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2013 | Book

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Engineering Mechanics 1

Statics

Authors: Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse

Publisher: Springer Berlin Heidelberg

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

Statics is the first volume of a three-volume textbook on Engineering Mechanics.

The authors, using a time-honoured straightforward and flexible approach, present the basic concepts and principles of mechanics in the clearest and simplest form possible to advanced undergraduate engineering students of various disciplines and different educational backgrounds.

An important objective of this book is to develop problem solving skills in a systematic manner.

Another aim of this volume is to provide engineering students as well as practising engineers with a solid foundation to help them bridge the gap between undergraduate studies on the one hand and advanced courses on mechanics and/or practical engineering problems on the other.

The book contains numerous examples, along with their complete solutions. Emphasis is placed upon student participation in problem solving. The contents of the book correspond to the topics normally covered in courses on basic engineering mechanics at universities and colleges.

Now in its second English edition, this material has been in use for two decades in Germany, and has benefited from many practical improvements and the authors’ teaching experience over the years. New to this edition are the extra supplementary examples available online as well as the TM-tools necessary to work with this method.

Table of Contents

Frontmatter
Introduction
Abstract
Mechanics is the oldest and the most highly developed branch of physics. As important foundation of engineering, its relevance continues to increase as its range of application grows.
The tasks of mechanics include the description and determination of the motion of bodies, as well as the investigation of the forces associated with the motion. Technical examples of such motions are the rolling wheel of a vehicle, the flow of a fluid in a duct, the flight of an airplane and the orbit of a satellite. “Motion” in a generalized sense includes the deflection of a bridge or the deformation of a structural element under the influence of a load. An important special case is the state of rest; a building, dam or television tower should be constructed in such a way that it does not move or collapse.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Basic Concepts
Abstract
Objectives: Statics is the study of forces acting on bodies that are in equilibrium. To investigate statics problems, it is necessary to be familiar with some basic terms, formulas, and work principles. Of particular importance are the method of sections, the law of action and reaction, and the free − body diagram, as they are used to solve nearly all problems in statics.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Forces with a Common Point of Application
Abstract
Objectives: In this chapter, systems of concentrated forces that have a common point of application are investigated. Such forces are called concurrent forces. Note that forces always act on a body; there are no forces without action on a body. In the case of a rigid body, the forces acting on it do not have to have the same point of application; it is sufficient that their lines of action intersect at a common point. Since in this case the force vectors are sliding vectors, they may be applied at any point along their lines of action without changing their effect on the body (principle of transmissibility). If all the forces acting on a body act in a plane, they are called coplanar forces.
Students will learn in this chapter how to determine the resultant of a system of concurrent forces and how to resolve force vectors into given directions. They will also learn how to correctly isolate the body under consideration and draw a free-body diagram, in order to be able to formulate the conditions of equilibrium.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
General Systems of Forces, Equilibrium of a Rigid Body
Abstract
Objectives: In this chapter general systems of forces are considered, i.e., forces whose lines of action do not intersect at a point. For the analysis, the notion moment has to be introduced. Students should learn how coplanar or spatial systems of forces can be reduced and under which conditions they are in equilibrium. They should also learn how to apply the method of sections to obtain a free-body diagram. A correct free-body diagram and an appropriate application of the equilibrium conditions are the key to the solution of a coplanar or a spatial problem.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Center of Gravity, Center of Mass, Centroids
Abstract
Objectives: In this chapter, definitions of the center of gravity and the center of mass are given. It is shown how to determine the centroids of bodies, areas and lines. Various examples demonstrate how to apply the definitions to practical problems.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Support Reactions
Abstract
Objectives: In this chapter, the most common kinds of supports of simple structures and the different connecting elements of multi-part structures are introduced. We will discuss their characteristic features and how they can be classified, so that the students will be able to decide whether or not a structure is statically and kinematically determinate. Students will also learn from this chapter how the forces and couple moments appearing at the supports and the connecting elements of a loaded structure can be determined. Here, the most important steps are the sketch of the free-body diagram and the correct application of the equilibrium conditions.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Trusses
Abstract
Objectives: A truss is a structure composed of slender members that are connected at their ends by joints. The truss is one of the most important structures in engineering applications. After studying this chapter, students should be able to recognise if a given truss is statically and kinematically determinate. In addition, they will become familiar with methods to determine the internal forces in a statically determinate truss.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Beams, Frames, Arches
Abstract
Objectives: Beams are among the most important elements in structural engineering. In this chapter it is explained how the internal forces in a beam can be made accessible to calculation.
The normal force, the shear force and the bending moment are introduced. Students will learn how to determine these quantities with the aid of the conditions of equilibrium. In addition, they will learn how to correctly apply the differential relationships between external loading and internal forces.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Work and Potential Energy
Abstract
Objectives: Students will become familiar with the concepts of work, conservative forces and potential energy. In addition, they will become acquainted with the principle of virtual work. After studying this chapter, students should be able to correctly apply this principle in order to determine equilibrium states in nonrigid systems as well as support reactions and internal forces and moments. Finally, it will be shown how to investigate the stability of equilibrium states of conservative systems with one degree of freedom.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Static and Kinetic Friction
Abstract
Objectives: Bodies in contact exert a force on each other. In the case of ideally smooth surfaces, this force acts perpendicularly to the contact plane. If the surfaces are rough, however, there may also be a tangential force component. Students will learn that this tangential component is a reaction force if the bodies adhere, and an active force if the bodies slip. After studying this chapter, students should be able to apply the Coulomb theory of friction to determine the forces in systems with contact.
Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall, Nimal Rajapakse
Backmatter
Metadata
Title
Engineering Mechanics 1
Authors
Dietmar Gross
Werner Hauger
Jörg Schröder
Wolfgang A. Wall
Nimal Rajapakse
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-30319-7
Print ISBN
978-3-642-30318-0
DOI
https://doi.org/10.1007/978-3-642-30319-7

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