Introduction to Structural Mechanics

Introduction to Structural Mechanics

DOI: 10.4018/978-1-4666-6379-4.ch001


Foreign visitors discovering a new country usually start by looking at a map of the place; they identify its regions and their characteristics; they try to acquire a mental chart of the new country. Naturally, they have to choose a city or cities in which they are going to spend long stays. Only in those specific places, the visitors will try to learn about the specifics: street names, places of interests, public transportation network, convenience stores, and so on. In this chapter, a general map of the structural mechanics (the “country” in which the reader of this book is going to “reside”) is first presented. Next, the theory of frames (the “city” that the reader of the book is going to know very well) is placed in this general context. After reading the chapter, the reader will slowly improve his/her knowledge of the specific topic until becoming an expert in the theme. It is fair to say that the theory of frames is equivalent to a Rio de Janeiro in Brazil or a Paris in France or a Saint Petersburg in Russia.
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1.1 Structural Mechanics, Its Goals, And Ways

The goal of structural engineering is to certify the structural integrity of machines, buildings and other solids during its normal operation and, also, during possible accidents or overloads. Structural engineering can be divided into two different but connected sub fields: structural design and structural mechanics. The former consists in the development and application of guidelines and rules that allow for the design of safe structures for a specific use. The latter has as a goal determining how the external forces and actions are distributed among the structural components of an object when its dimensions and properties are known. It is evident that it is not possible to design a structural component if the loads that it has to withstand are unknown. On the other hand, usually, the dimensions and properties of the structural components are not known if the structure has not been designed previously. Thus, in many cases, the process of structural certification is an iterative one where the techniques of the structural design and the structural mechanics are applied successively.

The present is a book on structural mechanics exclusively.

Structural mechanics can also be used as a tool for the “diagnosis” of existing structures, in the same way as medical imagenology techniques, such as computerized tomography, are used to diagnose a human patient (see Figure 1). This diagnose is sometimes called structural vulnerability assessment.

Figure 1.

“Diagnose” of (a, b) A human patient, (c, d) A structure

1a. MRI-Philips.JPG. (n.d.). Retrieved April 13, 2014 from PET-image.jpg. (n.d.). Retrieved April 13, 2014 from (n.d.). Retrieved July 25, 2010 from

In the engineering practice, structural mechanics concepts are usually applied through structural analysis programs. This field has two aspects. The first one is about the mathematical models or equations that describe the behavior of structures under mechanical loading; the second one is about the numerical procedures used to solve these equations. This book deals mainly with the former aspect although the basic notions of the latter are also considered. Table 1 presents a summary of the models used in the structural analysis.

Table 1.
Summary of structural mechanics models
Representation of the StructureRepresentation of the MaterialRepresentation of the DeformationRepresentation of the Loading
Solid theoryTheory of elasticitySmall strains and deformationsQuasi-static loadings
Beam and arc theoryTheory of plasticityLarge strain and deformationsDynamic loadings
Plate and shell theoryFracture Mechanics
Frame theoryDamage Mechanics

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