Question
Asked Feb 27, 2020
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Problem 4
2"
2"
8"
For the given cross sectional
area,
find:
(1) Centroid location measured from bottom
(2) What is the moment of inertia around centroidal axis (I,
6"
only)?
8"
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Problem 4 2" 2" 8" For the given cross sectional area, find: (1) Centroid location measured from bottom (2) What is the moment of inertia around centroidal axis (I, 6" only)? 8"

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Expert Answer

Step 1

Divide the given member into three different rectangular section:

Civil Engineering homework question answer, step 1, image 1

Step 2

Calculate the individual area and the distance of the CG from the x and y-axis of the rectangular sections.

Rectangle 1:

A1 = 12 x 2 = 24 in2

x1 = 12/2 = 6 in.

y1 = 2/2 = 1 in.

Rectangle 2:

A2 = 2 x 6 = 12 in2

x2 = 2/2 = 1 in.

y2 = 2 + 6/2 = 5 in.

Rectangle 3:

A3 = 2 x 6 = 12 in2

x3 = 2 + 8 + 2/2 = 11 in.

y3 = 2 + 6/2 = 5 in.

Step 3

Calculating the centroid position from the left and from the bottom position:

Civil Engineering homework question answer, step 3, image 1

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