Beginner Mechanics of Materials Course

Lesson 1 • Types of Loads and Supports

Categorizes axial, shear, bending, and torsional loads and common support conditions. Prepares students to identify load types before performing any analysis.

Lesson 2 • Introduction to Stress and Strain

Defines normal and shear stress and their corresponding strains. Anchors the chapter by establishing the two fundamental measurable quantities used throughout the course.

Lesson 3 • Equilibrium and Free-Body Diagrams

Applies static equilibrium equations to isolated bodies to find internal forces. Provides the analytical tool required for every stress calculation in the course.

Lesson 1 • Statically Indeterminate Axial Systems

Introduces compatibility equations to solve systems where equilibrium alone is insufficient. Extends axial analysis to real structures with redundant supports.

Lesson 2 • Axial Stress in Prismatic Members

Derives the average normal stress formula for constant cross-section bars. Establishes the simplest stress state as a baseline for more complex loading cases.

Lesson 3 • Stress Concentrations in Axial Members

Introduces stress concentration factors at geometric discontinuities such as holes and fillets. Prepares students to account for localized high-stress regions in design.

Lesson 4 • Deformation Under Axial Load

Applies Hooke's Law to compute elongation and contraction of axially loaded bars. Links stress and strain to measurable geometric change in a member.

Lesson 1 • Angle of Twist Calculation

Computes angular deformation of shafts under applied torques using material and geometric properties. Connects torsional stiffness to practical shaft performance requirements.

Lesson 2 • Power Transmission and Shaft Design

Relates transmitted power, rotational speed, and torque to size shafts for mechanical systems. Integrates stress and deformation limits into a practical design workflow.

Lesson 3 • Solid vs. Hollow Circular Shafts

Compares stress and twist in solid and hollow shafts for equivalent torque capacity. Guides material-efficient shaft design decisions.

Lesson 4 • Statically Indeterminate Torsional Systems

Solves torsional problems with redundant supports using compatibility of twist. Mirrors the indeterminate axial approach and reinforces the general solution method.

Lesson 1 • Bending Moment Diagrams

Constructs bending moment diagrams by integrating the shear diagram and applying moment jumps. Identifies the location and magnitude of maximum bending moment.

Lesson 2 • Diagrams for Common Beam Cases

Applies the diagramming process to simply supported, cantilever, and overhanging beams. Builds pattern recognition for standard loading configurations encountered in practice.

Lesson 3 • Shear Force Diagrams

Constructs shear force diagrams by integrating distributed loads and applying point load jumps. Develops the graphical skill needed to locate maximum shear in a beam.

Lesson 1 • Unsymmetric Bending

Analyzes bending about non-principal axes and locates the neutral axis for asymmetric loading. Prepares students for angle sections and other shapes without a vertical symmetry axis.

Lesson 2 • Bending of Composite Beams

Extends the flexure formula to beams made of two or more materials using the transformed-section method. Addresses practical cases such as reinforced concrete and bimetallic strips.

Lesson 3 • The Flexure Formula

Derives the bending stress distribution across a cross-section from moment equilibrium and strain compatibility. Provides the primary equation for beam bending stress analysis.

Lesson 4 • Section Modulus and Beam Design

Introduces the section modulus S as a single geometric efficiency metric for bending design. Guides selection of standard cross-sections based on allowable bending stress.

Lesson 1 • Shear Center of Open Sections

Locates the shear center as the point through which transverse load must act to prevent twisting. Demonstrates why loading off the shear center induces combined bending and torsion.

Lesson 2 • Shear Stress Formula for Beams

Derives the shear stress formula using the first moment of area Q and moment of inertia I. Establishes the governing equation for transverse shear stress in solid sections.

Lesson 3 • Shear Stress in Flanged Sections

Applies the shear formula to I-beams and T-sections, distinguishing web and flange contributions. Reveals why webs carry the majority of transverse shear in standard sections.

Lesson 1 • Plane Stress Transformation Equations

Derives equations for normal and shear stress on an inclined plane from known stress components. Provides the analytical foundation for finding stresses at any orientation.

Lesson 2 • Plane Strain Transformation

Applies analogous transformation equations to strain components and constructs Mohr's Circle for strain. Connects to experimental strain gauge measurements used in structural testing.

Lesson 3 • Mohr's Circle for Plane Stress

Constructs and interprets Mohr's Circle as a graphical tool for stress transformation. Reinforces the transformation equations through a visual and intuitive method.

Lesson 4 • Generalized Hooke's Law

Extends Hooke's Law to three-dimensional stress states using elastic constants E, G, and Poisson's ratio. Completes the stress-strain relationship needed for three-dimensional analysis.

Lesson 1 • Euler Buckling of Columns

Derives the Euler critical load formula for ideal columns and defines the slenderness ratio. Establishes the threshold compressive load beyond which a column becomes unstable.

Lesson 2 • Elastic Curve and Integration Method

Derives the differential equation of the elastic curve and integrates it to find slope and deflection. Establishes the fundamental analytical method for beam deflection calculation.

Lesson 3 • Statically Indeterminate Beams

Solves beams with redundant supports by combining equilibrium with deflection compatibility equations. Extends beam analysis to the continuous and propped-cantilever configurations common in practice.

Lesson 4 • Superposition Method for Deflection

Combines tabulated deflection formulas for simple cases to solve complex loading configurations. Provides a fast, practical alternative to direct integration for standard beam problems.