Mechanics I

Instance: 2024/2025 - 2S

Cycles of Study/Courses

Teaching language

Objectives

Learning outcomes and competences

Students must learn the main concepts of statics, solving problems involving the balance of bodies, identifying the actions on them and calculating the forces connecting them to the outside (reactions). They must correctly identify the different types of actions on structures, contact forces, distance forces acting on the mass and the respective moments and torques.
Learn to characterize the Coulomb dry friction forces generated by contact between surfaces and their effects, through some practical applications.

They should also learn to determine the center of mass of bodies and characterize their mass distribution by obtaining the inertia matrix.

At the end of the academic period, students are expected to:
- Be able to identify all actions, forces and moments on a given structure and draw the respective free body diagram;
- Know how to apply vector calculation to the study of 3D statics and master the concepts of static balance of systems of bodies;
- Regarding the analysis of structures, students must correctly identify the forces in the connections and determine them, with and without the presence of dry friction;
-Students should also learn to characterize areas and volumes by determining their centroid, center of mass, moments and products of inertia and obtain the respective inertia matrix.

Working method

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Students must have knowledge of vector algebra and integral calculus

L.EM004 Vector Algebra; Matrices; Determinants; Systems of Linear Equations; Linear Spaces, Transformations and Matrices; Eigenvalues and eigenvectors.
L.EM005 Functions and graphics. The concept of limit, the concept of continuity at a point and the derivative of a function.
L.EM010 Evaluation of double integrals over general regions in R2 using rectangular and polar coordinates. Calculation of triple integrals over regions of R3 using rectangular, cylindrical and spherical coordinates.

Program

STATICS - Introduction to vector mechanics applied to statics and presentation of the concepts of Force, Moment, couple and resultant of a force system. Static equilibrium in two and three dimensional systems. System Definition and its free body diagram. Introduction to structural mechanics: method of joints and method of sections in a simple truss. Introduction to the study of simple contact Friction (Coulomb).

GEOMETRY OF MASSES - Properties of surfaces and bodies. First moment of area and centroid. Theorems of Pappus-Guldinus. Second order moment of areas and solids and product of inertia. Transfer theorem (Steiner). Rotation of axes and relations between second moment and product second moment of area. Principal axes and matrix of inertia.

Mandatory literature

Complementary Bibliography

Teaching methods and learning activities

Two theoretical-practical classes (TP) of 2:00 hours per week (in an amphitheater), for all students + practical classes of 2:00 hours (in a room with 30 seats) every other week (15 in 15 days) for problem solving proposals and discussion of doubts raised by students.

All first-time students must also attend a bench laboratory session in which they carry out experimental work in groups of up to 7 students on the main subjects taught at the UC (expected duration of 1 hour). At the end of the session, they must submit a written report of the work carried out.

Attendance will be monitored in all classes.

keywords

Evaluation Type

Assessment Components

Amount of time allocated to each course unit

Eligibility for exams

Calculation formula of final grade

Classifications to be assigned: T1- 1st test; T2 - 2nd test; EF - final exam; TP - practical laboratory work

Approval in the UC implies that:

If T1>=8.0 and T2>=8.0
Final grade = 0.95*(0.5*(T1+T2))+0.05*TP>=10

If T1<8.0
Final grade = 0.95*EF+0.05*TP>=10

The final exam coincides with the appeal period for students who did not pass continuous assessment.

In the case of the appeal exam to improve grades, the higher of the two grades obtained will be considered.

Examinations or Special Assignments

It is not foreseen

Internship work/project

It is not foreseen

Special assessment (TE, DA, ...)

According to the FEUP regulations.

Classification improvement

 According to the FEUP regulations.

Observations