Essential Statics
Essential Statics in Engineering Mechanics Table of Contents
TABLE OF CONTENTS
Chapter 1 Some Concepts in Engineering Mechanics
1.1 Introducing Mechanics
Statics and Dynamics
Newton’s Laws of Particle Motion
Some Basic Concepts 3
A Quick Informal Peek at Particle Free Body Diagrams
1.2 On Units, Force and Weight
Dimensional Balance
On Force and Weight and Mass
1.3 On Prerequisite Mathematics and Representations of Physical Vectors
Review of Some Concepts from Mathematics
Vectors and Scalars
Introducing Vector Representations
1.4 Vector Directions and Resolution in Cartesian Coordinates
Cartesian Components of 2D Vectors
3D Vector Directions and Cartesian Representation
1.5 Practice and Assigned Problems
Chapter 2 Composition and Addition of (Force) Vectors
2.1 Problem Solving in Statics – General Approach
General Elements of a Solution Procedure
Setting-out the Solution
2.2 Addition of 2D Vectors by Graphical Approach
Procedure for Graphical Addition of (2D) Vectors
Permutations of the 2D Vector Addition Problem
2.3 Vector Addition by Resolution in Cartesian Coordinates
Procedure for Analytical Addition of Vectors
2.4 Examples of Vector Addition in 3D Space
2.5 Practice and Assigned Problems
Chapter 3 Equilibrium of Particles
3.1 Particle Interaction Forces and Free Body Diagram
Particle Free Body Diagram Procedure
Interaction of Particles with Their Environment
Introducing Friction
3.2 Ties, Struts, Cables and Springs
Tension and Compression, Ties and Struts
Ideal Cable and Interaction with Pulleys
Spring Behavior in Engineering Mechanics
3.3 Solution of Particle Equilibrium
Procedure for Equilibrium of Particles
Equilibrium of Particles in Two Dimensions
3.4 Equilibrium of Particles in Three Dimensions
3.5 Practice and Assigned Problems
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Table of Contents Essential Statics in Engineering Mechanics
Chapter 4 Moments, Couples and Distributed Loads
4.1 Moment of a Force about a Point
The Cross Product of Two Vectors
Methods of Computing the Moment of a Force about a Point
Moment of a Force about an Axis
4.2 Couples and the Couple Moment
Couple Generation and Moment of a Force-Pair Couple
Equivalent Force-Couple Systems
4.3 Concepts of Centers of Gravity, Mass, Volume and of Plane Areas
Center of Gravity, Center of Mass, and Centroid
Centroid of Plane Areas
4.4 Reduction of Distributed Normal Load
Reduction of Normal Traction and Center of Pressure
Reduction of a Line Load
4.5 Practice and Assigned Problems
Chapter 5 Equilibrium of Rigid Bodies
5.1 Rigid Body Equilibrium Equations
Equilibrium of Rigid Body Procedure
5.2 Equilibrium of Rigid Bodies in Two Dimensions
Two-Dimensional Rigid Body Support Reactions
Two-Force Members, Links and Three-force Members
Solution of Rigid Body Equilibrium Problems in 2D
5.3 Rigid Body Support Reactions in 3D and Degree-of-Freedom Constraints
3D Support Reactions 203
Statical Determinacy, Over- and Under-Constrained Systems
5.4 Equilibrium of Rigid Bodies in Three Dimensions
5.5 Practice and Assigned Problems
Chapter 6 Introducing Structural Analysis: Trusses and Frames
6.1 Structures: Types and Objective of Analysis
Trusses and their Applications
The Simple Truss
6.2 Analysis of Planar Simple Trusses by Method of Joints
Concept of Zero-Force Member
Method of Joints
6.3 Analysis of Planar Simple Trusses by Method of Sections
Procedure for Method of Sections
6.4 Analysis of Frames and Machine Elements
What are Frames?
Procedure for Frame Analysis
6.5 Practice and Assigned Problems
Chapter 7 Introducing Structural Design
7.1 Idea of Internal Stress, Compatibility and Equilibrium
Axially Loaded Member and Normal Stress
Transversely Loaded Member and Shear Stress
Longitudinal Member Subject to a Bending Moment
7.2 Moment of Inertia of Cross-section in Bending
Evaluation of Area Moment of Inertia of a Cross-section
Moment of Inertia of Composite Area
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Essential Statics in Engineering Mechanics Table of Contents
7.3 Open-Ended Design Problems
Open-Ended Design and Example
7.4 Computer Tool for Design Projects in Statics
Introducing Elements of Generalized Model for Computer Solution
Applications to Planar Trusses and Frames
Internal Loads at Interior Frame Sections: Beam Shear and Bending Moment Diagrams
7.5 Practice and Assigned Problems
Appendix A Review of Some Prerequisite Topics from Mathematics
A.1 Introduction
A.2 Geometry
Congruency of Angles
Triangle
Circle
Solid Geometry
A.3 Trigonometry
Definitions using A Right Triangle
Circle Definition
Periodicity and Symmetry
Some Identities
Angles and Sides of Any Triangle
A.4 Algebraic Equations
Quadratic Equation
Determinant and Inverse of A Square Matrix
Solution of A Linear System of Algebraic Equations
Nonlinear Systems and Iterative Techniques
A.5 Differential Calculus
Basic Derivatives
Product Rule
Quotient Rule
Chain Rule
A.6 Integral Calculus
Some Basic Integrals
Substitution Rule
Integration by Parts
Appendix B Solution of Tutorial Problems
Chapter 1 Tutorial Problems
Chapter 2 Tutorial Problems
Chapter 3 Tutorial Problems
Chapter 4 Tutorial Problems
Chapter 5 Tutorial Problems
Chapter 6 Tutorial Problems
Chapter 7 Tutorial Problems
Appendix C Dry Friction in Finite Surfaces
C.1 Coulomb Friction Analytical Model
Equilibrium of Rigid Bodies with Coulomb Friction Interfaces
C.2 Wedges and Screws
Wedges
Square Thread Power Screws
C.3 Thin Belts
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