Table of Contents
1. General Principles.
Mechanics. Fundamental Concepts. Units of Measurement. The International System of Units. Numerical Calculations.
2. Force Vectors.
Scalars and Vectors. Vector Operations. Vector Addition of Forces. Addition of a System of Coplanar Forces. Cartesian Vectors. Addition and Subtraction of Cartesian Vectors. Position Vectors. Force Vector Directed Along a Line. Dot Product.
3. Equilibrium of a Particle.
Condition for the Equilibrium of a Particle. The Free-Body Diagram. Coplanar Force Systems. Three-Dimensional Force Systems.
4. Force System Resultants.
Moment of a Force–Scalar Formation. Cross Product. Moment of a Force–Vector Formulation. Principle of Moments. Moment of a Force About a Specified Axis. Moment of a Couple. Equivalent System. Resultants of a Force and Couple System. Further Reduction of a Force and Couple System. Reduction of a Simple Distributed Loading.
5. Equilibrium of a Rigid Body.
Conditions for Rigid-Body Equilibrium. Equilibrium in Two Dimensions. Free-Body Diagrams. Equations of Equilibrium. Two- and Three-Force Members. Equilibrium in Three Dimensions. Free-Body Diagrams. Equations of Equilibrium. Constraints for a Rigid Body.
6. Structural Analysis.
Simple Trusses. The Method of Joints. Zero-Force Members. The Method of Sections. Space Trusses. Frames and Machines.
7. Internal Forces.
Internal Forces Developed in Structural Members. Shear and Moment Equations and Diagrams. Relations Between Distributed Load, Shear, and Moment. Cables.
Characteristics of Dry Friction. Problems Involving Dry Friction. Wedges. Frictional Forces on Screws. Frictional Forces on Flat Belts. Frictional Forces on Collar Bearings, Pivot Bearings, and Disks. Frictional Forces on Journal Bearings. Rolling Resistance.
9. Center of Gravity and Centroid.
Center of Gravity and Center of Mass for a System of Particles. Center of Gravity, Center of Mass, and Centroid for a Body. Composite Bodies. Theorems of Pappus and Guldinus. Resultant of a General Distributed Force System. Fluid Pressure.
10. Moments of Inertia.
Definitions of Moments of Inertia for Areas. Parallel-Axis Theorem for an Area. Radius of Gyration of an Area. Moments of Inertia for an Area by Integration. Moments of Inertia for Composite Areas. Product of Inertia for an Area. Moments of Inertia for an Area About Inclined Axes. Mohr's Circle for Moments of Inertia. Mass Moment of Inertia.
11. Virtual Work.
Definition of Work and Virtual Work. Principle of Virtual Work for a Particle and a Rigid Body. Principle of Virtual Work for a System of Connected Rigid Bodies. Conservative Forces. Potential Energy. Potential Energy Criterion for Equilibrium. Stability of Equilibrium.
A. Mathematical Expressions.
B. Numerical and Computer Analysis.