Solving for y in A(total)*y(horz centroidal axis): Where Did I Go Wrong?

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In summary, the conversation discussed a problem with calculating the centroid of a rectangular piece with a circular hole. The approach used was to subtract the area and centroid of the circle from the overall area and centroid of the rectangle. However, it was noted that this approach requires knowledge of the centroid of a semicircle, which was not given in the formula list. It was suggested to instead calculate the area and centroid of the entire rectangle and then subtract the area and centroid of the circular hole. The conversation also clarified that the centroid of a circle is easy to calculate, as it is simply the center.
  • #1
smr101
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Hi, having problems with (a) here, I'll show my attempt:

A1 = (0.025 * 0.05) - ((pi*0.01^2)/ 2)
1.093 x10^-3 m^2

A2 = (0.075 * 0.05) - ((pi*0.01^2)/2)
= 3.593 x10^-3 m^2

A(total)*y(horz centroidal axis) = A1y1 + A2y2

y = 1.093 x10^-3 * 0.0875 + 3.593x10^-3 * 0.0375 /(4.686x10^-3)
= 49.19 mm

Correct answer is 48.32 mm, any idea where I've gone wrong?

Thanks.
kgH1n.jpg
 
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  • #2
smr101 said:
Hi, having problems with (a) here, I'll show my attempt:

A1 = (0.025 * 0.05) - ((pi*0.01^2)/ 2)
1.093 x10^-3 m^2

A2 = (0.075 * 0.05) - ((pi*0.01^2)/2)
= 3.593 x10^-3 m^2

A(total)*y(horz centroidal axis) = A1y1 + A2y2

y = 1.093 x10^-3 * 0.0875 + 3.593x10^-3 * 0.0375 /(4.686x10^-3)
= 49.19 mm

Correct answer is 48.32 mm, any idea where I've gone wrong?

Thanks.
kgH1n.jpg
You would be better off calculating the area and centroid of the entire rectangular piece and subtracting from that the area and centroid of the circular hole.
The centroid of a circle is easy: it's the center.

The way you did the moments originally, you need to know the centroid of a semicircle, which is not given in your formula list.
 
  • #3
SteamKing said:
You would be better off calculating the area and centroid of the entire rectangular piece and subtracting from that the area and centroid of the circular hole.
The centroid of a circle is easy: it's the center.

The way you did the moments originally, you need to know the centroid of a semicircle, which is not given in your formula list.

Right, so the centroid, y, of the circle is just 75mm?
 
  • #4
smr101 said:
Right, so the centroid, y, of the circle is just 75mm?
Yes. The dashed lines on the figure are just there to locate the center of the circle relative to other parts of the cross section.

The centroids of simple figures like circles and rectangles should be learned, not least because they are pretty obvious.
 

1. What is the purpose of solving for y in this equation?

The equation A(total)*y(horz centroidal axis) is used to calculate the horizontal centroidal axis of a shape. By solving for y, we can determine the location of this axis, which is an important factor in many engineering and design calculations.

2. Can you explain the term "centroidal axis" in this equation?

The centroidal axis is the line that passes through the center of mass of a shape. It is the axis around which the shape can be balanced, and is used to measure the distribution of mass within the shape.

3. How do I know if my solution for y is correct?

To check if your solution for y is correct, you can substitute it back into the original equation and see if it satisfies the equation. You can also compare your solution to the known values for the centroidal axis of the shape.

4. What are some common mistakes when solving for y in this equation?

One common mistake is incorrectly identifying the total area, A(total). This can lead to an incorrect solution for y. Another mistake is not considering the units of measurement, as the units for A(total) and y must be consistent.

5. Are there any other methods for solving for y in this equation?

Yes, there are multiple methods for solving this equation, including graphical methods, numerical methods, and calculus-based methods. The best method to use will depend on the complexity of the shape and the available resources.

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