10 in 5) Find the centroid ( â, ŷ ) and Ix for the shape shown. Use a large rectangle and a small negative rectangle (which should have negative area and negative I, ) and the origin a shown. 4 in 6 in 10 in 15.5 in /6.5 in 1 5 in

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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Find the centroid (ˆˆ,xy) and Ix for the shape shown. Use a large rectangle and a small negative rectangle (which should have negative area and negative xI) and the origin a shown.

 

If the shape in problem 5 is used for a beam with Mmax = 25 k-ft, what is the maximum bending stress?

10 in
5) Find the centroid ( î, ŷ ) and Ix for the shape shown. Use a large
rectangle and a small negative rectangle (which should have
4 in
negative area and negative I) and the origin a shown.
6 in
10 in
6) If the shape in problem 5 is used for a beam with Mmax = 25 k-ft,
what is the maximum bending stress?
15.5 in
5 in
ul t
Transcribed Image Text:10 in 5) Find the centroid ( î, ŷ ) and Ix for the shape shown. Use a large rectangle and a small negative rectangle (which should have 4 in negative area and negative I) and the origin a shown. 6 in 10 in 6) If the shape in problem 5 is used for a beam with Mmax = 25 k-ft, what is the maximum bending stress? 15.5 in 5 in ul t
Expert Solution
Step 1

Solution:

Let large rectangle area  A1=10×15.5=155in2

Let small rectangle area A2=6.5×6=39in2

Mechanical Engineering homework question answer, step 1, image 1

We need to find the position of centroid x' and y' from the x-axis and y-axis shown in above figure.

To find x-coordinate of the centroid 

x-coordinate of centroid of area A1 (x1)=102=5in

x-coordinate of centroid of area A2 (x2)=4+62=7in

Then position of x-coordinate of the centroid of the section is given by,

x^=A1x1-A2x2A1-A2=155×5-39×7155-39=4.327in

 

To find y-coordinate of the centroid 

y-coordinate of centroid of area A1 (y1)=15.52=7.75in

y-coordinate of centroid of area A2 (y2)=5+6.52=8.25in

Then position of y-coordinate of the centroid of the section is given by,

y^=A1y1-A2y2A1-A2=155×7.75-39×8.25155-39=7.581in

The position of centroid is (4.327,7.581)

 

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