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Engineering Statics:
Open and Interactive
Daniel W. Baker, William Haynes
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Front Matter
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Colophon
About this Book
Acknowledgements
1
Introduction to Statics
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1.1
Newton’s Laws of Motion
1.1.1
Newton’s 1st Law
1.1.2
Newton’s 2nd Law
1.1.3
Newton’s 3rd Law
1.2
Units
1.2.1
Unit Systems
1.2.2
Units within Newton’s 2nd Law
1.2.3
Avoiding Common Unit Errors
1.3
Forces
1.4
Problem Solving
2
Forces and Other Vectors
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2.1
Vectors
2.2
One-Dimensional Vectors
2.2.1
Vector Addition
2.2.2
Vector Subtraction
2.2.3
Vector Multiplication by a Scalar
2.3
2D Coordinate Systems & Vectors
2.3.1
Rectangular Coordinates
2.3.2
Polar Coordinates
2.3.3
Coordinate Transformation
2.4
3D Coordinate Systems & Vectors
2.4.1
Rectangular Coordinates
2.4.2
Direction Cosine Angles
2.4.3
Spherical Coordinates
2.4.4
Cylindrical Coordinates
2.5
Unit Vectors
2.5.1
Cartesian Unit Vectors
2.5.2
Relation between Vectors and Unit Vectors
2.5.3
Force Vectors from Position Vectors
2.5.4
Unit Vectors and Direction Cosines
2.6
Vector Addition
2.6.1
Triangle Rule of Vector Addition
2.6.2
Graphical Vector Addition
2.6.3
Trigonometric Vector Addition
2.6.4
Orthogonal Components
2.6.5
Algebraic Addition of Components
2.6.6
Vector Subtraction
2.7
Dot Products
2.7.1
Calculation of the Dot product
2.7.2
Magnitude of a Vector
2.7.3
Angle between Two Vectors
2.7.4
Vector Projection
2.7.5
Perpendicular Components
2.8
Cross Products
2.8.1
Direction of the Vector Cross Product
2.8.2
Cross Product of Unit Vectors
2.8.3
Cross Product of Arbitrary Vectors
2.9
Exercises (Ch. 2)
3
Equilibrium of Particles
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3.1
Equilibrium
3.2
Particles
3.3
1D Particle Equilibrium
3.3.1
A simple case
3.3.2
Scalar Components
3.3.3
Two-force Bodies
3.3.4
General Procedure
3.4
2D Particle Equilibrium
3.4.1
Introduction
3.4.2
General Procedure
3.4.3
Force Triangle Method
3.4.4
Trigonometric Method
3.4.5
Scalar Components Method
3.4.6
Multi-Particle Equilibrium
3.5
3D Particle Equilibrium
3.5.1
Three-Dimensional Coordinate Frame
3.5.2
Free-Body Diagrams
3.5.3
Angles
3.5.4
General Procedure
3.6
Exercises (Ch. 3)
4
Moments and Static Equivalence
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4.1
Moment of Force
4.1.1
Magnitude of a Moment
4.1.2
Direction of a Moment
4.2
Scalar Addition of Moments
4.2.1
Scalar Components
4.2.2
Addition of Moments
4.3
Varignon’s Theorem
4.3.1
Parallel and Perpendicular Components
4.3.2
Horizontal and Vertical Components
4.3.3
Moment Cross Products
4.4
3D Moments
4.4.1
3D Cross Products
4.4.2
Moment about a Point
4.4.3
Moment about a Line
4.5
Couples
4.6
Equivalent Transformations
4.7
Statically Equivalent Systems
4.8
Exercises (Ch. 4)
5
Rigid Body Equilibrium
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5.1
Degree of Freedom
5.2
Free-Body Diagrams
5.3
Equations of Equilibrium
5.4
2D Rigid Body Equilibrium
5.5
3D Rigid Body Equilibrium
5.6
Stability and Determinacy
5.7
Equilibrium Examples
5.8
Exercises (Ch. 5)
6
Equilibrium of Structures
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6.1
Structures
6.2
Interactions between members
6.2.1
Load Paths
6.3
Trusses
6.3.1
Introduction
6.3.2
Simple Trusses
6.3.3
Solving Trusses
6.3.4
Zero-Force Members
6.4
Method of Joints
6.4.1
Procedure
6.5
Method of Sections
6.5.1
Procedure
6.6
Frames and Machines
6.6.1
Analyzing Frames and Machines
Procedure
Free-body diagram of structures
6.7
Summary
6.8
Exercises (Ch. 6)
7
Centroids and Centers of Gravity
