Appendix C. Moments of Composite Areas

C.1 Centroid

The plane area characteristics have special significance in various relationships governing stress and deflection of beams, columns, and shafts. Geometric properties for most areas encountered in practice are listed in numerous reference works [Ref. C.1]. Table C.1 presents several typical cases.

Table C.1. Properties of Some Plane Areas

1. Rectangle

A rectangle is shown with a point C (centroid) marked at its center. The breadth of the rectangle is marked "b" and the length is marked "h." An xy plane is drawn from the center point C. The length from the base to the x-axis is marked "h over 2."

A=bhIx=bh312Jc=bh(b2+h2)12

 

5. Circle

A circle shows a point C (centroid) marked at its center. An xy plane is drawn with its origin at point C of the circle. The distance from the base to the x-axis is marked as "r."

A=πr2Ix=πr44Jc=πr42

2. Right triangle

Get Advanced Mechanics of Materials and Applied Elasticity, 6th Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Start your free trial