Mechanics of Materials

Course Description

EGN2332C – Mechanics of Materials is a 3-credit-hour engineering science course that develops students' ability to analyze the deformation and stress in solid bodies under load. Also known as Strength of Materials, the course extends the equilibrium-of-rigid-bodies analysis from statics to address what happens internally to deformable bodies — covering stress and strain, axial loading, torsion, bending of beams, transverse shear, combined loading, stress transformations (Mohr's circle), beam deflection, column buckling, and an introduction to material failure theories.

EGN2332C is essentially equivalent in content to EGN3331C (Strength of Materials); the difference is primarily in curriculum positioning. EGN2332C is positioned as a sophomore-level (2000-level) course while EGN3331C is positioned as a junior-level (3000-level) course. Florida engineering programs vary in this curriculum positioning. The course is foundational to mechanical, civil, aerospace, and biomedical engineering practice — virtually any engineering work involving load-bearing components depends on the methods developed here.

The "C" lab indicator denotes integrated lecture and laboratory components, with hands-on testing of materials (tensile testing, beam bending, torsion testing, hardness testing) and the comparison of analytical predictions with experimental results. Students apply the equations of equilibrium from statics together with constitutive relationships (stress-strain behavior of materials) and geometric compatibility to solve problems that statics alone cannot address.

EGN2332C is a Florida common course offered at approximately 2 Florida institutions. EGN3331C (the more widely adopted junior-level designation) is offered at approximately 8 institutions. EGN2332C transfers as the equivalent course at all Florida public postsecondary institutions per SCNS articulation policy.

Learning Outcomes

Required Outcomes

Upon successful completion of this course, students will be able to:

• Apply foundational concepts of stress and strain, including normal stress, shear stress, normal strain, shear strain, units, and the engineering vs. true stress-strain distinction.
• Apply material constitutive behavior, including Hooke's law (σ = Eε), the modulus of elasticity, Poisson's ratio, the shear modulus, the relationship among elastic constants, and the engineering stress-strain diagram.
• Apply axial loading analysis, including stress in axially loaded members; deformation (δ = PL/AE); statically indeterminate axial problems; thermal stress; saint-venant's principle.
• Apply torsion of circular shafts, including shear stress in shafts (τ = Tc/J), angle of twist (φ = TL/JG), the polar moment of inertia J for solid and hollow circular shafts, statically indeterminate torsion problems, and power transmission applications.
• Apply bending of beams — stress analysis, including the flexure formula (σ = -My/I), the section modulus, bending stress at any point in a beam cross-section, and the proper application to symmetric beams.
• Apply transverse shear in beams, including the shear stress formula (τ = VQ/Ib), the shear stress distribution across common cross-sections (rectangular, I-beam, circular), and the engineering implications.
• Apply combined loading, including superposition of stresses from axial, torsional, and bending loads; the analysis of common combined-loading scenarios.
• Apply stress transformations, including the equations for plane stress transformation; principal stresses and principal directions; maximum shear stress; Mohr's circle for plane stress.
• Apply strain transformations at the introductory level, including plane strain transformation; principal strains; Mohr's circle for strain.
• Apply beam deflection analysis, including the integration method; the use of standard formulas for common loading cases; and the superposition method.
• Apply column buckling, including Euler's formula (P_cr = π²EI/L²), the slenderness ratio, the effects of end conditions, and the transition between elastic and inelastic buckling.
• Apply failure theories at the introductory level, including the maximum normal stress theory, maximum shear stress (Tresca) theory, and the distortion energy (von Mises) theory.
• Apply introductory pressure vessel analysis, including thin-walled cylindrical and spherical vessels; hoop stress and longitudinal stress.
• Demonstrate laboratory skills, including tensile testing, torsion testing, beam bending tests; comparison of theoretical predictions with experimental results.

Optional Outcomes

• Apply energy methods at the introductory level, including strain energy and Castigliano's theorem.
• Apply introductory finite element analysis (FEA), including the use of FEA software to verify analytical predictions.
• Apply principles to specific discipline contexts reflecting the program's emphasis.
• Apply fatigue analysis at the introductory level (cyclic loading, S-N curves, endurance limit).
• Apply introductory fracture mechanics, including stress intensity factor and fracture toughness at conceptual level.

