For the shaded area, determine the moments of inertia with respect to the given x and y axes.

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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 For the shaded area, determine the moments of inertia with respect to the given x and y axes.

PLEASE FOLLOW THE FORMAT FOR SOLUTION

1"
6"
3"
1"
2"
4"
Transcribed Image Text:1" 6" 3" 1" 2" 4"
2. Determine the moment of inertia of the T-section
shown in the figure about its centroidal X, axis.
Also, compute the radius of gyration of the area
with respect to the Xo axis.
-Xo
Solution:
-Xe
dz
The area can be dividded into two rectanales. I, for a rectangle isbh.
Solve first for the location of the centroidal axis xe
Y, in
7.
1, int
d, in
di=2
Ad, in
48
Parts
Area, in?
Ay, in
12
84
1
17(6)(2)' = 4
12
3
36
da=2
48
ㅎ(2)(6)"= 36
Total
24
120
40
96
120
24
ý= 5 in
Iso = 2ī, + ĽAd²
= 40 + 96
Io = 136 in*
Radius of gyration:
xo
136
sample format
24
Txe = 2.38 in
Transcribed Image Text:2. Determine the moment of inertia of the T-section shown in the figure about its centroidal X, axis. Also, compute the radius of gyration of the area with respect to the Xo axis. -Xo Solution: -Xe dz The area can be dividded into two rectanales. I, for a rectangle isbh. Solve first for the location of the centroidal axis xe Y, in 7. 1, int d, in di=2 Ad, in 48 Parts Area, in? Ay, in 12 84 1 17(6)(2)' = 4 12 3 36 da=2 48 ㅎ(2)(6)"= 36 Total 24 120 40 96 120 24 ý= 5 in Iso = 2ī, + ĽAd² = 40 + 96 Io = 136 in* Radius of gyration: xo 136 sample format 24 Txe = 2.38 in
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