# Statics

9369

### Department

Departamento de Engenharia Civil

6.0

### Teacher in charge

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

5

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..
2. Internal forces.
3. Relations among load, shear, and bending moment.
4. Diagrams of internal forces in isostatic structures.