Solid Mechanics I


The course is expected to provide the student a strong knowledge on the characterization of stress and strain states on solid bodies subjected to applied forces. The concepts of stress vector, stress and infinitesimal strain tensors are introduced, together with their dependencies on the referential used. Stress and strain invariants and methods to obtain principal stresses and strains are also taught.

The general stress-strain behavior for brittle and for ductile materials is taught, together with a more detailed analysis of this behavior for mild steel. Stress-strain relations are presented for materials with linear elastic behavior.

Two methodologies to obtain stresses and strains on general solids with applied loads are referred. First, the beam theory is introduced and its range of applicability specified. Equations for the determination of stresses, strains and displacements are deduced for the cases of beams subjected to axial loads and also torques. Secondly, for cases with more complex geometries, that cannot be properly analyzed with beam theory, a quick reference to the finite element method is made and a small problem is solved in the course work.

General characterization





Responsible teacher

António Paulo Vale Urgueira, Tiago Alexandre Narciso da Silva


Weekly - 5

Total - 70

Teaching language



It is recommended that students have obtained frequency/approval for the discipline Applied Mechanics I.


Mechanics of Materials, 3th / 4th / 5th / 6th Edition

Ferdinand P. Beer, E. Russell Johnston, Jr., John T. DeWolf, David F. Mazurek (5th / 6th Ed.), McGraw-Hill

Teaching method

Theoretical lectures and laboratory sessions.

Lab work.

Evaluation method

Continuous evaluation includes two group projects (TR1, TR2) and two quizzes (T1, T2). There is also the possibility to succeed in a final exam (E).

Practical works are mandatory and weight 15% for the final grade. In order to be able to access the final exam, the minimum average score of 10 must be attained.

Each written test as a weight of 35% in the final grade. The minimum score of 9,5 must be attained for the average classifications obtained in written tests in order to succeed continuous evaluation.

During written tests and exams students are only allowed to use a hand calculator from a brand and model specified on the list of autorized calculators for the high-school final exams of Fisics and Mathematics.

In order to succeed evaluation trough exam, a minimum score of 9,5 must be attained at the exam grade (E).

Final Grade (Continuous Evaluation) = 0,35 x (T1 + T2 ) + 0,15 x (TR1 + TR2)

Final Grade (Exam) = 0,7 x E + 0,15 x (TR1 + TR2)

Subject matter

Elasticity: Definition of stress. Stress vector. Normal stress and shear stress. Stress tensor. Equilibrium equations. Symmetry of the stress tensor. Transformation of stress. Principal stresses. Mohr''s circle for stress. Stress invariants. Analysis of strain. Strain tensor. Infinitesimal strain tensor. Mohr''s circle for strain. Strain measurement using strain gage. Principal axis. Compatibility equations. Linear elasticity. Generalized Hooke''s law. Young''s modulus and Poisson''s ratio. Isotropy. Plane stress and plane strain. Tensile test. Norm EN 10 002 - Tensile test of metallic materials. Models of material behaviour.

Axial loading: Linear members. Saint-Venant''s principle. Plastic deformations, residual stresses.

Torsion: Stresses and deformations in cylindrical shafts. Plastic deformations, residual stresses. Membrane analogy. Torsion of members with non-circular cross section. Thin-walled hollow shafts.


Programs where the course is taught: