Strength of Materials for Civil Engineering Course

Lesson 1 • Internal Forces in Structural Members

Introduces the method of sections to expose axial, shear, and moment resultants. These internal force concepts are the direct input to stress calculations.

Lesson 2 • Forces, Vectors, and Resultants

Covers vector algebra, force components, and resultant computation. Provides the mathematical toolkit used throughout all subsequent stress and deformation analyses.

Lesson 3 • Equilibrium of Rigid Bodies

Applies Newton's laws to stationary structures to find unknown reactions. Equilibrium conditions underpin every internal force calculation in later chapters.

Lesson 1 • Mechanical Properties from Testing

Interprets the tensile stress-strain diagram to extract key material properties. These properties are used in design calculations throughout the course.

Lesson 2 • Shear Stress and Shear Strain

Defines average shear stress in bolts, pins, and glued joints and introduces shear strain. Establishes the shear modulus as the elastic constant linking shear stress and strain.

Lesson 3 • Normal Stress and Axial Loading

Derives the average normal stress formula for prismatic bars under axial load. Connects internal axial force from equilibrium to cross-sectional stress distribution.

Lesson 4 • Normal Strain and Hooke's Law

Introduces axial strain and the linear stress-strain relationship for elastic materials. Provides the basis for computing elongation and deformation in structural members.

Lesson 1 • Composite Axial Members

Analyzes bars made of two or more materials bonded together under axial load. Applies compatibility of deformation and equilibrium to find stress in each material.

Lesson 2 • Thermal Stresses and Strains

Computes stresses induced when thermal expansion is restrained in indeterminate members. Combines thermal and mechanical deformations using superposition.

Lesson 3 • Stiffness Method for Axial Structures

Introduces the displacement-based stiffness approach as an alternative to the force method. Prepares students for matrix methods used in advanced structural analysis.

Lesson 1 • Angle of Twist Calculation

Computes angular deformation of shafts with constant and variable torque or cross-section. Applies superposition to multi-segment and indeterminate shaft problems.

Lesson 2 • Hollow Shafts and Thin-Walled Tubes

Extends torsion analysis to hollow circular and thin-walled closed sections. Introduces Bredt's formula for shear flow in non-circular closed sections.

Lesson 3 • Power Transmission and Shaft Design

Relates torque to power and rotational speed for mechanical and civil infrastructure applications. Applies allowable shear stress and twist limits to select shaft dimensions.

Lesson 1 • Beam Types and Loading Conditions

Classifies beams by support and loading type and establishes sign conventions. Correct sign conventions are essential for consistent diagram construction and stress calculation.

Lesson 2 • Introduction to Continuous Beams

Previews shear and moment behavior in statically indeterminate continuous beams. Motivates the need for advanced methods introduced in later chapters.

Lesson 3 • Differential Relationships and Diagram Rules

Derives the load-shear-moment differential relationships and applies them as diagram construction rules. Enables rapid, accurate diagram sketching without repeated section cuts.

Lesson 4 • Diagrams for Complex Loading

Constructs shear and moment diagrams for beams with combined concentrated, distributed, and applied moment loads. Addresses multi-span and overhanging configurations.

Lesson 1 • Composite and Reinforced Beams

Analyzes beams made of two materials using the transformed section method. Applies directly to reinforced concrete and timber-steel composite beam design.

Lesson 2 • Unsymmetric Bending

Extends bending analysis to sections without a vertical axis of symmetry or with inclined loads. Determines the neutral axis orientation and maximum stress for general loading.

Lesson 3 • Section Properties and Centroid

Computes centroids and moments of inertia for standard and composite cross-sections. Accurate section properties are prerequisite to correct stress and deflection calculations.

Lesson 4 • Flexure Formula Derivation

Derives normal stress distribution from geometric strain compatibility and Hooke's Law. Establishes the neutral axis location and the moment of inertia as key section properties.

Lesson 1 • Shear Center of Open Sections

Defines the shear center as the point through which transverse loads produce no twisting. Calculates shear center location for channels, angles, and other open profiles.

Lesson 2 • Shear Stress in Flanged Sections

Applies the shear formula to I-beams and T-sections, distinguishing web and flange contributions. Demonstrates why webs carry most shear in standard steel sections.

Lesson 3 • Built-Up Beam Fastener Design

Uses shear flow to determine the required spacing of nails, bolts, or welds in built-up beams. Connects shear flow theory directly to connection design practice.

Lesson 4 • Shear Flow in Thin-Walled Sections

Computes shear flow distribution in open thin-walled cross-sections under transverse loading. Shear flow is essential for locating the shear center and preventing torsion.

Lesson 1 • Energy Methods: Castigliano's Theorem

Applies Castigliano's second theorem to compute deflections and slopes in beams and frames. Provides a unified energy-based approach applicable to complex structural geometries.

Lesson 2 • Elastic Curve and Integration Method

Derives the differential equation of the elastic curve and integrates it to find slope and deflection. Boundary and continuity conditions are applied to evaluate integration constants.

Lesson 3 • Moment-Area Method

Uses the two moment-area theorems to compute slopes and deflections graphically. Efficient for beams with simple moment diagrams or when only specific values are needed.

Lesson 4 • Superposition Method for Deflections

Combines tabulated deflection formulas for standard cases to solve complex loading. Superposition is the fastest practical method for routine beam deflection calculations.