PART I 



MECHANICS OF MATERIALS 

 CHAPTER I 



ELASTIC PROPERTIES OF MATERIALS 



1. Introductory. In mechanics all bodies considered are assumed 

 to be perfectly rigid; that is to say, it is assumed that no matter 

 what system of forces acts on a body, the distance between any two 

 points of the body remains unchanged. 



It has been found by experiment, however, that the behavior of 

 natural bodies does not verify this assumption. Thus experiment 

 slmws that when a body formed of any substance whatever is acted 

 upon by external forces it changes its shape more or less, and that 

 when this change of shape becomes sufficiently great the body breaks. 

 It has also been found that the amount of change in shape necessary 

 to cause rupture depends on the material of which the body is made. 

 For instance, a piece of vulcanized rubber will stretch about eight 

 times its own length before breaking, while if a piece of steel is 

 stivtched until it breaks, the elongation preceding rupture is only 

 from T ^ to of its original length. 



2. Subject-matter of the strength of materials. Since the assump- 

 tion of rigidity upon which mechanics is based cannot be extended 

 to natural bodies, mathematical analysis alone is not sufficient to 

 determine the strength of any given structure. A knowledge of the 

 physical properties peculiar to the material of which the structure is 

 made is also essential. 



The subject-matter of the strength of materials, therefore, consists 

 of two parts. First, a mathematical theory of the relation between 

 the external forces which act on a body and its resultant change of 

 shape, by means of which the direction and intensity of the forces 

 acting at any point of the body may be calculated; and, second, an 



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