1. Engineering Structures and Materials

1 Structures / Materials SectionPage 1 CIVL 1101 --Civil Engineering Structures and IntroductionMechanics of Materials is a branch of applied mechanics that deals with the behavior ofsolid bodies subjected to various types of loading. This field of study is known by severalnames, including Strength of Materials and mechanics of deformable bodies. The solidbodies considered in this book include axially loaded members, shafts in torsion, thin shells,beams, and columns, as well as Structures that are assemblies of these components. Usuallythe objectives of our analysis will be the determination of the stresses, strains, and deflectionsproduced by the loads.

2 If these quantities can be found for all values of load up to the failureload, then we will have a complete picture of the mechanical behavior of the thorough understanding of mechanical behavior is essential for the safe design of allstructures, whether buildings and bridges, machines and motors, submarines and ships, orairplanes and antennas. Hence, mechanics of Materials is a basic subject in many engineeringfields. Of course, statics and dynamics are also essential, but they deal primarily with theforces and motions associated with particles and rigid bodies. In mechanics of Materials , wego one step further by examining the stresses and strains that occur inside real bodies that de-form under loads.

3 We use the physical properties of the Materials (obtained from experi-ments) as well as numerous theoretical laws and concepts, which are explained in succeedingsections of this analyses and experimental results have equally important roles in the study ofmechanicsof Materials . Onmanyoccasions, wewill makelogical derivationstoobtainformu-lasand equationsfor predictingmechanical behavior, but wemust recognizethat theseformu-las cannot be used in a realistic way unless certain properties of the Materials are properties are available to us only after suitable experiments have been carried out inthe laboratory.

4 Also, because many practical problems of great importance in engineeringcannot be handled efficiently by theoretical means, experimental measurements become historical development of mechanics of Materials is a fascinating blend of both theoryand experiment; experiments have pointed the way to useful results in some instances, andtheory has done so in others. Such famous men as Leonardo da Vinci(1452-1519) and GalileoGalilei (1564-1642) performed experiments to determine the strength of wires, bars, andbeams, although they did not develop any adequate theories (by today s standards) to explaintheir test results.

5 Such theories camemuch later. Bycontrast, thefamous mathematicianLeon-hard Euler (1707-1783) developed the mathematical theory of columns and calculated thetheoretical critical load of a column in 1744, long before any experimental evidence existed toshow the significance of his results. Thus, for want of appropriate tests, Euler s results re-mained unused for many years, although today they form the basis of column SectionPage 2 CIVL 1101 --Civil Engineering MeasurementsWhen studying mechanics of Materials from this book, you will find that your efforts aredivided naturally intotwoparts: first, understanding the logical developmentof theconcepts,and second, applying those concepts to practical situations.

6 The former is accomplished bystudying the derivations, discussions, and examples, and the latter by solving of the examples and problems are numerical in character, and others are algebraic torsymbolic). An advantage of numerical problems is that the magnitudes of all quantities areevident at every stage of the calculations. Sometimes these values are needed to ensure thatpractical limits (suchas allowable stresses) are not exceeded. Algebraicsolutions have certainadvantages, too. Because they lead to formulas, algebraic solutions make clear the variablesthat affect the final result.

7 For instance, a certain quantity may actually cancel out of the solu-tion, a fact that would not be evident from a numerical problem. Also apparent in algebraicsolutionsisthemannerin whichvariables affectthe results, such asthe appearanceof onevari-able in the numerator and another in the denominator. Furthermore, a symbolic solution pro-vides the opportunity to check the dimensions at any stage of the work. Finally, the most im-portant reason for obtaining an algebraic solution is to obtain a general formula that can beprogrammed on a computer and used for many different problems. In contrast, a numericalsolution applies to only one set of circumstances.

8 Ofcourse, youmust beadept atboth kindsofsolutions, hence you will find a mixture of numerical and algebraic problems throughout problems require that you work with specific units of measurements. The twoaccepted standards of measurement are the. International System of Units (SI) and the System (USCS). As you know significant digits are very important in our work in this section,three significant digitsprovides enough Normal Stress and StrainThe fundamental conceptsof stressand strain can be illustrated by considering aprismat-ic bar that is loaded by axial forcesPat the ends, as shown in Figure 1.

9 Aprismatic baris astraight structural member having constant cross section throughout its length. In this il-lustration, theaxial forcesproduce auniform stretchingof thebar; hence, the baris said to investigate the internal stresses produced in the bar by the axial forces, we make animaginary cut at sectionaa(Figure 1). This section is taken perpendicular to the longitudinalaxis of the bar; hence, it is known as across section. We now isolate the part of the bar to therightofthecutasafreebody. The tensileloadPacts atthe righthand end ofthe freebody; attheother end are forces representing the action of the removed part of the bar upon the part thatremains.

10 These forces are continuously distributed over the cross section, analogous to thecontinuous distribution of hydrostatic pressure over a submerged horizontal surface. The in-tensity of force (that is, the force per unit area) is called thestressand is commonly denoted bythe Greek letter (sigma). Assuming that the stress has a uniform distribution over the crosssection (see Figure 1), we can readily see that its resultant is equal to the intensity times theStructures/ Materials SectionPage 3 CIVL 1101 --Civil Engineering MeasurementsFigure 1. Bar in tension. LPxPPaaPaa dcross-sectional areaAof the bar.