STRENGTH OF MATERIALS

Strength of materials is a branch of applied mechanics that deals with the behavior of solid bodies

subjected to various types of loading. This field of study is known by several names, including

"Strength of materials" and "mechanics of deformable bodies."  The solid bodies considered in this

course include axially loaded members, shafts in torsion, beams, and columns, as well as structures that

are assemblies of these components. Usually the objectives of our analysis will be the determination of

the stresses, strains, bending and shear force, forces generated in truss members created by the loads.

If these quantities can be found for all values of load up to the failure load, then we will have a

complete picture of the mechanical behavior of the body.

A thorough understanding of mechanical behavior is essential for the safe design of all structures,

whether buildings and bridges, machines and motors, submarines and ships, or airplanes and antennas.

Hence, strength of materials is a basic subject in many engineering fields. Of course, statics and

dynamics are also essential, but they deal primarily with the forces and motions associated with

particles and rigid bodies. In this course, we will go one step further by examining the stresses and

strains that occur inside real bodies that deform under loads. We use the physical properties of the

materials as well as numerous theoretical laws and concepts, which will be explained as we

develop this course.

The historical development of strength of materials is a fascinating blend of both theory and

experiment; experiments have pointed the way to useful results in some instances, and theory has

done so in others. Such famous men as Leonardo da Vinci (1452-1519) and Galileo Galilei (15641642)

performed

experiments

to

determine

the strength of wires, bars, and beams, although they did

not develop any adequate theories (by today's standards) to explain their test results. Such theories

came much later. By contrast, the famous mathematician Leonhard Euler (1707-1783) developed the

mathematical theory of columns and calculated the theoretical  critical  load  of  a  column  in  1744, 

long  before  any  experimental evidence existed to show the significance of his results. Thus, for want

of appropriate tests, Euler's results remained unused for many years; although today they form the basis

of column theory. 

When studying strength of materials from this course, you will find that your efforts are divided

naturally into two parts: first, understanding the logical development of the concepts, and second,

applying those concepts to practical situations. The former is accomplished by studying the

derivations, discussions, and examples, and the latter by solving problems. Some of the examples and

problems are numerical in character, and others are algebraic or symbolic). An advantage  of 

numerical  problems  is  that  the  magnitudes  of  all  quantities  are evident at every stage of the

calculations. Sometimes these values are needed to ensure that practical limits (such as allowable

stresses) are not exceeded. Algebraic solutions have certain advantages, too. Because they lead to

formulas, algebraic solutions make clear the variables that affect the final result. For instance, a certain

quantity may actually cancel out of the solution, a fact that would not be evident from a numerical

problem.

Numerical problems require that you work with specific units of measurements and the only

accepted standard of measurement is the International System of Units (SI).