TORSION 



109 



Expressed in kilowatts instead of horse power, this formula 

 becomes 



(145) J> = 



where for steel p = 3.175, for wrought iron p = 3.627, and for cast 

 iron p = 4.576. 



64. Combined bending and torsion. In many cases shafts are 

 subjected to combined bending and torsion, as, for instance, when 

 a shaft transmits power by means of one or more cranks or pulleys. 

 In this case the bending moment M b at any point of the shaft pro- 

 duces a normal stress^? in accordance with equation (33), article 34, 

 that is, 



32Jf 6 



(146) 



P 



_ M h e 



and the torque M t produces a shearing stress q given by (138), 

 article 61, namely, 



(147) q = ^ = 



M t 



In more advanced works on the strength of materials, however, it 

 is shown that the maximum and minimum normal and shearing 

 stresses, resulting from any such combination as the above, are 

 given by the relations * 



min 



(148) 

 (149) 



Therefore, inserting in these expressions the values of p and q as 

 given above, the maximum and minimum normal and shearing 

 stresses in terms of the bending and twisting moments are found 

 to be 



+ Mf) ( called Rankine's formula), 



(150) 

 (151) 



min 



= 



7TD 3 



16 



min 



(called Guest's formula). 



Slocum and Hancock, Strength of Materials, Revised Edition, pp. 24-25. 



