

Reverse Osmosis

Solid Waste Management

Leachate

Chapter 17 Construction

Stages of Construction

Construction Documents

Submittals

Request for Information

Procurement Methods

Open Tendering

Restricted Tendering

Request for Proposal

Two-Stage Tendering

Request for Quotations

Single Source

Project Delivery Methods

Design-Bid-Build

Construction Management at Risk

Design-Build

Construction Operations and Methods

Machine Production

Production Cycle Time

Equipment Balancing

Scheduling

Gantt Charts

Critical Path Analysis

Program Evaluation and Review Technique

Earned Value Management

OSHA Regulations for Construction Projects

Rules of Construction

Site Layout

Emergency Response

Signs, Signals, and Barricades

Fall Protection

Quantity Estimating

Quantity Estimation for Excavations

Estimating Mortar Quantity between Bricks or Masonry Blocks

Chapter 18 Surveying

Glossary of Terms

Coordinate Systems

State Plane Coordinate System

Global Positioning System

Types of Surveys

Stationing

Chaining Techniques

Tension Correction

Temperature Correction

Sag Correction (Not in the FE Reference Handbook)

Angles and Distances

Azimuth

Bearings

Latitude and Departure

Northings and Eastings

Interior and Exterior Angles

Area of a Traverse by Coordinates

Area under an Irregular Curve

Traverse Closure

Transit Rule

Differential Leveling

Index