Moments of Inertia (for a Composite Area)

 

Example:  Find the moment of inertia, Ixx, for the shaded area shown in the figure on the left. 

All dimensions are in cm.

                      

 

Strategy:

First

Identify each part, its area, its centroid, and its centroidal axes.

Second

Obtain the moment of inertia for each part (by calculation or by table).

Third

Apply the parallel axis theorem if needed to transfer from the centroidal

axes to the desired parallel axes.

Fourth

Sum the contribution for each individual part as shown in the table below.

                                                 

As one option partition the composite area into two parts (shown above in the figure on the right). Part 1 is the entire rectangle (60 x 80) cm.  Part 2 is the “void” rectangle (20 x 60) cm.

 

                                   

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