129
OF ENGINEERING FOEMULÆ.
Moment of Inertia. (Graphic Construction.)
Divide the section into convenient layers; then
with auy scale set out successively on a horizontal
line lengths proportional to the area of each layer
respectively ; making the total length D B = the
area of the section ; also draw the perpendicular
D C — J D B; join B C, and from the points set
out as above draw vector lines radiating to C.
Then from the horizontal lines which passthrough
the centres of gravity of each layer respectively
draw lines parallel to each vector respectively as
shown in the diagram, forming a polygon. The
intersection of the lines bj in the polygon deter-
mines the position of the neutral axis.
The lines of the polygon are denoted by the
same letters as the vector lines to which they have
been drawn parallel.
c
Then if I = Moment of inertia,
A = Area of the section,
a — Area of the polygon an formed above,
I = A a.
The nearer the layers are together the more
accurate will be the result.