ENGN 221 • Midterm • Engineering Mechanics

Introduction and Fundamental Concepts

Units of Measurement and Numerical Calculations

Vector Operations, Vector Addition of Forces

Resultant Force Example 1

Vector Components Example

Resultant Force Example 2

Addition of Coplanar Forces

Resultant of Coplanar Forces Example 1

Cartesian Vectors

Cartesian Vectors Example 1

Cartesian Vectors Example 2

Cartesian Vectors Example 3

Position Vectors, Unit Vector and Force Vector Along A Line

Position Vector Example 1

Force Vector Example 1

Position Vector Example 2

Position Vector Example 3

Dot (Scalar) Product of Vectors

Dot Product Example 1

Dot Product Example 2

Dot Product Example 3

Chapter Review

Equilibrium, How to Draw a Free Body Diagram (FBD)

Coplanar Force Systems (Equilibrium in 2D)

Coplanar Force Systems Example 1

Coplanar Force Systems Example 2

Three Dimensional Force Systems (Equilibrium in 3D)

Three Dimensional Force Systems Example 1

Three Dimensional Force Systems Example 2

Chapter Review

What is Moment?

Moment of a Force: Scalar Formulation

Moment of a Force: Vector Formulation

Moment of a Force Example 1

Moment of a Force Example 2

Moment of Force Components: Varignon's Theorem

Moment of Force Components Example

Moment of a Force About an Axis

Moment About an Axis Example

Moment of a Couple

Moment of a Couple Example 1

Moment of a Couple Example 2

Simplification of a Force and Couple System

Reduction to a Given Point Example

Further Simplifications of a Force and Couple System

Reduction to a Single Force Example

Reduction of a Parallel Force System Example

Reduction of a Simple Distributed Loading

Distributed Loading Example

Chapter Review

Equilibrium in Two Dimensions

Free Body Diagram Example 1

Free Body Diagram Example 2

Equations of Equilibrium in 2-D

Equilibrium in 2-D Example 1

Equilibrium in 2-D Example 2

Equilibrium in 2-D Example 3

Equilibrium in 2-D Example 4

Two and Three Force Members

Equilibrium in Three Dimensions

Free Body Diagram in 3-D Example

Equations of Equilibrium in 3-D

Equilibrium in 3-D Example

Constraints and Statical Determinacy

Chapter Review

Simple Trusses, Method of Joints

Method of Joints Example 1

Method of Joints Example 2

Zero Force Members (ZFMs)

