Lý thuyết về COG shift trong bài toán lifting

Variations of Center of Gravity Following is an example of a CoG envelope centered on the calculated CoG, which corresponds to a rectangle whose sides are: (extracted from previous project general specification):
· The variation of the calculated location of the centre of gravity within a rectangle whose sides are equal to 10 % of the overall width and length for a deck, and 5 % of the overall width and length for a jacket, but not less than within a 2.0 m x 2.0 m square area for a deck.
· The variation of the minimum sling angle of 55°.
The variation of CoGs is applied in the SACS model by using dummy loads which are obtained from the following 2 cases:
· Fictitious couple force around X axis, Mox, which is dedicated to shift the CoG along the Y-axis.
· Fictitious couple force around Y axis, Moy, which is dedicated to shift the CoG along the X axis
Hình 1: Vị trí COG và các thông số

The fictitious couple force is assumed initially as a dummy load of any value and applied on the selected nodes in the model, thereof will be resulted moment load in X-axis (Mox) or in Y-axis (Moy). The both initial dummy loads then shall be combined with gravity loads and applied appropriate factors for obtaining the expected positions of CoG.
These fictitious forces could be applied on the selected joints at four corners of model in horizontal plane in order to ease the analysis.
Figures overleaf are examples how the fictitious forces are applied in the SACS model.
Hình 2: Nhập lực trong sacs.

Load case “COGX” above is created for generating moment in X-direction, Mox, while load case “COGY” is for generating moment in Y-direction, Moy.
The design variation of the CoG is shown in the figure below, then:
· Distance of CoG shift from theoretical CoG along X-axis is (+/-) dx/2.
· Distance of CoG shift from theoretical CoG along Y-axis is (+/-) dy/2.
If the weight of lifted object including Contingencies is “GRAV”, then the appropriate factors which corresponding to the expected positions of CoG are:
· Factors for shifting CoG in X-axis can be calculated :
αx = |GRAV| * (dx/2) / |Moy|,
Values of Moy and GRAV always taken are positive.
· Factors for shifting CoG in Y-axis can be calculated :
αy = |GRAV| * (dy/2) / |Mox|,
Values of Mox and GRAV are always taken are positive.