Strength of Materials

Course Description

EGN3331C – Strength of Materials is a 3-credit upper-division lecture course (often offered with an integrated laboratory component, indicated by the "C" suffix) in the Engineering: General taxonomy of Florida's Statewide Course Numbering System (SCNS). The course — also known as "Mechanics of Materials" — extends the principles of statics to the analysis of deformable bodies under load. Students learn to determine the stresses, strains, and deformations produced in engineering members by axial, torsional, flexural, and combined loadings, and to apply these results to the design and analysis of structural and mechanical components.

The course covers the concepts of normal and shear stress and strain, Hooke's law, mechanical properties of materials, axially loaded members, torsion of circular shafts, bending of beams, transverse shear, stress transformation (Mohr's circle), beam deflection, and column buckling. EGN3331C is a required course in mechanical, civil, aerospace, biomedical, and ocean engineering programs at Florida public universities and serves as the analytical foundation for upper-division courses in machine design, structural analysis, and finite element methods.

Learning Outcomes

Required Outcomes

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

• Define and compute normal stress, shear stress, normal strain, and shear strain, and apply Hooke's law to relate stress and strain in linearly elastic materials.
• Interpret stress-strain diagrams and identify mechanical properties such as modulus of elasticity, yield strength, ultimate strength, and ductility.
• Analyze axially loaded members, including statically determinate and indeterminate cases, thermal stresses, and stress concentrations.
• Apply the torsion formula to determine stresses and angles of twist in circular shafts under torsional loading.
• Determine bending stresses in straight and curved beams using the flexure formula.
• Determine transverse shear stresses in beams and analyze shear flow in built-up sections.
• Construct shear and bending-moment diagrams and use them to identify critical sections for design.
• Apply stress transformation using equations and Mohr's circle to determine principal stresses and maximum shear stresses.
• Compute beam deflections using integration, superposition, and the moment-area or virtual-work methods.
• Analyze column buckling using the Euler formula and apply effective length concepts to common end conditions.
• Apply principles of combined loading to analyze members subject to multiple simultaneous loads.

Optional Outcomes

Depending on institutional emphasis, students may also:

• Apply energy methods, including strain energy and Castigliano's theorem, to deformation analysis.
• Analyze thin-walled pressure vessels under internal pressure.
• Apply failure theories such as maximum-shear-stress (Tresca) and distortion-energy (von Mises) for ductile materials, and maximum-normal-stress for brittle materials.
• Conduct laboratory measurements of mechanical properties including tensile testing, hardness testing, and beam deflection experiments (when offered with the "C" lab component).
• Use computational tools (MATLAB, Python, or finite element software) to solve advanced strength-of-materials problems.

Major Topics

Required Topics

• Stress and Strain: Concepts of normal and shear stress; average and exact stress; normal and shear strain; allowable stress design.
• Mechanical Properties of Materials: Tension and compression tests; stress-strain behavior; modulus of elasticity, Poisson's ratio, modulus of rigidity; yield strength, ultimate strength, fracture.
• Axial Load: Saint-Venant's principle; elastic deformation of axially loaded members; statically indeterminate axially loaded members; thermal stress; stress concentrations.
• Torsion: Torsion formula for solid and hollow circular shafts; angle of twist; statically indeterminate torsion problems; power transmission; thin-walled tubes.
• Bending: Internal moments in beams; flexure formula for symmetric beams; unsymmetric bending; composite beams.
• Transverse Shear: Shear formula; shear stress in beams; shear flow in built-up sections.
• Combined Loadings: Combined axial, torsion, and bending; thin-walled pressure vessels.
• Stress and Strain Transformation: Plane-stress transformation equations; principal stresses and maximum shear stress; Mohr's circle for stress and strain.
• Beam Deflections: Elastic curve; integration of moment equation; method of superposition; moment-area method; virtual work for beams.
• Buckling of Columns: Euler buckling formula; effective length; secant formula; ideal versus real columns; design of columns.

Optional Topics

• Energy Methods: Strain energy; Castigliano's theorem; principle of virtual work for deflection analysis.
• Failure Theories: Maximum shear stress (Tresca); distortion energy (von Mises); maximum normal stress for brittle materials.
• Inelastic Bending and Torsion: Plastic bending; residual stresses; ultimate-strength concepts.
• Stress Concentrations: Use of stress concentration factor charts for design.
• Laboratory Component (when offered as 3331C): Tensile testing; hardness testing; beam deflection; column buckling; strain gage measurements.
• Computational Tools: MATLAB, Python, or introductory finite element analysis applied to strength-of-materials problems.

Resources & Tools

• Standard Textbooks: Mechanics of Materials by R.C. Hibbeler (most widely adopted in Florida); Mechanics of Materials by Beer, Johnston, DeWolf, and Mazurek; Mechanics of Materials by Gere and Goodno
• Online Homework Platforms: Pearson Mastering Engineering; McGraw-Hill Connect
• Lab Equipment (when offered as 3331C): Universal testing machine for tensile/compression tests; torsion testing apparatus; hardness testers (Rockwell, Brinell); strain gages and data acquisition systems; column buckling apparatus
• Computational Tools: MATLAB or Python for analytical solutions; ANSYS, Abaqus, or SolidWorks Simulation for introductory FEA exposure
• Reference Standards: ASTM standards for materials testing (ASTM E8 for tension testing, E18 for hardness, etc.); AISC Steel Construction Manual; appendix tables for moments of inertia and section properties

Career Pathways

Strength of Materials is a foundational course for nearly every engineering specialty involving structural or mechanical analysis. Successful completion supports progression into the following:

• Mechanical Engineering – Foundation for machine design, mechanical components, pressure vessels, and product reliability.
• Civil and Structural Engineering – Foundation for analysis and design of beams, columns, trusses, and structural connections in buildings and bridges.
• Aerospace Engineering – Foundation for analysis of airframe components, structural panels, and launch-vehicle structures, with strong relevance to Florida's Space Coast aerospace cluster.
• Biomedical Engineering – Foundation for orthopedic device design, prostheses, and tissue mechanics.
• Ocean Engineering – Foundation for offshore structures, marine vessels, and coastal infrastructure (relevant to Florida's coastal industries and FAU/UNF marine programs).
• Materials Engineering – Foundation for the analysis of material behavior under load and component design selection.

Special Information

FE Examination Preparation

Strength of Materials (also called "Mechanics of Materials") is one of the most heavily tested topic areas on the National Council of Examiners for Engineering and Surveying (NCEES) Fundamentals of Engineering (FE) examination. Mastery of stress, strain, axial loading, torsion, bending, deflection, and buckling — all developed in EGN3331C — is critical for FE preparation, the first step toward Professional Engineer (P.E.) licensure in Florida.

Course Number Variations

Some Florida institutions offer this course as EGN3331 (without the "C" lab indicator) when delivered as a lecture-only course; the "C" suffix denotes an integrated laboratory experience. Course content and learning outcomes are equivalent under Florida SCNS, and credits typically transfer between institutions with or without the lab component. Some programs also offer it under EML 3011 – Mechanics of Materials (e.g., FAMU-FSU College of Engineering).

Foundation for Upper-Division Coursework

EGN3331C is the prerequisite for upper-division courses including machine design, structural analysis, advanced mechanics of materials, finite element analysis, and ocean structural engineering. Strong preparation in this course is critical for success in the engineering major.