Moment Capacity Calculation of Cover Plate Reinforced Steel Beam?

[jayson34]

Hi Everyone,

Assuming there's a cover plate required on the bottom of a rolled I-beam, how should I calculate the capacity of the reinforced section? It's not a composite floor with shear studs, I only need to know the capacity of the reinforced steel section.

Since the reinforced section is now singly-symmetric, section F4 applies. Assuming a compact section and no LTB, limit state of compression flange yielding F4.1 should govern. However, I've seen people using the plastic section moment capacity. Also, AISC design guide 2 uses plastic section capacity for beams with web opening reinforcement where the sections are singly-symmetric.

The capacity based on compression flange yielding should be less than the plastic section moment capacity. I'm leaning toward using the code requirement, but it is conservative and will result in a very big cover plate.

Please help.

Thanks,
Jay

 

[dik]

Treat it as a composite section and weld the bottom plate to the W section as required to develop the composite action.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[BridgeSmith]

Calculate section modulus either as a composite, built-up section, or as you would a plate girder. It's pretty much the same thing; just depends on which approach is most familiar.

 

[jayson34]

Thanks for the replies. But I still don't think my question is addressed. The composite section is I-shaped, so section F4 of the steel spec needs to be checked. With compact elements and no LTB, compression flange yielding is going to govern, and the section capacity is based on the elastic section modulus for the top fiber. On the other hand, I've seen people using plastic section modulus for the entire composite section -- Do we know a code reference to back this up? The two different approaches will result in different cover plate sizes, obviously.

 

[Celt83]

You do use Section F4, and for the fully braced condition you are correct F4-1, compression flange yielding will govern however the Rpc term will usually end up as F4-9a which makes F4-1 simplify down to be equivalent to F2-1 so plastic section modulus ends up being applicable in a lot of instances.

F4-1: Mn = Rpc Myc

F4-9a: Rpc = Mp / Myc

Assuming F4-9a applies and Zx <= 1.6*Sx

F4-1, reduced: Mn = (Mp / Myc) * Myc = Mp

 

[jayson34]

Thanks, Celt83.

That makes sense, but if the initial sizing of the cover plate is too big, which makes Iyc/Iy<0.23, I can't rely on the web plastification factor per code. Is that correct?

 

[Celt83]

correct, but if you are adding that much additional steel plate area cover plating may not be your best reinforcing option. May want to look into adding a WT or if depth is constrained introducing additional floor beams to reduce the load.

 

[jayson34]

Thanks. I'm working on an exam prep question. The problem uses a 1-1/2" x 8" plate to reinforce a W16x40. In this case Iyc/Iy=0.16<0.23. The answer to the problem failed to check this ratio and just went directly using plastic section modulus. I mainly wanted to know if sticking to section F4 was the correct approach. Thanks again for your time and help.

 

[Celt83]

gotcha, ignore my example had the decimal place in the wrong spot, time for some coffee.

Email the example provider, or see if they have a published errata, that size cover plate is massive for the noted beam size.