Mechanics of Materials Course

Lesson 1 • Review of Static Equilibrium

Revisits free-body diagrams and equilibrium equations as prerequisites for internal force analysis. Bridges statics knowledge to deformable-body applications.

Lesson 2 • Strain Concepts and Deformation

Defines normal and shear strain as measures of deformation. Connects geometric changes in a body to the stress state introduced in the previous section.

Lesson 3 • Stress Concepts and Units

Defines normal and shear stress at a point and their mathematical expressions. Provides the conceptual basis for all subsequent stress analysis chapters.

Lesson 4 • Internal Forces and Stress Resultants

Introduces the method of sections to expose internal forces and moments. Establishes normal force, shear force, and bending moment as fundamental stress resultants.

Lesson 1 • Tension and Compression Testing

Describes the standard uniaxial test procedure and the resulting stress-strain curve. Provides the experimental foundation for all material property definitions used later.

Lesson 2 • Yield Criteria and Plasticity Basics

Introduces yield strength, proportional limit, and offset yield conventions. Prepares students to identify the onset of permanent deformation in design scenarios.

Lesson 3 • Elastic Material Properties

Defines Young's modulus, Poisson's ratio, and the shear modulus from test data. These constants appear in every deformation formula throughout the course.

Lesson 4 • Material Selection Considerations

Surveys metals, polymers, ceramics, and composites in terms of mechanical performance. Equips students to justify material choices based on strength, stiffness, and ductility requirements.

Lesson 1 • Axial Stress and Deformation Formulas

Derives the elastic deformation formula for prismatic and non-prismatic bars. Applies Hooke's law directly to compute elongation or shortening under axial load.

Lesson 2 • Thermal Loads and Misfit Strains

Combines thermal expansion with mechanical constraints to find thermally induced stresses. Extends indeterminate analysis to temperature changes and initial misfit conditions.

Lesson 3 • Inelastic Axial Behaviour

Extends axial analysis beyond the elastic limit to elastic-perfectly plastic models. Prepares students for residual stress calculations and limit-load concepts.

Lesson 4 • Statically Indeterminate Axial Members

Introduces compatibility equations to supplement equilibrium for indeterminate structures. Students learn to solve for unknown reactions and internal forces simultaneously.

Lesson 1 • Torsion of Non-Circular Sections

Introduces Prandtl's membrane analogy and closed thin-walled section formulas. Extends torsion analysis to rectangular bars and thin-walled structural tubes.

Lesson 2 • Statically Indeterminate Torsion Problems

Applies compatibility conditions to shafts with fixed ends or coupled segments. Mirrors the indeterminate axial approach within the torsion context.

Lesson 3 • Torsion Theory and Shear Stress Distribution

Derives the torsion formula assuming plane sections remain plane for circular cross-sections. Establishes the linear shear stress distribution as the basis for shaft design.

Lesson 4 • Power Transmission and Shaft Design

Relates transmitted power, rotational speed, and torque to size shafts for real machinery. Integrates allowable shear stress and angle-of-twist limits into a design procedure.

Lesson 1 • Beam Deflection by Integration

Integrates the moment-curvature relationship to obtain slope and deflection equations. Applies boundary conditions to determine integration constants for various support types.

Lesson 2 • Normal Stress in Pure Bending

Derives the flexure formula from kinematic and equilibrium assumptions for pure bending. Establishes the neutral axis concept and linear stress distribution across the section.

Lesson 3 • Shear Stress in Beams

Derives the shear stress formula for beams with rectangular and standard cross-sections. Identifies the maximum shear stress location and its role in beam failure.

Lesson 4 • Beam Deflection by Superposition and Energy

Uses superposition tables and Castigliano's theorem to find deflections efficiently. Provides practical alternatives to direct integration for complex loading patterns.

Lesson 5 • Shear Force and Bending Moment Diagrams

Constructs SFD and BMD for statically determinate beams under various load types. These diagrams are the essential input for all subsequent bending stress calculations.

Lesson 1 • Plane Stress Transformation Equations

Derives transformation equations for normal and shear stress on inclined planes. Establishes the mathematical framework for finding critical stress orientations.

Lesson 2 • Failure Theories for Ductile and Brittle Materials

Applies maximum-shear-stress and distortion-energy criteria to ductile materials and maximum-normal-stress to brittle ones. Enables safe design under combined loading.

Lesson 3 • Plane Strain Transformation

Applies analogous transformation equations to strain components in plane strain. Connects strain rosette measurements to principal strains and material stresses.

Lesson 4 • Mohr's Circle for Plane Stress

Constructs Mohr's circle as a graphical tool for stress transformation. Enables rapid identification of principal stresses, maximum shear, and stress on any plane.

Lesson 1 • Thick-Walled Cylinders and Press Fits

Derives Lamé equations for radial and hoop stresses in thick-walled cylinders. Extends to press-fit and shrink-fit contact pressure calculations.

Lesson 2 • Superposition of Stress Resultants

Combines normal and shear stresses from multiple load types at a critical point. Applies the principle of superposition to build the complete stress state for transformation.

Lesson 3 • Eccentric Axial Loading

Analyses members where the load line does not pass through the centroid, producing combined axial and bending stress. Introduces the kern concept for compression members.

Lesson 4 • Combined Bending and Torsion

Evaluates shafts and cranks under simultaneous bending moments and torques. Applies transformation equations and failure criteria to determine safe operating loads.

Lesson 1 • Effective Length and Boundary Conditions

Determines effective length factors for pinned, fixed, and mixed end conditions. Applies the effective length concept to real column configurations in structures.

Lesson 2 • Inelastic Buckling and Empirical Formulas

Addresses intermediate columns where yielding precedes buckling using tangent-modulus and empirical approaches. Bridges Euler theory to practical design specifications.

Lesson 3 • Eccentrically Loaded Columns

Analyses columns with load eccentricity using the secant formula. Combines bending amplification with axial stress to assess combined failure modes.

Lesson 4 • Euler Buckling of Ideal Columns

Derives the Euler critical load formula from the differential equation of the elastic curve. Establishes slenderness ratio as the key parameter governing buckling behaviour.