Solid Mechanics I
Code
3654
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Engenharia Mecânica e Industrial
Credits
6.0
Teacher in charge
António Paulo Vale Urgueira, João Mário Burguete Botelho Cardoso
Weekly hours
5
Total hours
98
Teaching language
Português
Objectives
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.
Prerequisites
It is recommended that students have obtained frequency/approval for the discipline Applied Mechanics I.
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.
Bibliography
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.
Evaluation method
Continuous evaluation includes one group project (TR) and two quizzes (T1, T2). There is also the possibility to succeed in a final exam (E).
The project is mandatory and account 20% for the final grade. In order to be able to access the final exam, the minimum score of 10 must be attained.
Each quiz as a weight of 40% in the final grade. The minimum score of 9 must be attained for the average of the classifications obtained in quizzes in order to succeed continuous evaluation.
The students that do not succeed one of the quizzes are allowed to repeat it at the date of the final exam.
In order to succeed evaluation trough exam, a minimum score of 9 must be attained at the exam grade (E).
Final Grade (Continuous Evaluation) = 0,4 x (T1 + T2 ) + 0,2 x TR
Final Grade (Exam) = 0,8 x E + 0,2 x TR