Applied Mechanics

Physics and Mathematics

Theoretical classes
In the theoretical classes, the expository method is used. The content is exposed through the joint use of the whiteboard and PowerPoint presentations. Discussions about the content presented are promoted and the active participation of each student is subject to evaluation.

Theoretical-practical classes
In theoretical-practical classes, the problem-based learning method is used. Students solve in-class exercises in which they apply the contents exposed in the theoretical classes. Additionally, Active learning methodologies will be used, using platforms such as Jamboard, Mentimeter, Kahoot, among others.

The objective of this course unit is to transmit to students the fundamental concepts and tools in the field of applied physics to Mechanical Engineering, namely in the field of statics.

It is intended that the content taught serves as a basic preparation for other course units, namely, the Strength of Materials and Machine Elements.

At the end of this course, the student should be able to execute free-body diagrams of a rigid body subjected to various force systems. Apply static equilibrium equations. Apply the Ritter’s method in the design of plane reticulated systems. Analyze friction on various machine elements. Calculate the centers of gravity of lines, areas and volumes. Determine the moments of inertia, products of inertia, principal axes and principal moments of inertia of areas.

1. Systems of Forces

Introduction. Types of forces: definitions and units. Principles of static. Moment and coordinates of a force. Moment of a force in relation to a point. Variation of the reduction center. Moment of a force relatively to an axis. Binaries/equivalent couples. Physical moment concept. Systems of forces: properties and coordinates. Variation of the reduction center. Varignon’s theorem.

2. Equilibrium of Rigid Bodies

Equations of equilibrium. Free body diagrams. Types of connections and reactions. Balance of systems plans. Equations of equilibrium. Equilibrium of three-dimensional systems.

3. Plane Reticulated Systems – trusses

Spatial reticulated structures. Notion of reticulated system. Classification of reticulated systems. Determination of the staticity of a system. Internal, external and general staticity. Triangulated systems. Resolution of plane reticulated systems, trusses. Method of the nodes. Ritter’s method. Description and applications of the method. Excess bars.

4. Friction

Introduction. Angles of friction. Coefficients of friction. Laws of dry friction. Wedges. Screws of square thread. Radial bearings – axle friction. Axial bearings – disc friction. Rolling resistance – wheels friction. Friction on belts/thongs.

5. Mass Geometry

Centers of gravity. Center of gravity of a two-dimensional body. Centers of gravity of areas and lines. Center of gravity of composite areas. Theorems of Guldinus-Pappus. Centers of gravity of volumes. Moments of Inertia – Definition. Radius of gyration of an area. Transposition of parallel axes – Steiner’s theorem. Moments of inertia of an area and of composite surfaces. Products of Inertia. Principal axes and principal moments of inertia. Mohr’s circle for moments and products of inertia. Moments and products of inertia of a body.

NAO

Recommended

TORRES, J. C. (1999). Mecânica I, Textos Pedagógicos. ISEC (available on Seção de Textos – ISEC)

BRANCO, R. S. (2008). Problemas de Mecânica Aplicada. ISEC (available on the Moodle and InforEstudante academic platforms)

BEER, F., JOHNSTON, R., & EISENBERG, E. (1998). Mecânica Vectorial para Engenheiros – Estática (6th ed.). Portugal: McGraw-Hill (available at the ISEC Library: 5-5-43)

BEER, F., JOHNSTON, R., MAZUREK, D., & EISENBERG, E. (2010). Vector Mechanics for Engineers (9th ed.). New York: McGraw-Hill (available at the ISEC Library: 5-5-61)

Complementary 

MUVDI, B., AL-KHAFAJI, A., & McNABB, J. (1997). Statics for Engineers. New York: Springer-Verlag (available at the ISEC Library: 5-5-41)

BEDFORD, A., & FOWLER, W. (2008). Engineering Mechanics – Statics (5th ed.). Addison-Wesley (available at the ISEC Library: 5-5-59)

MERIAN, J. (1994). Estática (2ª ed.). LTC – Livros Técnicos e Científicos.