Engineering Statics

F-21


Determine the moments of inertia Ixx and Iyy of the area shown with respect to centroidal axes respectively parallel and perpendicular to side AB.

To determine the centroidal axis, the area is separated into 
three rectangles.  The tabular method is then used by find the 
x-centroidal axis.  Note that measurements are taken from the 
right side of the area.  Hence the x-centroidal axis is .937 in. 
to the left of the right side of the channel iron.
For the moment of inertia about the rectangular area, 
(A<sub>1</sub>), x-centroidal axis is (1/12)hb<sup>3</sup>.
The moment of inertia of A<sub>1</sub> about the x axis is found by 
use of the transfer of axis theorem.
Note that d=3.375, the distance to the center of the member measured 
in the vertical direction.
Arithmetic is performed to get the final answer.
The moment of inertia of the vertical member is found.

The three moments of inertia are added. Notice that the moment of inertia of the first and third members are equal." >
Numeric values are substituted.
The total moment of inertia is found.
The moment of inertia of the first body about its centroidal axis is 
found.
The transfer of axis theorem is applied.
Numbers are substituted.  Notice that d = 1.5-.937.  1.5 is the 
distance from the centroidal axis of body 1 to the right side of 
the body and .937 was the distance found in the first step.
The moment of inertia of body 2 about its own centroidal axis is found.
The transfer of axis theorem is used.
Numbers are substituted.
The three moments of inertia are added to obtain the total.
Numbers are substituted.
The final answer is found.