Geometrical Properties of Common Shapes

Figure 2.14 : Properties of some common shapes

 

Table 2.2 : Properties of Common Shapes

 

Shape	A	$I_{xc}$	$I_{yc}$	$I_{xyc}$
A)Circle	$\pi R^2$	$\pi {R^4} \over 4$	$\pi {R^4} \over 4$	0
B)Rectangle	bh	${1 \over {12}} b h^3$	${1 \over {12}} h b^3$	0
C)Triangle	${1 \over 2} bh$	${1 \over {36}}b h^3$	-	${1 \over {72}} bh^2 (b-2d)$
D)Semicircle	${1 \over 2} \pi R^2$	$0.1098 R^4$	$0.3927R^4$	0

Note that the determination of the resultant force $F_R$ hinges on the knowledge of the position of the centroid for the given shape. The location of $CP$, the Center of Pressure depends upon the moment of inertia and the product of inertia. These are functions of the geometry only and can be calculated once the shape is given. Table 2.2 along with Figure 2.14 gives these properties for some of the common shapes.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney