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RC column Axial Load Equation - ACI

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Pedro Munoz wrote:

"The ACI 2002 Section 14.5 includes an equation for axially loaded walls that takes inot account k, l, and h for the wall section, I wonder if a similar equation could be proposed for axially loaded RC columns with minimum eccentricity that will fall outside the range of short columns say those in the intermediate range. I am sure that there should be enough test data that could be used to correlate a comprehensive equation that can be used for columns in the intermediate range and with minimum eccentricity to determine a Design Axial Load Strenght for a RC column of given cross section dimensions and unsupported length. This with the purpose of having a Design Axial Load Strength that can be incorporated into a Generalized Interaction Equation of Failure Surface for Axial load and Combined Biaxial moments. Does anyone in the Column Committes has comments to this proposal ?, AISC already has equaitons for axially loaded steel columns based on slendersess ratios, and it would be interesting to see how those eqautions for RC columns come out to be. Any  Comments and Suggestions from the ACI Column Committe Members, Researchers, Academic Investigators ?

Pedro R. Muñoz, Ph.D., P.E.
PRM Engineering, LLC
Haverhill, MA

Sounds like an intriguing idea.  Let me put forth a few points on both sides of the argument.

First, the equation in ACI Section 14.5.2 doesn't include any consideration of reinforcing.  For a wall, maybe that doesn't matter much; but it means that all the columns now designed with more than (I suppose) 1 percent reinforcing would not be able to be designed by this new equation, or else that the equation would have to get a lot more complicated.

Second, the allowable (factored) stress by 14.5.2 is 0.55 Fc', where Chapter 10 allows 0.85 x 0.85 or 0.72 Fc'; so the simplified form ends up costing about 25 percent of the capacity plus whatever the reinforcing represented.  This is what you expect for simplification, but there's usually a reason for making a wall a reasonable thickness (i.e. the contractor has to be able to get the mud down into the forms).  Columns may thus end up being penalized a lot more than walls by the simplification.

Third, there are a lot of columns whose moment puts the effective eccentricity well outside the kern.  Not as many walls have this problem, at least according to the person designing them.

Nonetheless, the idea is still interesting.  I once wrote a computer program, following the method used by CRSI, to analyze concrete columns and create interaction diagrams.  The programming was onerous, to say the least.  It was an extremely numerical, calculation-intensive procedure, and I can't help wondering whether we really know that much about how these columns behave to merit such a solution.  Frankly I doubt it.  In truth, anything based on a Whitney stress block and elastic-perfectly plastic rebar behavior is pretty approximate to begin with.  Even Whitney knew that, and said as much.  

And even if we really know the actual strength (almost a religious assumption), we then end up comparing it to forces arrived at by a poorly modeled structure run through an elastic analysis based on material properties we can only guess at and loads that somebody else guessed at for us (there's no way the partitions in my office weigh 20 psf), multiplied by load factors arrived at by people smoking cigars in small rooms after dinner (according to Ted Galambos, who would know).  ACI, after all, is the group who cavalierly said that the 1.4/1.7 load factors were the only true path in the commentary of one issue of 318, then blithely changed to 1.2/1.6 in the next issue without changing anything else (like the phi factor) for flexural design.

So maybe a radically simplified semi-rational method such as you propose has merit after all.  Personally I'd love to see a similar equation for columns.  It would be easy to pick on, but a lot of engineers would love to see something like that codified.

My two cents worth.

Mike Hemstad, P.E., S.E.
St. Paul, Minnesota

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