Page 91 - 4749
P. 91

back at an angle    –  angle at the point  K . The arc  KK    d
                                                                  1
           and  the  triangle  CKK   –    KK     dx .    Equating  the  right  of
                                 1         1   
           expression, we obtain
                                         d
                                          .                       (5.4)
                                    
                                          dx




















                                       Figure 5.5

             We  have  obtained  the  linear  law  of  distribution  of  angular
           deformitions  along  the  radius.  This  is  because  the  radius  in  the
           deformation process is not distorted.
             The  physical  aspect.  The  relation  between  stresses  and
           deformations is described by Hooke’s law in shear
                                     G .                            (5.5)
                                         
             Substituting the equation (5.4) in Hooke's law (5.5), we obtain
           the stress distribution law in torsion
                                          d
                                    G     .                         (5.6)
                                  
                                          dx
             Study  together  with  the  law  of  stress  distribution  (5.6)  the
           equilibrium equation (5.3), we obtain



                                          91
   86   87   88   89   90   91   92   93   94   95   96