Second Moment of An Area of Geometric Shape

The second moment of an area of a geometric shape can be determined by integration or the parallel-axis theorem. Imply

Moment of Inertia of Areas

Second Moment of Area of Rectangle

Second Moment about x' by Double Integration

The second moment of an area of a rectangle about the centroidal axis x' is

Second Moment about y' by Single Integration

The second moment of an area of a rectangle about the centroidal axis y' is

Second Moment about x by Parallel-Axis Theorem

The second moment of an area of a rectangle about the axis x is

Second Moment about y by Parallel-Axis Theorem

The second moment of an area of a rectangle about the axis y is

Polar Moment about C from Rectangular Moments of Inertia

The polar moment of an area of a rectangle about the centroid C is

Second Moment of Area of Circle

Second Moment about x'  by Double Integration

The second moment of an area of a circle about the centroidal axis x' is

Second Moment about y'  by Double Integration

The second moment of an area of a circle about the centroidal axis y' is

Polar Moment about C from Rectangular Moments of Inertia

The polar moment of an area of a circle about the centroid C is

Second Moment about A by Parallel-Axis Theorem

The second moment of an area of a rectangle about axis A is

Second Moment of Area of Triangle

Second Moment about x' by Single Integration

The second moment of an area of a triangle about the centroidal axis x' is

Second Moment about x by Parallel-Axis Theorem

The second moment of an area of a triangle about the axis x is