Which wood cross section can carry highest uniform load

[Blugga]

Which wood cross sectioπ caπ carry hïghest uπiform load

Homework Statement

Homework Equations

Moment of inertia for rectangle I=(1/12)bh³
τ=(VQ)/(I*b)
σ=(MV)/I

The Attempt at a Solution

I started by finding reactions at B and C
Then drew the sheer and moment diagrams (to save space i made it a link)
http://oi47.tinypic.com/qsmkxh.jpg
To find which cross section can withstand the biggest q, I found the moment of inertia about the z axis (neutral axis) for each figure.
(A)I_z=2*{((1/12)*8*2³)+[(2*8)*3²]}+2*{((1/12)*8*2³)+[(2*8)*1²]}
I_z=341.33 in⁴

(B)I_z=2*{((1/12)*8*2³)+[(2*8)*3²]}+2*{((1/12)*2*8³)}
I_z=469.33 in⁴

(C)I_z=2*{((1/12)*8*2³)+[(2*8)*5²]}+2*{((1/12)*2*8³)}
I_z=981.33 in⁴

(D)I_z=2*{((1/12)*8*2³)+[(2*8)*9²]}+2*{((1/12)*2*8³)+[(2*8)*4²]}
I_z=3285.33 in⁴

Because both of the equations I posted for τ and σ are dependent on Inertia, I figured since that when solving for (q) we would have to multiply by Inertia so whichever cross section has the biggest Inertia will also have a bigger (q). Therefore, cross section (D) was the pick. Was I right to assume this?
τ_max=[(6.5q)*Q(0)]/[3285.33*2]=65; where Q(0)=208. not sure about that value
∴q=315 lb/ft
σ_max=[(34.125lb-ft)(12in/ft)q*10]/3285.33=1800
∴q=1444.10 lb/ft and so the max q can be is 315 lb/ft

This is my first attempt so any help is appreciated.

 

[phinds]

I can't help you with the math but I can tell you that in the real world D is what is always used when strength is needed.

 

[Blugga]

I can't help you with the math but I can tell you that in the real world D is what is always used when strength is needed.

I guess it kinda helps prove my point, but I was kinda looking for a more mathematical response :)

 

[nvn]

Blugga: Is this a take-home test question? I currently cannot match your x1 = 10.5, on your shear diagram, yet. Are you sure x1 is correct? Try again. Therefore, I cannot match your bending stress equation yet.

Your shear stress equation looks fine. Your moments of inertia look fine. How will you know which cross section can carry the highest q if you do not check them? You will just guess?

Was I right to assume this?

No, I do not think so.

 

[Blugga]

It's a sort of take home quiz. The book doesn't go into depth into how to find this sort of info for these shapes. It just explains briefly for 1 or 2 wood boards, and i have 4.

I think you may be right about the X1 being off. I think x1 will just be 10.5ft - 4ft. So x1=6.5ft.
Therefore, M_max=13.125q.
Also, i guess my reasoning was that from the bending stress alone cross section (D) would be greatest. But i didn't count that the glued joints would make all the difference. I did try to find q_max for each cross section (but with the wrong M_max) and ended up with cross section (C) carrying the highest q. I'll rework the new figures in the morning. Thanks for the help.

 

[Blugga]

Blugga: We usually should not help on quiz or test questions. The PF Rules link at the top of each page says, "Do not ask for answers to exams."

I understand that, but this isn't an exam. It's a take home quiz/assignment. It's worth a very small percentage of the overall grade, about 0.7% and I already had half right so you were only helping with 0.35%. Only reason I asked was because the book was of no help and there was no one else I could ask (TA's and professors never have time). I guess it's best to get things wrong and never figure out how to do them then to bend the "rules" a little... :uhh:

But thanks for the help you did provide.