Calculating Q (first moment of inertia) above and below the neutral axis

In summary, the conversation discusses the calculation of Q, the first moment of inertia, for a shape made of 2 plates. The Q above and below the neutral axis should be equal, but the calculated values are not. The mistake is found in the calculation of Q above, where the distance from the centroid to the N.A. was incorrect. The correct distance is 3.875 inches, not 2.75 inches. The individual seeking help is grateful for the guidance and the opportunity to figure out the mistake on their own.
  • #1
tn3003
2
0

Homework Statement



This is the cross sectional are of the shape: http://img38.imageshack.us/i/shapep.jpg/"
It's made of 2 10"x1" plates. (Picture is not to scale)

Q (first moment of inertia) above and below the neutral axis should be the same. For some reasons, my calculated Q above is not equal to Q below the NA.


The Attempt at a Solution



Taking the datum at the bottom

y bar = (10*0.5 + 10*6) / (20) = 3.25"

Q above = 7.75 * 2.75 = 21.31

Q below = 2.25 * (2.25/2) + 10 * 2.75 = 30.03

21.31 =/= 30.03

Someone please point out my mistake.
 
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  • #2
Your Q below is corect, but in calculating thte Q above, the distance from the centroid to the N.A. is not 2.75. I think you may have just written down the wrong number.
 
  • #3
OK I see it now. The distance for Q above should be 7.75"/2 = 3.875"
I was using the centroid of the whole shape, which gave me 7.75" - 5" = 2.75" and that's wrong.

Thank you PhanthomJay for not giving out the answer and let me figure it out myself. I really appreciate it.
 
Last edited:

1. What is Q and why is it important in calculating moment of inertia?

Q represents the first moment of inertia and is a measure of an object's resistance to rotational motion. It is important because it determines how much force is needed to rotate an object about its axis.

2. How do you calculate Q above and below the neutral axis?

To calculate Q above the neutral axis, you need to multiply the area of the section above the neutral axis by the distance from the neutral axis to the centroid of that section. To calculate Q below the neutral axis, you need to multiply the area of the section below the neutral axis by the distance from the neutral axis to the centroid of that section. Finally, add these two values together to get the total Q value.

3. What does the neutral axis represent and why is it important in calculating Q?

The neutral axis is an imaginary line that divides an object into two equal sections, with one above and one below. It is important in calculating Q because it helps determine the centroid of each section and the distance from the neutral axis to the centroid, which are both necessary in the Q calculation.

4. How does Q affect an object's moment of inertia?

The larger the Q value, the greater the moment of inertia of an object. This means that it will require more force to rotate the object about its axis, making it more resistant to rotational motion. Conversely, a smaller Q value indicates a lower moment of inertia and less resistance to rotation.

5. Can Q be calculated for any shape or only certain ones?

Q can be calculated for any shape, as long as the shape is symmetrical about the neutral axis. This includes shapes such as circles, rectangles, and triangles. However, for irregular or asymmetrical shapes, Q cannot be calculated and other methods must be used to determine the moment of inertia.

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