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Introduction 



The strength of materials is the science more general of the strength of the machines and the constructions. Without its fundamental knowledge of the curse of the strength of materials it is not concevible the creation of diferent machines and mechanisms, civil and industrial constructions, bridges, lines of transmitions of energy, ships, airplanes, helicopters, turbomachinary and electric machines, nuclear equipment, rockets, etc.
Our subject owes much of its development to a great school of French mathematicians in the first half of the last century, of which the most outstandig names are Poisson, Lame, Navier, Poncelet, SaintVenant, and Boussinesq. Being mathematicians, they naturally considered their problem completely solved as soon as they had a formula relating stress to loading, and moreover they were convinced that they were working on a "practical" subject. Hence they gave to their subject the practical name resistance de materiaux, and their influence was so great that the name has persisted to this day among engineers in the Englishspeaking world. 



Hooke`s Law 



In the usual " tensile test" a bar of steel or other material is placed in a tensiletesting machine, and while it is slowly being pulled, readings are made of the pulling force and of the change in length (elongation) of the center portion of the bar. When these two quantities are plotted against each other, a diagram such as Fig. 1 results. In it we distinguish three stages, OA, AB, and BC. 






The elastic, linear behavior of a material in the region OA of Fig. 1 is known as "Hooke`s law". It states that the enlogation is proportional to the force, or expressed in a formula: 












The quantity e is the "unit elongation", or "strain", expressed in inches per inch and hence dimensionless. The pounds per square inch. Finally, E is a proportionality constant, which also must bbe expressed in pounds per square inch. It is known as the "modulus of elasticity", or also as "Young's modulus", after its inventor Thomas Young (17731829). 







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