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Zero-stress Column

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Jorge,
 
A plot of the axial load vs frequency squared
is a straight line. When you have one point above the horizontal axis (compression)
and one below the axis (tension), you can draw a straight line and get the frequency
corresponding to an unloaded column.
 
I am not sure I fully understand your question. By saying the column is framed
you imply it can't be directly seen. Yet there must be some way to measure its
frequency if you wish to go that way.
 
Gregory from Oz
 

Gregory:

OK. Assume that the frequency of the column having zero axial stresses is 25
Hz. A 10 Hz measure indicates that the column is in compression. A 60 Hz
measure indicates that the column is in tension. But, how to know that zero
stress occurs at 25 Hz, since the column is framed?

Jorge Jimenez, PE