Slenderness effect in column

[lutein]

Can anyone help me with this?
If I have analyzed the concrete structure with second order analysis and have also considered the cracking moment of inertia in the structure, can I use the short column design criteria for the column design? i.e. I can use the generated column tables in CRSI for short column.

Please help.
Thanks

 

[ishvaaag]

Theoretically yes since you have considered both the material and geometrical nonlinearities. That is, once properly and in consistent way with the analysis reinforced, you have proven you have a stable and strong enough structure at the factored level with all unfavourable phenomena considered, which is the target of life safety strength design.

So it is a matter of if the exact words in the enforceable code so permit, and the authorizing party is so wanting to admit, which may depend on a detailed exam of how you are entering the nonlinearities.

This said, the specified ways (through moment magnification) guide around ways of combination etc and it is good to keep an eye on them in any case.

 

[JAE]

Well...I'd say no...because you have not included second order effects along your column length.

If you modeled the frame using a two-joint stick element for your column (one joint at one floor and one joint at another floor) and performed a PDelta analysis on that frame, even with a reduced set of column section properties you have ONLY included second order effects due to sway-type deflections in the frame. You have not included the second order effects along the length of the member due to member distortions.

If you study the ACI code in chapter 10 you'll notice that they differentiate between the sway on non-sway frames and between sway and non-sway moments. When your frame sways sideways, you get a "delta" that is the story to story deflection. Thus, the axial load in the column "P" produces additional moment from that delta. But as your column gets more slender, it too will distort/deflect along its length and there will be a whole series of small "deltas" that also have that same axial load.

Imagine you have zero sway - no PDelta forces from sway. And you have a perfectly straight, stiff column - no "local" PDelta moments. Now assume that instead of the stiff, straight column, you have a curved or arched, thin column &quot". Still no sway, but you now have enormous secondary moments from any axial load applied.

Your computer model is NOT aware of these local deltas and the additional moment is not modeled unless you create your columns using a whole series of short segments, with joints located along the length of the column. Thus, as your matrix is solved, your model will truly generate both sway and non-sway second order effects.

See also the discussion in this thread:

thread167-5334


If you account for both of these effects, then yes, you could do your design assuming you have included magnified moments and simply use the CRSI tables OR you could use a program like PCACOL and assume a non-slender column (since you've already accounted for slenderness and sway in your model).

 

[ishvaaag]

I assumed in-member P-delta was included in the analysis, trough modeling of segments of representative inertias congruent with factored solicitations. If not, what JAE indicates respect in-member P-delta is paramount.

I however think special moment magnification is not anymore required, the moments resulting from the analysis -with short segments in the model, except if segments of an arch- are those that through amplification the simplified analysis tries to mimick, and you have them directly from analysis, once with effective sections congruent with the factored forces.

JAE is right in that you need to account for in-member buckling of the short segments -or use moment magnification for the stubby segments-, but the in-member P-delta magnification for these will be very small if stubby and initially straight. In case of doubt -say you have 4 segments in the column and you are not sure on whether significant curvature in some segment could be hidding further in-member unaccounted P-delta effects, magnify for the segments with the standin moments coming from the analysis with their ends unable to laterally displace, i.e., non-sway.

Material strength reduction factors need always be considered, however.

 

[lutein]

Thank you for your help. I am really getting a lot of info. from you guys. However, I have another question:

(1)
I understand the use of second order analysis and member buckling criteria. As we know, they are two different issue in design - Second order analysis is to obtain the "magnified" or "sway" forces, and the buckling criteria is to predict for the real strength of column due to bukcling failure before reaching the capacity.

I don't understand why isn't K being included in the colun strength formula butin the analysis part.

Please advise.

(2)
Furthermore, as I understand, Chapter 10 in ACI basically provides different moment magnification method with respect to how slender the column is based on KL/r ratio. A member curvature observation is to determine the K value by normograph method and furthere obtain the magnified momment. Such analogy is different from AISC in which it considers the K value in column strength formula and account for second roder drift by magnifiying the moment. I don't understand why are these two code different? Since the behaviour of frames and analysis are the same.

Please advise.

Thank you veyr much again.

 

[ishvaaag]

Before, proceeding with your last questions, I also note that when moment amplification is less than 10% one can find codes and texts that allow its entire dismissal. This surely acknowledges the conservative nature of the embedded enforcements. This supports the dismissal of moment magnification on account of the in-member buckling when one has considered a number of segments.

For initially straight members shown stable in sway or joint P-Delta this may well occurr above 4 segments but say, 6 to 10 segments should be in the range of allowable dismissal due to the low moment magnification required.

For initially curved elements if arches I would go preferably for separately statements of the buckling, and if not, always would consider the final in-member P-delta one way or another.

Now... On (1)
The second order analysis (say we keep it elastic in every segment, but the segments have embedded the degraded stiffness of the section) merely needs to re-state the geometry (and so the global stiffness matrix) and then calculate sucessive new cycles, stopping when all changes in deflections between cycles at all the calculated points are less than a selected value. This could be a problem in that if small they might grow indefinitely, but fortunately the analyzed structures if inestable soon show divergence, i.e., bigger displacements than in the previous cycle.

As you see from the description above, for that process no K slenderness (or on actual length amplification) factor is required, since it has nothing to do with what ongoing, which is merely a set of sucessive ordinary structural analyses for geometries calculated from the previous cycle. Normally you will have started with segments of mechanical properties consistent or conservative respect the final status at the factored level and you so need not to alter the member properties for every cycle, what you only would be doing with hand intervention old fashion (not even then, that used for the usual frame analyses iterative amplification of the lateral forces instead of modifcation of the global matrix stiffness).

Then when you see K for column behaviour is column buckling for some particular conditions of the column, end boundary conditions and in-member aligned and transverse loads if any, say, as the theoretical 2 for the usual loaded atop cantilever with fixed base and unrestrained atop, as a tool to facilitate the use of Euler's equation to properly describe the member buckling.

On (2)...
when I some years ago studied these things I saw the basis for both steel and concrete formulations. I am not presently knowledgeable enough nor have time to search the derivations, but I can attest that what I saw in general was consistent as an engineering tool. There were differences signaled by those that were making the studies, explanations and even recomendations of change, but the theoretical basis was consistent one and the same. Other thing is that there are not embedded particularizations necessary either by the nature of the structural system or the particularities of the code.