KKLATIOXS BETWEEN STKESS AND DEFOKMATION 31 



/7T <\ _ X + 



n ^4 + ^/~ x^ 

 From trigonometry, 



dx 

 dx 



Since </> is assumed to be very small, tan^ = ^, approximately, 

 and therefore 



. 

 whenc e 



By definition, 



H 



which expresses the relation between the elastic constants G, E, 



and /// . 



Problem 32. From the values of O and E, given in Article 22, determine the 

 value of m for cast iron. 



35. Measure of strain. In general, the unit deformation s is taken 

 as the measure of a strain. The calculation of s, however, involves 

 a knowledge of the modulus of elasticity E, and for many materials 

 the latter is difficult to determine. To obviate this difficulty, any 

 given strain may be compared with a linear strain which is pro- 

 duced by a unit stress equal to the maximum allowable unit stress. 

 The stress which would produce this linear strain is called the 

 equivalent stress. 



To illustrate the application of this method, consider a planar 

 i in which PI and p t denote the principal stresses and s lt s a 

 the corresponding unit deformations. Then, by Hooke's law, 



