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

ExAmpLE A.3
40 mm
Determine the moment of inertia about the x and y centroidal
axes for the zee shape shown.
6 mm
y
x
6 mm
30 mm
6 mm
Plan the Solution
After subdividing the zee shape into three rectangles, the moments
of inertia I x and I y will be computed using I c = bh 3 /12 and the
parallel-axis theorem.
SolutioN
The centroid location for the zee shape is shown in the sketch.
The complete calculation for I x and I y is summarized in the tables
on the next page.
40 mm
40 mm
(a) Moment of inertia About the x Centroidal Axis
18 mm
18 mm
(3)
6 mm
(2)
y
x
(1)
6 mm
30 mm
6 mm
I ci
(mm 4 )
⏐d i ⏐
(mm)
A i
(mm 2 )
d i 2 A i
(mm 4 )
I z
(mm 4 )
(1) 720 18.0 240 77,760 78,480
(2) 13,500 0 180 0 13,500
(3) 720 18.0 240 77,760 78,480
170,460
40 mm
40 mm
(b) Moment of inertia About the y Centroidal Axis
(3)
(2)
6 mm
17 mm
40 mm
y
17 mm
x
(1)
6 mm
30 mm
6 mm
I ci
(mm 4 )
⏐d i ⏐
(mm)
A i
(mm 2 )
d i 2 A i
(mm 4 )
I z
(mm 4 )
(1) 32,000 17.0 240 69,360 101,360
(2) 540 0 180 0 540
(3) 32,000 17.0 240 69,360 101,360
203,260
The moments of inertia for the zee shape are I x = 170,500 mm 4
and I y = 203,000 mm 4 .
Ans.
798