Page 47 - 4560
P. 47

Normal stress from exposure to bending moment determined by
          the formula
                                          M y
                                                ,                   (4.1)
                                    м
                                        S  (r   ) у
                                         н  н

          where y - the distance from the neutral line to the point where we
          determine the stress;  r  - the radius of curvature of the  neutral
                                 н
          layer;  S   F e  - static moment sectional area curve beam with
                  н
          respect to the neutral line;  e   - eccentricity, or the coordinates of
          the center of gravity sectional area relative to the neutral line;  F
          - cross sectional area of timber ,
                                           F
                                     r    dF  ,                      (4.2)
                                      н
                                          
                                          F  r
                         y
          where  r   r    – the  radius  of  curvature  of  an  arbitrary  layer
                     н
          with coordinate y.

















                                    Figure 4.4

          In  general  r   do  not  coincide  with  the  center  line  radius  of
                       н
          curvature,  i.e.  neutral  bending  line  curved  beam  does  not  pass
          through the center of gravity of the cross section, but shifted by
          an amount e  to the center of curvature of the beam.
          From (4.1) it follows that the strain   varies in height section is
                                               м
          not  linearly,  as  for  straight  beams,  and  on  hyperbolic.  Major
                                         47
   42   43   44   45   46   47   48   49   50   51   52