Allowable bending stress of rectangular plate

[PostFrameSE]

I'm using the 9th edition of the AISC steel manual and am getting myself all confused. I have a situation where I'm trying to use a steel .25" x 2.5" steel plate to stiffen an aluminum "beam" in bending. I'm orienting the plate such that I'm loading it in bending along the strong axis, where my Mom of I = .325in^4. I can only laterally brace this piece at 12" intervals. I suspect that when this thing is bent about the strong axis that my compression edge(not sure I can call it a flange as I'm basically just analyzing a prismatic rectangle) is going to buckle out of plane. I'm confused as to what my allowable bending stress would be for 36ksi plate steel.

How do I look at this in regards to Table B5.1? Do I even need to? It seems to me that I need to look at the "Unstiffened elements simply supported along one edge......." which gives me a limiting width-to-thickness ratio of 76/Fy^.5. Is that right? If so, then what do I do with that then in Chapter F? There is no axial load carried by this piece.....only bending.

Thanks for your help.

 

[nutte]

As you've noticed, the 9th edition doesn't do a good job of addressing strong-axis bending on a rectangular plate. Use the 13th edition, where specification F11 does deal with this case, including lateral torsionla buckling.

 

[PostFrameSE]

Wish I had one!

 

[rb1957]

remember too, dissimiliar materials ... "rule of mixtures"

 

[ash060]

PostFrameSE

The 2005 specification is available from AISC's website for free.

The manual tables are not there, but all of the spec is and that is all you need.

 

[racookpe1978]

Dissimilar metals corrosion and expansion/contraction - plus the extreme difficulty of 100% joining of the reinforcing plate (in steel) to the (more flexible!) aluminum base structure?

I don't recommend this configuration at all. Better to use a thicker Al plate. Then weld the Al-Al.

 

[DHKpeWI]

Be careful when designing welded aluminum sections.

Depending on the type of weld (longitudinal or transverse) the allowable stresses of a welded section can be significantly reduced. See the Aluminum Design Manual.

 

[JAE]

PostFrameSE - simply go to this link:

http://www.aisc.org/content.aspx?id=2884

...and download the FREE AISC specification (Specification for Structural Steel Buildings (ANSI/AISC 360-05)
) which is inside the 13th Edition.

 

[PostFrameSE]

I appreciate all of your responses. I'm dealing with a 2.5" x .25" thick member bent about the strong axis. Given 36ksi steel, a Cb=1.0 and Lb=12", could somebody confirm that my calcs are correct, in that my allowable bending stress would be 29,246psi and my moment capacity is 7,604in-lbs? If that's right, I'm comfortable with this methodology.

Thanks

 

[slickdeals]

Lb*d/t^2 = 480 < 1.9 E/Fy
Z= bt^2/4 = 0.3906 in^3
FyZx = 14.0625 k-in

I am getting an Mn based on equation F11-2 19.0791 k-in.

 

[PostFrameSE]

Thanks slickdeals,

If I break out my formula more it would look like this:
Mn = [1.52 - .274(480)*36/29,000]*My

That becomes 1.3567*My

My I believe should be 36*.26 = 9.36in-k since Sy=.25*2.5^2/6 = .26

Did you use Mp rather than My???

Therefore, I think Mn = 1.3567*9.36 = 12.69in-k.

My allowable moment capacity = 12.69/1.67 = 7.6in-k.

Assuming I'm wrong and you're right, where did I go wrong?

Thanks

 

[BAretired]

Ref. Theory of Elastic Stability by Timoshenko and Gere

For pure bending of a narrow rectangular section about its major axis:

M_cr = [&pi;][&radic;](E*Iy*G*J)/L

E = 29,000,000 psi
G = 12,000,000 psi
Iy = b*h³/12 = 0.003255 in^4
J = b*h³/3 = 0.01302 in^4
L = 12"

So M_cr = 31,800"# > My = 9375"#

Plastic moment, Mp = 14060"#

For an unbraced length of 12", lateral buckling does not appear to govern, so you can use the allowable stress specified by your code. I would not expect it to be as high as 29,246 psi, however.

BA

 

[slickdeals]

PostFrameSE:
Yes, you are right. It appears My should be used and not Mp because you are not reaching Mp.

 

[PostFrameSE]

Hopefully this is my last question. If we can agree that the yield moment is around 7.6in-k (including the 1.67 reduction factor), doesn't it follow that the allowable fiber bending stress is = to the M / S? If S is = .26in^3, then the fiber bending stress has to 29.2ksi right? Am I missing something BA??

Thanks all.

 

[nutte]

Your nominal moment, Mn, is higher than the yield moment, My, but not all the way to the plastic moment, Mp.

So, in theory and in line with the factor of safety, your stress diagram will not be linear. The extreme fiber stress will be 21.6 ksi (Fy/1.67). As you come down the member from the top fiber, the stress will remain 21.6 ksi, until you reach a point where it does start to decrease, until you have zero stress at the neutral axis.

In actuality, the extreme fiber stress is 29.2 ksi. Since this is below yield, the stress diagram will remain linear.

 

[BAretired]

PostFrameSE,

The moment, 'My' at first yield is:

My = Fy*S = 36,000*0.2604 = 9.375"k

I don't use the AISC code and I don't use ASD, so I can't remember for certain, but as I recall, the maximum allowable stress you can use is Fy/1.67 = 21.65"k which corresponds to an allowable moment of 5.6"k. This would suggest that one of us is missing something.

BA

 

[westheimer1234]

am kinda lazy to look for it.. where can i find how they come up with 0.75 for base plate

baseplate ASD
Fb = 0.75 Fy

 

[paddingtongreen]

westy, that is in the compact shape direction, he is bending in the other direction, the non-compact direction.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[nutte]

BA, the AISC equation is checking for lateral torsional buckling, which does control.

If it did not control, you'd be allowed to go to Mp, not just My, in which case the allowable moment would be 50% higher than the values you listed.

 

[BAretired]

nutte,

The original question in this thread was in respect to allowable stresses. Under no circumstances would you be able to go to Mp if you are using ASD. The maximum allowable stress using ASD is Fy/1.67 as I understand it.

As for the AISC equation, I can't comment because I don't have it, but the equation I provided earlier was for lateral torsional buckling of a narrow rectangular section according to Timoshenko and Gere. Are you saying it is wrong?

BA