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# Question about the interaction ratio for combined compression axial and moment formula4

## Question about the interaction ratio for combined compression axial and moment formula

(OP)
Hi there

I'm using the following formula from the AISC for the combined axial compression + moment

(a) when Pr/Pc ≥ 0.2

Pr/Pc + 8/9 ( Mrx/ Mcx + Mry/ Mcy ) ≤ 1.0

(b) when Pr/Pc < 0.2

Pr/2Pc + ( Mrx/ Mcx + Mry/Mcy ) ≤ 1.0

I have all the values ready to just plug and compute. The only one I am confused about is " Mcx " which is the available flexural strength in the strong axis "x" according to the AISC. I was able to find Mcy (the available flexural strength in the weak axis) no problem by using table 3-4, as it clearly states that the selection is by Zy. I looked up my value under ΦMn of course since I am using LRFD, when I was using table 3-4. SO then I went on to look for my Mcx value and I thought I could just go to table 3-2 since it says "selection by Zx" but I see 2 LRFD values for flexural strength, one marked Mrx and one with Mpx and so I assume that I have to be looking for Mn to apply to my interaction ratio formula . Should I just use table 3-10? since table 3-10 has the Mn . Any comments ? thank you

### RE: Question about the interaction ratio for combined compression axial and moment formula

Your strong axis moment capacity will depend upon the unbraced length you have for the member.
The unbraced length determines whether your member will fail in yielding or via lateral torsional buckling (assuming the shape is compact).

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### RE: Question about the interaction ratio for combined compression axial and moment formula

Z is the plastic section modulus. You can't use the plastic section modulus if your section buckles before it yields. As JAE mentioned, you need to make sure global buckling and local buckling are satisfied if you are going to be able to take advantage of the plastic strength of the section. Very dangerous to overlook buckling failure modes. You need to look at the graphs which plots phiMn with unbraced length. Be very careful with the tables - read the instructions before each. They will tell you important things such as self-weight not being included in the table capacities.

-Mac

### RE: Question about the interaction ratio for combined compression axial and moment formula

At the risk of making this too easy, check out Table 6-1 and the corresponding commentary. All information should be there in one place. As others have mentioned pay close attention to unbraced length for compression and flexure.

### RE: Question about the interaction ratio for combined compression axial and moment formula

All the "available" parameters in the equation (Pc, Mcx, and Mcy) must account for the unbraced length of the member.

You can use Table 4-1 for Pc (based on the unbraced length in both axes).
You can use Table 3-10 for Mcx (based on the unbraced length in the x-axis).
[EDITED] Find Mcy from Table 3-4 (see Hokie's post below)

Often with beam-columns you only have compression and strong axis bending so determining Mcy is typically unnecessary because you don't usually have Mry.

### RE: Question about the interaction ratio for combined compression axial and moment formula

(OP)
Okay thank you guys!

### RE: Question about the interaction ratio for combined compression axial and moment formula

As other people have noted the tables are a great tool but you need to understand how to use them and what their limitations are. I would advise going into the spec section (360-10) and cranking those numbers out by hand and then comparing them to the tables. That's the best way to learn and gain confidence in using the tables.

### RE: Question about the interaction ratio for combined compression axial and moment formula

Just a point of clarification regarding Mcy, the available flexural strength about the weak or y-axis. Since structural members do not experience lateral-torsional buckling about the weak axis, Mcy does not depend on an "unbraced length". Mcy is governed by yielding of the section or flange local buckling.

### RE: Question about the interaction ratio for combined compression axial and moment formula

Hokie, good point. Should make determining Mcy as easy as it gets.

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