CHAPTER VI 



TORSION 



92. Circular shafts. When a uniform circular shaft, such as 

 shown in Fig. 84, is twisted by the application of moments of oppo- 

 site signs to its ends, every straight line AB parallel to its a.\ 

 deformed into part of a helix, or screw thread, AC. The strain in this 

 case is one of pure shear and is called torsion, as mentioned in 

 cle 37. The angle <f> is called the angle of shear (compare Article 33), and 

 is proportional to the radius BD of the shall. The angle B is called tin- 

 angle of twist, and is proportional to the length AB of the shaft 



FIG. 84 



Fio. 86 



93. Maximum stress in circular shafts. (.'onsid.-r a section of 

 length dx cut from a circular shaft by planes perpendicular to its 

 axis (Fig. 85). Let dB denote the angle of twist for this section. 

 Then, since the angle of twist is proportional to the length of tin- 

 shaft, dB : 6 = dx : I ; whence 



Also, if < and dd are expressed in circular measure, 



and 

 Therefore 



BC = dB-BD = 



e 

 -7- = r- 



dx I 

 112 



