Faculdade de Ciências e Tecnologia

Statics

Code

9369

Academic unit

Faculdade de Ciências e Tecnologia

Department

Departamento de Engenharia Civil

Credits

6.0

Teacher in charge

João Carlos Gomes Rocha de Almeida, José Nuno Varandas da Silva Ferreira

Weekly hours

5

Teaching language

Português

Objectives

The course aims to develop the students’ analytical abilities and to provide a thorough understanding of the fundamental concepts of vector mechanics of bodies at rest (Statics). Students should be able to develop confidence and competence in applying the theoretical concepts and practical methodologies of Statics to solve equilibrium problems in a mathematical form and to understand the significance of any assumptions made to the solutions.

By the end of the semester the students should be able to:

1. Make the equilibrium of particles and rigid bodies in 2D and 3D;

2. Draw the free body diagrams of a structure;

3. Identify the types of loads and supports of a structure and determine the reactions of isostatic structures;

4. Establish relations among load, shear, and bending moment;

5. Determine the diagrams of internal forces in isostatic structures and trusses;

6. Calculate center of gravity, static moments and moments of inertia of sections.

Prerequisites

Background in mathematics needed to succeed in Statics: trigonometry and analitical geometry; differentiation and integration of single variable polynomials; solving simultaneous linear and quadratic equations.

Subject matter

  •  Introduction
  • Object of Statics
    1. Actions in Civil Engineering.
    2. General Principles of Mechanics
  • Systems of forces and moments.
    1. Reduction of a System of forces to one force and one couple.
    2. Equivalent Systems of Forces. Concurrent force systems.
    3. Parallel forces and their resultants.
  • Statics of particles. Equilibrium of a Particle.
  • Equilibrium of rigid bodies.
    1. Types of restraining and reactions at supports.
    2. Free body diagram.
  • Analysis of structures.
    1. Reactions at supports and connections.
    2. Equilibrium of the frames.
      1. Isostatic, hiperstatic and hipostatic structures.
    3. Isostatic trusses.
      1. Method of knots and method of the sections.
  • Equilibrium of isostatic structures..
    1. Various types of loading and support.
    2. Internal forces.
    3. Relations among load, shear, and bending moment.
    4. Diagrams of internal forces in isostatic structures.
  • Distributed Loads
    1. Centroids and centers of gravity.Centroids of areas and lines. Distributed Loads on Beams. Forces on submerged surfaces
    2. Moments of inertia of areas. Polar Moment of Inertia. Moments of inertia of composite areas. Theorem of the parallel axes. Moments and principal directions of inertia.

Teaching method

The teaching comprises lectures and practical classes using classical teaching methods supported by slides and computer based program.

The lectures intend to give the fundamental theoretical concepts, principles and methods, illustrating their application on simple problems needed for a better understanding.

The practical classes complement the lectures, solving a larger set of problems. Individual work, outside of the presencial classes, will be stimulated

Courses