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
126