Curved Beams-Introduction

Fig 1: C frame curved beam

     Curved beams are those which are same as that of straight beams but the only difference is(ofcourse these are curved shape)the neutral axis and the centroidal axis does'nt coincide in the case of curved beams,also the neutral axis gets shifted to the centre of curvature. There will be an eccentricity between them.In the adjacent fig. its a curved beam of C frame type(C shaped).We can clearly see the eccentricity between the neutral axis and the centroidal axis in the fig. Also the variation in bending stress along the depth of the cross section is hyperbolic.

Fig 2: Variation of Bending stress in curved beams

     In fig 1 Ri,Ro,Rn,R are the radii of innermost fibres,outermost fibres,neutral axis and centroidal axis respectively.'h' is the depth of the beam and 'b' is its width(rectangular cross section as if now).   The variation in bending stress is shown in fig 2.
It can be observed that the variation is hyperbolic which is different from that straight beams(which is straight).If we observe the figure,the stress in the inner layers(sigma b) which is tensile in nature is more than the stress in the outer layers(sigma o).
This property of curved beams leads to stress concentration(due to difference in stress levels),which should be eliminated as far as possible by the designer by getting the values of the stresses as closer as possible and get a uniform stress distribution as in the straight beams.