Second Moment of Area

The second moment of area is a geometric property of an area about a given axis.

List of Second Moments of Area for Common Shapes

I = \frac{π}{4} r^{4}

I = \frac{π}{4} (r_{2}^{4} - r_{1}^{4})

I = \frac{b h^{3}}{12}

The parallel axis theorem can be used to find the second moment of area about a different, parallel, axis from that already found.

I_{x} = I_{x^{'}} + A d_{y}^{2}

where:

$A$	is the area of the shape (m²);
$d_{y}$	is the perpendicular distance between the two axes (m);