ASCE 7-10 Redundancy Factor for 2-story X 1

[mbozzo]

A colleague and I were discussing this the other day. For the redundancy factor, ρ (rho) per ASCE 7-10, §12.3.4.2, option (b) states that if the SFRS consists of two bays of seismic force-resisting framing on each side of the structure, you can use a ρ = 1.0. Consider a steel OCBF configured in a 2-story X (e.g. figure C-F2.2 (a) of AISC 341-10). Can that be considered two bays? I've always assumed it cannot, because I usually think of one "bay" as being bounded by columns on each end. He posits that it can, because you have two braces, which act in both tension and compression. I looked through the commentary and couldn't find any further guidance. What are your opinions?

 

[mike20793]

In a single bay moment frame, there are two moment connections. Isn't that along the same logic your colleague is using? I agree with you that it needs to be bounded by columns on either end to constitute a bay, but this is a good question and I'm interested in other people's opinions.

 

[ajh1]

I think the answer is in ASCE 7-10 Table 12.3-3:
To meet the rho = 1.0 rule, removal of any one brace will not reduce the story strength more than 33%. That implies at least 4 elements taking load in a given plane. Realistically, removal of one tension brace when two tension and two compression braces are present might actually violate the 33% rule also depending on the relative tensile vs. compressive capacities. The two story X is basically one bay of an inverted V configuration on the first story and a V configuration on the second story.

 

[mbozzo]

I think the answer is in ASCE 7-10 Table 12.3-3:

You are correct in the sense that this is one way to determine whether or not you can use a ρ=1.0, but this option could require a fair amount of analysis depending on the building layout. Thus, for more regular structures, the code offers a second option to determine rho. The second option (the one I'm referring to in my question) requires no calculations or analysis to determine the value of rho.

That's a lot of words to essentially say you didn't quite answer my question. My question is this: assuming one is trying to use part (b) without further analysis of that code section, would a two story X frame count as two bays?

 

[jayrod12]

I would argue no. Two bays to me means there should be two locations in the same framing storey that are braced. Two stacked vertically don't provide any redundancy, which is what I gather the code is attempting to provide.

 

[WillisV]

No.

 

[KootK]

I vote no as well. A two story X looks a lot like an inverted chevron at the low floor. And that certainly wouldn't qualify for two-brace treatment. A two story X is, of course, a better system than stacked chevrons but I don't feel that's germane to the redundancy conversation. The only argument to the contrary that I can think of is a comparison to how concrete shear walls are treated. A single wall, if it's long enough, can be treated as two walls. A two story X brace is likely to be longer than one multiple of the story height.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[ajh1]

I would concur with the others that "two bays" must be two bays at the same story. Consider that the two conditions should logically be expected to result in about the same amount of bracing present.