Mechanics of Solids A
Introduction to the mechanical behavior of deformable bodies using tools from Mechanics of Materials with a Continuum Mechanics perspective. Static, linear problems with homogeneous-isotropic materials.
Instructor: Prof. José Luís M. Thiesen
Term: Spring
Location: UFSC — defined in CAGR
Time: Mondays and Wednesdays, 14:20–16:00
Course Description
This course introduces the mechanical behavior of deformable bodies using Mechanics of Materials tools within a Continuum Mechanics framework. The course covers static, linear problems with homogeneous, isotropic materials, and develops the student’s ability to perform basic structural integrity analysis and to design simple components such as bars and beams under tension, bending, and torsion.
Taught in Portuguese at UFSC. Course code: EMC5128.
Prerequisites
- MTM3121 — Linear Algebra
- EMC5132 — Statics
Assessment
Final grade is computed from four individual written exams:
MF = 0.1 × P1 + 0.3 × P2 + 0.3 × P3 + 0.3 × P4
- Pass: attendance ≥ 75% and MF ≥ 6.0
- Make-up exam (REC): available for MF between 3.0 and 5.5 → MFR = (MF + REC) / 2
| Exam | Date |
|---|---|
| P1 | April 1, 2026 |
| P2 | May 4, 2026 |
| P3 | June 8, 2026 |
| P4 | July 8, 2026 |
| REC | July 12, 2026 |
Textbooks
Main:
- Hibbeler, R.C., Mechanics of Materials, Prentice Hall, 5th ed., 2004.
- Mendonça, P.T., Resistência dos Materiais e Fundamentos de Mecânica dos Sólidos, Ed. Orsa Maggiore, 2021.
Supplementary:
- Gere, J.M. et al., Mechanics of Materials, Cengage Learning, 2009.
- Timoshenko, S.P.; Gere, J.M., Mechanics of Solids, Vols. 1–2, LTC, 1986.
- Gross, D. et al., Engineering Mechanics 1 & 2, Springer, 2013–2018.
- Popov, E.P., Introduction to Mechanics of Solids, Prentice Hall, 2012.
Schedule
| Week | Date | Topic | Materials |
|---|---|---|---|
| 1 | Introduction Course overview. Design concepts: conception, preliminary and detailed design, analysis. Types of analysis and models. Solid mechanics models: bars, beams, shells, solids. | ||
| 2 | Internal Forces I Review of statics. Reactions. Classification of internal forces in bars. Section method for isostatic bars and beams. | ||
| 3 | Internal Forces II Differential equilibrium equations. Normal force, shear force, and bending moment diagrams. Forces in trusses. | ||
| 4 | Stress Definition of stress. Uniaxial and shear stresses. Stress tensor. Classification of stress states: triaxial, plane, uniaxial, pure shear, hydrostatic. | ||
| 5 | Stress Transformation and Failure Criteria I Stress transformation. Mohr’s circle. | ||
| 6 | Stress Transformation and Failure Criteria II Failure criteria: maximum normal stress, maximum shear stress, and maximum distortion energy (von Mises). | ||
| 7 | Uniaxial Problems Applications: average stress, safety factor. Design and safety analysis of pins, bars under axial loads, columns. Stresses in trusses. | ||
| 8 | Strain Strain-displacement relations (normal and shear). Strain tensor. Strain transformation. | ||
| 9 | Constitutive Equations Hooke’s law for isotropic materials, Poisson’s ratio. Stress-strain diagrams. Axial deformation of bars under normal forces. | ||
| 10 | Bending I Normal bending stresses. Plane and oblique bending models. Combined bending and axial load. Maximum bending stress calculation. | ||
| 11 | Bending II — Asymmetric Cross-sections Bending in asymmetric cross-sections. Cross-sectional moments of inertia. Axis translation and rotation. Principal axes of inertia. Standard profiles. | ||
| 12 | Torsion Torsion model for circular cross-sections. Torsional moment diagrams. Stresses and strains due to torsion. Square and thin-walled sections. Hyperstatic torsion problems. | ||
| 13 | Shear in Beams Shear model for beams in bending. Shear flow. Shear center. Combined normal and shear stresses under bending and axial load. Principal stresses and failure criteria application. |