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ENGINEERING STATICS: OPEN AND INTERACTIVE

Daniel W. Baker, William Haynes

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 * Front Matterchevron_left
   * About this Book
     * 
   * Acknowledgements
 * 1 Introduction to Staticschevron_left
   * 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
   * 1.3 Forces
   * 1.4 Problem Solving
 * 2 Forces and Other Vectorschevron_left
   * 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 Orthogonal Components
     * 2.6.3 Graphical Vector Addition
     * 2.6.4 Trigonometric Vector Addition
     * 2.6.5 Algebraic Addition of Components
     * 2.6.6 Vector Subtraction
   * 2.7 Dot Products
     * 2.7.1 Magnitude of a Vector
     * 2.7.2 Angle between Two Vectors
     * 2.7.3 Vector Projection
     * 2.7.4 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 Particleschevron_left
   * 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 Equivalencechevron_left
   * 4.1 Direction of a Moment
   * 4.2 Magnitude of a Moment
     * 4.2.1 Definition of a Moment
   * 4.3 Scalar Components
   * 4.4 Varignon’s Theorem
     * 4.4.1 Rectangular Components
   * 4.5 3D Moments
     * 4.5.1 Moment Cross Products
     * 4.5.2 Moment about a Point
     * 4.5.3 Moment about a Line
   * 4.6 Couples
   * 4.7 Equivalent Transformations
   * 4.8 Statically Equivalent Systems
   * 4.9 Exercises (Ch. 4)
 * 5 Rigid Body Equilibriumchevron_left
   * 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 Structureschevron_left
   * 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 Gravitychevron_left
   * 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 Forceschevron_left
   * 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 Frictionchevron_left
   * 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 Inertiachevron_left
   * 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  dA=dx dy
       * Using  dA=dy dx
       * 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 Matterchevron_left
   * 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

🔗


CHAPTER 1 INTRODUCTION TO STATICS

🔗
Engineering Statics is the gateway into engineering mechanics, which is the
application of Newtonian physics to design and analyze objects, systems, and
structures with respect to motion, deformation, and failure. In addition to
learning the subject itself, you will also develop skills in the art and
practice of problem solving and mathematical modeling, skills that will benefit
you throughout your engineering career.
🔗
The subject is called “statics” because it is concerned with particles and rigid
bodies that are in equilibrium, and these will usually be stationary, i.e.
static.
🔗
🔗
The chapters in this book are:
 * Introduction to Statics— an overview of statics and an introduction to units
   and problem solving.
 * Forces and Other Vectors— basic principles and mathematical operations on
   force and position vectors.
 * Equilibrium of Particles— an introduction to equilibrium and problem solving.
 * Moments and Static Equivalence— the rotational tendency of forces, and
   simplification of force systems.
 * Rigid Body Equilibrium— balance of forces and moments for single rigid
   bodies.
 * Equilibrium of Structures— balance of forces and moments on interconnected
   systems of rigid bodies.
 * Centroids and Centers of Gravity— an important geometric property of shapes
   and rigid bodies.
 * Internal Forces— forces and moments within beams and other rigid bodies.
 * Friction— equilibrium of bodies subject to friction.
 * Moments of Inertia— an important property of geometric shapes used in many
   applications.

🔗
Your statics course may not cover all of these topics, or may move through them
in a different order.
🔗
Below are two examples of the types of problems you’ll learn to solve in
statics. Notice that each can be described with a picture and problem statement,
a free-body diagram, and equations of equilibrium.
🔗
Equilibrium of a particle: A  140 lb person walks across a slackline stretched
between two trees. If angles α and θ are known, find the tension in each end of
the slackline.
🔗
🔗
Person’s point of contact to slackline:
ΣFx=0−T1cos⁡α+T2cos⁡θ=0ΣFy=0T1sin⁡α+T2sin⁡θ−W=0
🔗
Equilibrium of a rigid body: Given the interaction forces at point C on the
upper arm of the excavator, find the internal axial force, shear force, and
bending moment at point .D.
🔗
🔗
Section cut FBD:
ΣFx=0−Cx+Fx−Vx−Nx=0ΣFy=0−Cy−Fy−Vy+Ny=0ΣMD=0+(dy)Cx+(dx)Cy−MD=0
🔗
The knowledge and skills gained in Statics will be used in your other
engineering courses, in particular in Dynamics, Mechanics of Solids (also called
Strength or Mechanics of Materials), and in Fluid Mechanics. Statics will be a
foundation of your engineering career.

🔗
Figure 1.0.1. Map of how Statics builds upon the prerequisites of Calculus and
Physics and then informs the later courses of Mechanics of Solids and Dynamics.
 * 1.1 Newton’s Laws of Motion
 * 1.2 Units
 * 1.3 Forces
 * 1.4 Problem Solving

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