Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

796
gEOMETRIC PROPERTIES
OF AN AREA
found by using the parallel-axis theorem. The moment of inertia for the composite area is
equal to the sum of the moments of inertia for the constituent shapes:
2
I =Σ ( I + d A)
c
If an area such as a hole is removed from a larger area, then its moment of inertia must be
subtracted in the summation above.
mecmovies
ExAmpLES
the Moment of inertia Game: Starting from Square one
A.4 A game that helps to build proficiency in moment of
inertia calculations for composite areas made up of rectangles.
A.5 Determine the centroid location and the moment of inertia
about the centroidal axis for a tee shape.
ExAmpLE A.2
30 mm
Determine the moment of inertia about the z and y axes for the flanged
shape shown in Example A.2.
71.0 mm
47.0 mm
z
y
6 mm
18 mm
90 mm
10 mm
Plan the Solution
In Example A.1, the flanged shape was subdivided into three rectangles.
The moment of inertia of a rectangle about its centroidal axis is given
by I c = bh 3 /12. To compute I z , this relationship will be used with the
parallel-axis theorem to compute the moments of inertia for each of
the three rectangles about the z centroidal axis of the flanged shape.
These three terms will be added together to give I z for the entire shape.
The computation of I y will be similar; however, the parallel-axis theorem
will not be required since the centroids for all three rectangles lie on the
y centroidal axis.
90 mm