TOKSION 117 



Problem 119. A steel shaft 5 in. in diameter is driven by a crank of 12-in. 

 throw, the maximum thrust on the crank being 10 tons. If the outer edge of the 

 shaft bearing is 11 in. from the center of the crank pin, what is the equivalent 

 in the shaft at this point ? 



Problem 120. A steel shaft 10 ft long between bearings and 4 in. in diameter 

 carries a pulley 14 in. in diameter at its center. If the tension in the belt on this 

 pulley is 250 lb., and the shaft makes 80 revolutions per minute, what is the maxi- 

 mum stress in the shaft and how many H.P. is it transmitting ? 



* 97. Resilience of circular shafts. In Article 73 the resilience of 

 a body was defined as the internal work of deformation. For a solid 

 circular shaft this internal work is 



where M is the external twisting moment and 6 is the angle of twist. 



From equation (54), = -^- = > and from equation (55), M = -- - 

 (tr Go, 2 



Therefore the total resilience of the shaft is 



and consequently the mean resilience per unit of volume is 



98. Non-circular shafts. The above investigation of the distribu- 

 tion and intensity of torsional stress applies only to shafts of circular 

 section. For other forms of cross section the results are entirely dif- 

 ferent, each form having its own peculiar distribution of stress. 



I '>r any form of cross section whatever, the stress at the boundary 

 jnAwt^tetejQgential. For if the stress is not tangential, it can be 

 resolved into two components, one tangential and the other normal 

 to the boundary ; and in Article 23 it was shown that such a normal 

 component would necessitate forces parallel to the axis of the shaft, 

 which are excluded by hypothesis. 



Since the stress at the boundary must be tangential, the circular 

 section is the only one for which the stress is perpendicular to a 

 radius vector. Therefore the circular section is the only one to which 

 the above development applies, and consequently is the only form of 



* For a brief course the remainder of this chapter may be omitted. 



