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# Applied Mechanics IA

7205

### Department

Departamento de Engenharia Mecânica e Industrial

7.5

### Teacher in charge

Raquel Albuquerque Soares Brás de Almeida

5

Português

### Objectives

The main objective of Applied Mechanics I is to provide the students the ability to:

• Solve problems involving the equilibrium of a particle and a rigid body.
• Calculate the position of the center of gravity of a body or a composite body.
• Carry out the analysis of trusses or a simple machine.
• Determinate the internal beam forces, shear and moment equations and diagrams, relations between distributed load, shear, and moment.
• Solve problems involving dry friction.
• Determinate the moments of inertia of simple and complex rigid bodies.
• Solve problems using the Principal of Virtual Work.

Simultaneously, through the teaching and learning practices, the students will develop their skills in problem solving and critical thinking and communication.

### Subject matter

1.     General principles.

2.     Free-Body Diagrams.

3.     Equilibrium of a particle.

• Coplanar force systems;
• Three-dimensional force systems.

4.     Equilibrium of a rigid body.

• Equilibrium in two dimensions;
• Equilibrium in three dimensions;
• Constraints for a rigid body.

5.     Center of gravity and centroid:

• Surfaces and curves;
• Bodies.

6.     Structural analysis:

• Trusses;
• Simple machines.

7.     Internal forces in beams:

• Internal forces developed in structural members;
• Normal, Shear and Moment equations and diagrams;
• Relations between distributed load, shear, and moment.

8.     Friction:

• Characteristics of dry friction.
• Problems involving dry friction.

9.  Moments of inertia:

Moments of inertia for areas:

• Parallel-axis theorem for an area;
• Radius of gyration of an area;
• Moments of inertia for an area by integration:
• Radius of gyration of an area;
• Moments of inertia of compose areas;
• Product of inertia;
• Axes and principal moments of inertia.

Mass Moments of inertia.

10. Principal of Virtual Work

### Bibliography

Vector Mechanics for Engineers – Statics, 7º Edition 2006

Ferdinand P. Beer, E. Russell Johnston & Elliot R. Eisenberg

Mc Graw Hill

or

Statics ( Engineering Mechanics) -12 Edition

Hibbeler, R. C.

Pearson Prentice Hall