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]

Under ASD, you are allowed to go to Mp. In the old ASD, for a wide flange, this was done using 0.66 Fy for the allowable, being a 10% increase over the normal 0.6 Fy, correlating to a general ratio of Zx/Sx for wide flange shapes equal to 1.10.

Under the current AISC 13th edition ASD, you're allowed to go to Fy Zx / 1.67 for your moment, if LTB doesn't control.

In this case, using AISC's LTB equations, you get a nominal moment higher than My, but less than Mp.

I'm not as familiar with the Timoshenko/Gere equations, so I can't comment on them. Regardless, the AISC equations do say that LTB controls.

 

[BAretired]

nutte,

I wasn't aware of the change to ASD, but I admit it makes sense.

I cannot believe there is such a huge difference in results between AISC and Timoshenko for lateral torsional buckling. Could you post the AISC equation for comparison?

BA

 

[nutte]

Here you go. A previous section says phi=0.90 and omega=1.67.

 

[BAretired]

nutte,
I'm still trying to understand the difference between your reference and mine and, for that matter between your code and mine. The following is another reference on lateral torsional buckling which appears to tie in with Timoshenko and Gere:

http://www3.imperial.ac.uk/portal/pls/portallive/docs/1/2075917.PDF

BA

 

[nutte]

BA:

The Timoshenko equation you posted is the same as Equation F11-4 in the AISC specification. Equation F11-3, the one that applies to our specific case, must be an for an inelastic buckling region.

Timoshenko: Mcr = pi*?(E*Iy*G*J)/L

F11-4: Fcr = 1.9 E Cb / (Lb*d/t^2)

We can manipulate Timoshenko's equation as such:

Iy = d*t^3/12
G = E/2.6
J = d*t^3/3

Mcr = pi*E^0.5*(E/2.6)^0.5*(d*t^3/12)^0.5*(d*t^3/3)^0.5/L

Mcr = 1.948*E*d*t^3/6/L

Multiply both top and bottom by d, resulting in:

Mcr = 1.948*E*d^2*t^3/6/L/d

Replace d*t^2/6 on top with Sx:

Mcr = 1.948*E*t^2*Sx/(L*d)

Remove Sx, to get Fcr, and pull t^2 to the bottom.

Fcr = 1.948*E/(L*d/t^2)

For Cb=1, this is AISC's equation, with 1.948 rounded to 1.9.

 

[BAretired]

nutte,

Yes, thanks for that. I guess we are in the inelastic buckling range with this problem. Tricky little devil, isn't it?

BA