Mechanics of materials centroidal question

[EITintraining]

Homework Statement

a beam is 12 cm wide and 10 cm long. Find the neutral axis, the area centroid and the distance between them.

Homework Equations

Yc=h/2

The Attempt at a Solution

Yc=10/2=5 cm.
I can't seem to find the area centroid of a rectangle. Any help? Thanks!

 

[pongo38]

Your question isn't clear to me. Do you mean "beam section"? The neutral axis would be a neutral plane, depending on the direction of loading. On the other hand, it seems a very trivial question. What do you think the answer is? If you were answering this in an exam, and had 15 seconds to answer it, what would you say to get a possible mark?

 

[EITintraining]

Well I thought that the answer would be the same for the neutral axis as for the area centroid, h/2. But the answer in the back says the area centroid is actually h/4. So the area centroid is half of the distance from the neutral axis?

 

[pongo38]

There is a proof (in my strength of materials book) that, under pure bending, the neutral axis is coincident with the centroidal axis. The circumstance in which this is not the case is when there is a combination of axial load and bending, The book could be wrong, as many authors in this forum will attest. On the other hand, the question could be a clumsy attempt to get you to look hard at the fundamentals. See if you can find that proof, and then go and teach it to an interested friend.

 

[DeeNos]

The area centroid of a rectangle is located at the intersection of its diagonals. In this case, the centroid will be located at the center of the rectangle, which is (6 cm, 5 cm). The distance between the centroid and the neutral axis (also known as the neutral axis offset) can be calculated using the formula: h/2, where h is the height of the rectangle. In this case, the distance would be 5 cm. It is important to note that the neutral axis of a rectangle is always located at the centroid of the shape. I hope this helps!