282
CONTINUOUS SYSTEMS
0
100
200
300
400
500
(b)
1 A/o= 227 000 kg
549l_
-100
_J________ I-------------JL_
-50
0
50
l
/
1
Displacement v(xjc), meters
Figure 10.14 Effect of ballast on critical pipeline displacements: (a) L = 244 m; (b)
L = 549 m.
Shown with asterisks in Table 10.3 are the pipeline lengths at which the
responses are unbounded. Note that the larger ballast mass (227000 kg instead
of 45 400 kg) increased the System stability for lengths of 183 m and 545 m, but
this additional ballast did not alleviate unbounded responses at lengths greater
than 610 m.
Shown in Figures 10.14a and 10.14b are typical stable pipe profiles corresponding to the peak transverse displacement v(L,tc) occurring during the 600
s simulations. Figure 10.14a shows that an increase of a factor of five in ballast
mass does little either to straighten the pipe to relieve its peak moment occurring near x = 75 m, or to reduce its peak deflection at x = L. These two profiles
correspond to critical times tc of 146 s and 264 s for the light and heavy ballast,