STRESSES AND STRAINS 123 



Let / represent the length of the body, in inches; e, the 

 deformation, in inches; and q, the unit strain. Then, 



<2 = y, or e = lq 



ELASTIC PROPERTIES 



It can be proved by experiment that when a certain unit 

 stress is created in a substance, a certain definite unit strain 

 is developed. If the unit stress is doubled, it will be found 

 that the unit strain also has doubled; that is, the alteration 

 of shape or the strain in a body is proportional to the force 

 applied to that body. This experimental fact is known as 

 Hooke's law. 



When a certain stress is created in a body a certain strain 

 is produced. When the stress is removed, the body returns 

 to its original shape, provided the unit stress has not been 

 too great. For each substance, however, there is a certain 

 maximum unit stress that the substance will stand and still 

 return to its original shape after the external forces are 

 removed. This unit stress is called the elastic limit of the 

 material. If a body is strained beyond the elastic limit, 

 it will maintain a permanent distortion, or set, even after 

 the strain forces are removed. Hooke's law, which is almost 

 exact for most materials below the elastic limit, does not hold 

 good for these materials above the elastic limit, as the 

 strain increases much more rapidly than the stress. Thus, 

 if the unit stress is doubled beyond the elastic limit, the unit 

 strain will be more than doubled. The unit stress that is 

 so great that the strain increases greatly with very little 

 increment of stress is called the yield point. For all prac- 

 tical purposes, with many materials the yield point com- 

 mences at the elastic limit. 



To restate Hooke's law, the ratio of the unit stress to the 

 unit strain for any substance is constant below the elastic 

 limit. This ratio of unit stress to unit strain is called the 

 modulus of elasticity, or coefficient of elasticity, which will be 

 represented by the symbol E. It is 



