AISC equations F4-9a and F4-9b?

[SteelPE]

I have an instance where I need to reinforce an existing beam. The building was constructed back in 1984 and consists of cantilever beam construction. I am trying to increase the load on the beam and I am getting killed by the unbraced length of the bottom flange (I am using the distance between the supports). My solution, at the moment, is to weld a plate on the bottom flange of the beam. I would like to avoid having to weld something to the top flange as there are stiffeners at the supports making continuity of the reinforcing difficult.

The problem I am having is with equation F4-9a and F4-9b of the AISC 13th edition manual in particular how these equations relate to table B4.1 case 11. In my instance for negative bending over the support I end up with the PNA in the flange of the beam therefore I do not know what to use for lam-pw. If I don't know lam-pw then I don't know if I should use equation F4-9a or F4-9b...... I am guessing that I would use F4-9a but I am not sure.

 

[JAE]

My guess would be that hp is zero.

In other words, your web never gets any compression in it so web buckling isn't a consideration and you'd use equation F4-9b.

 

[SteelPE]

JAE,

Are you sure a hp=0 would push you to equation F4-9b? My centroid is within the web, but my PNA is within the flange. Therefore I do have a value for hc but don't know what value I should use for hp in table B4.1 case 11.

 

[JAE]

So I guess you are saying that [λ]p would go to infinity with the hc/hp ratio exploding since hp = 0?

Thus you would always be less than [λ]p and use F4-9a?

I think this makes sense.

You might try contacting Dr. Don White who's paper/research formed the basis of the values in Table B4:

http://www.ce.gatech.edu/people/faculty/491/cv

 

[SteelPE]

Thanks JAE,

After some discussions with others I have decided to stay away from trying to reinforce my existing cantilevered beam and just install a new beam under the existing. This has to do with minimizing welding on the thin members of the existing beam (3/16" thick flanges). The existing structure is a metal building and I was trying to reinforce the rake beam for additional drift loading.

 

[JAE]

SteelPE - even though you are going with another option - the question you raise is a good one. I might like to see what the correct answer is. Perhaps I'll try to contact Dr. White with the question.