Applied Engineering Statics Course

Lesson 1 • Vector Operations in Two Dimensions

Covers addition, subtraction, and resolution of 2D vectors. Provides computational tools for decomposing forces into components.

Lesson 2 • Equilibrium Conditions in Two Dimensions

Formalises the three scalar equilibrium equations for 2D problems. Students apply sum-of-forces and sum-of-moments to simple bodies.

Lesson 3 • Newton's Laws Applied to Statics

Applies Newton's first and third laws to stationary bodies. Connects classical mechanics principles directly to equilibrium conditions.

Lesson 4 • Scalars, Vectors, and Force Basics

Introduces scalar vs. vector quantities and force representation. Builds the mathematical language needed for all subsequent equilibrium analysis.

Lesson 1 • Statical Determinacy and Stability

Introduces determinacy criteria to assess solvability before computing. Distinguishes stable, unstable, and redundant structural configurations.

Lesson 2 • Distributed Loads and Resultants

Converts distributed loads to equivalent point forces for FBD use. Covers uniform, triangular, and general load distributions.

Lesson 3 • Types of Supports and Reactions

Catalogues pin, roller, fixed, and link supports with their reaction components. Matching support type to reaction unknowns prevents under- or over-constraint errors.

Lesson 4 • Isolating a Body for Analysis

Teaches the process of mentally cutting a body free from its environment. Correct isolation is the prerequisite for applying equilibrium equations.

Lesson 1 • Beam Reactions Under Point Loads

Solves simply supported and overhanging beams with concentrated forces. Reinforces moment-sum strategy for efficient unknown isolation.

Lesson 2 • Frame and Machine Analysis

Decomposes multi-member frames into individual FBDs to find all member forces. Distinguishes two-force members from multi-force members for efficiency.

Lesson 3 • Cables and Pulleys

Analyses flexible cables under concentrated loads and pulley systems. Applies tension continuity and geometry to determine cable forces.

Lesson 4 • Beams with Combined Loading

Handles beams carrying point loads, distributed loads, and applied moments simultaneously. Builds problem-solving fluency for realistic loading scenarios.

Lesson 1 • Method of Joints

Solves truss member forces by applying equilibrium at each joint sequentially. Efficient for finding all member forces in small to medium trusses.

Lesson 2 • Truss Geometry and Assumptions

Defines ideal truss assumptions: pin joints, straight members, loads at joints only. Correct assumptions are the basis for valid two-force member analysis.

Lesson 3 • Space Trusses Introduction

Extends planar truss concepts to three-dimensional structures with six equilibrium equations per joint. Prepares students for 3D structural analysis.

Lesson 4 • Zero-Force Members and Shortcuts

Identifies zero-force members by inspection to reduce computational effort. Covers two standard geometric rules for rapid identification.

Lesson 1 • Shear and Moment by Sections

Uses the method of sections to compute V and M at specific locations. Builds analytical skill before introducing diagram construction.

Lesson 2 • Internal Force Concepts

Defines normal force, shear force, and bending moment at a cross-section. Establishes sign conventions critical for consistent diagram construction.

Lesson 3 • Shear Force Diagrams

Constructs complete shear force diagrams using load-shear relationships. Covers jumps at point loads and slopes under distributed loads.

Lesson 4 • Bending Moment Diagrams

Builds moment diagrams from shear diagrams using the shear-moment relationship. Identifies maximum moment location for design purposes.

Lesson 1 • Bearing and Disk Friction

Computes friction torque in journal bearings and flat disk clutches. Extends friction analysis to rotating machine components.

Lesson 2 • Friction in Block and Incline Problems

Applies Coulomb friction to blocks on flat and inclined surfaces. Covers tipping vs. sliding failure modes and their governing conditions.

Lesson 3 • Wedge and Screw Friction

Analyses self-locking wedges and power screws using friction principles. Determines mechanical advantage and self-locking conditions.

Lesson 4 • Belt and Rope Friction

Derives the capstan equation for tension ratio across a wrapped belt or rope. Applies to belt drives, rope brakes, and capstan devices.

Lesson 1 • Composite Body Method

Locates centroids of complex shapes by summing weighted sub-area contributions. Covers cutouts using negative area subtraction.

Lesson 2 • Centroids by Integration

Derives centroid coordinates using first-moment integrals for lines and areas. Builds analytical skill for irregular shapes without tabulated data.

Lesson 3 • Center of Gravity Concepts

Distinguishes centre of gravity, centre of mass, and centroid for uniform and non-uniform bodies. Establishes the physical meaning behind centroid calculations.

Lesson 4 • Pappus-Guldinus Theorems

Uses centroid path length and area to compute surface area and volume of revolution. Provides efficient alternatives to direct integration.

Lesson 1 • Parallel-Axis Theorem

Transfers moment of inertia from centroidal axis to any parallel axis. Essential for composite section analysis where sub-areas are offset from the overall centroid.

Lesson 2 • Product of Inertia and Principal Axes

Introduces product of inertia Ixy and Mohr's circle for area moments. Identifies principal axes where product of inertia vanishes for symmetric sections.

Lesson 3 • Second Moment of Area Defined

Defines moment of inertia of an area and its physical role in bending resistance. Distinguishes it from mass moment of inertia to prevent conceptual confusion.

Lesson 4 • Composite Section Analysis

Combines parallel-axis theorem with tabulated values to find I for built-up sections. Covers standard structural shapes: rectangles, circles, and I-sections.