TORSION 

 Therefore, substituting in equation (150), we have 



12,000 = -^L (364,230 + x/364,230 2 + 3p40 2 ) ; 



whence 



D = 6.725 in. 



and similarly, from equation (151), 



9000 = -H. V364,230 2 + 3p40 2 ; 



115 



whence 



= 5.842 in. 



The proper diameter for the shaft is then the larger of these two values, say 6| in. 



190. If the angle of twist for the wire in problem 186 is 9 = 40, how great is 

 the torsional moment acting on the wire ? 



191. Compare the angle of twist given by St. Tenant's general formula with 

 the values given by the special formulas in articles 67, 68, and 69. 



192. A steel shaft is required to transmit 300 H.P. at a speed of 200 revolutions 

 per minute, the maximum moment being 40 per cent greater than the average. 

 Find the diameter of the shaft. 



193. Under the same conditions as in problem 192, find the inside diameter of a 

 hollow circular shaft whose outside diameter is 6 in. Also compare the amount of 

 metal in the solid and hollow shafts. 



194. The semi-axes of the cross section of an elliptical shaft are 3 in. and 5 in. 

 respectively. What is the diameter of a circular shaft of equal strength ? 



195. An oak beam 6 in. square projects 4 ft. from a wall and is acted upon at 

 the free end by a twisting moment of 25,000 f t.-lb. How great is the angle of twist ? 



196. A steel shaft 10 ft. long between centers of bearings and 4 in. in diameter 

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

 is 250 lb., and the following side runs slack, what is the maximum stress in the 

 shaft, and how many H.P. is it transmitting when running at 80 R.P.M. ? 



197. Find the required diameter of a solid wrought-iron circular shaft which is 

 required to transmit 150 H.P. at a speed of 60 K.P.M. 



198. Find the angle of twist in problem 192. 



199. Find the angle of twist in problem 193 and compare it with the angle of 

 twist for the solid shaft in problem 198. 



200. How many H.P. can a hollow circular steel shaft of 15 in. external diam- 

 eter and 11 in. internal diameter transmit at a speed of 50 R.P.M. if the maximum 

 allowable unit stress is not to exceed 12,000 lb./in. 2 ? 



201. Find the diameter of a structural-steel engine shaft to transmit 900 H.P. 

 at 75 K.P.M. with a factor of safety of 10. 



202. Find the factor of safety for a wrought-iron shaft 5 in. in diameter which 

 is transmitting 60 H.P. at 125 R.P.M. 



203. A structural-steel shaft is 60 ft. long and is required to transmit 500 H.P. 

 at 90 R.P.M. with a factor of safety of 8, and to be of sufficient stiffness so that 

 the angle of torsion shall not exceed .5 per foot of length. Find its diameter. 



204. Under the same conditions as in problem 203, find the size of a hollow 

 shaft if the external diameter is twice the internal. 



