Page 126 - 4749
P. 126

1    d
                                      k         .
                                              ds
             Considering  the  smallness  of  deformations  ds   dx   and  the
           equation (6.30), we obtain
                                             2
                                  1   d    d y
                              k              .                    (6.32)
                                      dx   dx 2
             Equating  the  right  sides  of  equations  (6.31)  and  (6.32),  we
           obtain an approximate differential equation of the curved axis of a
           beam

                                  2
                                d y    M  z    x
                                             .                      (6.33)
                                dx 2    EJ
                                           z













                                      Figure 6.17

             The  sign  in  front  of  the  right  side  of  (6.33)  depends  on  the
           accepted  coordinate  system.  For  example,  for  the  coordinate
           system shown in fig. 6.17, the marks for curvature  k   y   x  and

           bending  moment  M     x   are  the  same,  so  the  right  side  of  the
                               z
           equation (6.33) is taken with a "plus". Differentiating the equation
           (6.33)  and  by  considering  the  equilibrium  equations  (6.1)  and
           (6.2), we obtain


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