Zero Force Members Example

Method of Joints Example 3

Method of Sections

Method of Sections Example 1

Method of Sections Example 2

Space Trusses

Space Trusses Example

Frames and Machines

Frames and Machines Example 1

Frames and Machines Example 2

Frames and Machines Example 3

Chapter Review

Internal Loadings in Structural Members

Internal Loadings at a Point Example 1

Internal Loadings at a Point Example 2

Shear and Moments Equations and Diagrams: Method of Sections

Diagrams with Method of Sections Example 1

Diagrams with Method of Sections Example 2

Relations Between Internal Loads: Graphical Approach

Diagrams with Graphical Approach Example 1

Diagrams with Graphical Approach Example 2

Cables with Concentrated Loads

Cables with Concentrated Loads Example

Cables with Distributed Loads

Cables with Distributed Loads Example

Cables with Their Own Weight

Chapter Review

Center of Gravity, Mass, Volume and Centroid of an Area

Centroid of an Area Under a Function Example 1

Centroid of an Area Under a Function Example 2

Centroid of a Curved Line

Centroid of a Composite Area

Centroid of a Composite Area Example

Centroid of a Composite Line Example

Centroid of a Composite Volume Example

Theorems of Pappus and Guldinus

Pappus and Guldinus Example

Chapter Review

Moment of Inertia Under a Function, Parallel Axis Theorem, Radius of Gyration

Moment of Inertia Under a Function Example

Moment of Inertia for Composite Areas

Moment of Inertia for Composite Area Example

Chapter Review

Structural Analysis: Trusses

Method of Sections Example 1

Structural Analysis: Trusses

Structural Analysis: Frames and Machines

Structural Analysis: Frames and Machines

Force Vectors: Resultant Force

Force Vectors: Resultant Force

Force Vectors: Resultant Force

Equilibrium of a Rigid Body: Support Reactions

Force System Resultants: Moment About a Point

Force System Resultants: Moment About a Point

Equilibrium of a Rigid Body in 3D

Structural Analysis: Trusses

Structural Analysis: Frames and Machines

Internal Forces: Shear Force and Bending Moment Diagrams (with Section Method)

Structural Analysis: Frames and Machines

Equilibrium of a Rigid Body in 3D

Structural Analysis: Trusses

Internal Forces

Practice Problem

Practice Problem

Practice Problem

Practice Problem

Internal Forces

Friction Belts

Friction

Structural Analysis: Frames and Machines

Equilibrium of a Rigid Body in 3D

Structural Analysis: Frames and Machines

Internal Forces: Shear Force and Bending Moment Diagrams

Friction

Area Moment of Inertia

Area Moment of Inertia

Area Moment of Inertia

Area Moment of Inertia

Moment of Inertia

Force Vectors

Force System Resultants

Moment About an Axis

Moment About a Point

Equilibrium of a Particle in 2D

Equilibrium of a Particle in 3D

Force System Resultants: Moment of a Force

Force System Resultants: Reduction to a Given Point

Force System Resultants

Equilibrium of a Particle

Equilibrium of a Rigid Body in 2D

Moment of a Force About an Axis

Equivalent Force and Couple System at a Point

Equilibrium of a Rigid Body in 3D

Vectors (Conceptual Question)

Equilibrium in of a Particle

Equilibrium of a Rigid Body in 2D

Equilibrium of Rigid Body in 2D

Moment of a Couple in 3D

Force System Resultants

Force System Resultants

Equilibrium of a Rigid Body in 3D

Equilibrium for Rigid Body in 3D

Equilibrium of Rigid Body in 3D

Equilibrium of Rigid Body in 3D

Equilibrium in 3D (Moment About an Axis)

Equilibrium in 3D (Moment About an Axis)

Force Vector Along A Line

Equilibrium of a Particle

Simplification of a Force and Couple System

Vectors (Resultant and Components Along Given Axes)

Vectors (3D Vectors and Direction Cosines)

Equilibrium of a Particle in 2D

Moment of a Force About an Axis

Force Vectors

Moment About a Point

Equilibrium of a Rigid Body in 2-D

Equilibrium of a Rigid Body in 2-D

Resultant Vector

Equilibrium of a Rigid Body

Equivalent Force and Moment at a Given Point

Equilibrium of a Rigid Body

Equilibrium of a Rigid Body

Force Vectors

Equilibrium of a Particle in 2D

Force Vectors and Moment About an Axis

Simplification of a Force System to a Given Point

Structural Analysis: Trusses

Structural Analysis: Trusses

Structural Analysis: Trusses

Structural Analysis: Frames and Machines

Structural Analysis: Frames and Machines

Structural Analysis: Frames and Machines

Internal Forces: Shear Force and Moment Diagrams

Internal Forces: Shear Force and Moment Diagrams

Structural Analysis: Frames and Machines

Structural Analysis: Frames and Machines

Structural Analysis: Trusses

Structural Analysis: Trusses

Internal Forces

Internal Forces: Shear Force and Bending Moment Diagrams

Internal Forces: Shear Force and Bending Moment Diagrams

Internal Forces: Shear Force and Moment Diagrams

Internal Forces: Shear Force and Moment Diagrams

Internal Forces: Shear Force and Moment Diagrams

Structural Analysis: Trusses

Structural Analysis: Frames and Machines

Structural Analysis: Frames and Machines

Internal Forces

Internal Forces: Shear Force and Moment Diagrams

Formula Sheet for All Chapters