
Engineering applications 315
mid-point, but the present maximal absolute value of stresses (moments)
appears at the end points, as shown in Figure 7.19. This phenomenon
results from the different external load distributions. In this problem, the
uid force f(x) is a decreasing function of pipeline deection w(x), and it is
clear that the deection of two ends is smaller than that of the mid-point.
This implies that the uid force at two ends is larger than that at mid-point.
Obviously the effect is different for uniform load distribution.
Figure 7.20 presents the critical velocities caused by the two types of
material failures: strength fa ...