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Concrete Column Biaxial Bending

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I am working on the design of some concrete columns with biaxial bending.  I don’t do a lot of these so a program like PCA Column is not feasible.  I am using the ACI Design handbook, Example 8, as a reference.  It is the reciprocal load method.  This is one of the 3 methods discussed in PCA Notes for the ACI 318.

 

I made a MathCAD sheet for the procedure.  It worked fine for the example problem.  Most of my columns worked fine.  I had one column where the method kind of blew apart on.  It occurred on a column with low bending moments.  When you calculate the values for Pnx and Pny using the equation Pnx=Rn*fc*Ag*h/ex, it becomes very large due to the low eccentricity.  I used the minimum eccentricities of 0.6+0.03*h or b. Same for Pny.  When you run the equation 1/Pni=1/[(1/Pnx)+(1/Pny)-1/Pno] you get a negative number because of the high Pnx and Pny.

 

Is there a valid range where this equation works and doesn’t?  Am I miss-applying it?

 

I created another MathCAD sheet using the load contour method and the column design had no problem.

 

Thanks for your insight.

 

Rich Lewis