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7.1
Weighted Averages
7.2
Center of Gravity
7.3
Center of Mass
7.4
Centroids
7.4.1
Properties of Common Shapes
7.4.2
Relations between Centroids and Center of Gravity
7.5
Centroids using Composite Parts
7.5.1
Composite Parts Method
7.5.2
Centroids of 3D objects
7.6
Average Value of a Function
7.7
Centroids using Integration
7.7.1
Integration Process
7.7.2
Area of a General Spandrel
7.7.3
Examples
7.8
Distributed Loads
7.8.1
Equivalent Magnitude
7.8.2
Equivalent Location
7.8.3
Distributed Load Applications
7.9
Fluid Statics
7.9.1
Principles of Fluid Statics
7.9.2
Fluid Statics Applications
7.10
Exercises (Ch. 7)
8
Internal Forces
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8.1
Internal Forces
8.2
Sign Conventions
8.3
Internal Forces at a Point
8.3.1
Interactive Internal Forces
8.4
Shear and Bending Moment Diagrams
8.4.1
Shear and Bending Moment Diagrams
8.5
Section Cut Method
8.6
Relation Between Loading, Shear and Moment
8.7
Graphical Method
8.8
Integration Method
8.8.1
Determining Loading Functions
8.8.2
Application of the Calculus Method
8.9
Geogebra Interactives
8.9.1
Concentrated Forces
8.9.2
Concentrated Force and Moment
8.9.3
Distributed Load
8.9.4
Combination Load
8.9.5
Arbitrary Load
8.10
Summary
8.11
Exercises (Ch. 8)
9
Friction
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9.1
Dry Friction
9.1.1
Coulomb Friction
9.1.2
Friction Angle and Friction Resultant
9.1.3
Normal Forces
9.1.4
Coulomb Friction Examples.
9.2
Slipping vs. Tipping
9.3
Wedges
9.4
Screw Threads
9.4.1
Screw Motion and the Right-hand rule
9.4.2
Screw Thread Properties
9.4.3
Moment to Reach Impending Motion
Applied Force Opposes Impending Motion
Applied Force Supports Impending Motion
9.5
Flexible Belts
9.5.1
Frictionless Belts
9.5.2
Friction in Flat Belts
Contact Angle
β
Belt Tension
Change in Belt Tension due to Friction
9.5.3
Torque in Belt Systems
9.5.4
V-Belts
9.6
Journal Bearings
9.6.1
Journal Bearing Friction
9.6.2
Rotating Shaft and Fixed Bearing
9.6.3
Fixed Shaft and Rotating Bearing
9.7
Rotating Discs
9.7.1
Disc Friction
9.7.2
Collar Bearings
9.7.3
End Bearings
9.7.4
Circular Arc Bearings
9.8
Exercises (Ch. 9)
10
Moments of Inertia
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10.1
Integral Properties of Shapes
10.1.1
Area
10.1.2
First Moment of Area
10.1.3
Moment of Inertia
10.1.4
Polar Moment of Inertia
10.1.5
Product of Inertia
10.2
Moments of Inertia of Common Shapes
10.2.1
Moment of Inertia of a Rectangle
Using
d
A
=
d
x
d
y
Using
d
A
=
d
y
d
x
Centroidal Moment of Inertia
10.2.2
Moment of Inertia of a Triangle
10.2.3
Moment of Inertia of a Differential Strip
10.2.4
Circles, Semicircles, and Quarter-circles
10.2.5
Summary of Integration Techniques
10.3
Parallel Axis Theorem
10.3.1
Derivation
10.3.2
Moments of Inertia Table
10.4
Composite Shapes
10.4.1
Composite Area Method
10.4.2
Structural Steel Sections
10.5
Polar Moment of Inertia
10.6
Radius of Gyration
10.7
Products of Inertia
10.8
Mass Moment of Inertia
10.9
Exercises (Ch. 10)
Back Matter
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A
Notation
B
Useful Mathematics
B.1
Distance Formula
B.2
Right Triangle Trigonometry
B.3
Oblique Triangle Trigonometry
B.3.1
Law of Sines
B.3.2
Law of Cosines
C
Properties of Shapes
C.1
Centroids of Common Shapes
C.2
Moment of Inertia of Common Shapes
D
Properties of Steel Sections
D.1
Angles
D.1.1
Angle Section-US
D.1.2
Angle Section-SI
D.2
Channels
D.2.1
Channel Section-US
D.2.2
Channel Section-SI
D.3
Standard Sections
D.3.1
Standard Section-US
D.3.2
Standard Section-SI
D.4
Wide Flange Sections
D.4.1
Wide Flange Section-US
D.4.2
Wide Flange Section-SI
Exercises
4.8
Exercises (Ch. 4)
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