How to Calculate Elastic Positive Bending Moment for Irregular Cross Sections?

[Temoor]

Hello
I just joined this forum and this is my first thread here. This is my assignment question. I'm supposed to find elastic positive bending capacities around the horizontal axes for the following cross section shown in pic. The elastic stress in tension is 10 ksi and in compression is 15 ksi. First i calculated "I" that is second moment of inertia, then i substituted in Moment = (I) x(stress) divided by c. I also have problem finding in c, because vertical length is not same. I posted my attempt as well.

 

[SteamKing]

Your calculations should ALWAYS have units attached to the quantities.

 

[Temoor]

Sure. But what about my method? is it correct? I don't know how to fund centroid :S

 

[SteamKing]

Since the section is not symmetrical about the horizontal axis, it looks like you have calculated the moment of inertia incorrectly. Your horizontal axis should be through the centroid of the section, which you haven't determined.

The rule at PF, and there is a template here:
https://www.physicsforums.com/showpost.php?p=3977513&postcount=2

you should try to post the entire problem as given to you without paraphrasing it if possible.

 

[SteamKing]

Sure. But what about my method? is it correct? I don't know how to fund centroid :S

If you don't know anything about centroids, no, your method is not correct.

First moment of area? Does that ring a bell?

If you've studied how to calculate moment of inertia (or the second moment of area), you must have studied what the first moment of area is used for and how it is calculated.

 

[Temoor]

i know how to find centroid, but in this case as you can see the lower side its thickness is 2 inches and for upper it is 1 inces, In this case i don't know how to find it.

 

[Temoor]

sure i will post photo of entire problem now.

 

[SteamKing]

i know how to find centroid, but in this case as you can see the lower side its thickness is 2 inches and for upper it is 1 inces, In this case i don't know how to find it.

Your statement contradicts itself.

Review this pdf and see if you can't figure out how to calculate the centroid of your section:

http://www.ce.memphis.edu/3322/Pdfs/PaulsPDFs/Centroids and Moment of Inertia Calculation.pdf

 

[jtbell]

Please write out the text of the problem, instead of just posting a photo of it. It's OK to use a photo for diagrams that you can't simply "write", but it's not OK to use a photo for the whole thing.

Check your private messages by clicking the "Notifications" link at the top right of this page.

(Aside to other readers: this post was moved here from one of the non-homework forums, which is why it doesn't follow the usual template for the homework-help forums.)

 

[Temoor]

@jtbell: It won't happen next time.

 

[pongo38]

As people use different sign conventions, you should state yours. Does 'positive' mean 'tensile' or 'compressive'?

 

[Temoor]

Positive mean tensile and negative means compressive but my method above is wrong.

 

[Temoor]

@steam king: This is my calculation of centroid. See it i calculated it right?

 

[Temoor]

Please help me, i have to submite this question tomorrow. It holds 20 percent of my total grading. Please help me.

 

[SteamKing]

I'm sorry, but you are still not understanding the correct method of calculation for the centroid.

You chose the long way to calculate the centroid by splitting up the section into four pieces. This is fine, although the long way, but then you went and subtracted the void inside the section, which is incorrect.

Instead of re-doing all this work, find the first moment of the outer section and remove the inner void from it.

 

[Temoor]

Formula for finding moment of inertia is I = 1/12 bh^3 ?? Am I right?

 

[SteamKing]

Yes. But you still have to find the inertia of the section about its centroid, which means you've got to find the correct centroid location.

 

[nvn]

Temoor: Your centroid (y_bar) is currently incorrect. Recompute each number having a blue slash in the attached file. And recompute y_bar.

Your formula in post 16 is correct, but you still need to add the parallel axis theorem to it.