Major Topics

Required Topics

• Concepts of Stress: Normal stress (σ = F/A); shear stress (τ = V/A); units (Pa, MPa, GPa, psi, ksi); average stress vs. stress at a point.
• Concepts of Strain: Normal strain (ε = δ/L); shear strain (γ in radians); units (dimensionless or strain in microstrain); the relationship between strain and deformation.
• Material Behavior: The engineering stress-strain diagram for ductile materials; the diagram for brittle materials; ductile vs. brittle failure.
• Hooke's Law and Elastic Constants: σ = Eε; the modulus of elasticity E; Poisson's ratio ν; the shear modulus G; the relationship G = E/[2(1+ν)]; typical values for common engineering materials.
• Axial Loading — Stress and Deformation: Average normal stress in axially loaded bars; the deformation formula δ = PL/AE; statically determinate axial problems.
• Statically Indeterminate Axial Loading: The compatibility condition; the simultaneous use of equilibrium, force-deformation, and compatibility equations.
• Thermal Stress: Thermal strain (ε = αΔT); thermal stress arising from constrained thermal expansion.
• Torsion of Circular Shafts: The torsion formula; the polar moment of inertia J; the angle of twist; statically indeterminate torsion; power transmission.
• Bending of Beams — Stress: The flexure formula; the section modulus; the moment of inertia for common cross-sections; the assumption of pure bending.
• Transverse Shear in Beams: The shear stress formula; the shear stress distribution across rectangular cross-sections; shear stress in I-beams and other common cross-sections.
• Combined Loading: Superposition of stresses from axial, torsional, and bending loads; the analysis of common combined-loading problems.
• Stress Transformations: The plane stress transformation equations; principal stresses; the maximum shear stress; the orientations of principal stress and maximum shear stress.
• Mohr's Circle: The graphical representation of plane stress; the construction of Mohr's circle; reading principal stresses, maximum shear stress, and stress on any oriented plane.
• Beam Deflection: The differential equation of the elastic curve (EI d²y/dx² = M(x)); integration to find slope and deflection; deflection formulas for common loading cases; the superposition method.
• Column Buckling: Euler's formula for ideal columns; end condition factors; the slenderness ratio; the limit of Euler's formula at the proportional limit.
• Failure Theories: The maximum normal stress theory; the maximum shear stress (Tresca) theory; the distortion energy (von Mises) theory; the application to design with factor of safety.
• Pressure Vessels: Thin-walled cylindrical pressure vessels (hoop stress, longitudinal stress); thin-walled spherical vessels.
• Laboratory Component: Tensile testing; construction of stress-strain curves from test data; torsion testing; beam bending tests; the comparison of analytical predictions with experimental results.

Optional Topics

• Energy Methods: Strain energy in axial, torsional, and bending loading; Castigliano's theorem for deflection.
• Introductory FEA: Finite element analysis at the introductory level; the use of FEA software.
• Fatigue Analysis: Cyclic loading; the S-N curve; endurance limit.
• Fracture Mechanics: Introduction to stress intensity factor and fracture toughness.

Resources & Tools

• Common Texts: Mechanics of Materials (Hibbeler — the most widely adopted text); Mechanics of Materials (Beer/Johnston/DeWolf/Mazurek); Mechanics of Materials (Gere/Goodno); Mechanics of Materials (Philpot)
• Online Platforms: Mastering Engineering (Pearson — paired with Hibbeler); Connect (McGraw-Hill — paired with Beer/Johnston); WebAssign (Cengage)
• Software: MATLAB or Python for numerical solutions; FEA software (ANSYS, SolidWorks Simulation, ABAQUS — institutional licensing); Excel for tabular calculations
• Lab Equipment: Universal testing machine (UTM); torsion testing apparatus; beam bending fixtures; strain gauges; hardness testing; standard test specimens (ASTM tensile specimens)
• Reference Resources: ASTM International (astm.org) — material testing standards; ASM International handbooks; engineering material property databases (MatWeb at matweb.com); Roark's Formulas for Stress and Strain

Career Pathways

Mechanics of materials is foundational to mechanical, civil, aerospace, biomedical, and materials engineering careers — see EGN3331C for the comprehensive list of career pathways. The course's content is essentially identical to EGN3331C, with the same downstream career applications.

Special Information

EGN2332C vs. EGN3331C

Florida engineering programs vary in their mechanics of materials course coding:

• EGN2332C – Mechanics of Materials (this course) — Sophomore-level designation used at approximately 2 institutions.
• EGN3331C – Strength of Materials — Junior-level designation used at approximately 8 institutions.

Content is essentially equivalent; the difference is primarily in curriculum positioning. Programs that put statics in year 2 (EGN2312) typically put mechanics of materials in year 2 as well (EGN2332C); programs that put statics in year 3 (EGN3311) typically put mechanics of materials in year 3 (EGN3331C).

General Education and Transfer

EGN2332C is a Florida common course number that transfers as the equivalent course at all Florida public postsecondary institutions per SCNS articulation policy.

Course Format

EGN2332C is offered primarily in face-to-face format due to the integrated lab component. Hybrid versions (online lecture + on-campus lab) are common; fully online versions with virtual labs are increasingly available but less common given the hands-on nature of the laboratory work.

Position in the Engineering Curriculum

EGN2332C is typically taken in the second year of engineering study, after statics is completed. The course is then a prerequisite for many subsequent courses including machine design, structural analysis, aircraft structures, reinforced concrete design, steel design, mechanical vibrations, and composite materials.

FE Exam Preparation

Mechanics of materials is consistently a major content area on the FE Mechanical, FE Civil, FE Aerospace, and FE Other Disciplines exams. EGN2332C directly prepares students for this content, supporting career pathways toward Professional Engineer (PE) licensure.

Difficulty and Time Commitment

Mechanics of materials is consistently identified as among the most challenging engineering science courses. The course requires substantial out-of-class time (typically 8-12+ hours per week beyond class time) and disciplined practice with problems. The visual-spatial demands (visualizing stress states, transformations, and beam behavior) add to the difficulty.

Prerequisites

EGN2332C typically requires:

• EGN2312 (Engineering Analysis - Statics) or EGN3311 (Statics) with grade of C or better — provides the equilibrium and internal force foundation
• MAC2311, MAC2312, MAC2313 (Calculus I, II, III) with grades of C or better
• MAP2302 (Differential Equations) recommended at most institutions and required at some, for the beam deflection content

Students should have current proficiency in calculus, differential equations, and statics before beginning EGN2332C.