TORSION 



115 



whence 



(59) 





As safe values for the maximum unit shear q' Ewing recommends 

 9000 Ib./in. 2 fur wrought iron, 13,500 lb./in. 2 for steel, and 4500 lb./in. 2 

 for cast iron.* Inserting these values of q' in formula (59), it becomes 



(60) 



where for steel /A = 2.88, for wrought iron /-i = 3.29, and for cast 

 iron fi = 4.15. 



Formulas (59) and (60) were deduced under the assumption that 

 the action of the external moment was uniform. In many cases, how- 

 ever, this assumption is not verified. For example, if a shaft is driven 

 by one or more cranks, the mo- 

 ment varies periodically. Under V~ 

 such conditions the diameter of J 

 the shaft should be somewhat 

 larger than the value of d given 

 by equation (60). 







cio 



Problem 115. Kind the diameter 

 of a solid wrought-iron circular shaft 

 whirh is rfijuiivl to transmif l.~,oH.p. FIG. 86 



at a speed of 00 revolutions per minute. 



Problem 116. A steel shaft is required to transmit 800 H.P.'at a speed of 200 

 r -volutions per minute, the maximum moment being 40 per cent greater than the 

 average. Find tin- diameter of th- shaft. 



Problem 117. I'nd. -r the same conditions as in Problem 110, find the inside 

 diamrter of a hollow circular shaft whose outside diameter is 6 in. Also corn- 

 par, the amount of metal in the solid and hollow shafts. 



Problem 118. H<>\v many H.I', can a hollow circular steel shaft of 15 in. exter- 

 nal dianiftcr and 11 in. internal diameter transmit at a speed of 50 revolutions per 

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



96. Combined bending and torsion. When a shaft transmits power 

 by means of a crank or pulley, it is subjected to combined bending 

 and torsion. For example, if a force P acts at a point A in the 

 crank pin shown in Fig. 86, the bending moment at any point C of 



* Ewing, The Strength of Materials, p. 190. 



