Time (s)

Fig。  7。 RPDs of forward  leg。

increases rapidly in the first stage (i。e。, 0–700 s)。 During this period, the total vertical reaction force of the four pinions on chord F1 increases and the reaction forces of the pinions on chords F2 and F3 decrease until they are very close which can be seen from Fig。 8。 That is to say, percentage of the bending moment caused by wind loads, which is resisted by the vertical reaction force of the pinions, changes from 100% (a 100% fix system) at the beginning of the simulation to nearly 7% (a 93% floating system) in a time of about 700 s。 Some gaps are closed gradually to improve the horizontal resistance as shown in Fig。 9。 From 700 to 1300 s (the second stage), the vertical reaction forces of chord F1 and chords F2 and F3 only have a little change, which means that the system remains mainly as a floating system。 More gaps are closed and shear forces are induced to act on the leg in the contact region。 The difference between the vertical reaction forces of the pinions on chord F1 and chords F2 and F3 increases from 1300 to 1600 s (the third stage) and the difference decrease from 1600 to 1800 s (the fourth stage), which lead to the  percentage increment and decrement of the bending moment resisted by pin- ions  for  these  two  stages,  respectively。 Consequently,

RPD growth speeds up and then slows down。 From the above mentioned descriptions, it can be seen that the RPD growth speed depends on the difference between the vertical reaction forces of pinions on chord F1 and chords F2 and F3。 Similar phenomena can be found for port leg and starboard leg。 If RPD limitation or ultimate bearing capacity of any pinion is reached, RPD correc- tion operation may be   required。

Member forces are also available  from simulation。 To keep away from local collapse (i。e。, material failure or buckling), member forces of the diagonal and hori- zontal braces within the jacking regions can be taken out and compared with their ultimate load capacities。 For example, member forces of two horizontal and two di- agonal members are displayed in Fig。 10。 It is very easy to find the maximum force on a member and the time that the maximum force occurs。 If any member force exceeds its load capacity, RPD correction operation should be performed to reduce the gap   forces。

The simulated jack-up unit was analyzed with em- pirical equations to predict the maximum RPD value under 1100 kN wind load before the simulation work was carried out。 The predicted maximum RPD at time

论文网Fig。  6。 Jacking status at different  time。

in time domain and all the information obtained are coincident, the numerical method is more reliable and accurate than the empirical one。

0 200       400       600       800     1,000    1,200    1,400    1,600 1,800

Time (s)

5。3。Wind  load effect

The horizontal wind load acting on the hull varies seriously with the sea state conditions。 Four cases under wind loads of 2200, 1100, 550 and 0 kN have been simulated for the jack-up unit with three legs pinned。 Comparisons of RPDs and vertical reaction forces of pinions for the forward leg have been carried out and shown in Figs。 11 and 12,  respectively。

Fig。  8。 Vertical reaction forces of pinions on forward   leg。

0 200      400      600      800    1,000   1,200   1,400   1,600   1,800