MOMENTS AND CENTROIDS 47 
(3) A plane figure is formed by removing from a triangle ABC 
(Fig. 45) triangles ADE and FHK. It is required to find the centroid 
of the figure. ; 
The centroids of the triangles ABC, ADE, and FHK are first deter- 
mined by the intersections of their medians. Conceive that the triangle 
ABC is made of very 
thin sheet metal, and 
that it is suspended 
from its centre of 
gravity by a string. 
The tension R in the 
string would be equal 
to. the weight (or area) 
of the triangle. The 
upward force R would 
be balanced by the 
downward forces W, P, 
and Q, where W is the 
weight (or area) of the 
shaded figure acting at 
its centre of gravity G (as yet unknown), P is the weight (or area) of 
the triangle FHK acting at its centre of gravity, which is known, and 
Q is the weight (or area) of the triangle ADE acting at its centre of 
gravity, which is known. The parallel forces R, P, and Q are completely 
known, and G, their centre, is the centroid required. The force and 
funicular polygons for finding G are not shown. 
To work this example by calculation proceed as follows :— 
R=area of ABC= 4x 4} x 24 =4} square inches. 
P=area of FHK =} x 14 x $=, square inch. 
2 
Q=area of ADE=(7}) x $1.9 square inch. 
W =shaded area= R —- P- Q= $3 -  — 95 = $3 square inches. 
Distance of centroid of ABC from BC =} x 44 =14 inches. 
Distance of centroid of FHK from BC = 44 — 14 - 3 x 14 =2 inches. 
Distance of centroid of ADE from BC = 44 —% x 14=3} inches. 
Distance of centroid G from BC =z. 
Take forces parallel to BC, and take moments about B, then 
te x lg =e x 244% x 3444230. Hence x= 1+ inches. 
Taking the forces parallel to AB, and taking moments about B, the 
distance y of the centroid G from AB is found to be £ inch. 
Further examples on the determination of centroids will be found 
later on in this chapter in connection with moments of inertia. 
66. Centre of Pressure and Centre of Stress.—If a plane figure be 
subjected to fluid pressure, the point in the plane of the figure at which 
the resultant of the pressure acts is called the centre of pressure. If 
a plane figure be a section of a bar which is subjected to stress, the point 
in the plane of the section at which the resultant of the stress acts is 
called the centre of stress. 
If the pressure or stress be uniform over the figure, then the centre 
of pressure or centre of stress coincides with the centroid of the figure. 
