Solid Mechanics I
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.
General characterization
Code
3654
Credits
6.0
Responsible teacher
Pedro Samuel Gonçalves Coelho, Tiago Alexandre Narciso da Silva
Hours
Weekly - 4
Total - 70
Teaching language
Português
Prerequisites
It is recommended that students have obtained frequency/approval for the discipline Applied Mechanics I.
Bibliography
F. P. Beer, E. R. Johnston, Jr., J. T. DeWolf, D. F. Mazurek. Mecânica dos Materiais / Resistência dos Materiais / Mechanics of Materials (diversas edições). McGraw-Hill.
R. C. Hibbeler. Mechanics of Materials (diversas edições). Pearson.
L.S. Srinath. Advanced Mechanics of Solids. McGraw-Hill.
A.P. Boresi, R.J. Schmidt. Advanced Mechanics of Materials. John Wiley \& Sons.
J. N. Reddy (2010). Principles of Continuum Mechanics - A Study of Conservation Principles with Applications. Cambridge Uni. Press.
Teaching method
This subject is taught in theoretical and practical classes. In lectures, the fundamental concepts are presented together with their demonstration. In practical classes, students are expected to discuss previously proposed problems.
The main aim of the lecture method, self-study and practical work is to motivate students to solve problems, making a decisive contribution to the training of mechanical engineers capable of meeting the requirements of the business community, as well as giving them an understanding of the application of the subjects in research.
Note: Classes (time with teachers) should be utilised to the full, and prior preparation is essential.
Evaluation method
This subject can be passed by continuous assessment or by exam, and practical work is fundamental to teaching.
The assignments are compulsory and count for 30% of the final grade. In order to pass the subject and sit the exam, or to pass the subject by continuous assessment, you must:
- hand in at least 75% of the weekly challenges;
- have an average mark of 10 or more on practical assignments.
There are 2 practical assignments (TP1, TP2) and they are carried out by groups of 3 students (detailed information in the practical assignment guide).
Continuous assessment consists of the 2 practical assignments (TP1, TP2), 2 tests (T1, T2) and attendance obtained by handing in the weekly challenges. The tests can be replaced by an exam (E), in the case of assessment by exam.
In order to pass the assessment by exam, the exam mark must be equal to or greater than 9.5.
Weekly challenges: The aim of these challenges is to keep all students active in their learning process. The challenges are set weekly, according to specific information, and are compulsory to validate compulsory attendance in MS1.
The challenges will not be graded quantitatively, but students will be given feedback on their work. As mentioned above, to validate attendance in MS1 each student must hand in at least 75% of the weekly challenges, each of which has 2 components: solving a problem and assessing the solution to the same problem submitted by a fellow student. Please note that these challenges will tend to be akin to a homework assignment, nothing more. (ATTENTION: anyone who fails to hand in the weekly challenges will be prevented from taking the subject, as they will not be able to fulfil minimum attandance).
This year we are doing tests instead of 3 tests:
The option of 3 tests is related to the adjustment of continuous assessment to the 3 major themes of the UC.
But this year we''re only doing 2 tests. Thus:
- T1: Assessed subject: Elasticity | Weight: 35% | Date: 7th week of the semester.
- T2: Assessed subject: Traction/Compression + Torsion | Weight: 35% | Date: by the 14th week of the semester.
To pass the course by continuous assessment, the average mark obtained in the tests must be higher than 9.5.
During the tests and exams, students may only use a calculator of a make and model that appears on the list of machines authorised for the National Final Examinations of Secondary Education for the subjects of Physics and Mathematics.
Final Grade (Continuous Assessment) = 0,35 (T1 + T2 ) + 0.15 (TP1 + TP2)
Final Grade (Exam) = 0.7 E + 0.15 (TP1 + TP2)
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. 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.