Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019

More complex shapes can be built up from individual rectangular sections. The section property can be calculated for each rectangle and the combined section property calculated for the combination.

The section properties of a composite shape are defined as follows:

The total second moment of area of the shape is determined by using the parallel axis theorem (see section 6.1.4) with I’ being the 2^nd moment of area of each individual component:

The solution is best laid out as a table, with a row for each element of the cross section. This is shown in the spreadsheet at the link below:

AA-SM-001-002 Section Properties – General

The spreadsheet first calculates the combined section properties about the origin:

 This table is used to determine the centroid of the combined rectangles.

The spreadsheet then recalculates the section properties about the centroid of the combined rectangles:

There are different spreadsheets that allow analysis of various composite rectangular sections at the links below:

AA-SM-001-004 Section Properties – General with Angles – moment distribution

AA-SM-001-005 Section Properties – General with Angles – Really Small Format

AA-SM-001-006 Section Properties – General with Angles – Weighted area – moment distribution

AA-SM-001-007 Section Properties – General with Angles – weighted area – moment distribution – small format