Moments of Inertia Click here for Parallel Axis Theorem

Key Concepts: The moment of inertia, I, is an important property of an area. It is the

"second" moment of an element of area about axes y and z (using integration) such as

(see figure below)

I_zz = ʃ y² dA I_yy = ʃ z² dA

The moment of inertia is frequently calculated about the centroidal axes of the X-section.

The parallel axis theorem then provides a convenient method to calculate the moment of

inertia about any parallel axes to the centroidal axes.

In a Nutshell: The analysis of stresses in beams uses the moment of inertia of area in its

calculation. Common X-sections include rectangular, box, tee, circular, and annular. The table

below contains the moments of inertia of areas for rectangular and circular X-sections.

I_yy I_zz

Rectangular Area	(1/12) hb^3	(1/12) bh^3
Circular Area	(1/4)π r^4	(1/4)π r^4

X-sections can be combined to form composite sections such as a box section, a tee section

or an annular section. Strategy: Use superposition to calculate the moment of inertia of

composite sections.

Click here for examples. Click here for a discussion for composite sections.

Return to Notes on Statics

Copyright © 2019 Richard C. Coddington
All rights reserved.