Strength of Materials Course

Lesson 1 • Support Reactions and Determinacy

Analyses pin, roller, and fixed supports and classifies structures as statically determinate or indeterminate. Determines which analysis methods apply to a given structure.

Lesson 2 • Equilibrium of Rigid Bodies

Covers conditions for static equilibrium and moment balance. Provides the analytical basis for determining support reactions in structural members.

Lesson 3 • Forces and Vector Representation

Introduces scalar versus vector quantities and force resolution into components. Establishes the mathematical language used throughout all subsequent chapters.

Lesson 1 • Stress-Strain Diagrams and Material Behaviour

Interprets tensile test data to identify elastic, yielding, and fracture regions. Establishes material property vocabulary used in all design calculations ahead.

Lesson 2 • Shear Stress and Bearing Stress

Introduces average shear stress in bolts, pins, and welds, plus bearing stress at contact surfaces. Extends stress analysis to fastened and connected members.

Lesson 3 • Normal Stress Under Axial Loading

Derives the normal stress formula from internal force resultants. Connects equilibrium concepts to the intensity of force per unit area on a cross-section.

Lesson 4 • Factor of Safety and Permissible Stress

Applies safety factors to convert material strength into permissible design stress. Introduces the engineering judgment required for safe structural sizing.

Lesson 1 • Hooke's Law and Elastic Moduli

Establishes the linear relationship between stress and strain for isotropic materials. Introduces Young's modulus, modulus of rigidity, and bulk modulus as design constants.

Lesson 2 • Creep, Fatigue, and Fracture Basics

Introduces time-dependent creep, cyclic fatigue, and brittle fracture as failure modes. Connects material behaviour to the service life considerations in structural design.

Lesson 3 • Elastic versus Plastic Deformation

Distinguishes recoverable elastic deformation from permanent plastic deformation. Provides the conceptual basis for yield criteria introduced in later chapters.

Lesson 1 • Statically Indeterminate Axial Structures

Introduces compatibility equations to supplement equilibrium for indeterminate systems. Solves for unknown reactions and internal forces in redundant axial members.

Lesson 2 • Elastic Deformation of Axial Members

Derives the axial deformation formula from Hooke's law and equilibrium. Applies the formula to single-segment and multi-segment prismatic bars.

Lesson 3 • Stress Concentrations in Axial Members

Quantifies local stress amplification near holes, notches, and fillets using concentration factors. Demonstrates why geometric discontinuities govern fatigue and fracture design.

Lesson 1 • Angle of Twist and Shaft Stiffness

Calculates angular deformation of shafts under applied torque using material and geometric properties. Extends to multi-segment shafts with varying cross-sections or materials.

Lesson 2 • Torsion of Non-Circular and Thin-Walled Sections

Applies Bredt's formula to closed thin-walled sections and introduces warping in open sections. Expands torsion analysis beyond circular geometry to structural profiles.

Lesson 3 • Torsion Formula for Circular Shafts

Derives the torsional shear stress distribution assuming plane sections remain plane. Establishes the polar moment of inertia as the key geometric property for shaft design.

Lesson 1 • Flexure Formula and Bending Stress

Derives the elastic flexure formula from plane-sections and Hooke's law assumptions. Calculates normal stress distribution across symmetric and unsymmetric cross-sections.

Lesson 2 • Shear and Moment Diagram Construction

Constructs V and M diagrams by integration and graphical methods for various load cases. Identifies critical sections where maximum stress occurs for design purposes.

Lesson 3 • Internal Shear and Bending Moment

Defines internal shear force and bending moment at any beam cross-section using equilibrium. Introduces sign conventions essential for consistent diagram construction.

Lesson 4 • Composite and Unsymmetric Beam Bending

Analyses beams made of two or more materials using the transformed-section method. Extends bending theory to sections with no axis of symmetry in the loading plane.

Lesson 1 • Differential Equation of the Elastic Curve

Derives the beam deflection differential equation from curvature-moment relationships. Establishes boundary and continuity conditions needed for integration solutions.

Lesson 2 • Statically Indeterminate Beams

Solves propped cantilevers and continuous beams using compatibility and superposition. Determines redundant reactions and draws complete shear and moment diagrams.

Lesson 3 • Direct Integration Method

Solves the elastic curve equation by successive integration for standard load cases. Applies boundary conditions to determine constants of integration and deflection equations.

Lesson 4 • Moment-Area Method

Uses the first and second moment-area theorems to find slopes and deflections graphically. Particularly efficient for beams with variable moment of inertia or stepped sections.

Lesson 1 • Yield and Fracture Failure Criteria

Applies von Mises and Tresca criteria for ductile yielding and maximum normal stress for brittle fracture. Enables quantitative safety assessment under multiaxial stress states.

Lesson 2 • Pressure Vessels and Thin-Walled Structures

Derives hoop and longitudinal stresses in cylindrical and spherical pressure vessels. Applies combined stress analysis and failure criteria to pressurised structural components.

Lesson 3 • Combined Axial, Bending, and Torsion

Superimposes stress resultants from multiple load types at critical points on a cross-section. Identifies the most stressed location as the starting point for failure assessment.

Lesson 4 • Strain Transformation and Rosette Analysis

Applies transformation equations to strain and interprets strain gauge rosette data. Connects measured surface strains to principal stresses via material constitutive relations.