2025
Mechanics of Materials
Name: Mechanics of Materials
Code: EME13094L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mechanical Engineering
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
Students should already possess consolidated knowledge on the topics of Applied Mechanics, Mathematical Analysis, and Linear Algebra.
The objective of this unit is to provide students with fundamental knowledge on the field of classic Solid Mechanics.
Students shall develop the required skill set to approach. on a balanced and rational way, solid mechanics problems, to understand the stress distribution in the material for different loading conditions, and to apply an appropriate yield criterion.
Students should also develop the capability to consult available bibliography on the topic in an organised and independent way, identifying a-priori the appropriate context in order to solve problems of greater complexity.
The objective of this unit is to provide students with fundamental knowledge on the field of classic Solid Mechanics.
Students shall develop the required skill set to approach. on a balanced and rational way, solid mechanics problems, to understand the stress distribution in the material for different loading conditions, and to apply an appropriate yield criterion.
Students should also develop the capability to consult available bibliography on the topic in an organised and independent way, identifying a-priori the appropriate context in order to solve problems of greater complexity.
Contents
1. Stress analysis. Concept of stress, normal stress and shear stress. Stress matrix. Equations of equilibrium. Stress invariants. Principal stress. Plane stress state. Mohr's circle.
2. Strain analysis. Concept of deformation and distortion. Strain matrix. Strain invariants. Deviatoric strains. Principal strains. Plane strain state.
3. Stress-strain relations. Generalised Hooke's law. Hooke's law for isotropic materials. Elastic properties of materials. Elastic energy of deformation.
4. Centroids. Area moments of inertia.
5. Torsion of circular sections. Torsion of rectangular sections. Torsion of closed thin wall profiles. Composite beams.
6. Internal forces. Internal forces diagrams. Concentrated and distributed loads.
7. Bending. Pure and simple bending. Multi-axis bending. Combined bending and axial force, or with torsion. Equation of the Elastic Curve.
8. Yield criteria.
2. Strain analysis. Concept of deformation and distortion. Strain matrix. Strain invariants. Deviatoric strains. Principal strains. Plane strain state.
3. Stress-strain relations. Generalised Hooke's law. Hooke's law for isotropic materials. Elastic properties of materials. Elastic energy of deformation.
4. Centroids. Area moments of inertia.
5. Torsion of circular sections. Torsion of rectangular sections. Torsion of closed thin wall profiles. Composite beams.
6. Internal forces. Internal forces diagrams. Concentrated and distributed loads.
7. Bending. Pure and simple bending. Multi-axis bending. Combined bending and axial force, or with torsion. Equation of the Elastic Curve.
8. Yield criteria.
Teaching Methods
During theoretical classes, the fundamental concepts will be presented and debated using Powerpoint presentations and videos. Theoretical-practical classes will include summaries and exercises and are oriented to the practical application of the fundamental concepts introduced during the theoretical classes.
Assessment
Assessment can be either through tests during the semester or final exam. In the case of an assessment throughout the semester, the following formula will be used for calculating the final mark:
Final mark: NF = 0.35*NF1+0.45*NF2+0.2*NT
Where: NF1: First Test NF2: Second Test NT: Thematic work with report
In the case of assessment by exam, the final mark will be the highest mark obtained:
Final mark: NF = Max(EN,ER)
Where: E1: Exam in first call E2: Exam in second call
Final mark: NF = 0.35*NF1+0.45*NF2+0.2*NT
Where: NF1: First Test NF2: Second Test NT: Thematic work with report
In the case of assessment by exam, the final mark will be the highest mark obtained:
Final mark: NF = Max(EN,ER)
Where: E1: Exam in first call E2: Exam in second call
Teaching Staff
- Gonçalo Nuno Guerreiro de Jesus Silva [responsible]
Certificações
