178
DOCK ENGINEERING.
The same principle may be applied to finding the common centre of
gravity of two areas. Let A CD B (tig. 102) and C F H E be two areas,
whose respective centres of gravity are Gj and G2. Join Gj G2. From Gj
and G2 draw two parallel lines, in this case horizontal, but, generally
speaking, preferably perpendicular to Gj G2, and inake G(J proportional
to the area C F H E, and G2 K proportional to the area A C D B. Join J K.
The intersection of J K and G1 G2 at the point, O, gives the common centre
of gravity of the two areas.
Sections of dock walls, when not actually forming any simple geometrical
figure, may be subdivided into a number of such figures. The combined
centre of gravity for the whole figure can then be obtained by the method
just described, taking the areas successively and finding the joint centre for
each pair. Or any of the following methods may be employed :--
1. In fig. 103 a wall section is shown divided into 3 rectangles. E is
the centre of gravity of the topmost rectangle, A C D B, found by inter-
Fig. 104.
secting diagonals. F and H, in like manner, are the centres of gravity
for the other two rectangles. Join EF and take a point G such that
EG area OLMJ „.
----= --------- -. Then G is the common centre ot gravity for the two
GF area ACDB
rectangles. Join G II and take a point K such that
GK area L NO P
KH = areas ACDB + CLMJ’
K is the centre of gravity of the whole figure.
2. The point K may be found by combining the co-ordinates of the