Calculating theoretical principle second moments of an L shaped section

[Roomie]

Homework Statement

Hi, I'm trying to complete my laboratory write up over my christmas break, and I'm struggling to understand how to do part of it. I emailed the lab demonstrator on December 9th, and the head of labs on the 18th and I've had no reply off either, so I'd really appreciate it if you guys could try and help me!

I need to calculate the theoretical value of the principle second moment of area for an L shaped section. Using a Mohr's circle apparently.

Here is a scan of the lab sheet explaining what I need to do.. I just don't understand how:

Homework Equations

http://dl.dropbox.com/u/630750/Screen%20Shot%202011-12-23%20at%2010.08.40.png

The Attempt at a Solution

If someone can try to explain what I'm supposed to do that would be so helpful! Thank you.

 

[vela]

The lab sheet seems pretty straightforward:

1. Calculate I_A.
2. Calculate I_B.
3. Calculate I_{AB{/sub].
   [*]Follow the instructions on how to construct Mohr's circle from those values.}
   

_{What part are you having trouble with and what specifically is the problem?}

 

[Roomie]

The lab sheet seems pretty straightforward:

1. Calculate I_A.
2. Calculate I_B.
3. Calculate I_{AB{/sub].
   [*]Follow the instructions on how to construct Mohr's circle from those values.}
   

_{What part are you having trouble with and what specifically is the problem?}

<sub>Thanks for the reply, I just don't know how to calculate IA, IB or IAB.

Is there a formula I should know?</sub>

 

[vela]

Do you know how to calculate the moment of inertia about an axis?

 

[Roomie]

Do you know how to calculate the moment of inertia about an axis?

It isn't something I've done a considerable amount of work on, I'm used to using the formulas for common shapes such as beams & cylinders.

But looking through my textbook I've found some examples.

They demonstrate using Ix and Iy, but they're Ia and Ib in my problem I think.

They split it up into sections and then sum them?

using http://dl.dropbox.com/u/630750/Screen%20Shot%202011-12-23%20at%2014.00.29.png

If that's right, how do I get I_AB from that? Average them? Or add them?

Plus how do I convert these values from IA and IB to the proper Ix and Iy?

Thanks for your help!

 

[vela]

It isn't something I've done a considerable amount of work on, I'm used to using the formulas for common shapes such as beams & cylinders.

But looking through my textbook I've found some examples.

They demonstrate using Ix and Iy, but they're Ia and Ib in my problem I think.

Right. x, y and A, B are just labels for the axes.

They split it up into sections and then sum them?

using http://dl.dropbox.com/u/630750/Screen%20Shot%202011-12-23%20at%2014.00.29.png

Yes, that's what you want to do to find I_A and I_B. The moments of inertia about the center of mass for common shapes are tabulated, so there's no need to derive them again. For an axis that doesn't pass through the center of mass, you use the parallel-axis theorem.

If that's right, how do I get I_AB from that? Average them? Or add them?

By definition, you have
$$I_{AB} = \int_A ab\ dA$$which for a rectangular section turns out to be $I_{AB}=a_\mathrm{cm}b_\mathrm{cm}A$. So, again, calculate I_AB for each piece and then sum them.

(Sometimes, you'll see a negative sign in the definition. It shouldn't matter here though.)

Plus how do I convert these values from IA and IB to the proper Ix and Iy?

You use Mohr's circle.

 

[Redbelly98]

Moderator's note: thread moved to Engineering, Comp Sci, & Technology

In the future, please post engineering homework in Engineering, Comp Sci, & Technology instead of Introductory Physics