Chapter 1 Introduction 1

1.1 Mechanics

1.2 Basic Concepts

1.3 Units

1.3.1 SI Units

1.3.2 Customary Units

1.3.3 Conversion between Systems of Units

1.4 Numerical Calculations

1.5 Problem-solving Strategy

1.6 Computational Software

Chapter 2 Vector Analyis

2.1 Introduction

2.2 Vectors

2.2.1 Definition of a Scalar and a Vector

2.2.2 Vector Addition

2.2.3 Multiplication of a Vector by a Scalar

2.2.4 Vector Components

2.2.5 Resolution of a Vector into Components

2.3 Forces and Their Characteristics

2.3.1 Concurrent Coplanar Forces

2.4 Three-dimensional Cartesian Coordinates and Unit Base Vectors

2.4.1 Unit Base Vectors

2.4.2 Vector Equality in Component Notation

2.4.3 Vector Addition by Components

2.4.4 Multiplication of a Vector by a Scalar

2.4.5 Vector Subtraction

2.4.6 General Unit Vectors

2.4.7 Vector Directions in Space

2.4.8 Matrix Notation for Vectors

2.5 Computation of Vector Operations

2.6 Components of a Vector in Nonorthogonal Directions

2.7 Systems of Linear Equations

2.7.1 Matrices

2.8 Scalar Product of Two Vectors

2.8.1 Applications of the Scalar Product

2.9 Vector Product or Cross Product

2.9.1 Multiple Products of Vectors

2.10 Direct Vector Solutions

Chapter 3 Particle Equilibrium

3.1 Free-body Diagrams of a Particle

3.2 Equilibrium of a Particle

3.3 Springs

3.4 Statically Indeterminate Problems

3.5 Special Sections

3.5A Introduction to Friction

3.5B Keystone of the Arch

Chapter 4 Rigid Bodies: Equivalent Force Systems

4.1 Rigid Bodies

4.2 Modeling of Rigid Bodies and Moment of a Force

4.3 Moment of a Force about a Point in Space

4.3.1 Direct Vector Solutions

4.4 Varignon’s Theorem

4.5 Moment of a Force about an Axis

4.6 Moment of a Couple

4.7 Equivalent Force Systems

4.8 Special Equivalent Force Systems

4.8.1 Concurrent Force Systems

4.8.2 Coplanar Force Systems

4.8.3 Parallel Force Systems

4.9 General Equivalent Force Systems

4.9.1 The Wrench 160

Chapter 5 Distributed Forces: Centroids and Center of Gravity

5.1 Introduction

5.2 Center of Mass and Center of Gravity

5.2.1 Center of Mass

5.2.2 Center of Gravity

5.3 Average Position: Centroids of Areas, Volumes, and Lines;The First Moment

5.3.1 Centroid of an Area

5.3.2 Centroid of a Volume

5.3.3 Centroid of a Line

5.3.4 Centroid of a Curve in Space

5.4 Theorems of Pappus and Guldinus

5.5 Centroids of Composite Bodies

5.6 Distributed Loads on Beams

5.7 Forces Due to Fluid Pressure Acting on a Submerged Surface

5.7.1 Buoyancy

Chapter 6 Equilibrium of Rigid Bodies

6.1 Introduction

6.2 Supports for a Two-dimensional Model

6.3 Supports for a Three-dimensional Model

6.4 Free-body Diagram

6.5 Equilibrium of a Rigid Body in Two Dimensions

6.5.1 Solution Strategy

6.5.2 A Two-Force Member

6.5.3 A Three-Force Member

6.6 Equilibrium of a Rigid Body in Three Dimensions

6.6.1 Constraints

6.7 Statically Indeterminate Reactions and Improper Constraints

Chapter 7 Analysis of Structures

7.1 Introduction

7.2 Planar Trusses

7.3 Simple Trusses

7.4 Method of Joints

7.5 Method of Joints Using Matrix Techniques

7.6 Method of Sections

7.7 Space Trusses

7.8 Compound Trusses

7.9 Frames and Machines

Chapter 8 Internal Forces in Structural Members

8.1 Introduction

8.2 Internal Forces in a Member

8.3 Types of Loading and Supports in Beams

8.4 Shear and Bending Moments in Beams

8.4.1 Relationship between the Load Distribution, the Shear Force, and the Bending Moment

8.5 Discontinuity Functions for Beam Equations

8.6 Cables

8.6.1 Cable Subjected to Concentrated Loads

8.6.2 Cables Supporting Loads Distributed Uniformly along a Horizontal Line

8.6.3 Cable Supporting Loads Distributed Uniformly along its Own Length

Chapter 9 Friction

9.1 Introduction

9.2 Coulomb Friction

9.3 Wedges

9.4 Square-Threaded Screws

9.5 Belt Friction

9.5.1 V-belts

9.6 Bearings

9.7 Thrust Bearings, Collars, and Clutches

9.8 Rolling Resistance

Chapter 10 Moments of Inertia

10.1 Introduction

10.2 Second Moment of an Area

10.2.1 Determination of the Second Moment of an Area by Integration

10.3 Polar Moment of Inertia

10.4 Second Moment of an Area about Centroidal Axes for Specific Areas

10.5 Parallel-Axis Theorem for the Second Moment of Area

10.6 Radius of Gyration of an Area

10.7 Second Moments of Composite Areas

10.8 Principal Second Moments of Area

10.8.1 Product Moment of an Area, or Product Moment of Inertia

10.8.2 Rotation of Axes

10.9 Mohr’s Circle to Determine Principal Second Moments of Area

10.10 Eigenvalue Problem

10.11 Mass Moments of Inertia

10.11.1 Parallel-Axis Theorem

Chapter 11 Virtual Work

11.1 Introduction

11.1.1 Work—By a Force or Moment

11.2 Virtual Work

11.3 Principle of Virtual Work for a System of Connected Rigid Bodies

11.4 Finite Work of a Force and Moment

11.5 Conservative Forces and Potential Energy

11.6 Potential Energy and Equilibrium

11.7 Stability of Equilibrium

Appendix

Solution of Systems of Linear Equations

Gauss–Jordan Reduction

Inverse of a Matrix

Solution of Vector Equations

Statics Index Dictionary

Answers

Index