AISC 360-16 - Ch. C Stability - Tau-b Stiffness Adjustment Factor

[Futzin]

The Direct Analysis Method is nothing new, so when I started digging around for interpretations of the subject requirement, I was surprised I didn't find any verbiage in any of the spec commentary, the front matter of the manual, existing eng-tips posts, AISC DG28, etc... to satisfy my intellectual curiosity.

Spec. Section C3(b) states that "(a)n additional factor, τ[sub]b[/sub], shall be applied to the flexural stiffnesses of all members whose flexural stiffnesses are considered to contribute to the stability of the structure." So what members are those? My initial interpretation was that in a moment-resisting frame structure, this provision applies only those beams and columns that comprise the moment frame(s). This would make sense since lateral stability of a moment frame is highly dependent on the beam/column stiffness ratios. For a braced frame structure, I initially thought this provision did not apply at all since stability is provided via the axial stiffness of brace elements; no LFRS members are resisting lateral loads via flexure.

Then the gears got turning and I begun questioning the validity of my interpretation. Take for instance collector element beams in a braced frame structure that transfer diaphragm forces axially to braced frame bays. Assuming these beams also support gravity loads, then they are subject to both axial and flexural forces. Although these flexural forces are not induced by lateral loads, they could be amplified due to P-small delta effects when carrying substantial axial load. I would certainly consider flexural bucking of a collector beam to compromise the stability of a structure.

Extending this thought to what could be considered a level of absurdity that I'm fairly confident isn't the intent of the code, does not the flexural stiffness of a column contribute to it's axial compacity even when not subject to transverse loading? After all, radius of gyration is a function of the moment of inertia... If that's true, then couldn't the failure of a gravity column cause a supported diaphragm to fail... so on and so forth.

Anyway, curious what the community's thoughts are here. I have a habit of wanting to know the exact intent of every code provision which sometimes leaves me down the proverbial creek w/o a paddle. Thanks.

 

[le99]

See note below C3(b):

User Note: Taken together, Sections (a) and (b) require the use of 0.8τb times the nominal elastic flexural stiffness and 0.8 times other nominal elastic stiffness for structural steel members in the analysis.

 

[Futzin]

@le99 - Right. The user note below C3(a) recommends applying the 0.8 factor to all member stiffnesses across the board to avoid artificial distortions. This is no big deal, easy to accomplish. The τ[sub]b[/sub] factor, however, is a function of the axial demands on each particular member the provision applies to. It cannot be applied across the board. The alternative is to apply the additional notional load in all load combos which penalizes the structure as a whole. In an effort to avoid the global penalization, and to reduce the workload of performing the iteration for all members, what members do Section C3(b) actually apply to?

Note: I'm aware software codes are available to perform the iteration automatically, but I'm not too fond of the "black box" nature of these code driven program features.

 

[le99]

I think the language is quite clear that the factor should apply to all "flexural" members (primary) as opposed to those elastic members (secondary), for which the dominant action/concern is axial. I could be wrong though.

 

[Settingsun]

The theoretical ideal is probably all members, but practically probably unbraced members is enough (by comparison to what is permitted in the effective length method).

 

[Futzin]

@steveh49 I'm coming around to that line of thinking. After reading through DG28 again, they seem to indicate the factor only comes into play for "heavily-loaded beam-columns". Running some numbers on the structures I'm working on, the P[sub]u[/sub]/A doesn't get anywhere close to 50% (two-story moment frame that's controlled by seismic drift). Perhaps this situation occurs more frequently in low seismic/low wind situations where the columns are proportioned primarily for gravity loads.