130 RESISTANCE OF MATERIALS 



Similarly, the unit deformation s 2 of a fiber on the surface of the 



shaft is 



- D 



From Hooke's law, = E, we have, therefore, for the unit stress 

 s 



p l on the inside of the disk 



1=-,=^ 



and for the unit stress p 2 on the surface of the shaft 



p,_ A-D 



Adding these two equations to eliminate the unknown quantity Z>, 

 the result is 



where K denotes the allowance, or difference in diameter of shaft 

 and hole. For a thick disk or heavy ring this allowance K may be 

 determined from the nominal diameter D of the shaft by means of 

 the f ollowing empirical formulas : * 



For shrinkage fits, K 

 For pressed fits, 

 For driven fits, 



For thin rings, however, the allowance given by these formulas 

 will be found to produce stresses in the ring entirely too large for 

 safety. In deciding on the allowance for any given class of work 

 the working stresses in shaft and ring may first be assigned and 

 the allowance then determined from the formulas given below, so 

 that the actual stresses shall not exceed these values. 



* S. H. Moore, Trans. Am. Soc. Mech. Eng.,Vo\. XXIV. 



