Engineering Statics

F-23


Two 102x102x12.7mm angles are welded to a 12mm steel plate as shown. Determine the moments of inertia of the combined section with respect to the centroidal axes respectively parallel and perpendicular to the plate.

The body shown is separated into three sections.  The channels are 
standard shapes, hence their areas and centroidal moments of inertia are 
gotten from tables.
The x centroidal axis is in the center by symmetry.  The y centroidal 
axis is found by use of the tabular method.
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 = 30 - 28.2 + 12.  30 is the distance from the bottom of 
the angle to the centroid.  28.2 is the distance from the bottom of 
the plate to the composite centroid (found in step 1) and 12 is the 
thickness of the plate.
The moment of inertia of the plate is found about its x centroidal axis.
The transfer of axis theorem is used from the plate.
The total moment of inertia is the sum of the three moments of inertia.
Numbers are substituted.  Note that the moments of inertia of bodies 1 
and 2 are equal.
Arithmetic is performed to get the answer.
The moment of inertia about the y axis is found for the angle by means 
of the transfer of axis theorem.
Numbers are substituted.  Note that d = (250/2) - 30.  250/2 is the center of 
the entire body and 30 is the location of the centroid of the angle as measured 
from the edge of the angle.
Numbers are substituted for the moment of inertia of the plate about the 
y axis.
The total moment of inertia is gotten by adding the three moments of inertia.
Numbers are substituted.
Arithmetic gives the final answer.