kl/r greater than 100 1

[ILLINI99]

I have a project that has resulted in tall piers with a kl/r over 100 (drilled shafts to columns above ground). This disallows the use of the magnified moments used in AASHTO 5.6.4.3. AASHTO references the use of a "more refined procedure" for kl/r>100, but that is all that is given. I have been unable to find much on what is acceptable for this more refined procedure. I have used both Midas and Group to get my loads (including second order effects), but have not reduced the axial or moment capacities due to these. I would assume there is another way to produce the "magnified moments", or reduce the interaction diagram, but i have not found any example/article that covers this. Any guidance/help would be appreciated.

 

[BridgeSmith]

Generally, the 'more refined analysis' would be an FEA. Sometimes, depending on the loading and restraint conditions, a P-delta (moment due to axial force multiplied by eccentricity) approach is sufficient. The P-delta analysis can be very straightforward, or fairly complicated. For loads are applied at the top, so there is single curvature, and the eccentricity limited by the connection to the superstructure, the upper bound for moment is just the max axial load multiplied by max eccentricity that can can occur. For loads applied to the columns, things become much more complicated, and an FEA is usually employed.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[ILLINI99]

Rod,

Midas is an FEA program. I have run P-delta analysis (this is what i meant by saying I included second order effects) on it, but my concern is changes in the interaction diagram for a slender column. At some point, buckling behavior will control, and typical interaction diagrams are based on short columns (i.e., no buckling). The short column interaction diagrams work well with lower kl/r values, but they should be affected by the height of the column at some point.

Thanks,
Illini99

 

[BridgeSmith]

I don't see that the capacity of the column cross section is reduced due to slenderness. My understanding is that the 'capacity' of the column overall to carry axial load is reduced because the moments are magnified by the second order effects. So, I believe the interaction diagrams would still be valid, but the applied moment you combine with the axial load would be what you calculate (get from the analysis) including the second order effects.

Of course, that is all based on the assumption of an uncracked section. If the deformation is large enough to crack the section, then things get messy. Designing slender columns with cracked sections generally doesn't work anyway, because the reduced moment of inertia results in even larger deflections, resulting in larger P-delta moments, leading to a progressive collapse of the column.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[ILLINI99]

The axial capacity of a column (not the cross section, but the cross section for a given kl) will go down when kl/r gets large enough and buckling becomes your failure mechanism. What I am getting from your comments is you do not believe the axial load in the column will get high enough to buckle, essentially limiting yourself to the bottom of the interaction diagram through the use of typical column sizes. If I have a high kl/r, it would not be a typical column size for a given height.

I look at this as 2 calculations. The first is calculating the Loads and additional P-Delta moment. Then second is producing an interaction diagram that takes slenderness into account, so I do not ignore column buckling in the design. Is this approach flawed?

Thanks,
Illini99

 

[rapt]

You either use
- a simplified model with a moment magnifier to determine the increased moment from buckling in cases where it is allowed, or

- you do a more complex second order analysis to determine the increased effects from buckling.

The interaction diagram does not change.

The available axial capacity changes because the moment is higher so you are further out in the interaction curve where axial capacity is reduced due to the increased moment.

 

[BridgeSmith]

The way I'm looking at it, the capacity, i.e. the stress and strain limits, of the reinforced concrete doesn't change because the slenderness of the column changes. What changes is the moment applied, specifically the moment on the column increases by P multiplied by delta.

I don't see any reductions on the capacity for an RC column where kl/r is < 100, only a magnification of the moment that it must be designed for. The only thing different when kl/r exceeds 100 is that the 'magnification' becomes more extreme and more difficult to find a relatively simple equation that approximates the increase due to the 2nd order effects. So they limit the range of applicability of the moment magnification equations.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[BridgeSmith]

Well said, rapt. I was trying to get there, but I took the scenic route and got lost.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[rapt]

BridgeSmith,

I like it simple!