RELATIONS BETWEEN STRESS AND DEFORMATION 29 



For this reason K is called the coefficient of cubical expansion (or 

 contraction) of the body. 



From this definition it is evident that for temperature stresses the 

 coefficient of cubical expansion is three times the coefficient of linear 

 expansion. 



From Article 9, for linear tensile strain, 



Consequently, in this case, 



Since the prism is certainly not decreased in volume by a tensile 

 strain. A' cannot be negative and therefore m 2 > 0, or m > 2. If 

 m = 2, A' = 0, which means 

 that the body is incompressi- 

 ble. Therefore 2 is the l..\\. r 

 limit of Poisson's constant. 



33. Modulus of elasticity 

 of shear. In an elementary 

 prism subjected tn simple 

 angular deformat i< >n 



occurs, as shown in l-'i.u r . 16. Flo 16 



Let the angle of deformat inn 



<f> be expressed in < ircular measure. Then, for materials which con- 

 form to Hooke's 1 



JH 



'G, 



7 



:it called tin- modulus of elasticity of shear, or 



modulus of rigidity. Since tin- an^le $, expressed j n circular measure, 

 is an abstract number, G must have the dimensions of q, and can 

 therefore be expressed in lb./in. 2 , as hi the case of Young's modulus. 

 ilat-d values of the modulus of elasticity of shear and ultimate 

 shearing .strength for various substances are given in Article 22. 



Problem 28. A |-in. wrought-iron bolt has a diameter of .62 in. at base of 

 :. with a nut | in. thick. What force acting on the nut will strip the thread 

 off the bolt ? 



