Engineering Statics

F-19


Determine the moment of inertia and radius of gyration of the shaded area with respect to the y axis.
The given area is separated into three distinct rectangles. 
The area of each rectangle and the total area are found.
For the moment of inertia about area 1's (A<sub>1</sub>) centroidal axis 
is (1/12)hb<sup>3</sup>.
The moment of inertia of A<sub>1</sub> about the y axis is the 
<i>centroidal moment of inertia</i> plus the terms for the transfer 
of axis theorem, A<sub>1</sub>d<sup>2</sup>.
Numeric values are substituted.
The moment of inertia of body A<sub>1</sub> about the x axis is found. 
The moment of inertia of body A<sub>3</sub> is equal to the moment of 
inertia of body one.  This saves us calculations.
The moment of inertia of A<sub>2</sub> about the x axis is the 
centroidal moment of inertia since the two axes coincide.
The three moments of inertia are added.
Numeric values are substituted.
The total moment of inertia is found.
The radius of gyration is the square root of the moment 
of inertia divided by the area.  It is the radius of a hoop 
which has the same moment of inertia as the given area.
Numeric values are substituted.
The radius of gyration is found.